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QUEENSLAND UNIVERSITY OF TECHNOLOGY
SCHOOL OF PHYSICAL AND CHEMICAL SCIENCES
NOVEL APPROACHES TO THE DESIGN OF DOMESTIC SOLAR HOT WATER SYSTEMS
Submitted by Raniero Alberto GUARNIERI to the School of Physical and Chemical Sciences,
Queensland University of Technology, in partial fulfilment of the requirements of the degree of
Doctor of Philosophy.
2005
Novel approaches to the design of domestic solar hot water systems iii
Keywords Domestic Solar Hot Water Systems, Concentrating Optics, Compound Parabolic
Collectors, Solar Selective Surface, Self-Pump, Air Heater Panel, Compact Heat
Exchanger, Sun-Earth Geometry
Novel approaches to the design of domestic solar hot water systems v
Abstract
Domestic solar hot water units, if properly designed, are capable of providing all hot water
needs in an environmentally friendly and cost-effective way. Despite 50 years of
development, commercial technology has not yet achieved substantial market penetration
compared to mainstream electric and gas options. Therefore, alternate designs are warranted
if they can offer similar or greater performance for a comparable cost to conventional units.
This study proved that such alternatives are possible by designing and testing two novel solar
hot water systems (SHWS).
The first system used compound parabolic collector (CPC) panels to concentrate solar
energy and produce steam. The steam moved from a rooftop downward into a heat exchange
pipe within a ground level water tank, heating the water, condensing and falling into a
receptacle. The operation was entirely passive, since the condensate was pulled up due to the
partial vacuum that occurred after system cooling. Efficiencies of up to 40% were obtained.
The second system used an air heater panel. Air was circulated in open and closed loop
configuration (air recycling) by means of a fan/blower motor and was forced across a
compact heat exchanger coupled to a water tank. This produced a natural thermosiphon flow
heating the water. Air recycling mode provided higher system efficiencies: 34% vs. 27%.
The concurrent development of an analytical model that reasonably predicted heat transfer
dynamics of these systems allowed 1) performance optimisation for specific input/starting
operating conditions and 2) virtual design improvements. The merit of this model lay in its
acceptable accuracy in spite of its simplicity.
By optimising for operating conditions and parameter design, both systems are capable of
providing over 30 MJ of useful domestic hot water on clear days, which equates roughly to
an increase of 35°C in a 200 L water tank. This will satisfy, on average, daily hot water
requirements for a 4-person household, particularly in low-latitude regions (eg. Queensland).
Preliminary costing for these systems puts them on par with conventional units, with the
passive, remotely coupled, low maintenance, CPC SHWS comparable to higher end models.
The air heater SHWS, by contrast, was much more economical and easier to build and
handle, but at the trade-off cost of 1) the need for an active system, 2) increased maintenance
and running costs and 3) the requirement for a temperature control mechanism that would
protect the panel body by dumping hot air trapped inside if stagnation were to occur.
Novel approaches to the design of domestic solar hot water systems vii
Table of Contents
Keywords ...............................................................................................................iii
Abstract ................................................................................................................... v
Table of Contents ................................................................................................vii
Nomenclature ...................................................................................................... xiv
List of Diagrams, Images and Figures ............................................................. xx
List of Tables ..................................................................................................... xxix
Statement of Original Authorship ................................................................... xxxi
Acknowledgments ..........................................................................................xxxiii
Chapter 1 Introduction ...............................................................1
1.1 Solar energy and domestic solar hot water production .................................... 1
1.2 Conventional SHWS ........................................................................................ 2
1.3 Problems and disadvantages with existing systems ......................................... 5
1.4 Aims and objectives ......................................................................................... 5
1.5 Brief outline of approach to new designs......................................................... 6
1.6 Rationale behind the selection, construction and operation of the designs developed ......................................................................................................... 7
Chapter 2 Solar radiation and solar geometry..........................10
2.1 Introduction .................................................................................................... 10
2.2 Solar energy and solar radiation..................................................................... 10
2.3 Air mass atmospheric transmittance model ................................................... 11
2.4 Sun-earth geometry ........................................................................................ 13
2.5 Solar geometry and panel layout/orientation ................................................. 16
Novel approaches to the design of domestic solar hot water systems viii
Chapter 3 Concentrating devices.............................................23
3.1 Introduction .................................................................................................... 23
3.2 Concentration ................................................................................................. 23
3.2.1 Upper limit for concentration .......................................................... 25
3.3 The Compound Parabolic Collector (CPC).................................................... 26
3.3.1 Conceptualisation of the CPC and the “edge-ray” principle ........... 28
3.4 Exploring CPC orientations and collection times .......................................... 30
Chapter 4 Heat transfer............................................................47
4.1 Introduction .................................................................................................... 47
4.1.1 Conduction heat transfer.................................................................. 47
4.1.2 Convection heat transfer .................................................................. 48
4.1.3 Radiation heat transfer ..................................................................... 49
4.2 Selected heat transfer equations and other relationships................................ 50
4.2.1 Convection in SHWS....................................................................... 51
4.2.1.1 Free convection between a flat plate and the surroundings.... 51
4.2.1.2 Forced convection between a flat plate and the surroundings............................................................................ 52
4.2.1.3 Free convection from horizontal cylinders............................. 53
4.2.1.4 Free convection from vertical cylinders................................. 53
4.2.1.5 Forced convection from horizontal or vertical cylinders ....... 54
4.2.1.6 Free convection between flat plates ....................................... 54
4.2.1.7 Free convection between concentric cylinders....................... 56
4.2.1.8 Forced convection in a corrugated triangular duct................. 56
4.2.2 Radiation in SHWS.......................................................................... 58
4.2.2.1 Radiation exchange between a convex object and a large enclosure ................................................................................. 59
Novel approaches to the design of domestic solar hot water systems ix
4.2.2.2 Radiation exchange between flat plates ................................. 59
4.2.2.3 Radiation exchange between two concentric cylindrical surfaces .............................................................................. 60
4.2.3 Conduction in SHWS ...................................................................... 61
4.2.3.1 Conduction between concentric cylinders ............................. 61
4.3 Thermal network formulation and energy balance equations ........................ 61
4.4 Energy and power in fluid flow and fluid storage.......................................... 64
4.5 Heat exchanger effectiveness-NTU method .................................................. 65
Chapter 5 Fluid mechanics and hydraulics ..............................68
5.1 Introduction .................................................................................................... 68
5.2 Pressure losses................................................................................................ 68
5.2.1 Pressure in fluids ............................................................................. 69
5.2.2 Energy and “head”........................................................................... 69
5.2.3 Head (pressure) losses ..................................................................... 71
5.2.4 Minor losses..................................................................................... 72
5.3 Thermohydraulics .......................................................................................... 74
5.3.1 Poisseuille’s Law for laminar flow.................................................. 74
Chapter 6 Solar Hot Water System with Passive Downward
Vapour Phase Heat Transport.................................75
6.1 Introduction .................................................................................................... 75
6.1.1 Basic design considerations............................................................. 76
6.2 Concentrating systems – a review.................................................................. 80
6.3 Solar Geometry and panel layout/orientation................................................. 83
6.4 Heat transfer ................................................................................................... 85
Novel approaches to the design of domestic solar hot water systems x
6.4.1 Collector panel energy balance equations and relationships for heat transfer modes .......................................................................... 87
6.4.2 Conveyance infrastructure / transfer line......................................... 94
6.4.3 Hot water tank and exchanger ......................................................... 96
6.4.4 Summary of solution process for the entire system......................... 98
6.5 Experimental work: prototype and system construction ................................ 99
6.5.1 System components ......................................................................... 99
6.5.2 First prototype collector panel ....................................................... 105
6.5.3 Second prototype ........................................................................... 107
6.5.4 Third prototype .............................................................................. 109
6.6 Results and discussion.................................................................................. 113
6.6.1 Modelling results ........................................................................... 113
6.6.2 Experimental results from prototypes............................................ 121
6.6.2.1 First Prototype (Figure 6.31) ........................................... 121
6.6.2.2 Second Prototype (Figure 6.32)....................................... 122
6.6.2.3 Third Prototype (Figure 6.33).......................................... 123
6.6.3 Comparison of the 3 prototypes (Figure 6.34)............................... 125
6.6.4 Water tank...................................................................................... 126
6.7 Conclusions and discussion.......................................................................... 128
6.7.1 Performance of the downward vapour heat transport SHWS........ 128
6.7.2 Elements construction and materials used ..................................... 131
6.7.3 Model predictions compared with experimental results. ............... 133
Chapter 7 - Air-to-water heat transfer solar hot water system with
heat exchanger-water tank coupling .....................135
7.1 Introduction .................................................................................................. 135
Novel approaches to the design of domestic solar hot water systems xi
7.1.1 Basic design for the construction and operation of the air-to-water heat exchanger-coupled tank SHWS ................................... 135
7.2 Types of solar air heating panels.................................................................. 139
7.3 Heat transfer ................................................................................................. 142
7.3.1 Air heating collector panel ............................................................. 143
7.3.2 Collector panel energy balance equations and relationships for heat transfer modes ........................................................................ 145
7.3.3 Conveyance system energy balance equations and relationships for heat transfer modes (pipes and bends) ..................................... 149
7.3.4 Heat exchanger energy considerations and power gain in the water .............................................................................................. 151
7.3.5 Centrifugal Fan-Motor ................................................................... 155
7.3.6 Water Tank heat gains and losses .................................................. 157
7.3.7 Summary of solution process for the entire system ....................... 158
7.4 Thermohydraulic assessment of airflow ...................................................... 159
7.4.1 Pressure losses................................................................................ 159
7.5 Experimental work: construction details...................................................... 161
7.5.1 System components........................................................................ 162
7.6 Results ........................................................................................................ 173
7.6.1 First prototype ................................................................................ 173
7.6.2 Second prototype............................................................................ 185
7.6.2.1 Open loop operation mode .............................................. 186
7.6.2.2 Closed loop operation mode............................................ 194
7.6.3 Determination of head loss and pressure drops in the system ....... 200
7.6.4 Thermosiphon effective radius and linear fluid flow approximation................................................................................ 205
7.6.5 Exploring exchanger effectiveness variation under system operation ........................................................................................ 208
7.7 Discussion .................................................................................................... 215
Novel approaches to the design of domestic solar hot water systems xii
7.7.1 Air heater system elements ............................................................ 215
7.7.2 Economics ...................................................................................... 220
7.7.3 Model prediction results................................................................. 220
7.8 Conclusions .................................................................................................. 222
Chapter 8 - Economic analysis..................................................223
8.1 SWHS with passive downward vapour phase heat transport ....................... 224
8.2 SHWS incorporating an air heater collector panel and heat exchanger-water tank coupling ................................................................................................ 227
Chapter 9 General discussion, conclusions and avenues for
future work.............................................................231
9.1 SHWS with passive downward vapour phase heat transport ....................... 233
9.2 SHWS with an air heater collector panel and heat exchanger-water tank coupling ........................................................................................................ 240
Appendix A – Mathematical relationships and calculations in
solar geometry and CPC orientation................... 250
Appendix B – Etendue invariant and optical concentration....... 255
Appendix C – Mathematical formulation for the design of the
CPC shape and the horizontal fin profile ............ 258
Appendix D – Heat transfer parameters and pipe friction .........265
Appendix E – Analytical expressions for the heat transfer
dynamics of the CPC panel SHWS .................... 270
Novel approaches to the design of domestic solar hot water systems xiii
Appendix F – Analytical expressions for the heat transfer
dynamics of the air heater panel SHWS.............275
Appendix G – Polynomial approximations of physical
properties of air and water ..................................284
Appendix H – Air/water heat exchanger and fan-blower motor.290
Appendix I – Anemometer calibration.......................................292
Bibliography ............................................................................295
References ............................................................................296
Novel approaches to the design of domestic solar hot water systems xiv
Nomenclature
α Solar altitude angle / Absorptivity
β Inverse of the temperature
αr Heliz angle of roughness for a pipe with internal corrugation
αt Thermal diffusivity (m2/s)
Γ Total emissive power (W/m2)
γ Specific weight (kg/m2·s2)
δ Declination
Δ Angular surface error for CPC
Δx Thickness of material
ΔΤ Temperature difference
Δp Pressure difference
φ Latitude
Φv Volumetric flow rate
ϕ Panel azimuth angle
ϕS Solar azimuth angle
θ Panel tilt angle
ρ Rotation angle about the normal to the collector panel plane
ω Twist angle
η Dynamic viscosity (kg/m·s) / Efficiency
ε Emissivity / Heat exchanger effectiveness / Pipe wall roughness factor
ε’ Modified heat exchanger effectiveness
ν Kinematic viscosity (m2/s)
σ Stefan-Boltzmmann constant
ρ Reflectivity / Density
τ Transmissivity
τatm Atmospheric transmittance
τod(l) Optical depth for radiation traversing a medium of thickness ‘l’
θa CPC acceptance half-angle
θc CPC collection angle
θinc Incidence angle: the angle between the surface and the solar beam
Novel approaches to the design of domestic solar hot water systems xv
θSN’ Angle between the solar vector and the normal to the panel surface
θSP’ Angle between the solar vector and the vector normal to the panel surface and
to the line-axis of the CPC
θz Zenith angle
a Aperture radius of an optical system
A Area
Arat Area ratio between the surfaces of concentric cylinders
At=Ad Pipe cross-sectional area
C Concentration ratio / combined electrical motor efficiency
Cp Specific heat at constant pressure(kJ/kg·°C)
(also: Cair, Cw for air and water, respectively)
D Diameter
Dh Hydraulic Diameter
Dp Pipe diameter
dr Roughness pitch for a pipe with internal corrugation
dx Element surface length for air panel absorber
er Roughness height for a pipe with internal corrugation
ET Equation of time
f Friction factor / Focal length of parabola
F Force
F’ Collector efficiency factor
Fij Radiation shape factor for radiation exchange from surface i to surface j
g Acceleration of gravity
Gcb Attenuated irradiance on the Earth’s surface after traversing the atmosphere
(Gcb = S = I)
GcbN Attenuated irradiance on a surface for normal solar incidence
Go Extraterrestrial radiation at the boundary of the Earth’s atmosphere
Gr Grashof number
GSC Solar constant
h = lh Hot water column height in the thermosiphon circuit
hf Head losses
hm Minor pressure losses
hn Reduction in cold water column height in the thermosiphon circuit
Novel approaches to the design of domestic solar hot water systems xvi
hs Hour angle
H Head pressure (m)
Hs Plate spacing for double-cover collector panel
hT Heat transfer coefficient
K Overall attenuation factor for solar radiation traversing the atmosphere /
Pressure loss coefficient
k Thermal conductivity
kλ Wavelength dependent extinction coefficient for solar radiation traversing the
atmosphere
KE Kinetic Energy
l Length / Solar panel length / Pipe length / Height
L Characteristic length
l0 Atmosphere thickness for normal solar incidence
LH Enthalpy of vapourisation (kJ/kg)
llocal Local longitude
LST Local standard time
lST Standard time meridian
m Body mass / air mass ratio
m& Mass flow rate
n Day number / Refractive index
Nu Nusselt number
P Perimeter / Power
Pd Wetted perimeter of a duct
p Pressure
PE Pressure Energy
Pr Prandtl number
pr Rib spacing for a pipe with internal ribbed corrugation
Px_act Heat transfer experienced by fluid in heat exchanger
Px_max Maximum possible heat transfer
q Heat flow (W)
Q Total heat flow (W)
r Pipe radius
R Reflectance
Ra Rayleigh number
Novel approaches to the design of domestic solar hot water systems xvii
Re Reynolds number
RT Thermal resistance (W/m4·°C)
ST Solar time
t Thickness of material
T Temperature
Tci Temperature of the cold fluid at input/output port ‘i’ of exhcanger
Thi Temperature of the hot fluid at input/output port ‘i’ of exhcanger
UL Total heat loss coefficient
U(θu) Rotation matrix about an arbitrary vector VU by an angle θu
v Fluid velocity
vm Mean fluid velocity
VN Unit vector normal to panel surface
VN’ Unit vector normal to panel surface after panel orientation
VNpol VN in polar coordinates
VP Unit vector normal to both VN and the line-axis of the collector
VP’ Unit vector normal to both VN’ and the line-axis of the orientated collector
VPpol VP in polar coordinates
VS Solar vector
VSN’ Projection of the solar vector on the axes of VN’
VSP’ Projection of the solar vector on the axes of VP’
VST Projected solar vector on the transverse plane of the CPC panel
V& Volume flow rate
w Width / Aperture width of an optical system
W Body weight (kg)
Ws Slat width for double-cover collector panel
X, Y, Z Rotation matrices about the x, y and z-axes, respectively
ZE Potential Energy
Subscripts and Supersripts
A Related to CPC collector panel absorber
F Related to CPC collector panel absorber sheath
C Related to CPC and Air Heater collector panel cover
Novel approaches to the design of domestic solar hot water systems xviii
V Related to CPC cavity
B Related to back of the air heater absorber panel
Q Related to heat losses from the double cover of the air heater panel to the
environment
amb Related to the ambient, usually temperature (Tamb)
mot Denotes fan/blower motor property or characteristic
ab Related to the air heater absorber
Related to the air streams flowing over or under the air panel absorber
e Related to the side walls of the air heater panel
h Related to the hot fluid
c Related to the cold fluid / Related to convection heat trasfer
k Related to conduction heat trasfer
r Related to radiation heat trasfer
i Related to point, port, or object of measurement
s Related to steam properties or characteristic (ηs)
f Relates to a fluid property or characteristic (Tf)
sky Related to the sky (Tsky)
forced Denotes forced convection mode
free Denotes free convection mode
cond Related to steam condensate
tank_cond Related to condensation occurring in the heat exchanger loop of the tank
tot_cond Related to total steam condensate
stag Related to stagnation temperature
eff Denotes an effective measurement or quality
in Denotes input condition or internal location
out Denotes output condition or external location
w, water Denotes water characteristic
w Denotes internal pipe wall
x Denotes heat exchanger characteristic
f Indicates evaluation of property at film temperature
cyl Related to a cylindrical geometry
opt Related to the optical properties of the CPC
eff Effective
cpc Related to the CPC
iair
Novel approaches to the design of domestic solar hot water systems xix
fin Related to CPC absorber-boiler fin
ins Related to insulation material
T Related to the water storage tank
tube Related to CPC absorber-boiler tube
Novel approaches to the design of domestic solar hot water systems xx
List of Diagrams, Images and Figures
Figure 1.1 A conventional close-coupled thermosiphonic solar hot water system... 2
Figure 1.2 Schematic for the vapour phase downward heat transport SHWS.......... 6
Figure 1.3 Schematic for the air-to-water heat exchanger tank-coupled SHWS...... 7
Figure 2.1 Solar radiation travel distance through the atmosphere ........................ 11
Figure 2.2 Sun path diagrams for seasonal times for a temperate austral latitude.. 13
Figure 2.3 Collection angle comparison between a flat plate and a concentrator .. 15
Figure 2.4 Cartesian coordinate system for collector panel.................................... 17
Figure 2.5 Plane of a CPC before and after azimuth rotation................................. 18
Figure 2.6 Tilt angle for the plane of the CPC........................................................ 18
Figure 2.7 Tilt and twist angles for the plane of a CPC.......................................... 19
Figure 2.8 Effective azimuth and tilt angles for the plane of a CPC and angle of incidence for direct solar radiation ........................................................ 20
Figure 2.9 Radiation collection and acceptance angles for an arbitrary CPC layout ..................................................................................................... 22
Figure 3.1 Magnifying glass ................................................................................... 24
Figure 3.2 Cone concentrator (longitudinal profile) ............................................... 25
Figure 3.3 Off-axis aberrations (coma) for a parabolic trough mirror.................... 26
Figure 3.4 CPC configurations for different absorber types................................... 27
Figure 3.5 Projection of incoming solar ray on transverse CPC plane, normal to the surface.............................................................................................. 28
Figure 3.6 Edge-ray principle for 2D CPC ............................................................. 29
Figure 3.7 The CPC profile as compounded parabolic segments........................... 29
Figure 3.8 Irradiation profile and collection times for east-west orientation and north facing collector, i.e., twisted to the latitude angle........................ 31
Figure 3.9 Irradiation profile and collection times for north-south alignment and north facing collector, i.e., tilted to the latitude angle .................... 32
Novel approaches to the design of domestic solar hot water systems xxi
Figure 3.10 Irradiation profile and collection times for northeast-southwest aligned collector, tilted to the latitude angle ......................................... 33
Figure 3.11 Irradiation profile and collection times for northwest-southeast aligned collector, twisted to the latitude angle ...................................... 34
Figure 3.12 Irradiation profile and collection times for east-west aligned collector, twisted to the latitude angle and tilted east ........................... 35
Figure 3.13 Irradiation profile and collection times for east-west aligned collector, twisted to the latitude angle, tilted east & rotated 5° about its normal............................................................................................... 36
Figure 3.14 Irradiation profile and collection times for east-west aligned collector, twisted to the latitude angle, tilted east & rotated 10° about its normal............................................................................................... 37
Figure 3.15 Irradiation profile and collection times for east-west aligned collector, twisted to the latitude angle, tilted east & rotated 20° about its normal............................................................................................... 38
Figure 3.16 Irradiation profile and collection times for east-west aligned collector, twisted to the latitude angle, tilted east & rotated 30° about its normal............................................................................................... 39
Figure 3.17 Irradiation profile and collection times for east-west aligned collector, with a 30° twist angle and a 20° tilt – summer solstice......... 40
Figure 3.18 Irradiation profile and collection times for east-west aligned collector, with a 30° twist angle and a 20° tilt – winter solstice ........... 41
Figure 3.19 Irradiation profile for a northwest facing collector with a 20° tilt, before and after a +25° ρ-rotation – summer solstice ........................... 42
Figure 3.20 Irradiation profile for a northwest facing collector with a 20° tilt, before and after a +25° ρ-rotation – winter solstice.............................. 43
Figure 4.1 Convection, conduction and radiation heat transfer (qc, qk, qr, respectively) for a hot plate exposed to a cool environment, Tp > Tair.. 47
Figure 4.2 Parallel flat plates with slats for convection suppression...................... 55
Figure 4.3 Corrugation parameters for circular ducts............................................. 58
Figure 4.4 Concentric cylinder arrangement for two radiating surfaces ................ 60
Novel approaches to the design of domestic solar hot water systems xxii
Figure 4.5 Thermal circuit schematics for heat transfer through the roof of a shed........................................................................................................ 62
Figure 4.6 Double pipe heat exchanger .................................................................. 65
Figure 5.1 Fluid element in a pipe section at height ‘h’ above reference level ...... 70
Figure 6.1 Sketch for the downward vapour heat transport SHWS........................ 76
Figure 6.2 CPC main plane rotations...................................................................... 83
Figure 6.3 CPC collection and acceptance angles .................................................. 84
Figure 6.4 CPC cross-section.................................................................................. 85
Figure 6.5 Heat transfer modes............................................................................... 87
Figure 6.6 Double cover model .............................................................................. 87
Figure 6.7 Thermal network resistance for the CPC heat transfer model............... 88
Figure 6.8 Solutions algorithm flow chart for simulation of heat transfer in the system and calculation of relevant parameters ...................................... 92
Figure 6.9 Assessment of heat losses for an experimental transfer line ................. 94
Figure 6.10 Truncated CPC profile used (scale 1:3)............................................... 100
Figure 6.11 Schematic of the fin and tube copper absorber ................................... 100
Figure 6.12 Absorber-boiler array of 7 fins & tubes connected to header/footer tubes and return water pipes prior to blackening (2nd prototype) ........ 101
Figure 6.13 Reservoir tank (from final prototype).................................................. 103
Figure 6.14 Hot water tank ..................................................................................... 104
Figure 6.15 Insulated vapour transfer line (trajectory indicated by red arrows) .... 104
Figure 6.16 CPC modules and 1st prototype ........................................................... 105
Figure 6.17 Vertical fin profile CPC mould before and after aluminium lining .... 105
Figure 6.18 Header tube of the 1st prototype and transfer line connection............. 106
Figure 6.19 Double-panel 2nd prototype with reservoir tank in the centre ............. 107
Figure 6.20 7-CPC module structure with reflective lining in metal case.............. 108
Figure 6.21 Single-module 3rd prototype with reservoir tank to the right .............. 110
Figure 6.22 Fin and tube copper array before and during maxorb layering ........... 110
Novel approaches to the design of domestic solar hot water systems xxiii
Figure 6.23 CPC structure with reflector material Silverlux™ (still covered with protective foil) and maxorb-lined boiler array .................................... 111
Figure 6.24 Steam production from 3rd prototype .................................................. 111
Figure 6.25 Collection and orientation layout for 3rd prototype showing collector and reservoir on the roof and the storage tank at ground level ........... 112
Figure 6.26 Performance plots for variations in CPC wall reflectance .................. 114
Figure 6.27 Performance plots for single- and double-cover collector models...... 115
Figure 6.28 Total steam production for a typical CPC panel over 5 hours ............ 118
Figure 6.29 Steam power produced for various CPC concentration ratios ............ 119
Figure 6.30 Daily steam energy produced for various CPC concentration and emittance values .................................................................................. 120
Figure 6.31 Efficiency results for the 1st CPC prototype........................................ 121
Figure 6.32 Efficiency results for the 2nd CPC prototype....................................... 122
Figure 6.33 Efficiency results for the 3rd CPC prototype ....................................... 124
Figure 6.34 Prototypes performance comparison ................................................... 125
Figure 6.35 Water tank temperature for no-load conditions over 6 consecutive clear days............................................................................................. 126
Figure 6.36 Hot water storage tank, transfer pipe and condensate receptacle........ 128
Figure 6.37 Water tank temperature for no-load conditions over 12 consecutive days showing stagnation water temperature........................................ 133
Figure 7.1 Sketch for the air-to-water heat exchanger-coupled tank SHWS........ 136
Figure 7.2 Longitudinal view for 3 different air-heating flat-plate solar panels .. 140
Figure 7.3 Transverse view for 2 different air-heating solar panels with multi-channel absorber plates ....................................................................... 140
Figure 7.4 Longitudinal view for 2 different air-heating flat-plate solar panels using alternative absorber type............................................................ 141
Figure 7.5 Transverse view of 1st prototype with a V-shaped absorber panel and triangular fins ...................................................................................... 144
Figure 7.6 Heat transfer modes for a) double channel flat and b) V-shaped absorber configurations ....................................................................... 145
Novel approaches to the design of domestic solar hot water systems xxiv
Figure 7.7 Thermal resistance network for absorber panel configurations of Figure 7.6............................................................................................. 148
Figure 7.8 Pipe section / schematic for air pipe heat loses to the environment .... 149
Figure 7.9 Thermosiphon and hot water stratification for the SHWS heat exchanger and tank .............................................................................. 152
Figure 7.10 V-corrugated absorber panel with fins and polystyrene housing ........ 162
Figure 7.11 1st prototype air heater absorber panel with air diffuser sections and double cover ........................................................................................ 162
Figure 7.12 1st prototype air heater panel on movable tilted base .......................... 163
Figure 7.13 1st prototype on work bench with fan blower and variable power supply .................................................................................................. 164
Figure 7.14 Devices used in the determination of airflow rates ............................. 164
Figure 7.15 2nd prototype large scale air heater panel on tilt-adjustable frame ...... 165
Figure 7.16 Absorber panel profile and panel construction.................................... 166
Figure 7.17 Heat exchanger employed in the SHWS ............................................. 167
Figure 7.18 Hot water tank and heat exchanger ..................................................... 168
Figure 7.19 Upper view of centrifugal fan-blower attached to heat exchanger...... 169
Figure 7.20 2nd prototype air heater panel & SHWS in operation .......................... 170
Figure 7.21 Measurement of pressure drop in mm H2O gauge across a pipe section.................................................................................................. 172
Figure 7.22 Output air temperature vs. airflow rate for different panel configurations ...................................................................................... 174
Figure 7.23 Collector efficiency vs. airflow rate for different panel configurations ...................................................................................... 174
Figure 7.24 Output air temperature vs. airflow rate for finned V-corrugated absorbers for an input air temperature of 20°C ................................... 177
Figure 7.25 Efficiency vs. airflow rate for a V-corrugated absorber of various fin lengths.................................................................................................. 177
Figure 7.26 Output air temperature vs. airflow rate for finned V-corrugated absorbers for an input air temperature of 60°C ................................... 178
Novel approaches to the design of domestic solar hot water systems xxv
Figure 7.27 Efficiency vs. airflow rate for a V-corrugated absorber of various fin lengths ................................................................................................. 178
Figure 7.28 Output air temperature vs. airflow rate for input air at 20°C and different panel configurations ............................................................. 179
Figure 7.29 Efficiency vs. airflow rate for input air at 20°C and different panel configurations...................................................................................... 180
Figure 7.30 Output air temperature vs. airflow rate for input air at 40°C and different panel configurations ............................................................. 180
Figure 7.31 Efficiency vs. airflow rate for input air at 40°C and different panel configurations...................................................................................... 181
Figure 7.32 Output air temperature vs. airflow rate for input air at 60°C and different panel configurations ............................................................. 181
Figure 7.33 Efficiency vs. airflow rate for input air at 60°C and different panel configurations...................................................................................... 182
Figure 7.34 Variation of the ouput air temperature for 20°C input air based on different D/L ratios.............................................................................. 183
Figure 7.35 Efficiency air temperature for 20 °C input air temperatures based on different D/L ratios.............................................................................. 183
Figure 7.36 Variation of the ouput air temperature for 40°C input air based on different D/L ratios.............................................................................. 184
Figure 7.37 Efficiency air temperature for 40 °C input air temperatures based on different D/L ratios.............................................................................. 184
Figure 7.38 Experimental and numerical temperature variations vs. time of the day for the elements of the 2nd prototype air heater panel and SHWS in open loop mode ............................................................................... 186
Figure 7.39 Experimental results and numerical fit for determination of exchanger effectiveness (eq. 7.24) for an airflow rate of 61 L/s in open loop mode ................................................................................... 187
Figure 7.40 Experimental measurements and numerical predictions for power delivered to the water vs. exchanger output air temperature for various thermosiphon pipe radii (eq. 7.22) and for an airflow of 61 L/s in open loop operation.............................................................. 188
Novel approaches to the design of domestic solar hot water systems xxvi
Figure 7.41 Experimental temperature variations and numerical predictions over a wide range of irradiance values for the 2nd SHWS prototype in open loop mode ................................................................................... 189
Figure 7.42 Experimental and numerical output air temperature variations for the 2nd prototype air heater panel vs. time of the day in open loop mode.191
Figure 7.43 Experimental results and numerical prediction for power delivered to the water vs. time of the day for open loop operation and for 61 L/s airflow ...................................................................................... 192
Figure 7.44 Temperature measurements for a vertical profile of the water in the storage tank for open loop operation of the system and for 61 L/s airflow.................................................................................................. 193
Figure 7.45 Experimental and numerical temperature variations vs. time of the day for the elements of the 2nd prototype air heater panel and SHWS in closed loop mode............................................................................. 194
Figure 7.46 Experimental results and numerical fits for determination of exchanger effectiveness (Equation 7.24) for an airflow rate of 63 L/s in open loop mode ............................................................................... 195
Figure 7.47 Experimental measurements and numerical predictions for power delivered to the water vs. exchanger output air temperature for varius thermosiphon pipe radi (eq. 7.56) and for an airflow of 63 L/s in closed loop operation....................................................................... 196
Figure 7.48 Experimental temperature variations and numerical predictions over a wide range of irradiance values for the 2nd SHWS prototype in closed loop mode................................................................................. 197
Figure 7.49 Experimental results and numerical prediction for power delivered to the water vs. time of the day for 63 L/s airflow in closed loop mode .................................................................................................... 198
Figure 7.50 Temperatre measurements for a vertical profile of the water in the storage tank for 63 L/s airflow in closed loop mode ........................... 199
Figure 7.51 Schematic of conveyance infrastructure: pipes, elbows, fittings and other elements...................................................................................... 200
Figure 7.52 Pressure drop measurement setup for water flow in the heat exchanger............................................................................................. 205
Novel approaches to the design of domestic solar hot water systems xxvii
Figure 7.53 Experimental measurements for pressure drops vs. water flow rates in the heat exchanger and equation fits showing a linear response below 12 cc/s ....................................................................................... 206
Figure 7.54 Experimental measurements for the modified effectiveness vs. water flow rates in the heat exchanger and exponential equation fits to the data ...................................................................................................... 210
Figure 7.55 Experimental measurements for the modified effectiveness vs. ‘ Cm ⋅& ’ product quotient between water and air. An exponential equation fits the data well.................................................................... 210
Figure 7.56 Predicted values for modified effectiveness vs. water flow rate from the exponential expression of Equation 4.74 ...................................... 211
Figure 7.57 Variation of exchanger efficiency vs. water flow rate obtained from the experimental fit for modified effectivness .................................... 213
Figure 9.1 Original near-horizontal heat exchanger and proposed vertical arrangement for hot water stratification .............................................. 238
Figure B1 General optical system and the étendue invariant ............................... 255
Figure B2 The étendue for a general optical system (measure of angular displacement shown for y-coordinate) ................................................ 256
Figure B3 Two dimensional concentrator of acceptance angle 2θ and output angular range 2θ’................................................................................. 256
Figure C1 Construction of the CPC profile.......................................................... 258
Figure C2 Comparison of the fraction of radiation incident on the aperture of a CPC for different CPC scenarios (assuming perfect reflectivity) ....... 261
Figure C3 Compound parabolic profile for the horizontal absorber concentrator261
Figure C4 Truncated CPC .................................................................................... 264
Figure D1 Friction factors for vs. Reynolds number for various pipe roughness and diameter ratios and for laminar, transitional and turbulent flow .. 268
Figure G1 Plots of the linear fits for thermal diffusivity, kinematic viscosity and thermal conductivity of air vs. temperature.................................. 286
Figure G2 Plots of polynomial fits for specific heat and density of air vs. temperature.......................................................................................... 287
Novel approaches to the design of domestic solar hot water systems xxviii
Figure G3 Plots of the polynomial fits for selected physical properties of air vs. temperature .......................................................................................... 289
Figure H1 Picture-schematic of original heater core used as a heat exchanger.... 290
Figure H2 Picture-schematic of the fan/blower.................................................... 291
Figure I1 Speed profile for airflow in the pipes vs. transverse distance and polynomial fit ...................................................................................... 293
Figure I2 Correlation between anemometer readings and known air speed values showing a strong linear fit to the data. ..................................... 294
Novel approaches to the design of domestic solar hot water systems xxix
List of Tables
Table 1.1 Sizing recommendations for SHWS ....................................................... 8
Table 1.2 Energy and water volume targets for SHWS design............................... 9
Table 2.1 Quantities in Sun-Earth geometry ......................................................... 15
Table 6.1 Assumed efficiencies for basic system components ............................. 76
Table 6.2 Assumed energy and power requirements: Mode #1 ............................ 77
Table 6.3 Average irradiance and minimum collector area required: Mode #1.... 78
Table 6.4 Assumed energy and power requirements: Mode #2 ............................ 78
Table 6.5 Average irradiance and minimum panel area required: Mode #2 ......... 78
Table 6.6 Water conditions and required mass for boiling ................................... 79
Table 6.7 Real heat transfer modes in the system ................................................. 86
Table 6.8 Simplified heat exchange modes........................................................... 87
Table 6.9 Heat transfer model parameters for thermal network of Figure 6.7...... 89
Table 6.10 Numerical results for a panel with a single cover (no sheath) and for various absorber emittance values......................................................... 93
Table 6.11 Efficiency prediction for all prototypes .............................................. 125
Table 6.12 Collector efficiency parameters........................................................... 126
Table 6.13 Energy collection and heat losses for the water in the tank ................ 127
Table 6.14 Prediction of average system steam for truncation effects and different pipe losses from the plots of Figure 6.30 ............................. 129
Table 7.1 Assumed efficiencies for basic system components ........................... 135
Table 7.2 Assumed energy and power requirements for 6-hour operation ......... 136
Table 7.3 Average irradiance for minimum absorber area required during OPEN LOOP operation mode ............................................................. 138
Table 7.4 Average irradiance for minimum absorber area required during CLOSED LOOP operation mode ........................................................ 139
Table 7.5 Heat transfer model parameters for thermal network of Figure 7.7.... 147
Novel approaches to the design of domestic solar hot water systems xxx
Table 7.6 Numerical results for the complex double cover profile of Figure 7.22 for various airflow rates (Figure 7.6a absorber profile) ........................ 175
Table 7.7 Theoretical and experimental pipeline pressure drops.......................... 201
Table 7.8 Comparison of different values for the thermosiphon effective radius 207
Table 8.1 Projected costing for the first system developed.................................. 225
Table 8.2 Projected costing for the second system developed............................. 228
Table 8.3 Tentative sale prices for commercial versions of the SHWS............... 229
Table 9.1 Proposed materials for construction of the solar air heater panel: insulation, body structure and outer casing ......................................... 242
Table A1 Input/Output data for the solar geometry modelling program............. 254
Table E1 Modelling relationships ....................................................................... 270
Table G1 Thermal diffusivity and kinematic viscosity for air at atmospheric pressure................................................................................................ 285
Table G2 Thermal conductivity, specific heat and density for air at atmospheric pressure ........................................................................... 285
Table G3 Selected properties for water at atmospheric temperature .................. 288
Table H1 Specifications for the heat exchanger core.......................................... 290
Table H2 Specifications of the fan/blower motor ............................................... 291
Novel approaches to the design of domestic solar hot water systems xxxi
Statement of Original Authorship
The work contained in this thesis has not been previously submitted for a degree or
diploma at any other higher education institution. To the best of my knowledge and
belief, the thesis contains no material previously published or written by another
person except where due reference is made.
Signed:
Date:
Novel approaches to the design of domestic solar hot water systems xxxii
Novel approaches to the design of domestic solar hot water systems xxxiii
Acknowledgments
It is interesting how one can have different, or opposing, opinions on similar subjects
at different times of one’s life. Sometimes these might seem so contradictory that one
is left questioning how could it have ever been possible to think/act/talk/feel the way
we did before. What can be very good or pleasant at some point could become the
opposite at a later stage and vice-versa.
I had a very different view when I started this project: what I expected and wanted
and –most importantly– the reasons why I thought it was valuable. Most of it has
changed for the better.
The project has had much more value than what I anticipated and for reasons I had
not considered back then. I have greatly benefited from the interactions with other
people, which besides from the acquisition and use of academic knowledge for the
development of this venture, have allowed me to see, consider and honour other
probably even more significant aspects of humanness. The constant struggle for
“happiness” and the life we craft trying to achieve this has made me feel that it
ultimately all means a state of being/mind/existence, which apparently little has to do
with externalities but more with how we interact, bond and connect with other fellow
beings. For me, this PhD has been another milestone in the constant search for this
state and I acknowledge it as such, with its pleasant and not so pleasant events, and
am grateful to the Universe for having been able to live it.
There are many that have been part of this conjunct journey. The following is by no
means a comprehensive list and I apologise beforehand if anyone who reads this
feels left out. I do not want to be unfair to anyone, but I will address a few people
that clearly stand out:
First and foremost I wish to express my deep appreciation to my principal supervisor,
Ian Edmonds, whom from the start continuously and steadily supported me offering
his unconditional assistance in all matters related to this project. He provided the
testing facilities and on site tools that enabled the practical aspects of the project to
be carried forward from the start up to its completion. What most impressed me,
Novel approaches to the design of domestic solar hot water systems xxxiv
however, is Ian’s total focus on the creation and promotion of benevolent aspects of
technology in society and how he devotes himself wholeheartedly to such pursuits,
helping in the process those that come near him in a equally embracing way. This is
admirable. Maria, Ian’s wife, was always very dear to me, and supportive in any way
she could during the extensive periods I spent at their place. She treated me like a
member of her family and this is something for which I will remain always grateful.
My associate supervisor, Greg Michael, also provided very useful and timely
support, complementing the supervisory role shared by him and Ian. It was actually
thanks to Greg back in 2000 that I first knew about the possibility of doing this PhD
and it was after we spoke about it that everything was set in motion. Greg provided
his own, refreshing, view in tackling different problems, suggesting alternate
solutions drawn from his unique experience as a scientist and lecturer. At times he
was also a good devil’s advocate engaging the team in a pseudo-Socratic method of
discovery in the search for the solution to obstacles. Dear supervisors, I would
certainly enjoy the opportunity to continue working with you both in any related
projects and research that may become available in the future.
Special thanks go to our industry partner, Peter Sachs Industries Pty Ltd, for their
input and assistance during the first stage of the project in relation to the vapour
downward heat transport system. The interaction with them provided very useful
insight, particularly into the commercial and manufacturing areas of this technology,
so necessary in the comprehensive assessment of the feasibility of the solar hot water
units developed as domestic hot water alternatives.
Although I spent most of my time outside university premises during this research, I
recognise and am grateful for the help provided by academic and administrative staff
working “behind the scenes” so that everything ran smoothly for me. I am sure there
are many I am not even aware of. To all of you, a big THANK YOU for helping me
out. I particularly wish to thank Elizabeth Stein for her ongoing support in this regard
with her quick and sharp on-the-spot answers and solutions to every question I had
and situations in which I were involved. A/P Brian J Thomas was always there,
providing support and counsel when it was most sought with the distinct kindness
and care for the student that characterise him. The School of Physical Sciences aided
Novel approaches to the design of domestic solar hot water systems xxxv
me financially in the attendance of a paper presentation at the 2001 International
Solar Energy Society congress held in Adelaide. This was a great opportunity that
exposed me for the first time to the broader academic and current developments of
technologies in this field. I am most appreciative for this assistance.
There are those who have helped me indirectly in this process and their input and
support at earlier stages of my life has made it possible for me to be where I am now.
My mother and father are top on this list, together with my ‘other’ mom (my nanny).
They have not only given me all the emotional and physical support from very early
in life but have also supported me during the PhD to the best of their ability (despite
living on the other side of the world). My sisters are included here as well, with their
best wishes and unflinching faith in me.
My family-friends in the faith are next. They all cheered my decision of going ahead
with this research and remained excited and positive throughout, reminding me of the
greater good in all actions we engage ourselves in when done selflessly. Particular
thanks go to Venkat and Tim for their direct input during the final editing process.
Venkat, you are THE rock for all the youth and for everyone who crosses your path.
A special thanks to my dear friend, Ross Thompson, who provided invaluable
support with his simple, yet empowering self-insight techniques and methods for the
uncovering and development of human potential. I enjoyed every moment I spent in
your company and consider myself fortunate for having had that chance.
My last words of appreciation go undoubtedly to my wife, Mila. She has certainly
been there throughout these years of continuous ups and downs, taking the role of
nurturing wife and best friend with the utmost love for me. Thank you, my dear, for
your effort and care ☺.
Brisbane, 17 December 2004
Chapter 1 - Introduction
1.1 Solar energy and domestic solar hot water production
Most forms of energy available on Earth are a direct or indirect expression of solar
energy. It either manifests as kinetic or thermal energy, or is stored as chemical
energy in plants (photosynthesis). The direct expression of solar radiation as heat is
the most palpable form of solar energy we can experience. Past and present
implementation of solar energy applications1 (eg. solar clocks, passive solar
architecture) have demonstrated its usefulness.
Domestic hot water has been a common need in society. In the past, the heating of
water was only achievable by using energy extracted from the burning of renewable
(mainly wood) and non-renewable (gas, coal, oil) resources. With the advent of
electricity, electric domestic hot water systems have become mainstream, together
with the more refined gas water heaters that rely on the non-renewable fuel.
Depending on the nature of electricity production, it can have a high impact on the
environment by increasing greenhouse gases due to the burning of coal, oil and gas
in electricity power plants. In Economics, this is evidenced in the so-called
“externality costs”2, which is the ongoing financial burden borne by society as a
whole and not reflected in market transactions.
In any case it has an associated high cost to produce and –very importantly– has an
invasive effect on our biosphere. Solar energy on the other hand is environmentally
safe and totally free. Solar energy is "clean" energy.
Domestic solar hot water systems (DSHWS) have been developed in Australia with a
commercial aim since the 1960s. They date back to 1964 involving the Department
of Mechanical Engineering-CSIRO3, Australia. Patents had been sought for solar air
heating systems (SAHS) to heat water even before4 this. Since then, full commercial
development of the now well-known thermosiphon solar hot water system has led to
many modifications, refinements and improvements over the original designs.
Novel approaches to the design of domestic solar hot water systems
Chapter 1 - Introduction
2
Currently, there are two mainstream types of SHWS: the passive thermosiphon
close-coupled system and the pump-driven remotely-coupled system. The description
and operation of commercial SHWS is widely available in the literature (for
additional information, refer to bibliography). However, a brief explanation of the
operation and benefits of the two basic systems is given next.
1.2 Conventional SHWS
Most solar hot water systems (SHWS) consist of three basic parts:
• Collector panels with heat absorbing media
• Circulation system for hot fluid
• Water storage tank
Solar radiation reaching the collectors is converted into heat and a proportion of the
heat is transferred to the tank by the circulation system. This allows the supply and
temporary storage of hot water for a house or building. These systems are used for
domestic and commercial solar hot water heating. The systems are usually mounted
on rooftops and, as mentioned above, are classed as close-coupled or remotely-
coupled, depending on the location of the storage tank in relation to the panels.
The basic configuration of a thermosiphon (close-coupled) hot water system and
system components is depicted in Figure 1.1:
Figure 1.1 A conventional close-coupled thermosiphonic solar hot water system
Novel approaches to the design of domestic solar hot water systems
Chapter 1 - Introduction
3
Purpose of each of the components
Collectors: Their function is to efficiently convert solar radiation to heat and
transfer the heat to the liquid, which flows through the circulation system. In the
simplest of systems, the liquid is the water to be heated and there is no exchange
compartment in the tank. There are two types of collectors:
i) Plate and tube: An absorber plate made of copper or aluminium to which
copper pipes are bonded.
ii) Flooded plate: An absorber plate which is made by bonding together
moulded sheets of metal (usually of mild steel) containing channels
through which liquid may flow.
Storage tank: This is the reservoir for the heated water, which has been
transferred by the circulation system. There are two types of storage tanks; low
pressure copper and high pressure steel. Mains pressure tanks are usually vitreous
enamel lined to protect the steel from harsh water conditions and are fitted with a
sacrificial anode in electrical contact with the steel that will corrode first if cracks
in the enamel appear. The anode has to be replaced every 5 years.
Circulation system: In a close-coupled configuration, the circulation system is
usually a natural thermosiphon process. As the liquid heats it becomes less dense
and rises towards the tank. It enters the top of the tank while the cooler liquid
leaves the bottom and flows into the collectors.
Control and protection system: This is a combination of valves designed to
maintain pressure and temperature levels in the tank below specified levels.
Auxiliary heater: This is the backup system for heating water when solar energy
is insufficient. It is usually electrically or gas operated.
Heat dump: This is a protruding attachment from the tank to the exterior for
dumping heat to the surroundings when the hot water approaches boiling point.
Novel approaches to the design of domestic solar hot water systems
Chapter 1 - Introduction
4
Conduction, convection and radiation losses are minimised by the use of bulk
insulation of the collectors and storage tank. Convection is reduced by the use of
transparent covers (usually glass) over the absorber plate. Radiation from the
absorbers is also reduced by the use of selective surface materials with high
absorptance for solar radiation and low emittance in the thermal spectrum.
All forms of domestic solar water heating used extensively today are variations of the
original thermosiphon hot water system.
Collector improvements have been mainly achieved in better automated and
expedited production processes as well as in the use of better solar selective surfaces
for panel absorbers. Water storage tanks have been modified to include heat
exchanger compartments with heating fluids, other than water, used in the circulation
system. This is especially useful for regions where freezing conditions can occur.
Tank construction and internal wall linings, sacrificial anodes, insulation, etc, have
also been subject of better engineering and manufacturing standards.
The market has also seen the introduction of some SHWS using concentrating
collectors and evacuated tube collectors instead of flat collector plates with the
promise of added advantages. To date, solar hot water systems of this and other kinds
are being produced in China, Portugal, Spain, Israel, Turkey, Australia and the USA.
In Australia, Federal and State governments are actively encouraging the use of
alternative, environmentally friendly, energy sources as a replacement for fossil fuel
dependence by means of industry and community awareness programs in the form of
legislation, subsidies and grants. The Queensland Government is currently offering
rebates5 of up to $750 per household for the installation of new SHWS. The rebate
scheme is intended to last until the end of 2005. The Federal Government has a
Renewable Energy Certificates scheme6 through which further savings, up to $1500,
can be made on the purchase price. Each eligible solar water heater has a deemed
amount of these certificates associated with it, and they can be either assigned or
traded (sold) to receive a financial benefit. Additionally, some manufacturers offer
additional discounts on their product range that combined with the rebate and
certificates can add up to substantial savings for the end-user. Considering that a
Novel approaches to the design of domestic solar hot water systems
Chapter 1 - Introduction
5
typical SHWS costs between $2000 and $3000, the savings may offset the original
price bringing the net cost close to that of a conventional electric hot water system
($700-$1100). Despite this and due to the lack of community awareness on the
subject, general perception is that SHWS are an expensive option and so, penetration
of SHWS in Queensland and Australia, generally, is still low.
1.3 Problems and disadvantages with existing systems
There are two main characteristics of conventional SHWS that can be considered
problematic or non-advantageous. In thermosiphon systems, requiring the tank to be
placed above the panels can be a source of inconvenience for various reasons:
installation difficulty, stress placed on rooftops, servicing and repairing difficulties,
non-integration with architectural concepts (aesthetics), decommissioning difficulty.
The disadvantage of remotely-coupled systems is the added complexity of a pump
and associated control system and the additional running and maintenance costs.
As part of this project, two new SHWS were developed together with a simulation
model that predicted the performance of these
1.4 Aims and objectives
The study set out to explore and design DSHWS without the inconveniences
mentioned above. The objectives were:
- Development of a collector-boiler steam generation passive downward heat
transfer prototype for solar water heating
- Development of an air-to-water heat transfer prototype for solar water heating
- Assembly of a full scale domestic SHWS with the above devices
- Usage of low cost, “off-the-shelf” and environmentally friendly materials
- Field-testing and comparison of experimental results with prediction models
- Economic analysis and feasibility as an alternative to current SHWS
Novel approaches to the design of domestic solar hot water systems
Chapter 1 - Introduction
6
1.5 Brief outline of approach to new designs
In the first system7 (Figure 1.2), from water stored in a small roof level reservoir,
energy concentrating panels produce steam that travels downwards to a ground level
water tank.
Figure 1.2 Schematic for the vapour phase downward heat transport SHWS
Through a heat-exchanging copper loop inside the tank, steam gives up heat to the
water, condenses in the process and flows into a collection tank. After daily
operation, when the system cools down the unit recharges itself by drawing the
condensate formed during the day back up to the reservoir tank due to the partial
vacuum formed in the panels. This is a self-pumped system requiring no control
mechanisms or the aid of active (e.g. pump) or passive (e.g. valve) components to
operate.
The second system (Figure 1.3) is based on an air-heating solar panel. A fan-blower
delivers the hot air into a radiator type heat exchanger, which is connected to a hot
water tank. Despite requiring the use of active components, it was less expensive to
manufacture and install thatn the steam based system
Condensate tank
Steam heat exchanger
(optional: heat exchanger coil for indirect hot water draw-off)
Hot water tank
Footer pipe
Header
Water heater & boiler panel
Down-coming Steam
Water reservoir
Novel approaches to the design of domestic solar hot water systems
Chapter 1 - Introduction
7
Figure 1.3 Schematic for the air-to-water heat exchanger-tank coupled SHWS
The design of these two systems went hand-in-hand with the study and development
of theoretical models that could predict their performance with reasonable accuracy.
Chapters 2 through 5 give the basic theory of solar geometry, concentrating optics,
heat transfer, fluid mechanics and hydraulics used to simulate performance. Chapter
6 deals with the steam generator system and chapter 7 deals with the air heater
system. Chapter 8 gives a brief economic appraisal for each system. General
conclusions, discussions and speculation for future work are given in chapter 9
1.6 Rationale behind the selection, construction and operation of
the designs developed
The Australian Greenhouse Office (AGO) has suggested that the average use of hot
water in a domestic situation is about 50 L per person per day. This has been used by
state government institutions in advisory fact sheets and technical notes8-9
10 as a
guideline in the selection of household SHWS. For a family of four, this equates to
Hot water tank
Fan/blower
Air Heater Panel
(optional: return pipe forclosed-loop operation)
Hot air
Heat exchanger
Novel approaches to the design of domestic solar hot water systems
Chapter 1 - Introduction
8
200 L daily usage. Also, it is necessary to be able to store additional amounts of hot
water for times when the weather does not provide sufficient insolation. Suggested
figures for SHWS sizing9 are given in Table 1.1:
Table 1.1 Sizing recommendations for SHWS
No. of persons served
Hot water delivery (L/day)
Approximate tank size (L)
1-2 120 180
3-4 200 300
5-6 300 440
It is possible to obtain near boiling point temperatures with conventional domestic
hot water systems. However, it is sufficient to have temperatures between 60°-70°C
for all domestic activities. A storage temperature of around 60°C is the maximum
advisable10F
11 for pressurised water storage tanks that work with direct draw-off (water
displacement tanks). For non-pressurised tanks, heat is drawn-off indirectly by mains
water passing through an immersed heat exchanger coil in the hot water (see optional
attachment in Figure 1.2). In this case the water storage temperature must be higher,
about 70°C, in order to provide enough heat transfer from water-to-coil to obtain a
hot water output comparable to that of pressurised tanks. The two SHWS of the
project were designed for use with non-pressurised tanks. The reasons for this are
listed below:
- The non-pressurised hot water tank with electrical heating element is the least
expensive tank option available. These tanks do not require strengthening to
withstand high pressures (0.5 mm sheet copper tank is adequate) and do not
have the associated maintenance inconveniences of mains pressure tanks,
where valves and sacrificial anodes must be replaced.
- The tanks have been used in Queensland for over 50 years and perform very
well when properly sized for domestic requirements.
- The tanks allow the possibility of retrofitting a solar hot water option of the
type described in this work via an extra pair of inlet and outlet ports.
Novel approaches to the design of domestic solar hot water systems
Chapter 1 - Introduction
9
Both systems were designed to have the storage tanks at ground level. Reasons for
this are:
- The tank is located where it can be serviced easily
- There is the possibility of better shelter from the elements (less wear, less heat
losses)
- Reduction of installation costs (no lifting of tanks or accommodation on roofs)
- Reductions of other collateral costs like roof reinforcing for heavy water tanks
- Better integration with pre-existing architecture (less invasive, better
aesthetics)
The following energy target was then chosen for the design of both SHWS:
Table 1.2 Energy and water volume targets for SHWS design
Daily heating requirement: 200 L of water by 30 °C – 35 °C
Energy required: 25 – 30 MJ
The target figure of 30 MJ/day corresponds to the recommended peak daily thermal
load for large SHWS sizing for low-latitude regions of Australia11F
12 (e.g., most of
Queensland).
The reader may wish to turn directly to chapters 6 and 7, which describe the
development of the two novel SHWS and where reference is made to the basic
theory (chapters 2, 3, 4 and 5) as required.
Chapter 2 - Solar radiation and solar geometry 2.1 Introduction
Prediction of SHWS performance over time requires the knowledge of, and the
capacity to model, solar irradiation patterns and trends for objects of arbitrary shapes
under different conditions and locations worldwide.
2.2 Solar energy and solar radiation
The amount of energy per unit time per unit area received from the sun outside the
earth’s atmosphere at the mean earth-sun distance is termed the solar constant, GSC.
A value of (1367 ± 23) W/m2 is used by many references 12F
13. The extraterrestrial
radiation, however, will vary due to the earth’s elliptical orbit around the sun with
the consequential variation in the earth-sun distance. An approximate expression for
extraterrestrial radiation as a function of the day of the year13F
14 is given in Equation
2.1.
⎥⎥⎦
⎤
⎢⎢⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛ ⋅⋅+⋅=
36536003301 ncos.GG SCo (2.1)
n is the day number starting from the beginning of a calendar year, i.e., 1 < n <365
The amount of incoming radiation that is not reflected back into space is attenuated
by the earth’s atmosphere due to absorption and scattering. Direct or beam radiation
reaches the surface with very little directional change. Radiation from the rest of the
sky hemisphere that has been scattered and eventually reaches the surface is termed
diffuse radiation. The combination of both direct and diffuse radiation is termed
global radiation.
The measurements of solar radiation in this study are all measurements of global
radiation.
Novel approaches to the design of domestic solar hot water systems
Chapter 2 - Solar radiation and solar geometry
11
2.3 Air mass atmospheric transmittance model
Direct radiation on its way to the surface will traverse a certain atmospheric distance,
which will depend on the solar altitude angle, α (Figure 2.1). It is this distance that
accounts for attenuation of all sorts. It is minimum when the sun is directly above the
point of consideration (zenith point or maximum altitude angle, α = 90°).
Figure 2.1 Solar radiation travel distance through the atmosphere
Attenuation in the atmosphere can be quantified from Bouger’s Law for attenuation
of monochromatic light in a gas:
∫⋅=
⋅−D
dxk
, eI)l(I 00
λ
λλ (2.2)
Where kλ is the position- and wavelength-dependent (monochromatic) attenuation
coefficient and D is the distance travelled in the gas.
Solar radiation is not only not monochromatic, but the attenuation coefficients are
strongly dependent on the position of travel. To determine the attenuated irradiance
an approximation can be made by assuming a single, overall, attenuation factor, ‘K’
which varies with distance:
ldK
)l(cb
l
eGG∫
⋅=⋅−
00 (2.3)
The integral of Equation 2.3 is also known as the optical depth of the medium, τod(l).
For normal solar incidence (α = 90°), l = l0, and if τod(lo) = τo, the expression for direct
normal solar radiation is:
α
O
S Z
Earth’s surface
Atmosphere limit
Sun Zenith
l0 l
Novel approaches to the design of domestic solar hot water systems
Chapter 2 - Solar radiation and solar geometry
12
oeGGcbNτ−⋅= 0 (2.4)
GcbN represents the irradiance value on the surface of the earth for perpendicular
incidence arising from direct radiation.
For different solar altitude angles (from Figure 2.1):
αsinm
ll 1
0
≈= (2.5)
The quantity m, known as air mass ratio, is the ratio of an oblique path through the
atmosphere to the path when the sun is directly overhead. The approximation to the
right of Equation 2.5 may be used for solar altitude angles above 20° at sea level.
From this it is possible to formulate a general relationship for irradiance on the
surface for any solar altitude angle: m
cb eGG ⋅−⋅= 00
τ (2.6)
There are several approximations and empirical relationships offering closed forms
and ease of calculation for Gcb and the air mass ratio.
In this study the following expressions for global irradiation and air mass ratio have
been used14F
15:
( ) 584342 6146141229 .h
esinsinm −⋅⎥⎦
⎤⎢⎣⎡ ⋅−⋅+= αα (2.7)
2
0950650
0
m.m.cb ee
GG ⋅−⋅− +
= (2.8)
The air mass ratio is corrected for altitude15F
16, h. The relation 0GGcb is also called the
atmospheric transmission factor, or just atmospheric transmittance, τatm.
Irradiation on a flat surface, Gcb, is:
incatmcb cosGG θτ ⋅⋅= 0 (2.9)
where θinc is the angle between the surface and the solar beam.
Novel approaches to the design of domestic solar hot water systems
Chapter 2 - Solar radiation and solar geometry
13
2.4 Sun-earth geometry
Solar energy input on collector panels is dependent on the following factors:
- Date & Time
- Latitude
- Climatic conditions
- Collector panel orientation
- Geometric properties of the solar collector
The earth’s axis is tilted at an angle of 23.45° relative to the orbital plane. This tilt is
the main cause of the seasonal variations as the earth orbits the sun. It is convenient
to assume an apparent daily motion of the sun across the sky for all solar geometrical
calculations. This motion varies cyclically throughout the year and is defined by the
angle of declination, δ (Table 2.1). This angle varies ±23.45°, affecting the angle of
incidence of solar radiation on the surface of the earth and causing seasonal
variations in the length of the day.
For an observer on earth, the position of the sun can be completely specified by the
solar altitude angle, α, and the solar azimuth angle, ϕS. (Figure 2.2). These
quantities define the solar vector, VS.
(a) (b)
Figure 2.2 Sun path diagrams for seasonal times for a temperate austral latitude
N
Noon
8 am
6 am mid-winter
mid-summer Equinoxes
23.45°
23.45°
-40° Lat.
N
S α
ϕS
Summer
Winter
Equinox
W
Noon
8 am
6 am
VS
Novel approaches to the design of domestic solar hot water systems
Chapter 2 - Solar radiation and solar geometry
14
The time used in solar charts, diagrams and calculations is the solar time, ST, which
is often different from local standard time, LST, as this can apply over several
degrees of longitude (and 1° of longitude is equal to 4 minutes of standard time).
( ) ETminllLSTST localST ⋅⋅−+=o
4 (2.10)
lST and llocal are the standard time meridian and the local longitude, respectively. ET
is the equation of time, which is a correction factor that accounts for irregularities in
the earth’s speed around the sun.
Another fundamental quantity is the hour angle, hs, based on the 24 hours required
for the sun to “move” 360° around the earth.
omin
noonsolarlocalfromutesminhs
4= (2.11)
The determination and profiling of solar irradiance on panels of arbitrary orientation
is expressed in terms of panel azimuth, tilt, angle of incidence and solar altitude
angle, which, in turn, are related to the more fundamental quantities of hour angle,
latitude and declination. These quantities are summarised in Table 2.1
Solar geometry and sun-earth geometric relationships are well known and
documented in several sources16F
17,17F
18. Methods for determining solar radiation falling
on arbitrary tilted and tracking flat surfaces are also readily available18F
1919F20F
-21F
22.
The method is much more complex for a system of limited collection times, like
many types of concentrating collectors, and in particular the geometry of the
compound parabolic collectors (CPC) used in this project and explained in detail in
chapter 3. CPC collection times depend on their design, layout and orientation. While
a flat plate collector lying horizontally on the ground will collect sunrays for the
whole day, a concentrating device or CPC will collect for a limited time, due to a
restricted collection angle, θa < 90° (Figure 2.3)
Novel approaches to the design of domestic solar hot water systems
Chapter 2 - Solar radiation and solar geometry
15
Table 2.1 Quantities in Sun-Earth geometry
Quantities Description
Solar altitude angle, α The angle between the horizontal and the line to the sun.
Solar zenith angle, θz The angle between the vertical and the line to the sun.
Solar azimuth angle, ϕS The angle between a due north line0F
∗ and the projection of beam radiation on the horizontal plane.
Latitude, φ The angular location north or south of the equator.
Declination, δ The angular position of the sun at solar noon (i.e., when the sun is on the local meridian) with respect to the plane of the equator.
Hour angle, hs The angular displacement of the sun east or west of the local meridian due to rotation of the earth on its axis.
Angle of incidence, θinc The angle between the beam radiation on a panel and the normal to that panel.
Panel tilt angle, θ The angle between the surface of the panel and the horizontal plane.
Panel azimuth angle, ϕ The angle between the projection of the line-axis of the panel normal to the horizontal plane and due north line.
Atmospheric transmittance, τatm
Determined by natural and induced climatic conditions and geographical location.
Figure 2.3 Collection angle comparison between a flat plate and a concentrator
The general process for determining radiation collected by a solar panel over a day
involves:
1. Specifying the orientation of the panel
2. Determining the position of the sun in the sky over the day
3. Determining radiation intercepted over the day (for how long and in what way
the absorber elements of the panel “see” the sun)
∗ This definition holds for locations in the southern hemisphere. The converse is true (due south line) for the northern hemisphere.
Concentrating collector
θa
Flat plate collector
θa = 90°
Novel approaches to the design of domestic solar hot water systems
Chapter 2 - Solar radiation and solar geometry
16
For flat plates it is enough to specify azimuth and tilt angles to define the collectors'
layout because of symmetrical properties. For any orientation, (i.e. any combination
of azimuth and tilt angles) a collector of this type can be rotated by any angle, ρ,
about it’s normal and still have the same available incoming solar radiation. This is
not the case for a CPC panel, where additional angles are required to properly
determine energy collection times. The irradiance falling on the input plane of a CPC
panel will be the same as for a flat plate panel, but the actual collection times which
are dependent on the geometrical construction of the CPC, will vary with its position.
Existing mathematical relationships for calculation of general orientational aspects of
arbitrarily orientated fixed CPCs 22F
23-23F24F25F26F
27 are not straightforward as for flat plate
collectors. Derivations of such relationships focus on the determination of solar
energy input and collection times, but in doing so do not follow a standard approach.
One method of determining energy collection by fixed CPCs, which may be simpler
and more intuitive, is via a two-step process (section 2.5, next):
- Making use of algorithms and mathematical relationships for solar geometry and
terrestrial radiation calculations for arbitrary tilted surfaces.
- Considering additional relationships for the non-symmetrical characteristics of
arbitrary CPC panel layouts that, together with the solar vector, allow for proper
determination of collected solar energy.
2.5 Solar geometry and panel layout/orientation
1. Specifying the orientation of the panel
The location and layout for solar collector panels may be specified by a combination
of the following rotation angles in a 3D Cartesian system (Figure 2.4):
For a flat plate collector
· Azimuth angle, ϕ, about the normal to the plane (z-axis) (Figure 2.5)
· Tilt angle, θ, about the transverse axis of the plane (Figure 2.6)
Novel approaches to the design of domestic solar hot water systems
Chapter 2 - Solar radiation and solar geometry
17
For a CPC
· Azimuth and tilt angles as for the flat plate (θ and ϕ)
· Twist angle, ω, about the longitudinal axis of the plane (Figure 2.7)
· Rotation angle, ρ, about the normal to the plane in its final orientation1F
*
The CPC plane is identified by the unit vector normal to its surface, VN. Successive
operations of azimuth, tilt and twist result in a new positioning of this vector which
then indicates the position and orientation of the CPC plane. Changes in the actual
CPC layout can be tracked by following changes to another unit vector, VP, normal
to both VN and the line-axis of the collector (Figures 2.5 through 2.7). The final panel
position is then given by a {θ,ω,ϕ} combination and the final CPC position by
{θ,ω,ϕ,ρ}. With this in mind, the orientation of the panel can be redefined from what
is termed effective azimuth, ϕeff, and effective tilt, θeff. These are the angles that, if
applied to the plane of the CPC at starting point, give an equivalent location of the
panel as what the {θ,ω,ϕ} triad gives: {θeff, ϕeff}orientation ≡{θ,ω,ϕ}orientation
These effective angles can then used to determine the available radiation falling on
the aperture plane of the CPC depending on the position of the sun in the sky. A
general outline of how the process may be implemented is given next.
Specifying the orientation of the panel: step-by-step approach
Step 0 (starting conditions): A convenient starting position for the CPC panel is
lying flat (horizontally) with a North-South line-axis alignment as shown in
Figure 2.4.
Figure 2.4 Cartesian coordinate system for collector panel
* This extra degree of rotation has been referred to as “skewness” in the literature26 and presented as a useful parameter that could allow the optimisation of year-round energy collection for CPC devices.
N
S
E
W
y
z
x
Novel approaches to the design of domestic solar hot water systems
Chapter 2 - Solar radiation and solar geometry
18
For simplicity and illustration, only one CPC is shown on the panel. All rotations
refer to this panel.
Step 1: An azimuth angle, ϕ, is then given (rotation about the normal to the surface).
Figure 2.5 Plane of a CPC before and after azimuth rotation
Step 2*: A tilt angle, θ, is also given (rotation about the transverse axis of the panel).
Figure 2.6 Tilt angle for the plane of the CPC
At this point, the orientation of a flat plate collector relative to the starting position is
uniquely determined by these two angles.
Step 3 2F
∗: A twist, ω, angle follows (rotation about the longitudinal axis of the panel).
This angle allows for an extra degree of movement and is required for a CPC
collector.
∗ The panel may be first tilted and then twisted or vice-versa. It is noted that these operations are not commutative, i.e, tilting_and_then_twisting ≠ twisting_and_then_tilting.
θ
VN
VP VN
ϕ
VP
VN
Novel approaches to the design of domestic solar hot water systems
Chapter 2 - Solar radiation and solar geometry
19
Figure 2.7 Tilt and twist angles for the plane of a CPC
Step 4: Another rotation angle, ρ, about the normal to the surface is allowed.
Once the azimuth, tilt and twist angles are applied, it is possible to further rotate the
panel about the normal to its surface, in the same way the azimuth angle is given in
the beginning. This could be useful for investigating changes in radiation collection
times for a given {ϕ,θ,ω,ρ} panel position. The orientation remains the same but the
CPC position changes, therefore collection times also change (Figure 2.5).
Step 5: Redefining panel orientation based on effective azimuth and tilt angles
The final orientation of the CPC panel is defined by the coordinates of the unit vector
normal to its surface, VN’. This vector is expressed in polar coordinates by the tilt
and azimuth angles of its position resulting from all the rotations previously applied
(effective angles). As stated before, these angles produce the same orientation result
if applied to the plane of the CPC at starting point, but without requiring a twist
about the longitudinal axis (Figure 2.8). This is convenient since it enables
straightforward calculation of the angle of incidence, θinc, on the CPC plane from the
solar vector determination and from conventional relationships for flat surfaces,
which only require the tilt and azimuth of the surface. From the angle of incidence
the solar irradiance can be found. The calculation takes into account other quantities
as given by Table 2.1.
ωθ
VP
VN
Novel approaches to the design of domestic solar hot water systems
Chapter 2 - Solar radiation and solar geometry
20
Figure 2.8 Effective azimuth and tilt angles for the plane of a CPC and angle of incidence for
direct solar radiation
2. Determining the position of the sun in the sky during the day
The position of the sun is given by the solar unit vector, VS = {1,α,ϕS}, based on the
solar azimuth and altitude angles as defined in Figure 2.2. It was mentioned earlier
that these quantities are derived from the (more fundamental) hour angle, declination
and latitude angle and it was shown above that these three are sufficient for
determining irradiance falling on the CPC plane as far as solar position is concerned.
However, for the actual CPC collection times, it is necessary to determine the actual
azimuth and altitude of the sun and its relative position to the line-axis of the CPC.
For horizontal surfaces, the angle of incidence from direct solar radiation is the
zenith angle of the sun, which is the complementary angle to the solar altitude angle,
i.e., θz = 90-α. Calculation for solar altitude can, therefore, make use of the
relationships for irradiance on flat surfaces with no tilt.
The solar azimuth angle, ϕS, may (theoretically) vary between 0° and 360°, with the
angle convention as given previously and will depend on the declination, δ, the
latitude, φ, and the number of hours per day, n (refer to appendix A).
y x ϕ
θ ω
VN’
z
y
z
x
θeff
ϕeff VN’
θinc
Novel approaches to the design of domestic solar hot water systems
Chapter 2 - Solar radiation and solar geometry
21
3. Determining radiation intercepted by the CPC over the day, i.e.,
determining radiation collection times
The collection characteristic of the CPC is basically given by what is termed the
acceptance half-angle, θa (Figure 2.3). For collection to occur, this is the minimum
angle-value required between the projection of the solar vector on the transverse
plane perpendicular to the collector’s surface and the normal to the surface. From the
previous discussion, collection times for the CPC can then be determined as follows:
a) The collection angle, θc, between the projected solar vector on the transverse
plane, VST, and the normal to the collector’s surface, VN’, can be found for all
solar positions over the day. This is done by (Figure 2.9):
- Calculating the angles between the solar vector, VS, and VP’ and VN’, which
will give θSP’ and θSN’, respectively.
- Determining the projection of the solar vector on the axes of VP’ and VN’,
giving VSP’ and VSN’, and noting that tan(θc) = VSP’/VSN’ (Appendix A).
b) This angle can then be compared with the acceptance half-angle, θa, and if it is
smaller, collection is acknowledged.
Geometrical and analytical relationships that may be used for implementing the
process discussed so far are given in Appendix A. The computational process has
been detailed 3F
∗, based on the operations that would be required to produce the results
desired.
∗ Appendix A actually serves as a guide for implementing such process
Novel approaches to the design of domestic solar hot water systems
Chapter 2 - Solar radiation and solar geometry
22
Figure 2.9 Radiation collection and acceptance angles for an arbitrary CPC layout
y
z
x
VP’
VS
VN’
θa
VSP’
VSN’
VST
θSN
θSP
θc
Chapter 3 - Concentrating devices 3.1 Introduction
The maximum value for solar irradiance falling on the Earth’s surface cannot exceed
the value for the solar constant (1367 W/m2 - Chapter 2). The actual value received at
its peak, and for specific locations and times of the year, is more like 1100 W/m2. A
value of 1000 W/m2 (1 peak sun) has been chosen in solar research and engineering
for standardisation purposes as a figure for maximum irradiation attainable.
The Stefan-Boltzmann equation for blackbody radiation indicates the total emissive
power, Γ, in W/m2 radiated by a black body (perfect radiator) at a certain absolute
temperature. It enables calculation of an upper limit to the temperature of an object,
were it to completely absorb (and re-irradiate) this power:
Γ=⋅ 4Tσ (3.1)
where 42810675 Km/W. ⋅×= −σ , the Stefan-Boltzmann constant. At 90 °C a black
body radiates about 1000 W/m2.
Since there are other heat loss mechanisms (eg. convection, conduction) it is
uncommon for an object to reach temperatures close to the boiling point of water
under normal exposure to the sun (1000 W/m2). Clearly, for high temperature
processes (like steam production) flat plate collectors are unsuitable. The solution to
this situation is to increase the power density reaching the element of interest by
using concentrating devices.
3.2 Concentration
The development of most ideas and concepts in this section and supporting
appendices follows closely the treatise on non-imaging optics and concentration
given by Welford and Winston (see bibliography).
Novel approaches to the design of domestic solar hot water systems
Chapter 3 - Concentrating devices
24
A concentrator is an optical system that receives a certain power density and delivers
a higher power density to the element to be heated. The ratio of these two quantities
is the concentration factor, which depends on geometrical and optical system design.
The concentration ratio is defined as the ratio between the input and output aperture
areas of the optical system.
'
'
AAC =
ΓΓ
= (3.2)
For a two-dimensional system: 'wwC = w = aperture width (3.3)
For a three-dimensional system: 2
2
'aaC = a = aperture radius (3.4)
And for a black body it follows that the temperature can be increased from
T to T’, where: TCT' ⋅=4 (3.5)
Concentrators can be reflectors or refractors, can be image forming (e.g. lens arrays,
parabolic dishes) or non-imaging. They can have two- and three-dimensional axes of
symmetry (such as cylindrical surfaces) and can be continuous or segmented.
An example of an image forming concentrator is a magnifying glass (Figure 3.1). If
sunlight is perpendicular to the plane of the lens and an object is near the focal
distance, the concentration can be high enough to elevate the temperature at the focal
point above 300°C. For instance, for a lens diameter of 50 mm that produces a focal
“spot” of 6 mm diameter, the concentration factor (Equation 3.4) is about 8.3. For
this case Equation 3.5 yields an upper temperature limit, T’, of about 340°C.
Figure 3.1 Magnifying glass
50 mm 6 mm
f
Novel approaches to the design of domestic solar hot water systems
Chapter 3 - Concentrating devices
25
An example of a simple (but inefficient) non-imaging concentrator is a truncated
cone formed from reflective material (Figure 3.2). Radiation entering from the larger
aperture of the cone will tend to be “squeezed” on its way down the other end,
resulting in a concentrated output.
Figure 3.2 Cone concentrator (longitudinal profile)
3.2.1 Upper limit for concentration
The concentration ratio defined as the ratio of the output to input aperture dimensions
of the system (Equations 3.3 and 3.4) is termed the geometrical concentration ratio.
However, for every optical system there is a particular physical quantity that depends
on the spatial and angular displacement of input and output rays which remains
invariant throughout that system. This is the étendue invariant and it allows for the
determination of an optical expression for concentration ratio as well as the
maximum theoretical value obtainable. Derivation of the optical concentration from
the étendue is given in Appendix B and the expressions for maximum concentration
for 2D and 3D systems are:
θsinC D
max12 = (3.6)
θ23 1
sinC D
max = (3.7)
Where θ is the acceptance half-angle of the concentrator system.
Refractive imaging devices, like the magnifier, suffer aberrations and coma and fall
short from attaining the maximum concentration ratio, by a minimum factor of 2 for
2D systems and 4 for 3D systems27F
28. Image forming mirror systems (like parabolic
Collected ray
Ray sent
Novel approaches to the design of domestic solar hot water systems
Chapter 3 - Concentrating devices
26
troughs) that focus rays parallel to their axis on a focal point, have no spherical or
chromatic aberrations. However, off-axis beams can be highly aberrated (Figure 3.3).
Figure 3.3 Off-axis aberrations (coma) for a parabolic trough mirror
For higher concentrations coma effects will be stronger and off-axis incoming rays
will be reflected farther away from the focal point. The output aperture area
(absorber area) must be increased in order to capture these rays and the increase will
depend on how much deviation from the normal is tolerable. However, an increase in
collection area means a decrease in concentration. Mirror concentrators must
therefore be constantly directed towards the sun with high precision and accuracy in
order to minimise these effects.
There is a family of non-imaging devices known as the compound parabolic
collectors (CPC) which do not suffer from these problems and can deliver high
concentration ratios attaining the theoretical limit without sun tracking.
3.3 The Compound Parabolic Collector (CPC)
The CPC concept was proposed and developed in the 1960's 28F
29,29F
30 and shortly after
found considerable use in solar energy applications30F
31,31F
32 and continues to do so32F
33-33F34F
35.
The term "compound parabolic" is derived from the fact that it is formed from two
parabolic segments joined by one or more arc segments. Different CPC
configurations are obtained for different absorber-recievers (Figure 3.4).
a) Normal incidence b) Oblique incidence (θ < 90°)
Axis of symmetry
θ
Axis of symmetry
Novel approaches to the design of domestic solar hot water systems
Chapter 3 - Concentrating devices
27
(a) (b) (c)
Figure 3.4 CPC configurations for different absorber types.
The CPC comes very near in achieving the maximum theoretical concentration
possible, being limited basically by construction and material imperfections and
other practical problems35F
36.
Energy collection will occur when the angles between the projection of the incoming
rays on the transverse plane perpendicular to the collector’s surface and the normal to
the surface are less than, or equal to, θa (θc ≤ θa). If θc = θa the incoming rays are
extreme rays (Figure 3.5).
For the CPC configurations of Figure 3.4, the profile of the reflector consists of:
- an involute of the absorber (arc of a circle) inside the area defined by the rays
tangent to the absorbers at ±θ (dotted lines) and…
- a curve outside, such that a ray parallel to the extreme rays, falling on this curve
(wall of the CPC) and being reflected by it, touches the absorber tangentially (at
one of its extremes in the case of flat receivers).
For example, for the vertical fin this corresponds to:
- a circular arc segment (with centre at the top of the absorber and radius a/2)
beneath and inside the dashed lines and…
- two tilted parabolic sections outside the lines, where any extreme rays falling on
these will be reflected such that they are just tangent to the absorber (they just
touch the absorber top).
Novel approaches to the design of domestic solar hot water systems
Chapter 3 - Concentrating devices
28
Figure 3.5 Projection of incoming solar ray on transverse CPC plane, normal to the surface
3.3.1 Conceptualisation of the CPC and the “edge-ray” principle
The CPC must be an optical system such that rays entering the input aperture within
a certain angular acceptance range are all admitted at the output aperture. The task is
then to produce reflector shapes that accomplish this. For ideal concentrators,
extreme input rays become extreme output rays. This is known as the edge-ray
principle. Although it is not sufficient (cannot be proven) to guarantee ideal
concentration in non-imaging optical concentrator systems, in practice it is found that
designs based on this principle have very high concentration ratios, and so it is a
valuable heuristic tool for concentrator design.
An example of a simple collecting 2D CPC is given in Figures 3.6 and 3.7. It is
designed to concentrate the light from an input aperture w down to a smaller aperture
w’ where a collector/absorber is placed (eg. flat plate, photovoltaic panel, etc). The
acceptance half-angle is θ and so the concentrator will have an angular acceptance
range of ±θ about its axis. In Figure 3.6, the blue rays are extreme rays that get
reflected from the upper section of the concentrator to point P’. Likewise, extreme
rays being reflected from the lower section will end up at point P (red ray). Rays
entering the system at a larger angle of incidence (green ray) will be turned back. All
other rays will be collected at some point over the extension of the exit aperture.
θcθa
Novel approaches to the design of domestic solar hot water systems
Chapter 3 - Concentrating devices
29
Figure 3.6 Edge-ray principle for 2D CPC
The parabolic reflector shape has the property that any ray parallel to the axis of the
parabola will be reflected to the focal point. In the design of Figure 3.6, it is required
for all extreme rays incident on the upper reflector wall to be reflected to point P’.
The reflector shape is therefore obtained as a section of a parabola with focus at P’
and axis parallel to the direction of the extreme rays. The lower reflector wall is
obtained in an analogous way. Figure 3.7 shows the parabolas, their axes and focal
points for both CPC segments.
Figure 3.7 The CPC profile as compounded parabolic segments
2θ
θ
P'
P
w'
w
Parabola axis (for upper reflector section)
o
Blue and red rays are extreme rays (θ) that are collected at the rim of the aperture exit. The green ray has a direction greater than θ and is reflected back
P’ P
2θ
Novel approaches to the design of domestic solar hot water systems
Chapter 3 - Concentrating devices
30
Concentrating devices constructed in this way will have profiles made up of
compounded parabolic segments, hence the name for these concentrators4F
*.
Formalisation of the CPC profile derivation based on the geometrical relationships of
the parabolic segments and their mathematical formulation is given in Appendix C
together with the derivation and construction of the horizontal absorber profile.
3.4 Exploring CPC orientations and collection times
Being able to fully determine CPC shapes, layouts and orientations, daily irradiance
profiles and collection times for a CPC configuration were explored for various
positions/orientations and for different times of the year. Figures 3.8-3.20 plot these
for a few select orientations. The latitude used in these examples was the latitude for
Brisbane, Queensland – Australia: φ = -27.5°. The day was counted from the
beginning of the calendar year and for most of the plots it corresponded to the
autumn equinox, March 21st- 22nd (day = 81) when the declination is zero.
The irradiance profiles show the amount of energy intercepted over the day by a CPC
with a 30° acceptance half-angle (concentration ratio of 2). The collection versus
time plots show the variation of the collection angle, θc, over the day and whether or
not its values fall within the admittance range of ±30°. The CPC icon on the top-right
corner of the irradiance plots represents the layout for the collector plane after all
rotations have been applied. The line-axis of the collector is represented by the
position of this icon, indicating the azimuth rotation. After this rotation, the panel can
be tilted or twisted or both. The red dot indicates a tilt in the given direction. The
yellow dot indicates a twist in the given direction. The effect of the optional
ρ-rotation is shown for the later plots as a potential useful parameter for year-round
orientation optimisation for energy collection.
*Not all non-imaging concentrators are made of compound parabolic segments as it depends on the nature of the exit aperture or energy collection absorber/receiver. An example of this is the circular absorber concentrator profile shown in fig. 3.4a, which has no parabolic sections.
Novel approaches to the design of domestic solar hot water systems
Chapter 3 - Concentrating devices
31
(a)
(b)
Figure 3.8 Irradiation profile and collection times for east-west orientation and north
facing collector, i.e., twisted to the latitude angle
6 7 8 9 10 11 12 13 14 15 16 17 180
100
200
300
400
500
600
700
800
900
Irradiance variation over a day
Hour of the day
Irrad
ianc
e (W
/m²)
Latitude = -27.5° Day = 81 Original azimuth = 90° Original tilt = 0° Twist = 27.5° ρ-rotation = 0° Effective azimuth = 0° Effective tilt = 27.5° Concentration ratio = 2 Acceptance angle = 30°
N
E
S
W
6 7 8 9 10 11 12 13 14 15 16 17 18-90
-75
-60
-45
-30
-15
0
15
30
45
60
75
90
Hour of the day
Solar energy collection times over a day
Angle collection limits
Ang
le ( θ
c ) bet
wee
n th
e no
rmal
to th
e su
rfac
e an
d th
e so
lar v
ecto
r pr
ojec
tion
on th
e tr
ansv
erse
pla
ne p
erpe
ndic
ular
to th
e su
rfac
e
Novel approaches to the design of domestic solar hot water systems
Chapter 3 - Concentrating devices
32
(a)
(b)
Figure 3.9 Irradiation profile and collection times for north-south alignment and north
facing collector, i.e., tilted to the latitude angle
6 7 8 9 10 11 12 13 14 15 16 17 18 0
100
200
300
400
500
600
700
800
900
Irradiance variation over a day
Hour of the day
Irrad
ianc
e (W
/m²)
Latitude = -27.5° Day = 81 Original azimuth = 0° Original tilt = 27.5° Twist = 0° ρ-rotation = 0° Effective azimuth = 0° Effective tilt = 27.5° Concentration ratio = 2Acceptance angle = 30°
N
EW
S
6 7 8 9 10 11 12 13 14 15 16 17 18 -90
-75
-60
-45
-30
-15
0
15
30
45
60
75
90
Hour of the day
Solar energy collection times over a day
Angle collection limits
Ang
le ( θ
c ) bet
wee
n th
e no
rmal
to th
e su
rfac
e an
d th
e so
lar v
ecto
r pr
ojec
tion
on th
e tr
ansv
erse
pla
ne p
erpe
ndic
ular
to th
e su
rfac
e
Novel approaches to the design of domestic solar hot water systems
Chapter 3 - Concentrating devices
33
(a)
(b)
Figure 3.10 Irradiation profile and collection times for northeast-southwest aligned
collector, tilted to the latitude angle
6 7 8 9 10 11 12 13 14 15 16 17 180
100
200
300
400
500
600
700
800
900
Irradiance variation over a day
Hour of the day
Irrad
ianc
e (W
/m²)
Acceptance angle = 30°Concentration ratio = 2
Effective tilt = 27.5° Effective azimuth = 45°
ρ-otation = 0° Twist = 0° Original tilt = 27.5° Original azimuth = 45°
Day = 81 Latitude = -27.5°
N
E
S
W
6 7 8 9 10 11 12 13 14 15 16 17 18-90
-75
-60
-45
-30
-15
0
15
30
45
60
75
90
Hour of the day
Solar energy collection times over a day Angle collection limits
Ang
le ( θ
c ) bet
wee
n th
e no
rmal
to th
e su
rfac
e an
d th
e so
lar v
ecto
r pr
ojec
tion
on th
e tr
ansv
erse
pla
ne p
erpe
ndic
ular
to th
e su
rfac
e
Novel approaches to the design of domestic solar hot water systems
Chapter 3 - Concentrating devices
34
(a)
(b)
Figure 3.11 Irradiation profile and collection times for northwest-southeast aligned
collector, twisted to the latitude angle
6 7 8 9 10 11 12 13 14 15 16 17 18 0
100
200
300
400
500
600
700
800
900
Irradiance variation over a day
Hour of the day
Irrad
ianc
e (W
/m²)
Latitude = -27.5° Day = 81 Original azimuth = 315° Original tilt = 0° Twist = -27.5° ρ-otation = 0° Effective azimuth = 45° Effective tilt = 27.5° Concentration ratio = 2 Acceptance angle = 30°
N
E
S
W
6 7 8 9 10 11 12 13 14 15 16 17 18 -90
-75
-60
-45
-30
-15
0
15
30
45
60
75
90
Hour of the day
Solar energy collection times over a day Angle collection limits
Ang
le ( θ
c ) bet
wee
n th
e no
rmal
to th
e su
rfac
e an
d th
e so
lar v
ecto
r pr
ojec
tion
on th
e tr
ansv
erse
pla
ne p
erpe
ndic
ular
to th
e su
rfac
e
Novel approaches to the design of domestic solar hot water systems
Chapter 3 - Concentrating devices
35
(a)
(b)
Figure 3.12 Irradiation profile and collection times for east-west aligned collector, twisted
to the latitude angle and tilted east
6 7 8 9 10 11 12 13 14 15 16 17 180
100
200
300
400
500
600
700
800
900
Irradiance variation over a day
Hour of the day
Irrad
ianc
e (W
/m²)
Latitude = -27.5° Day = 81 Original azimuth = 90°Original tilt = 30° Twist = 27.5° ρ-rotation = 0° Effective azimuth = 51.35° Effective tilt = 39.81°
Concentration ratio = 2Acceptance angle = 30°
N
E
S
W
Ang
le ( θ
c ) bet
wee
n th
e no
rmal
to th
e su
rfac
e an
d th
e so
lar v
ecto
r pr
ojec
tion
on th
e tr
ansv
erse
pla
ne p
erpe
ndic
ular
to th
e su
rfac
e
6 7 8 9 10 11 12 13 14 15 16 17 18-90
-75
-60
-45
-30
-15
0
15
30
45
60
75
90
Hour of the day
Solar energy collection times over a day Angle collection limits
Novel approaches to the design of domestic solar hot water systems
Chapter 3 - Concentrating devices
36
(a)
(b)
Figure 3.13 Irradiation profile and collection times for east-west aligned collector, twisted
to the latitude angle, tilted east & rotated 5° about its normal
6 7 8 9 10 11 12 13 14 15 16 17 18 0
100
200
300
400
500
600
700
800
900
Irradiance variation over a day
Hour of the day
Irrad
ianc
e (W
/m²)
Latitude = -27.5° Day = 81 Original azimuth = 90° Original tilt = 30° Twist = 27.5° ρ-rotation = 5°
Effective azimuth = 51.35° Effective tilt = 39.81° Concentration ratio = 2 Acceptance angle = 30°
N
E
S
W
6 7 8 9 10 11 12 13 14 15 16 17 18 -90
-75
-60
-45
-30
-15
0
15
30
45
60
75
90
Hour of the day
Solar energy collection times over a day
Angle collection limits
Ang
le ( θ
c ) bet
wee
n th
e no
rmal
to th
e su
rfac
e an
d th
e so
lar v
ecto
r pr
ojec
tion
on th
e tr
ansv
erse
pla
ne p
erpe
ndic
ular
to th
e su
rfac
e
Novel approaches to the design of domestic solar hot water systems
Chapter 3 - Concentrating devices
37
(a)
(b)
Figure 3.14 Irradiation profile and collection times for east-west aligned collector, twisted
to the latitude angle, tilted east & rotated 10° about its normal
6 7 8 9 10 11 12 13 14 15 16 17 180
100
200
300
400
500
600
700
800
900
Irradiance variation over a day
Hour of the day
Irrad
ianc
e (W
/m²)
Latitude = -27.5° Day = 81 Original azimuth = 90° Original tilt = 30° Twist = 27.5° ρ-rotation = 10°
Effective azimuth = 51.35° Effective tilt = 39.81°
Concentration ratio = 2Acceptance angle = 30°
N
E
S
W
Ang
le ( θ
c ) bet
wee
n th
e no
rmal
to th
e su
rfac
e an
d th
e so
lar v
ecto
r pr
ojec
tion
on th
e tr
ansv
erse
pla
ne p
erpe
ndic
ular
to th
e su
rfac
e
6 7 8 9 10 11 12 13 14 15 16 17 18-90
-75
-60
-45
-30
-15
0
15
30
45
60
75
90
Hour of the day
Solar energy collection times over a day
Angle collection limits
Novel approaches to the design of domestic solar hot water systems
Chapter 3 - Concentrating devices
38
(a)
(b)
Figure 3.15 Irradiation profile and collection times for east-west aligned collector, twisted
to the latitude angle, tilted east & rotated 20° about its normal
6 7 8 9 10 11 12 13 14 15 16 17 18 0
100
200
300
400
500
600
700
800
900
Irradiance variation over a day
Hour of the day
Irrad
ianc
e (W
/m²)
Latitude = -27.5° Day = 81 Original azimuth = 90° Original tilt = 30° Twist = 27.5° ρ-rotation = 20°
Effective azimuth = 51.35° Effective tilt = 39.81° Concentration ratio = 2 Acceptance angle = 30°
N
E
S
W
6 7 8 9 10 11 12 13 14 15 16 17 18 -90
-75
-60
-45
-30
-15
0
15
30
45
60
75
90
Hour of the day
Solar energy collection times over a day
Angle collection limits
Ang
le ( θ
c ) bet
wee
n th
e no
rmal
to th
e su
rfac
e an
d th
e so
lar v
ecto
r pr
ojec
tion
on th
e tr
ansv
erse
pla
ne p
erpe
ndic
ular
to th
e su
rfac
e
Novel approaches to the design of domestic solar hot water systems
Chapter 3 - Concentrating devices
39
(a)
(b)
Figure 3.16 Irradiation profile and collection times for east-west aligned collector, twisted
to the latitude angle, tilted east & rotated 30° about its normal
6 7 8 9 10 11 12 13 14 15 16 17 180
100
200
300
400
500
600
700
800
900
Irradiance variation over a day
Hour of the day
Irrad
ianc
e (W
/m²)
Latitude = -27.5° Day = 81 Original azimuth = 90° Original tilt = 30° Twist = 27.5° ρ-rotation = 30°
Effective azimuth = 51.35° Effective tilt = 39.81°
Concentration ratio = 2Acceptance angle = 30°
N
E
S
W
6 7 8 9 10 11 12 13 14 15 16 17 18-90
-75
-60
-45
-30
-15
0
15
30
45
60
75
90
Hour of the day
Solar energy collection times over a day
Angle collection limits
Ang
le ( θ
c ) bet
wee
n th
e no
rmal
to th
e su
rfac
e an
d th
e so
lar v
ecto
r pr
ojec
tion
on th
e tr
ansv
erse
pla
ne p
erpe
ndic
ular
to th
e su
rfac
e
Novel approaches to the design of domestic solar hot water systems
Chapter 3 - Concentrating devices
40
(a)
(b)
Figure 3.17 Irradiation profile and collection times for east-west aligned collector, with a
30° twist angle and a 20° tilt – summer solstice
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 0
100
200
300
400
500
600
700
800
900 Irradiance variation over a day
Hour of the day
Irrad
ianc
e (W
/m²) Latitude = -27.5°
Day = 356
Original azimuth = 90° Original tilt = 20° Twist = 30° ρ-rotation = 0°
Effective azimuth = 36.05° Effective tilt = 35.53° Concentration ratio = 2 Acceptance angle = 30°
N
E
S
W
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 -90
-75
-60
-45
-30
-15
0
15
30
45
60
75
90
Hour of the day
Solar energy collection times over a day
Angle collection limits
Ang
le ( θ
c ) bet
wee
n th
e no
rmal
to th
e su
rfac
e an
d th
e so
lar v
ecto
r pr
ojec
tion
on th
e tr
ansv
erse
pla
ne p
erpe
ndic
ular
to th
e su
rfac
e
Novel approaches to the design of domestic solar hot water systems
Chapter 3 - Concentrating devices
41
(a)
(b)
Figure 3.18 Irradiation profile and collection times for east-west aligned collector, with a
30° twist angle and a 20° tilt – winter solstice
6 7 8 9 10 11 12 13 14 15 16 17 180
100
200
300
400
500
600
700
Irradiance variation over a day
Hour of the day
Irrad
ianc
e (W
/m²) Latitude = -27.5°
Day = 171 Original azimuth = 90° Original tilt = 20° Twist = 30° ρ-rotation = 0°
Effective azimuth = 36.05° Effective tilt = 35.53°
Concentration ratio = 2Acceptance angle = 30°
N
E
S
W
6 7 8 9 10 11 12 13 14 15 16 17 18-90
-75
-60
-45
-30
-15
0
15
30
45
60
75
90
Hour of the day
Solar energy collection times over a day
Angle collection limits
Ang
le ( θ
c ) bet
wee
n th
e no
rmal
to th
e su
rfac
e an
d th
e so
lar v
ecto
r pr
ojec
tion
on th
e tr
ansv
erse
pla
ne p
erpe
ndic
ular
to th
e su
rfac
e
Novel approaches to the design of domestic solar hot water systems
Chapter 3 - Concentrating devices
42
(a)
(b)
Figure 3.19 Irradiation profile for a northwest facing collector with a 20° tilt, before and
after a +25° ρ-rotation – summer solstice
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 0
100
200
300
400
500
600
700
800
900
1000 Irradiance variation over a day
Hour of the day
Irrad
ianc
e (W
/m²)
Latitude = -27.5° Day = 356 Original azimuth = 315° Original tilt = 20° Twist = 0° ρ-rotation = 0°
Effective azimuth = 315° Effective tilt = 20° Concentration ratio = 2 Acceptance angle = 30°
S
W E
N
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 0
100
200
300
400
500
600
700
800
900
1000 Irradiance variation over a day
Hour of the day
Irrad
ianc
e (W
/m²)
Latitude = -27.5° Day = 356 Original azimuth = 315° Original tilt = 20° Twist = 0° ρ-rotation = 25°
Effective azimuth = 315° Effective tilt = 20° Concentration ratio = 2 Acceptance angle = 30°
S
W E
N
Novel approaches to the design of domestic solar hot water systems
Chapter 3 - Concentrating devices
43
(a)
(b)
Figure 3.20 Irradiation profile for a northwest facing collector with a 20° tilt, before and
after a +25° ρ-rotation – winter solstice
6 7 8 9 10 11 12 13 14 15 16 17 180
100
200
300
400
500
600
Irradiance variation over a day
Hour of the day
Irrad
ianc
e (W
/m²)
Latitude = -27.5° Day = 171 Original azimuth = 315° Original tilt = 20° Twist = 0° ρ-rotation = 25°
Effective azimuth = 315° Effective tilt = 20° Concentration ratio = 2Acceptance angle = 30°
S
W E
N
6 7 8 9 10 11 12 13 14 15 16 17 180
100
200
300
400
500
600
Irradiance variation over a day
Hour of the day
Irrad
ianc
e (W
/m²)
Latitude = -27.5° Day = 171 Original azimuth = 315° Original tilt = 20° Twist = 0° ρ-rotation = 0°
Effective azimuth = 315° Effective tilt = 20° Concentration ratio = 2Acceptance angle = 30°
S
W E
N
Novel approaches to the design of domestic solar hot water systems
Chapter 3 - Concentrating devices
44
At solar noon, the incidence angle θinc on the plane of the collector is equal to the
absolute value of the difference between the latitude and the declination.
δφθ −=noon_inc (3.13)
During equinox, θinc_noon = φ (since δ = 0) and the results from Figure 3.8 show that
an east-west aligned collector, facing north, with a twist angle equal to the latitude
angle, maximises energy collection. Any other orientation (e.g., Figures 3.9-3.11)
will result in less collection times and also reduced available energy. However, in
order for the collector to work properly, a tilt angle must be present so that the water
is gravity-fed into the boilers and steam can be produced and delivered adequately.
Figure 3.12 shows an orientation for this case where a tilt angle is used, and the
collector faces northeast. Collection is biased towards the morning hours, due to the
tilt, and ends earlier in the afternoon.
Figure 3.9 shows the usual orientation for flat panel collectors, facing due north and
tilted to the latitude angle. Since the CPC under consideration has an acceptance
half-angle of 30°, in this orientation, the collection period is limited to 2 hours before
and after solar noon time (i.e., 4 hours total).
Figures 3.10 and 3.11 have essentially the same panel (not CPC) orientation, facing
due northeast, with the collector tilted and twisted as indicated. The available energy
falling on the panel is the same in both cases but collection times are different due to
the CPC layout, which is substantially different for each.
Figures 3.13-3.16 have the same panel orientation as Figure 3.12 but include the
effect of applying the ρ-rotation. Note how the effect in this case is only a restriction
in CPC collection (as in the example above). The available energy falling on the
plane of the CPC is the same, but collection times are reduced.
Optimisation of CPC energy collection for any date of the year is not a
straightforward exercise (except perhaps for the equinoxes). Different dates will
require different orientations. There is no single optimal orientation. Satisfying a
Novel approaches to the design of domestic solar hot water systems
Chapter 3 - Concentrating devices
45
maximisation criterion on a regular basis (monthly, or even quarterly) is far from
practical since it would require constant adjustment of the collector, defeating the
purpose of having a stationary concentrator in the first place. A compromise must be
reached by selecting an orientation that will satisfy winter and summer requirements
as best as possible. A first approximation for this year-round single orientation is the
one which maximises collection during equinox with early morning bias and a slight
winter bias: an east-west aligned collector, with a twist angle greater than the latitude
angle and a shallow tilt angle for operational purposes (this makes for a northeast
facing collector). Results for the summer and winter solstices with this CPC
orientation for Brisbane are given by Figures 3.17 and 3.18, respectively. In this
situation collection is sacrificed during summer for the benefit of an increased energy
collection during winter. It is standard practice to incorporate a winter bias design, or
setup, in SHWS in order to maximise collection during this season since less
radiation is available and the load on the system is higher.
In reality, most SHWS are mounted on roofs that constrain their orientation leaving
little flexibility in the selection of azimuth and tilt angles (not to mention twist
angles) precluding optimal collection. In most cases, panels rest on roof surfaces
relying on roof pitch angle with its attendant shortcomings.
An annual optimal collector configuration requires a study of the varying conditions
from seasonal changes and collection restrictions imposed by the site.
It has been suggested that once CPC panels are located on a roof, optimisation may
follow by conveniently “skewing” the collector25, which is similar to giving the panel
a ρ-rotation as mentioned in this study. An example of how this can be done and the
effect it may have is given by Figures 3.19 and 3.20 which show the difference in
energy collection for a SHWS located flush on a northwest facing roof, with a 20°
pitch, before and after a ρ-rotation of 25°, and for summer and winter solstices. The
rotation angle was selected ad-hoc. For the winter solstice, the application of this
rotation biases the energy collection earlier in the day. Collection starts and finishes
about 45 and 85 minutes earlier, respectively. Although the overall collection time
decreases, the early available irradiance is much higher than what is available in the
last 85 minutes of operation. The total energy collected for the rotated configuration
Novel approaches to the design of domestic solar hot water systems
Chapter 3 - Concentrating devices
46
is higher than for the original orientation. This rotation, therefore, enhances steam
production for the day, making better use of the available energy falling on the plane
of the collector.
On the other hand, for the summer solstice it is evident from Figure 3.19 that there is
a total decrease in collection times and energy collection. The first 55 minutes of
collection are eliminated with this rotation rendering this configuration seemingly
inefficient. However, the irradiance available in the first 50 minutes is the lowest of
the entire collection time. This means that the fraction of energy collected during this
period is smaller that at any other comparable period during the day and is close to
about 15% of the total collectable energy. The application of this rotation may be
justified on the grounds that little inconvenience may be experienced by this energy
decrease in summer (due to less demand and overall lower heat losses) offsetting
appreciable winter gains (higher load on the system).
The above brief examination points to the need for a more detailed inspection
covering additional dates and actual steam production. It is possible that in the
example above, actual optimisation involves an even stronger winter bias (i.e., ρ >
25°). What this shows is that the application of a ρ-rotation can improve year-round
collection for a particular SHWS orientation. An optimisation of this nature could be
built into the solar geometry and panel orientation programming code and would
certainly be an avenue for improvement in the future.
Chapter 4 - Heat transfer 4.1 Introduction
The energy exchanged between bodies of different temperatures is called heat
transfer. It occurs via three different mechanisms (or modes of transfer):
• Conduction
• Convection
• Radiation
An example of these transfer modes is sketched in Figure 4.1 for a cooling hot plate.
Figure 4.1 Convection, conduction and radiation heat transfer (qc, qk, qr, respectively) for a hot
plate exposed to a cool environment, Tp > Tair
In solar thermal processes, a way of assessing heat transfer amongst the elements of
the systems (eg., SHWS) is required for system design and performance prediction.
4.1.1 Conduction heat transfer
This transfer mode occurs in a body when a temperature gradient exists, where heat
travels to the region of lower temperature. The heat transfer rate in this case is
proportional to the temperature gradient times the area through which heat transfer
occurs (Figure 4.1):
x qk
qr
Tair
A
TP
qc
Novel approaches to the design of domestic solar hot water systems
Chapter 4 - Heat transfer
48
xTAkqk ∂
∂⋅⋅−= (4.1)
Equation 4.1 is also known as Fourier’s Law of heat conduction. The proportionality
constant, k, is the thermal conductivity of the material. The negative sign indicates
that heat flows to the region of low temperature, as required by the 2nd law of
thermodynamics.
4.1.2 Convection heat transfer
This transfer mode occurs when fluids come in contact with solid objects. Heat
transfer in this case is proportional to the temperature difference between the fluid
and object’s surface and the surface area in contact by the fluid (Figure 4.1):
( )fscc TTAhq −⋅⋅= (4.2)
This is also known as Newton’s Law of cooling. Parameter hc is the convection heat
transfer coefficient and is temperature-dependent. It can be calculated analytically for
some (rather simple) systems and must be found experimentally, or inferred by using
computational fluid dynamics (CFD), in more complex scenarios.
There are two kinds of convection modes:
a) Free convection
When natural buoyant forces occur as a consequence of density differences in a fluid
that has come in contact with the surface of an object at a different temperature. An
example of this is the heat loss on the top (hot) cover of a flat plate solar collector
when no wind is blowing over it.
b) Forced convection
When a fluid is forced past the surface of an object at a different temperature. Due to
the higher fluid velocity, more heat can be transferred between fluid and object. An
example would be the same collector plate as before under windy conditions.
Novel approaches to the design of domestic solar hot water systems
Chapter 4 - Heat transfer
49
4.1.3 Radiation heat transfer
This transfer mode occurs via electromagnetic radiation emission and absorption
between bodies of different temperatures and is termed thermal radiation. It requires
no solid medium to propagate. The most obvious example of this is solar radiation
collected on the Earth’s surface. In Chapter 3, it was mentioned that the total
emissive power of a blackbody, or perfect emitter of thermal radiation, was
proportional to the fourth power of its temperature, as given by the Stefan-Boltzmann
equation (Equation 3.1). This can be re-written for energy rate emission, or power,
as:
4TAqr ⋅⋅= σ (4.3)
Since there are no perfect radiators, Equation 4.3 represents an upper limit for
radiation emission of real bodies. To account for this, a quantity known as emissivity,
ε, and defined as the ratio between the emissive power of a body to the emissive
power of a blackbody at the same temperature, is introduced in the previous
equation. Furthermore, during radiation heat exchange between finite surfaces, not
all the radiation emitted by one surface will reach the other, since some will be lost to
the surroundings. This is influenced by physical and geometrical properties of the
surfaces and is quantified by the parameter known as the view, or shape, factor, F12.
For radiation exchange between two surfaces, the net thermal energy transfer from
surface-1 to surface-2 can be approximated by:
( )
22
2
12111
1
42
411221
111AFAA
TTqq rr
⋅−
+⋅
+⋅
−−⋅
=−= ↔↔
εε
εε
σ (4.4)
The emissivity of “real” surfaces is dependent on wavelength, temperature and the
physical and geometrical properties of the surface. In order to use a constant value
for emissivity (and enable an otherwise nearly impossible analytical calculation), the
following assumptions are made:
- Radiation properties are independent of wavelength
- Surfaces are diffuse (radiation emitted equally in all directions)
Novel approaches to the design of domestic solar hot water systems
Chapter 4 - Heat transfer
50
- Surface temperatures are uniform
- Incident energy over the surfaces is uniform
When radiation interacts with matter, part of it is reflected, part is absorbed and for
translucent materials, part is transmitted. The following equation is obtained from the
1st law of thermodynamics and establishes a relationship between the fraction of
radiation reflected, ρ, the fraction absorbed, α, and the fraction transmitted, τ:
1=++ ταρ (4.5)
For bodies that are opaque to thermal radiation, τ = 0. The absorptivity of a body for
a given wavelength is equal to the emissivity of that body, i.e., α = ε. This is called
Kirchhoff’s identity.
In the following sections, heat transfer equations pertaining to the elements of the
SHWS developed are detailed and discussed.
4.2 Selected heat transfer equations and other relationships
Heat flow by convection, radiation and conduction between two arbitrary surfaces
may be expressed in a general form by the following equation:
)TT(hAQ T 211 −⋅⋅= (4.6)
Where: Q = heat or flow of thermal energy (W)
A1 = area of the surface (m2)
hT = heat transfer coefficient (W/m2 ·°C)
T1 -T2 = ΔT = the difference in temperatures between the elements (°C)
Equation 4.6 was the relation used in all heat transfer mode calculations in this study.
For additional information of the different parameters and quantities used hereafter,
refer to Appendix D.
Novel approaches to the design of domestic solar hot water systems
Chapter 4 - Heat transfer
51
4.2.1 Convection in SHWS
The general expression for the convection heat transfer coefficient involving flat
plates, hT, is:
LkNuhT ⋅= (4.7)
Nu is the Nusselt number, k is the thermal conductivity of the fluid (W/m ·°C) and L
is the characteristic length (m).
Convection problems usually rely on finding the Nusselt number in order to obtain
the heat transfer coefficient and finally the heat transferred, via Equation 4.6. The
characteristic length, L, depends on the actual convection situation, relating on most
occasions to the main dimension of the heated surface.
4.2.1.1 Free convection between a flat plate and the surroundings
Different empirical expressions for Nusselt number calculations have been used in
the simulation of the two SHWS developed. The reasons owe to operational
differences between them and the availability of additional resources during
development of the second system.
For the vapour phase downward heat transport SHWS
For isothermal plates, the following relationships were employed36F
37:
⎪⎩
⎪⎨⎧
≤<⋅⋅
⋅≤≤⋅⋅=
11631
6441
10108150
108102540
ff
fff
RaforRa.
RaforRa.Nu
( )( )b.
a.8484
Raf is called the Rayleigh number, which is the product of two other quantities, the
Grashof, Gr, and Prandtl, Pr, numbers (Appendix D).
Novel approaches to the design of domestic solar hot water systems
Chapter 4 - Heat transfer
52
For the air-to-water heat exchange SHWS
The heat transfer coefficient for an isothermal plate of arbitrary tilt angle was
calculated from the following relationships37F
38:
a) Horizontal plate (from Appendix D)
( ) 10110
lH10tHH NuNuNu += (4.9)
4.2.1.2 Forced convection between a flat plate and the surroundings
For an isothermal flat plate the following relationship was used38F
39:
21
31
x3320Nu RePr. ⋅⋅= (4.10)
The quantity Rex is called the Reynolds number. It is an indicator of the nature of the
flow; whether it is laminar, transitional or turbulent. Fluid flow over a surface is
influenced by its proximity to the surface, which will cause it to develop a particular
velocity flow profile. The flow is laminar when the fluid behaves as if it could be
characterised by a series of juxtaposed layers, moving uniformly, where the path of
individual fluid particles do not cross each other. In this case, adjacent fluid layers
move at nearly the same velocity. The flow becomes turbulent when paths of
individual fluid particles are erratic and cross each other, as if in the presence of a
random churning action. The flow is transitional during the process when it departs
from being laminar and advances towards turbulence.
For this case, x = l, since the entire length of the collector was considered. The heat
transfer coefficient for forced convection was averaged over this length and the result
was twice the value obtained from Equation 4.7:
forcedforced hchc ⋅= 2 (4.11)
And the final result for the convection heat transfer coefficient, hc, between a flat
plate and the surroundings was:
Novel approaches to the design of domestic solar hot water systems
Chapter 4 - Heat transfer
53
[ ]maxccc forcedfree
h,hh = (4.12)
For the air-to-water SHWS developed in the later stages of this project (Chapter 7), it
was necessary to determine the heat losses from large circular pipes carrying hot air.
Calculation of convection heat transfer over cylinders enabled this. The most
conservative approach in this case was to take the maximum value between free and
forced convection over horizontal and vertical pipes.
4.2.1.3 Free convection from horizontal cylinders
The air-heating system was designed as a split system, with the heating panel located
on the roof and the tank at ground level. The heating/exchange fluid was hot air and
it was transported downward via vertical plastic pipes. In a general case, however, a
system like this could also require horizontal pipes, or be mainly composed of them,
like when it is all set at the same level (e.g., tank and panel at ground level).
A conservative expression was used for the Nusselt number over a wide range of
Rayleigh numbers39:
( )
26
1
916
169
559013870600
⎪⎪⎪
⎭
⎪⎪⎪
⎬
⎫
⎪⎪⎪
⎩
⎪⎪⎪
⎨
⎧
⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢
⎣
⎡
⎥⎦⎤
⎢⎣⎡ +
⋅+=
Pr.
Ra..Nu freeH (4.13)
Where:
4.2.1.4 Free convection from vertical cylinders
In this case, vertical cylinders were treated as vertical flat plates by using the
following expression38:
Novel approaches to the design of domestic solar hot water systems
Chapter 4 - Heat transfer
54
( )9
4
169
41
49201
670680
⎥⎦⎤
⎢⎣⎡ +
⋅+=
Pr.
Ra..Nu freeV (4.14)
Where: 92 1010 << Ra
4.2.1.5 Forced convection from horizontal or vertical cylinders
A comprehensive relationship for the Nusselt number in such case is given next:
( )
54
85
41
32
31
21
2820001
401
62030⎥⎥⎦
⎤
⎢⎢⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛+⋅
⎥⎦⎤
⎢⎣⎡ +
⋅⋅+=
Re
Pr.
PrRe..Nu forced (4.15)
Where: 72 1010 << Re
In all cases of convection over pipes, the characteristic length was equal to the
diameter of the pipe, Dp.
The final (conservative) result for the convection heat transfer coefficient over
cylinders, hc_cyl, was:
[ ] maxforcedVHcyl_c h,h,hh = (4.16)
4.2.1.6 Free convection between flat plates
In this case, the Nusselt number was the ratio of pure conduction resistance to a
convection resistance and it can be seen that if Nu =1, substituting Equation 4.7 into
4.6 reduces to Equation 4.1, meaning that conduction would become the heat transfer
mode. The characteristic length for this situation was the interplate spacing distance.
Two relationships were used here39F
40:
- One for the parallel plate convection
Novel approaches to the design of domestic solar hot water systems
Chapter 4 - Heat transfer
55
- A second one for evaluation of convection suppression if slats are present
between the plates (as is the case for the top cover of the second system
developed)
For parallel plates with tilt angles, θ, from 0° to 75°, the Nusselt number was found
from the following expression:
(4.17)
The ‘+’ superscript means that only positive, or zero, values were to be taken.
In the case of slats between the plates, the following relationship defining a ratio for
Nu with and without slats was used to asses the magnitude of convection suppression
(Figure 4.2):
[ ][ ] 1
1130
111
580280
28021
≥⋅⋅
⋅⋅⋅= slats_no
max..
max.
slats_no
slats Nuif,ZRa.
,RaCC.
NuNu
(4.18)
(4.19)
Where C1 and C2 are derived from experimental correlations for different slat aspect
ratios, Ws/Hs, and C2 for different tilt angles as well; 40° ≤ θ ≤ 90°. If 0° ≤ θ ≤ 45°,
C2 ≅ 1. Note that Hs is the plate spacing.
Figure 4.2 Parallel flat plates with slats for convection suppression
( )45−= θcosZ
( )+
+
⎥⎥
⎦
⎤
⎢⎢
⎣
⎡−⎟⎟
⎠
⎞⎜⎜⎝
⎛ ⋅+⎥
⎦
⎤⎢⎣
⎡⋅
−⋅⎥⎥⎦
⎤
⎢⎢⎣
⎡
⋅⋅
−⋅+= 15830
17081811708144113
161 θθθ
θ cosRacosRacosRa
.sin.Nu.
H
W
θ
Novel approaches to the design of domestic solar hot water systems
Chapter 4 - Heat transfer
56
For tilt angles between 0° and 45° and Ws ≈ Hs (conditions appropriate for the
second system developed in this study):
C1 ≅ 0.145, C2 ≅ 1, 0.82 ≤ Z ≤ 1
Given the above and rewriting Equation 4.18:
[ ][ ]
[ ][ ]
max.
max.
slats_no
slats
max.
max.
,Ra.
,Ra.
NuNu
,Ra.
,Ra.
11070
1160
1130
1160280
280
280
280
⋅
⋅≤≤
⋅
⋅ (4.20)
If Nu > 1, the ratio above is independent of the Rayleigh number and for this
particular case it would mean that the presence of slats actually increased convection
by about 23% to 50%, which would have been undesirable.
4.2.1.7 Free convection between concentric cylinders
The following relationship was used in this case38:
⎪⎩
⎪⎨⎧
≤<⋅⋅⋅≤≤⋅⋅
=116200
64290
10108400108102110
δδ
δδδ RaforRa.
RaforRa.Nu .
.
( )( )b.
a.214214
The expression for the heat transfer coefficient was different in this case due to the
geometry of the surfaces involved:
⎟⎠⎞⎜
⎝⎛⋅
⋅=
2
12 r
rlnr
Nukhcδ (4.22)
Where: r2|r1 = Outer|inner cylinder radius (m)
δ = r2 - r1
4.2.1.8 Forced convection in a corrugated triangular duct
A V-corrugated absorber was used in the air panel of the first prototype developed
for the second system (Figures 7.5 and 7.10). Heated air was forced over and under
this absorber. It was necessary to determine convection arising from this process.
Novel approaches to the design of domestic solar hot water systems
Chapter 4 - Heat transfer
57
Calculating the heat transfer for air flowing in a triangular duct could approximate
convection heat transfer in a V-shaped absorber. In particular, it was desirable to
explore convection for an apex angle of ϑ ≈ 90°, which was relevant for the system
under consideration. Experimental and theoretical studies have been performed for
turbulent flow in finned equilateral40F
41 and isosceles ducts41F
42 (besides other geometries)
and the results can be used for the situation at hand.
Fluid flow in ducts and tubes is subject to frictional resistance from the walls.
Experimental correlations between the friction factor and the Reynolds number have
been developed, since the Reynolds number represents the status of the flow
(laminar, transitional or turbulent) and depends on the dimensions of the resistive
surface and the properties of the fluid. The Moody diagram (Appendix D) shows this
dependency graphically, where the friction factor is plotted versus the Reynolds
number for a series of relative roughness values and for laminar, transitional and
turbulent flow.
An expression for the Nusselt number for smooth circular ducts used in this study is
provided below 42F
43:
( )1Pr87.1207.1
PrRe83
221
−⋅⎟⎠⎞⎜
⎝⎛⋅+
⋅⋅=
f
fNusmooth (4.23)
For: ⎪⎩
⎪⎨⎧
<<⋅<<
5501054000 6
Pr.Re
For turbulent flow in smooth isosceles triangular ducts of apex angle, ϑ, equal to 90°,
experimental evidence40 suggests that friction factors can be calculated using the
same correlations developed for friction in circular ducts. Therefore, it would seem
possible to hypothesise that a similar equivalence exists between roughened
triangular and circular ducts with ribs or fins.
2000 < Re < 4000 ← Laminar flow
Turbulent →flow
↑ ↑
Novel approaches to the design of domestic solar hot water systems
Chapter 4 - Heat transfer
58
Given the absence of specific results pertaining to this situation, if this assumption is
extended to heat transfer behaviour, it is possible to make use of correlations
developed for heat transfer of turbulent flow in circular ducts with internal triangular
fins43F
44 as an approximation to the behaviour of turbulent flow in a V-corrugated
absorber, also with triangular fins and apex angle, ϑ=90.
Substituting Equation 4.23 in 4.24 allowed calculation of the Nusselt number,
Nurough, for the V-corrugated absorber approximation for various corrugation
parameters (Figure 4.3). Using this result in Equation 4.7 provided the convection
heat transfer coefficient (where L = Dh).
71
70240
29021021200360
906421⎪⎭
⎪⎬⎫
⎪⎩
⎪⎨⎧
⎥⎦
⎤⎢⎣
⎡⋅⎟
⎠⎞⎜
⎝⎛⋅⎟
⎠⎞⎜
⎝⎛⋅⎟
⎠⎞⎜
⎝⎛⋅⋅+= −
−.
.r
.
r
r.
r
r.
smooth
rough Prdp
deRe.
NuNu α (4.24)
Figure 4.3 Corrugation parameters for circular ducts
4.2.2 Radiation in SHWS
From Equations 4.4 and 4.6:
( ) ( )211
12122
2
11
1
42
41
111TTAh
FAAA
TTq rr −⋅⋅=
⋅+
⋅−
+⋅
−−⋅
=
εε
εε
σ (4.25)
The general form for the radiation heat transfer coefficient between two surfaces is:
er = roughness height
dr = roughness pitch
αr= heliz angle of roughness
pr = rib spacing
dr
pr
er
αr
Novel approaches to the design of domestic solar hot water systems
Chapter 4 - Heat transfer
59
( ) ( )( )
22
12
121
1
212
22
1
111A
AF
TTTThh rT
⋅⋅−
++−
+⋅+⋅==
εε
εε
σ (4.26)
Where: σ = 5.6697 x 10-8 W/m2·K4 (Stefan-Boltzmann constant)
εi & Fij as defined in section 4.1.3
4.2.2.1 Radiation exchange between a convex object and a large enclosure
This situation applies when a convex object is completely enclosed by a very large
concave surface. In this case, 0AA 21 → and practically no radiation emitted from
the object is reflected back, so 112 →F . From Equation 4.4:
( )42
4111 TTAqr −⋅⋅⋅= εσ (4.27)
( ) ( )212
22
11 TTTThr +⋅+⋅⋅= εσ (4.28)
This expression is used in the case of a flat plate cover at temperature TC radiating to
the sky at temperature Tsky. It is convenient to rewrite Equation 4.28 with reference to
the ambient temperature, Tamb, for reasons that will become apparent in section 4.3:
( )( )ambC
skyCcCS TT
TThr
−
−⋅=
44
εσ (4.29)
Where: 2305520 ambsky T.T ⋅=
4.2.2.2 Radiation exchange between flat plates
An approximation is done in this case assuming that all the radiation is transferred
between the plates and none is lost, so 112 →F (strictly speaking, this is true for
infinite plates). Since A1 = A2 = A, from Equation 4.4:
Novel approaches to the design of domestic solar hot water systems
Chapter 4 - Heat transfer
60
( )111
21
42
41
−+
−⋅⋅=
εε
σ TTAqr (4.31)
( ) ( )
111
21
212
22
1
−+
+⋅+⋅=
εε
σ TTTThr (4.32)
4.2.2.3 Radiation exchange between two concentric cylindrical surfaces
The approximation of total radiation heat exchange was also used in this case with
112 →F and A1 ≠ A2 (Figure 4.4). The resulting relationship from Equation 4.4 was:
( )( )
2
1
2
2
1
42
411
11rr
TTrqr
⋅−
+
−⋅⋅=
εε
ε
σ (4.33)
( ) ( )( )
2
1
2
2
1
212
22
1
11rr
TTTThr
⋅−
+
+⋅+⋅=
εε
ε
σ (4.34)
Figure 4.4 Concentric cylinder arrangement for two radiating surfaces
For computational simplicity and conservative reasons (i.e., upper bound value), a
unity radiation shape factor, F12 = 1, was used in the calculations.
r1
r2
l
Novel approaches to the design of domestic solar hot water systems
Chapter 4 - Heat transfer
61
4.2.3 Conduction in SHWS
Conduction heat transfer in SHWS panels is a minor heat loss mechanism compared
to convection and radiation, which cover most of the heat exchange that occurs.
Efficient flat plate collectors and non-imaging concentrating collectors are contained
in well insulated housings, making these losses very small and so, they can be
neglected for simplicity and first order approximation calculations. For double
glazing covers, conduction between the covers may be the main heat transfer mode
and has been acknowledged accordingly (section 4.2.1.6). Conduction is important,
however, in the assessment of heat losses from hot water tanks.
4.2.3.1 Conduction between concentric cylinders
Heat flow via conduction between cylinders is useful to determine heat losses in hot
water tanks that are surrounded by an outer cylindrical casing with insulation
between them. A simple expression for the actual heat transfer in this case is 44F
45:
( )12
1
2
2 TT
rrln
Lkq cyl_k −⋅⎟⎠⎞
⎜⎝⎛
⋅⋅=
π (4.35)
Where: r2|r1 = Outer|inner cylinder radius (m)
4.3 Thermal network formulation and energy balance equations
Heat transfer processes may be represented by thermal resistance networks using an
analogy with Ohm's law. Solar energy systems may be modeled this way45F
46 and some
thermal analyses of flat plate and CPC collectors have incorporated this technique 46F
47.
ResistanceThermalDifferencePotentialThermal
FlowHeat = ( )T
T hA
TR
TQ⋅
Δ=
Δ=
1
1 (4.36)
Novel approaches to the design of domestic solar hot water systems
Chapter 4 - Heat transfer
62
The thermal network analogy is useful for obtaining the heat gains and losses
(Q values) by solving for combinations of parallel and series thermal resistances
which represent the modelled heat transfer modes.
Assuming that the example given in Figure 4.1 is a flat roof of a shed and that heat is
only lost via the roof, simplified heat transfer modes can be modelled as follows:
Figure 4.5 Thermal circuit schematics
for heat transfer through the roof of a shed
Since all the heat is lost through the roof, the energy balance relationships are:
Q = qc_shed = qk_roof = (qc_roof + qr_roof) (4.37)
Where:
(4.38)
(4.39)
(4.40a)
(4.40b)
(4.41)
Tir
Tor
qr_roof →
Tamb
Tshed
qk_roof →qc_shed →
Tsky
qc_roof → Rcs Rkr
Rcr
Rrr
cs
irshedshed_c R
TTqQ −==
kr
orirroof_k R
TTqQ −==
cr
amborroof_c R
TTq −=
⎪⎪
⎩
⎪⎪
⎨
⎧
−
−
=
∗rr
ambor
rr
skyor
roof_r
RTT
RTT
q
Tir Tor
qr_roof →
Tamb Tshed
qk_roof →qc_shed →
qc_roof → Rcs Rkr
Rcr
Rrr *
and also
qk_roof
qr_roof Tamb
Tshed
qc_roof
qc_shed
Tir
Tor
Novel approaches to the design of domestic solar hot water systems
Chapter 4 - Heat transfer
63
If Tshed, Tsky and Tamb are known, Q can be found as a function of these temperatures
and of the R-values by solving Equations 4.38 through 4.41. From this, the unknown
temperatures, Tir and Tor, can also be found and consequently, all heat transfer values
can be found.
Equation 4.40b corresponds to the second schematic where the radiation transfer
resistance has been referenced to Tamb (Rrr). This is done for convenience of
calculation, since it simplifies the solution of the network. In this case, the radiation
heat transfer coefficient is also referenced to the ambient temperature (hrr) as given
by Equation 4.29. By contrast, the radiation heat transfer coefficient when normally
referenced to Tsky (hrr) is given by Equation 4.28.
By combining Equations 4.38 and 4.39 it is easy to arrive at:
(4.42)
This is equivalent to considering both resistors in series and solving for Q at the
temperature nodes, Tshed and Tor.
From Equations 4.40, 4.41 and 4.42, Q is solved as a function of the three
temperatures and of the R-values:
r_eqkrcs
ambshed
RRRTT
Q++
−= (4.43)
(4.44)
BA
ambrrskycrshedB
RRTRTRTR
Q++
⋅−⋅−⋅=
1 (4.45)
(4.46)
(4.47)
The thermal resistances are the inverse of the heat transfer coefficients as defined in
4.51, which in turn are given by the relationships presented in the previous section.
krcs
orshed
RRTTQ
+−
=
rrcrB RRR +=
krcsA RRR +=
∗
∗
+⋅
=rrcr
rrcrr_eq RR
RRR
And also:
*
*
Novel approaches to the design of domestic solar hot water systems
Chapter 4 - Heat transfer
64
These values are temperature dependent, so the solution to the system is not purely
that of a standard linear equations system. The solution process requires an iterative
procedure, where the equations are simultaneously solved for all temperatures over
many cycles. For each cycle, new temperature values are found and fed back into the
system for the following cycle. The process continues in a converging manner until
the temperatures obtained remain virtually constant in subsequent iterations. Detailed
explanation for each of the systems developed is given in sections 6.4.1 and 7.2.2.
4.4 Energy and power in fluid flow and fluid storage
Thermal energy gained or lost by a body during a heat transfer process is expressed
in terms of the temperature change undergone by the body, the body mass and the
capacity to experience this change. This energy variation is expressed as:
( )fip TTCmQE −⋅⋅== (4.48)
Where: m = body mass (kg)
Cp = specific heat of the body at constant pressure (kJ/kg·°C)
In a similar way, thermal power transferred by a body of fluid is given as:
( )fip TTCmP −⋅⋅= & (4.49)
Where: m& = mass flow rate of fluid (kg/s)
The energy and power transferred during phase change of a fluid is given by:
Hphasephase LmQE ⋅== (4.50)
Hphase LmP ⋅= & (4.51)
Where: LH = Enthalpy of vapourisation (kJ/kg)
Equations 4.48 and 4.49, together with Equation 4.6 form the basis of heat flow
evaluation in all calculations performed in this work.
Novel approaches to the design of domestic solar hot water systems
Chapter 4 - Heat transfer
65
4.5 Heat exchanger effectiveness-NTU method
If input fluid temperatures in a heat exchanger are known and the effectiveness of the
exchanger in transferring a certain amount of heat can be determined, it is possible to
predict output fluid temperatures. The following development was used for the tank-
exchanger-coupled thermosiphon system (Chapter 7) as a means for determining the
temperature of the output hot water from the heat exchanger.
For illustration, consider the simple double-pipe heat exchanger of Figure 4.6, where
fluid B is the hot fluid. Fluid flow may be either parallel flow (fluids A & B flowing
in the same direction) or counterflow (fluids flow in the opposite direction). The
effectiveness is determined differently for each.
Figure 4.6 Double pipe heat exchanger
In parallel flow: 1221 AABB TTTT >>>
In counterflow:
211
221
AAB
ABB
TTT
TTT
>>
>> and it is possible for: 21 BA TT >
In counterflow, the output temperature of the cold fluid can lie between the input and
output temperatures for the hot fluid. This is the situation for the output hot water in
the tank-exchanger loop of the system incorporating the air heater panel. Given this
situation and even though the heat exchanger used is not physically like the one
pictured above, as a first approximation the exchanger was taken as a “black box”
input/output element with a behaviour similar to counterflow operation and so the
effectiveness was determined as for a counterflow system.
1 2
Fluid B
Fluid AParallel flow
Counterflow
TA2
TB2
TB1
TA1
Novel approaches to the design of domestic solar hot water systems
Chapter 4 - Heat transfer
66
The effectiveness-NTU method (NTU: number of transfer units) defines exchanger
effectiveness as the ratio of the actual to the maximum possible rate of heat
transfer47F
48:
max_x
act_x
PP
transferheatpossibleimummaxtransferheatactual
==ε (4.52)
Assuming no losses, the actual rate of heat transfer is given by the rate of energy loss
of the hot fluid or by the equal rate of energy gain of the cold fluid.
For parallel flow: ( ) ( )1221 cccchhhh||
act_x TTCmTTCmP −⋅⋅=−⋅⋅= && (4.53)
For counterflow: ( ) ( )2121 cccchhhhact_x TTCmTTCmP −⋅⋅=−⋅⋅=↔ && (4.54)
Where subscripts h and c refer to hot and cold fluid, respectively.
The maximum possible rate of heat transfer occurs when one of the fluids undergoes
the maximum temperature change available in the exchanger. This is the temperature
difference between the input hot air and input cold water temperatures to the
exchanger of the air heater prototype system. Only the fluid with the minimum value
of heat capacity rate ( )minCm ⋅& can undergo this maximum temperature change.
The maximum possible heat transfer is: ( ) ( )inletinlet chminmax_x TTCmP −⋅⋅= & (4.55)
For counterflow operation there are two possible relationships for effectiveness,
depending on which fluid has the minimum heat capacity rate:
Hot fluid → ( )( ) 21
21
21
21
ch
hh
chhh
hhhh
max_x
act_xh TT
TTTTCmTTCm
PP
−−
=−⋅⋅−⋅⋅
==&
&ε (4.56a)
Cold fluid → ( )( ) 21
21
21
21
ch
cc
chcc
cccc
max_x
act_xc TT
TTTTCmTTCm
PP
−−
=−⋅⋅−⋅⋅
==&
&ε (4.56b)
With increasing and decreasing fluid temperatures it is possible for both fluids to
share the role of having the minimum value of heat capacity at different times. The
Novel approaches to the design of domestic solar hot water systems
Chapter 4 - Heat transfer
67
“swap over” point occurs when ( ) ( )hc cmcm && = and the effectiveness is expressed
as 48F
49:
⎭⎬⎫
⎩⎨⎧
−−
−−
=21
21
21
21
ch
cc
ch
hh
TTTT
,TTTT
maxε (4.57)
It is noted that the same effectiveness value can be obtained for two different fluid
temperatures 49F
50 and two different flow rates. In the characterisation of heat
exchangers where the effectiveness is an input parameter in the model used to obtain
other parameters (as was the case with this study), the use of relationship 4.57 will
therefore not allow their unequivocal determination. For cases like these, a single
expression termed as “modified” effectiveness, ε’, has been proposed for empirical
prediction models50F
51:
( )( )21
21
21
21
chhh
cccc
ch
hh'
TTCmTTCm
TTTT
−⋅⋅−⋅⋅
=−−
=&
&ε (4.58)
This expression can be obtained by dividing Equation 4.54 by ( )21 chcc TTCm −⋅⋅& .
It was concluded from experimental measurements performed on the SHWS
incorporating the air heater panel that under steady-state conditions and the high
irradiance levels used, the water (which was also the cold fluid) was the fluid that
underwent the maximum energy change (see section 7.2.4 for details). The
effectiveness is then given by Equation 4.56b. This equation is useful in determining
the output temperature of the cold fluid, Tc1, if the other temperatures are known and
the effectiveness can be found.
Novel approaches to the design of domestic solar hot water systems
Chapter 4 - Heat transfer
68
Chapter 5 - Fluid mechanics and hydraulics 5.1 Introduction
In systems like those described in this work, the elements therein present a resistance
to fluid flow, causing pressure drops which modify the flow, influencing operation.
In the specific case of the SHWS with the air heating panel, where the airflow is
driven by a fan or blower, the energy expenditure of the motor used to circulate the
air must be considered in the final determination of a total, or effective, efficiency of
the system. The effective efficiency in this broader sense can be considered as51F
52:
AGPP
cb
net_moteff_watereff ⋅
−=η (5.1)
CPP motnet_mot = (5.2)
Pwater_eff is the effective power gained by water in the tank, Pmot_net is the net
pumping power required and Pmot is the pumping power of the motor. C is the
combined efficiencies of the fan, motor, transmission line and electricity generation
processes.
There are two types of friction losses in pipes: main, or head, losses and minor
losses. The first type deals with the resistance to flow offered by straight pipe
sections while the second one refers to bends, fittings, valves and other elements
present in a pipe system. Knowing the pressure losses in a piping system and the
pumping power required allows for sizing considerations of motors and pumps.
5.2 Pressure losses
This section shows the fundamentals of fluid mechanics necessary to understand and
determine pressure losses in pipeworks.
Novel approaches to the design of domestic solar hot water systems
Chapter 5 - Fluid Mechanics and hydraulics
70
5.2.1 Pressure in fluids
If a force, F, is applied uniformly over a certain area, At, the pressure over that area,
p, is given as the ratio between these two quantities:
tt dAadm
dAdFp ⋅
== (5.3)
For fluid flow in pipes, At is the cross-sectional area of the pipe.
The volume occupied by a fluid is related to its mass via the mass density:
dVdm
=ρ (5.4)
ldAdV t ⋅= (5.5)
dmldAt =⋅⋅ρ (5.6)
Combining Equations 5.3 and 5.6:
lap ⋅⋅= ρ (5.7)
In dealing with many situations involving pressures in fluids, often the forces causing
the pressures are the weight of the fluids, or fluid elements (such as the pressure at
the bottom of a hot water tank). In this case:
hp ⋅= γ (5.8)
g⋅= ργ (specific weight) (5.9)
5.2.2 Energy and “head”
It is necessary to understand the concept of a “head” related to the energy that a
flowing fluid carries.
Consider a pipe section and fluid element as in Figure 5.1
Novel approaches to the design of domestic solar hot water systems
Chapter 5 - Fluid Mechanics and hydraulics
71
Figure 5.1 Fluid element in a pipe section at height ‘h’ above reference level
There are three forms of energy that the fluid carries in its movement: potential,
kinetic and pressure energy.
Potential Energy is related to the weight of the fluid and its height above a reference
point:
hWhgmZ E ⋅=⋅⋅= (5.10)
Kinetic Energy is related to the mass and velocity of fluid flow:
gvWvmK E ⋅
⋅=
⋅=
22
22
(5.11)
Pressure Energy related to the work required to force the fluid over a certain distance
against the pressure:
lFPE ⋅= (5.12)
From Equations 5.3, 5.6 and 5.12:
ρmpPE
⋅= (5.13)
Total energy is the sum of Equations 5.10, 5.11 and 5.13:
ρmpvmhgmE ⋅
+⋅
+⋅⋅=2
2
(5.14)
From Equations 5.9 and 5.14 and rearranging, the expression for total energy as a
“head”, H, is defined:
v
lh
Novel approaches to the design of domestic solar hot water systems
Chapter 5 - Fluid Mechanics and hydraulics
72
γp
gvhH
gmE
+⋅
+==⋅ 2
2
5F
* (5.15)
pressure head
velocity head
elevation head
Pressure drops will be a consequence of the friction exerted by the pipes and
elements affecting fluid flow. To determine these drops it is necessary to know the
behaviour of the fluids in closed circuits. Particularly, it is necessary to know if fluid
flow is laminar or turbulent and what the friction factors are for each section of the
pipe under study (section 4.2.1.8). By calculating Reynolds numbers, friction factors
and other parameters, the friction losses can be found.
5.2.3 Head (pressure) losses
The losses from friction flow in channels and ducts are given by the well-known
D’Arcy-Weisbach formula:
gv
Dlfhf
h2
2⋅⋅= (5.16)
t
v
AareationalseccrossrateflowVolumetric
vΦ
=−
= (5.17)
Dh, l, v and f are the hydraulic diameter, the length of the pipe the fluid velocity and
the friction factor, respectively.
Substituting 5.17 for the mean velocity in D.11 and noticing that x = Dh:
t
vh
AD
Re⋅
Φ⋅=
ν (5.18)
Substituting 5.18 for the Reynolds number in D.14:
* Note that this equation has length units
Novel approaches to the design of domestic solar hot water systems
Chapter 5 - Fluid Mechanics and hydraulics
73
2
7781750
−
⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛⋅⋅Φ⋅
⋅=t
v
AD
ln.fν
(5.19)
Finally, substituting 5.17 and 5.19 in 5.16, the head loss for each pipe section is:
g
A
Dl
AD
ln.hf i
i
t
iv
i
i
t
ivii 27
781750
2
2⎟⎟⎠
⎞⎜⎜⎝
⎛Φ
⋅⋅⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
⋅⋅Φ⋅
⋅=
−
ν (5.20)
Total head loss from all straight pipe sections is then: ∑=i
ifTOT hfh _
5.2.4 Minor losses
Calculation of minor losses will be dependent on the number of fittings, valves and
other obstacles that affect the flow in any way. Therefore, in order to find these
losses it is necessary to know exactly how many attachments of this nature are part of
the piping system.
Minor losses are usually expressed by specifying a “loss coefficient”, K, as a ratio of
the head loss through the element to the velocity head of the fluid in the system.
The resultant expression is: ( )g
vhK m
22= (5.21)
Therefore, minor head losses are given by:
gA
Kg
vKhv
m 22
2
2 ⎟⎠⎞⎜
⎝⎛Φ
⋅=⋅= (5.22)
Loss coefficients can be determined from experimental data and in most cases are
function of the geometry of the element only. Tabulated values for fittings, bends,
tees and valves are available in the literature52F
53.
Novel approaches to the design of domestic solar hot water systems
Chapter 5 - Fluid Mechanics and hydraulics
74
For sudden expansions and contractions, where turbulent fluid suddenly encounters
an increased or reduced space, plots of K-values versus input/output diameter ratios
(for a pipe system) and empirical relationships are used:
Sudden expansion of cross section: 2
2
1exp 1 ⎟⎟
⎠
⎞⎜⎜⎝
⎛−=
AA
K (5.23)
Sudden contraction of cross section: 2
1
21420 ⎟⎟⎠
⎞⎜⎜⎝
⎛−⋅≈
AA
.Kcon (5.24)
Where A1 and A2 are the cross sectional upstream (first) and downstream (second)
conduits areas, respectively.
Friction coefficients for other elements, such as heat exchangers and collector panels,
are much more complicated to determine and are usually case-specific to the
particular situation under study.
The total minor head losses are given by: ∑=i
iimTOT g
vKh2
2
_ (5.25)
Therefore, total head loss by adding Equations 5.20 and 5.25 is:
∑∑ +
⎪⎪
⎭
⎪⎪
⎬
⎫
⎪⎪
⎩
⎪⎪
⎨
⎧⎟⎠
⎞⎜⎝
⎛Φ
⋅⋅⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛
⋅⋅
Φ⋅⋅=
−
i
ii
j
tj
jv
j
j
tj
jvjTOT g
vK
A
DL
AD
ln.H227
7817502
2
2
ν (5.26)
By knowing the total pressure losses, the required pumping power and the effective
efficiency for the system can be found.
vFtlF
tE
P net_motnet_motnet_mot
net_mot ⋅=⋅== (5.27)
( )tt
net_motnet_mot Av
AF
P ⋅⋅= (5.28)
pΔ vΦ
Novel approaches to the design of domestic solar hot water systems
Chapter 5 - Fluid Mechanics and hydraulics
75
From Equations 5.8, 5.9 and 5.28:
TOTvTOTvvnet_mot HgHpP ⋅⋅⋅Φ=⋅⋅Φ=Δ⋅Φ= ργ (5.29)
5.3 Thermohydraulics
5.3.1 Poisseuille’s Law for laminar flow
It has been shown for laminar flow that the volume of a liquid flowing through a tube
is directly proportional to the pressure difference driving the liquid, p, and
proportional to the fourth power of the tube radius, r.
Poiseuille's law accurately describes the flow of liquids through pipes as long as
laminar flow exists:
lpr
v ⋅⋅Δ⋅⋅
=Φη
π8
4
(5.30)
Where: r = radius of pipe
η = viscosity of water
Δp = pressure difference
l = length of pipe
This relationship is of particular interest in the case of natural thermosiphon flow as
occurring in the air-to-water heat exchanger of the second system developed in this
study and referred to in chapter 7. In this case, Δp =ρ·g·h, where the pressure is given
by the density differences of hot and cold water columns of length ‘h’ in the
thermosiphon system (Figure 7.9).
Chapter 6 - Solar hot water system with passive
downward vapour phase heat transport 6.1 Introduction
This solar water heater was composed of six sections:
• Heat collection elements: concentrating collector panels and absorber-boiler tube
arrays where water is converted into steam.
• Roof reservoir (20 L) that supplies cold water to the collector
• Conveyance infrastructure: header and footer tubes and and insulated copper pipe
that transport steam to the water storage tank.
• Storage tank: an insulated 200 L tank.
• Heat exchanger: a short copper loop located inside the tank where steam
condenses and gives off heat to the storage water.
• Condensate receptacle: a container under the water tank for condensate collection.
The concentrating collectors generate steam, which flows down the transfer line into
the exchanger coil in the tank, heats the water, condenses and ends up as condensate
in the receptacle. A partial vacuum forms in the collector after cooling, pulling the
condensate back up to recharge the collector chambers and reservoir tank. Even
though high temperatures and steam production have been achieved by using flat
plate collectors53F
54, such temperatures are easier to obtain with concentrating optics.
The main developments were:
1. The design and implementation of the concentrating collectors
2. Roof reservoir water supply
3. Separation of the steam and water
4. The downward steam transfer system
5. Steam to water heat exchange mechanism
6. The night time recharge process
Novel approaches to the design of domestic solar hot water systems
Chapter 6 - Solar hot water system with passive downward vapour phase heat transport
77
6.1.1 Basic design considerations
To meet the proposed daily target of 30 MJ (Table 1.2), the following efficiencies
were assumed as a starting point for system design (Figure 6.1):
Table 6.1 Assumed efficiencies for basic system components
Elements required Efficiencies Steam to water heat exchange 80% or higher
Collector panel 40% or higher TOTAL SYSTEM ~32% or higher
Figure 6.1 Sketch for the downward vapour heat transport SHWS
The steam-to-water heat exchange efficiency of Table 6.1 included the efficiency of
the transfer line, the efficiency of the exchange coil and the efficiency of the tank for
heat retention. The combined efficiency was assumed to be about 80%, provided the
transfer pipeline and water tank were well insulated. Operation of the system was
assumed to occur in the following way:
As the tank water temperature increased the efficiency of the steam/water heat
exchanger would decrease. The efficiency of the tank would also decrease, although
to a lesser extent. For the steam, zero efficiency would be expected as the tank water
approached 100°C. A stagnation temperature below 100°C would set in when heat
gains from the steam and heat losses from the tank were in equilibrium. In this
situation most steam would flow to the receptacle, which would then serve as a heat
dumping mechanism.
Water tank
Heat exchanger
Receptacle
Reservoir tank(optional: hot water draw-off coil)
Collector panel
Novel approaches to the design of domestic solar hot water systems
Chapter 6 - Solar hot water system with passive downward vapour phase heat transport
78
A copper pipe loop would be used as the steam/water heat exchanger and placed near
the bottom of the tank. Since the cold condensate would return to the roof reservoir
at the end of the day it would be desirable for it to not come in contact with the
stored hot water. However, its placement at the bottom of the tank would result in
mixing of hot and cold water inside the tank with little stratification expected. Even
so, the bottom of the tank would always have the coldest water.
The system would operate only on clear days, when irradiance values were high
enough to enable steam production. In many places in Australia and particularly in
Queensland, cloudless and clear skies are the norm throughout the dry period
extending from April to November. Most SHWS in use in Australia do not give
significant output during overcast days. During winter, when the load on SHWS is
the highest and ambient temperatures are low, a system can produce a considerable
amount of hot water since irradiance values close to 1000 W/m2 can still be obtained
(section 6.6.2.3).
As concentrating collectors have limited collection angles, orientation of the panels
greatly affects performance. Two different panel orientations were considered
hypothetically for comparison and evaluation of potential performance:
Mode #1
For a north-facing panel with a 30° collection half-angle and optimum tilt, the system
would be expected to operate for 4 hours on clear days with an average irradiance of
about 880 W/m2 (Figure 3.9). Tables 6.2 and 6.3 summarise the required
performance based on these conditions and the assumptions of table 6.1.
Table 6.2 Assumed energy and power requirements: Mode #1
Required daily energy in the water (from Table 1.2): 25 – 30 MJ Required average power into water (4 hours): 1740 – 2100 W Required average power output from panel: 2175 – 2600 W Required average power into system: 5400 – 6500 W
Novel approaches to the design of domestic solar hot water systems
Chapter 6 - Solar hot water system with passive downward vapour phase heat transport
79
Table 6.3 Average irradiance and minimum collector area required: Mode #1
Average irradiance over 4 hours: 880 W/m2 Absorber aperture area required: 7.4 m2
The absorber area was determined from the required average power into the system.
Mode #2
For an east-facing 30° tilted panel with optimum twist angle and same half-angle, the
system would be expected to collect energy for most of the day. However, it would
be expected to operate with an average panel efficiency of 0.4 for about 5 hours
(between 8:00 am and 1:15 pm) when the irradiance values falling on the aperture
area were over 600 W/m2 (Figure 3.12). The average irradiance during this period
would be expected to be around 820 W/m2. Tables 6.4 and 6.5 indicate the required
performance of the system.
Table 6.4 Assumed energy and power requirements: Mode #2
Required daily energy in the water (from Table 1.2): 25 – 30 MJ Required average power into water (5.25 hours): 1320 – 1580 WRequired average power output from panel: 1650 – 1975 WRequired average power into system: 4125 – 4940 W
Table 6.5 Average irradiance and minimum panel area required: Mode #2
Average irradiance over 5.25 hours: 820 W/m2 Absorber aperture area required: 6.0 m2
If the efficiencies of the system and/or the average irradiance happened to be lower
than the assumed values of Tables 6.1, 6.3 and 6.5, the concentrator aperture would
have to be either increased to compensate for the lower power outputs or have a more
efficient design.
It also appeared from the above that the east facing panel would be a better
arrangement for optimum energy collection and minimal use of resources. Actual
performance of the units, however, was measured mainly for a north facing
Novel approaches to the design of domestic solar hot water systems
Chapter 6 - Solar hot water system with passive downward vapour phase heat transport
80
configuration owing to testing location constraints (reduced solar window and the
unfeasibility of having an optimum twist angle).
The amount of water required for boiling was determined from the required daily
energy into the water and the cold water temperature. The total energy in the water
was given by:
- The phase-change energy from steam to 100°C condensate
- The sensible heat from 100°C to cold condensate
For a cold condensate at 20°C, the sensible heat is about 10% of the heat available
from condensation. Therefore, for simplicity and to be conservative, only the energy
from the heat of vaporisation of the condensing steam was used in design
calculations. From chapter 4:
LmEsteam ⋅= (4.65)
Table 6.6 Water conditions and required mass for boiling
Required daily energy in the water: 25 – 30 MJ Cold water temperature (Twater_cold ≅ Tamb): 20 °C Boiling water temperature (Tsteam): 100 °C Enthalpy of vapourisation for water (L): 2260 J/g Required mass of water for boiling: 11 – 13 kg
It was necessary to have significantly more than this amount of water in the roof
level reservoir so that the system would not boil dry. The roof reservoir was designed
for 20 L capacity.
The estimated total panel areas required was (6–7 m2). Actual panel dimensions were
constrained to a maximum of 2.4 m × 1.2 m = 2.9 m2, due to material availability so
the system was designed with a double-panel configuration (~5 m2).
The theoretical framework for concentrating devices was given in Chapter 3 with
emphasis on non-imaging concentrators and specifically compound parabolic
collectors, CPC, since these were the designs of choice for this system. Imaging and
non-imaging concentrators have been developed and used for solar applications for
Novel approaches to the design of domestic solar hot water systems
Chapter 6 - Solar hot water system with passive downward vapour phase heat transport
81
over 30 years and there have been many collector designs studied, tested and
implemented54F
55. However, not much has been done in relation to their integration
with SHWS where flat plate collectors have dominated as the fluid heating elements.
6.2 Concentrating systems – a review
Concentrators have mainly been studied, proposed and used for non-domestic hot
water production, for example: detoxification of contaminated water55F
56,56F
57 and
improved steam generation57F
58; electricity production58F
59, cooking59F
60 and sterilisation
purposes60F
61 and also photovoltaic electricity applications 61F
62,62F
63.
Relatively inexpensive concentrators have been designed and proposed for SHWS to
improve collector performance and most of these63F
64 have involved the use of the non-
imaging CPC type. Asymmetric concentrators with simple absorber configurations
have been shown to be suitable for direct water heating64F
65,65F
66.
Many variations and modifications have been made to proposed CPC geometries,
some of which include: CPC truncation for cost reduction, easier manufacture and
building integration, double-trough arrangements for increased performance66F
67, two-
stage arrangements for increased concentration67F
68,68F
69 and compact design69F
70, “hybrid”
designs of imaging and non-imaging devices70F
71,71F
72 introduction of baffles in collector
cavities to reduce heat losses72F
73, etc.
Integrated collector storage (ICS) SHWS for domestic use incorporating both
symmetric and asymmetric concentrators have demonstrated their capability in
achieving moderate temperatures with lower thermal losses than conventional flat
plates73F
74. They also offer comparable performance, or better, if high reflectance
materials are used74F
75, are configurable so that the entire integrated system requires
less auxiliary boosting75F
76 and represent a reduction in material costs71,76F
77. Better
aesthetic building integration is also alleged for ICS systems.
A conventional CPC with novel absorber geometry77F
78, convection suppression
mechanisms and lowered optical losses has also shown an improved performance
Novel approaches to the design of domestic solar hot water systems
Chapter 6 - Solar hot water system with passive downward vapour phase heat transport
82
over flat plates and evacuated tube collectors up to 100°C with comparable, or
potentially lower, costs.
These studies demonstrate that concentrating collectors can replace flat plate
collectors by offering equal or better performance for similar costs.
In many cases, however, the design of the collectors can still represent an added
complication. The introduction of asymmetric geometries, for example, may imply
reflector dimensions that could be bulky and difficult to integrate, and even maintain,
with conventional building structure, especially in the case of ICS systems.
Realistically, “pleasant aesthetic integration” is a matter of subjectivity and lifestyle,
and does not benefit from large or awkwardly shaped structures on domestic roofs.
Additionally, the generation and use of steam as the heat transfer medium has not
received much attention. As such, concentrators proposed as alternatives for hot
water production are not necessarily geared towards high performance at higher
temperatures, although they might be capable of doing so.
The initial stages of this work aimed at producing a self-pumped domestic SHWS of:
- Completely passive operation and low maintenance.
- Remotely coupled components (panels on roof and water tank at ground level)
- Simple and inexpensive elements, where possible (steam as heat transfer fluid)
Examples of self-pumped systems, capable of domestic use, have been proposed78F
79,79F
80,
modelled80F
81 and operated81F
82,82F
83. They have considered low boiling point fluids, other
than water, which have not required concentration techniques and have therefore
used conventional flat plate collectors. They share common advantages with the
system proposed in this project (e.g., passive operation and remotely coupled).
However, they suffer from a few disadvantages such as lower heat of vapourisation
for phase-change energy transfer, technical difficulties in their elaboration and the
use of certain passive control mechanisms, requiring a maintenance routine.
A passive downward heat transport system, using water, was proposed in 1988 and
considered the use of an adjustable concentrating collector with evacuated tubes83F
84. A
Novel approaches to the design of domestic solar hot water systems
Chapter 6 - Solar hot water system with passive downward vapour phase heat transport
83
subsequent simulation84F
85 devised a full scale model that operated successfully over a
height of one storey to advance the model.
Non-imaging asymmetric concentrators, also with evacuated tubular absorbers, have
been developed and tested85F
86 for solar cooking with a similar passive downward
transfer principle. This and the previous system were sealed requiring high-pressure
protection valves. The solar cooker had a somewhat bulky collector-absorber unit
due to the high-load seasonal winter bias incorporated into reflector design.
The present work has taken into account these advantages and disadvantages.
Non-maging concentrators for steam generation were considered prudent. In the
interest of marketability, the dimensions of the collector would necessarily have to be
comparable to those of conventional flat plates. The use of readily available, “off the
shelf” if possible, materials and devices would improve the chances of a
cost-effective system.
It was clear that the CPC was the element of choice for the following reasons:
- Stationary
- Flexible and highly configurable for different absorber geometries.
- Relatively simple manufacturing compared to other concentrating devices
- Proven efficacy for steam generation
- Relative construction simplicity and set-up of a symmetric vs. asymmetric CPC
In this study, CPC vertical and horizontal fin profiles (Figure 3.4) were tested as a
modular array of concentrators and were put together in what became the first
prototype constructed. For subsequent prototypes, the horizontal fin profile was
chosen exclusively for two main reasons:
- The upper face of the horizontal fin receives radiation directly entering the
aperture area of the collector, while the lower face receives radiation via the
reflector. The vertical fin profile is totally dependent on the reflector, therefore
more affected by optical losses introduced in the reflection process. The
horizontal fin profile also allows for using lower cost materials that somewhat
compromise on optical efficiency.
Novel approaches to the design of domestic solar hot water systems
Chapter 6 - Solar hot water system with passive downward vapour phase heat transport
84
- Convection heat losses are expected to be lower for the horizontal fin, since hot
air under the plate at the involute section is partially trapped.
Modelling of sun-earth geometrical relationships and heat transfer dynamics in the
collector-boiler assemblies was done to predict the behaviour of the system.
6.3 Solar Geometry and panel layout/orientation
Determination of energy collection for the CPC geometry was obtained as an
extension to the methods applicable to flat surfaces, where it was possible to
manipulate position and orientation of a CPC to suit any situation. The mathematical
treatment proposed for this was given in Chapter 2 and detailed in Appendix A.
Starting with a horizontal CPC panel and a north-south line-axis alignment, it was
possible to rotate the panel in 4 different ways (Figure 6.2) in order of importance
(tilt and twist are user preferred).
1. An azimuth rotation, ϕ, about the normal to the plane
2. A tilt,θ, or rotation about the transverse axis Main rotations
3. A twist, ω, or rotation about the longitudinal axis
4. A rotation, ρ, normal to the plane after reaching its final orientation (optional)
Figure 6.2 CPC main plane rotations
Azimuth angle
y
z
x ϕ
Tilt angle
y
z
x
θ
Twist angle
y
z
xω
θ
⎭⎬⎫
Novel approaches to the design of domestic solar hot water systems
Chapter 6 - Solar hot water system with passive downward vapour phase heat transport
85
By knowing the relative positions between the sun, the CPC and the plane orientation
(Figure 6.3), it was possible to determine the irradiance and collection times over a
day.
Figure 6.3 CPC collection and acceptance angles
The recirculation in the collector requires a tilted configuration. The simplest
arrangement that satisfies this is orientation mode #1 (section 6.1.1): a north-facing
panel tilted to the latitude angle. Other possible configurations were also explored in
Chapter 3, such as orientation mode #2, which is the tilted east-facing panel with a
twist angle and which appears to be the most efficient for energy collection.
The first prototype was orientated according to mode #2 while the second and third
prototypes as by mode #1, with the third (and last) prototype the only one for which
long term measurements were taken and with collection times of approximately 4
hours per day (Figure 3.9a).
VS
θc
θa
VN’
VST
Novel approaches to the design of domestic solar hot water systems
Chapter 6 - Solar hot water system with passive downward vapour phase heat transport
86
6.4 Heat transfer
The next part in performance prediction of the CPC configuration was the study of
heat transfer modes in the CPC absorber-boiler arrays.
A cross section of the CPC profile and element description is given below:
The system comprises:
• Top cover
• CPC reflector
• Absorber-boiler
• Insulation
Figure 6.4 CPC cross-section
The simulation of heat transfer and thermodynamic processes in multicomponent
systems is complex. Analytical solutions that account for all interactions between all
constituents and the surroundings are difficult to obtain.
Simulation models and different approaches proposed for solar water heating designs
can be divided in two main types:
- Models which rely on algebraic manipulation of well-established analytical
relationships for heat transfer modes.
- Models which rely on numerical approximations. Time-dependent equations for
temperatures, pressures, and fluid motion within the systems are solved in this
manner.
Models of the first type77,86F
87-87F88F
89 produce results in a relatively shorter time and offer a
more direct analysis and understanding of the heat transfer intricacies of the systems
under study but require much more simplification. Numerical solutions obtainable
from modular simulation programs89F
90,90F
91 provide the most complete and accurate
Novel approaches to the design of domestic solar hot water systems
Chapter 6 - Solar hot water system with passive downward vapour phase heat transport
87
results, but require relatively long user experience and appreciable expertise to
exploit full model capabilities. They also require higher capital investments.
The analytical model approach was employed in the present work. Table 6.7 lists the
heat transfer interactions of the steam production system:
Table 6.7 Real heat transfer modes in the system
Heat exchange in this system occurs between
Cover and environment Absorber and cover Reflector and absorber Reflector and cover Reflector and insulation Insulation and environment
Heat transfer modes between enclosures of arbitrary shapes and sizes and their
surroundings are very difficult to determine analytically. Even empirical equations
are scarcely available. This is especially the case for convection heat transfer. To
date, there appear to be no general relationships applicable to a wide range of cases
involving arbitrary enclosures91F
92. Most of them relate to rectangular and box-type
(parallelepiped) arrangements. In the heat transfer analysis undertaken, several
assumptions were made and simplifications introduced to be able to tackle the
modelling process in a simple, yet accurate way, so to produce acceptable results:
1. Temperatures are constant and uniform for absorber-boilers
2. Heat capacity effects of all elements are negligible
3. Temperature drop across the cover is negligible
4. Conduction losses through insulation are insignificant
5. Radiation exchange between grey bodies with form factors equal to 1
6. Optical properties only vary discretely for solar and thermal spectral differences
7. The system is equal to a concentric cylinder arrangement for convective transfer
8. Heat generated from reflector absorptance ends up on the top cover
The simplified heat transfer model used was based on the following interactions:
Novel approaches to the design of domestic solar hot water systems
Chapter 6 - Solar hot water system with passive downward vapour phase heat transport
88
Table 6.8 Simplified heat exchange modes
Heat exchange in the system is described by modelling convection and radiation transfer modes between:
Cover and environment Absorber and cover
Reflector and absorber Reflector and cover*
*single, combined, transfer mechanism for both modes.
The simulation also considered a system with a
cover on top of the CPC structure and a second
cover in the form of a semi-cylindrical sheath
around each absorber.
The energy balance equations for heat exchanged due to convection and radiation are
described in the following section (refer to nomenclature page for description of
variables and subscripts):
6.4.1 Collector panel energy balance equations and relationships for heat
transfer modes
For top cover (C)
( ) ( ) ( ) ( ) ( )ambCCCFCACFFFCFCCCCCC TTAhrhcTTAhrhcrAIAI −⋅⋅+=−⋅⋅++−⋅⋅⋅+⋅⋅ 1τα (6.1)
For sheath (F)
( ) ( ) ( ) ( )CFFFCFCFAAAFAF TTAhrhcTTAhrhc −⋅⋅+=−⋅⋅+ (6.2)
For absorber (A)
( ) ( ) ( )FAAAFAFCCACAC TTAhrhcrAAIAI −⋅⋅+=⋅⋅−⋅+⋅⋅ ττ (6.3)
It is assumed that the sheath does not absorb radiation.
Figure 6.6 Double cover model
4444 34444 21
0η⋅= IS
Figure 6.5 Heat transfer modes
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To solve these equations to find the temperatures of each element and ultimately the
heat losses the thermal resistance network formulation explained in Chapter 4 was
employed. The thermal network corresponding to this model is shown in Figure 6.7
and an explanation of the parameters used is given in Table 6.9:
(a)
(b)
Figure 6.7 Thermal network resistance for the CPC heat transfer model
The model did not explicitly consider transfer modes associated with the reflector
surface. During operation, depending on the reflectivity of the material used on the
walls of the collector, more or less incoming radiation was reflected onto the
absorbers. Even though high reflectance values were possible, there was always a
certain amount of energy absorbed in the walls and subsequently exchanged in the
system, in the form of radiation and convection. The reflector walls, therefore,
radiated energy to the absorber and cover. A convection flow within the CPC cavity
(in addition to that arising by heat losses from the absorber) was also established.
For simplicity it was assumed that, because the absorber was relatively small (about
31 the area of the reflectors), the energy absorbed by the reflector walls eventually
ended up on the top cover of the CPC. This is the reason why the thermal network
shows a constant heat source, QK, at the TC node. QK includes the combination of
convection and radiation modes for the reflector, which is equal to the energy it
absorbs (QR) and this is why it is considered as a single constant. The other
component, QC, refers to absorption of solar radiation by the cover. The QK input on
the cover raises its temperature and has the effect of contributing to higher overall
system efficiencies.
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Table 6.9 Heat transfer model parameters for thermal network of Figure 6.7
Parameters Description
Temperatures: TA Absorber-boiler (TA = 100°C) TF 2nd cover (sheath) TA > TF > TC TC Top cover
Tamb Ambient temperature Thermal resistors
(RT = 1/A·hT):
RRAF Radiation mode RCAF Convection mode
Absorber → Sheath
RRFC Radiation mode RCFC Convection mode
Sheath → Cover
RRCS Radiation mode Cover → Sky
RCCS Convection mode Cover → Environment Equivalent resistors
(Req= {Σ RT-1}-1):
Radiation-convection thermal factors combined
RA Absorber → Sheath RF Sheath → Cover RC Cover → Environment
Input factors: S Attenuated solar energy reaching absorbers
QO Heat losses from the absorber boiler QK= QR + QC Input heat term arising from:
-Transfer modes linked to CPC walls (QR) -Radiation absorbed by top cover (QC)
Another important point to notice is that, whilst convection resistance from the cover
to the surroundings, RCCS, was naturally referenced to the ambient temperature, the
radiation resistance from the cover to the sky, RRCS, was also referenced to this
temperature when it should rather be the sky temperature. The reasons behind this
are explained in section 4.3 and it is mainly for simplicity in the solution of the
thermal network. The expressions and calculations for the heat transfer coefficients
were taken from various sources as referred to in Chapter 4 and are given in
Appendix E. Examples of typical numerical results for these losses are given in
Table 6.10.
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Qualitative explanation of model simulation and heat flow in the system:
1) Heat input
a) Radiation admitted by the CPC traverses the top cover where most of it is
transmitted (~90%), a fraction is reflected and a fraction is absorbed.
b) Transmitted radiation reaches the CPC walls, where most is reflected (~95%)
onto the absorber-boilers and a small portion is absorbed within the walls.
c) Radiation reaching the boilers is mostly absorbed (90-95%)).
d) The energy absorbed by the boilers is equal to the energy falling on the CPC
plane modified and attenuated by the optical efficiency of the system. This
optical efficiency incorporates the transmittance, reflectance and absorptance
values of the components involved.
e) The ‘S’ parameter shown in the thermal resistance network is this final
energy reaching the absorber-boiler.
2) Heat losses
a) Part of the energy absorbed is used in the production of steam by heating and
boiling water. The rest is lost by convection and radiation.
b) The model was analysed in steady-state mode of steam production. Under
these conditions, the model considered a constant temperature for the
absorber-boiler fixed at boiling point (TA = 100°C) 6F
*.
c) Thermal resistors RRAF and RCAF represent the energy losses from the absorber
to the second cover (sheath) due to radiation and convection, respectively.
d) Thermal resistors RRFC and RCFC represent the energy losses from the sheath
to top cover.
* In reality, temperatures will vary and will be higher at the edges of the fins, but will be close to boiling point in the tubules where water is vapourised
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e) Finally, thermal resistors RRCS and RCCS represent the energy losses from the
top cover to the ambient.
The problem lay in solving this network in order to find all temperature values, T,
and ultimately heat values, Q.
In principle, heat flow can be calculated from the thermal resistance network
formulation by finding R and T values as explained in chapter 4. However, the
thermal resistance values are not fixed, but are dynamic quantities that depend on the
temperatures and the temperatures depend on the R-values and on the heat flow.
The network was reduced to equivalent thermal resistors as shown in Figure 6.7. It
was further reduced by adding RA and RF, since the heat flow from absorber to sheath
and from sheath to cover is the same (QO). This eliminated parameter TF and
simplified the calculations.
From the network, it can readily be seen that:
AOAF RQTT ⋅−= (6.4)
FOFC RQTT ⋅−= (6.5)
By algebraic manipulation, it is possible to show that:
CFA
CKSAO RRR
RQTTQ
++⋅−−
= (6.6)
If RF is set to zero, the second cover is not considered and the problem reduces to
that of a single cover CPC/absorber-boiler.
Solution process
The solution for finding the temperatures and the heat loss of the panel was based on
the iterative approach for thermal networks (chapter 4). The following flow chart
illustrates the different steps through which the solutions algorithm was applied.
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Figure 6.8 Solutions algorithm flow chart for simulation of heat transfer in the system
and calculation of relevant parameters
By solving the balancing equations, the iteration process looped until previous and
new temperatures differed by 0.01 °C. Once this point was reached the process ended
and the desired temperatures and heat flow values were found, allowing
determination of the efficiency of the system.
Convective and radiative heat transfer coefficients are calculated (hconv, hrad)
Equivalent thermal resistance values (RA, RF, RC) are calculated
QO is determined (eq. 6.22)
If |TFnew - TF| > tol or |TCnew - TC| > tol
Else
New TF is found (eq. 6.20): TFnew
New TC is found (eq. 6.21): TCnew
Previous values replaced by new ones:
TF = TFnew TC = TCnew
END
Temperature input
TA & TS: known values
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Table 6.10 Numerical results for a panel with a single cover (no sheath) and for various absorber emittance values
Emittance of the absorber (ε) Calculated and given parameters 0.1 0.3 0.6 0.9
Absorber length 2.25 m Fin width 0.05 m
Fin surface width 0.10 m CPC Aperture (truncated) 0.16 m
Optical efficiency 0.8 Average irradiance 900 W/m2
Temperatures: ° C Tamb 20 TA 100 TC 42.3 45.5 49.6 53.2
Heat transfer coefficients: W/m2·°C HRAC 0.93 2.83 5.76 8.76 HCAC 2.36 2.32 2.26 2.20 HRCS
6.39 6.49 6.63 6.75 HCCS 8.08 8.39 8.76 9.05
Equivalent resistors: °C/W RA
* 1.35 0.86 0.56 0.41 RC 0.19 0.19 0.18 0.18
Total heat loss: [A· (RA + RC
)]-1 W/m2·°C
U 1.8 2.6 3.8 4.8 * Absorber-cover heat transfer resistance values are calculated based on the absorber area
Cover-ambient heat transfer resistance values and total heat loss from the CPC are calculated based on the cover (CPC aperture) area
Table 6.10 shows that the heat losses are under 5 W/m2·°C for a worst-case scenario
of high absorber emittance. Less is expected if a selective surface is used for the
absorbers (as was the case in this study). The main contributors to changes in overall
heat loss are the convection and radiation losses from the absorber to the cover. The
losses from the cover to the ambient have very little impact, and in fact do not
change significantly.
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6.4.2 Conveyance infrastructure / transfer line
Steam produced in the absorber-boiler section traveled down the transfer line into the
exchanger loop inside the water tank. The heat lost in this trajectory had to be
minimised and adequately predicted for overall performance evaluation.
These losses were calculated and assessed experimentally by setting up at 10 m long
equivalent pipeline, transferring steam from one end to the other and measuring
condensate formed in the transfer line and steam collected at the output (Figure 6.9).
Figure 6.9 Assessment of heat losses for an experimental transfer line
The pipeline was insulated with 25 mm thick fabric-protected polyester tubes, slit in
the middle. Five of these tubes were used and joined together with masking tape. The
set-up included a condensate trap and a graduated cylinder for accurate measurement
of total condensate volume (Figure 6.9).
The volume of the water collected in the trap arising from condensation in the pipe
gave an indication of the losses. From equations 4.49 and 4.51:
( )TCpLVQ Hcondpipeloss Δ⋅+⋅⋅= &ρ (6.7)
Where condV& is the volume flow rate, ρ is the density of the condensate formed in the
pipe, ΔT is the temperature difference between condensate and ambient values and
LH is the enthalpy of vapourisation.
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Experimental measurements took about 20 minutes with a condensate volume of
(73 ± 1) cc and condensate temperatures of 93 °C at pipe exit. From equation 6.7
about 150 W are required to produce this amount of steam condensate.
The calculated value for pipe heat loss (from equation 4.35) was about 170 W,
where, T1 = Tamb = 25° C ± 2 °C, κtube= 0.058 W/m2·°C (at 25°C), r2 = 31.4 mm,
r1 = 6.4 mm.
Power losses from the pipe depend on the ambient temperature and are not constant.
However, for simplicity and since ambient temperatures did not vary much during
system operation, a fixed figure, initially of 150 W, was used in the overall
performance calculation of the SHWS, where the experimental measurements were
considered more reliable that the calculated value. This figure was later reduced to
100 W since a different material (Armaflex™) with 33% lower thermal conductivity
was used as thermal insulation for the transfer line (section 6.2.2).
Solution process
Power going into the water due to steam condensation was determined as:
Vcond_ktanpipe_lossout_panelin_steam LVPPP ⋅⋅=−= &ρ (6.8)
Vcond_tot LV ⋅⋅ &ρ
150 W (as mentioned above)
Where cond_totV& is the total condensate volume rate, which was due to pipe losses and
heat exchange in the tank. cond_ktanV& is the condensate volume rate from heat
exchange in the copper loop inside the tank. The difference between the two is the
volume rate of condensation that occurred in the transfer line.
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6.4.3 Hot water tank and exchanger
A commercial tank was used and modified to include the heat exchanger. Energy
gained from steam condensation occurred essentially via: 1) the phase change from
steam to water, and 2) the sensible heat transfer from hot water condensate as it
travelled through the exchanger
While heat transfer remained relatively constant during initial stages of operation, it
decreased as the temperature of the water in the tank rose. A stagnation water
temperature, Tstag, was reached, where the effective energy gained by hot water was
equal to the tank losses. The system gained much more heat from steam phase
change than from the hot condensate resulting from this change.
In a situation like this, the highest contribution that sensible heat could have to the
overall energy gain of the water in the tank, and for water at 20 °C, is about 15% that
of steam. In reality it would be less, since the water in the tank would desirably never
be allowed to go below 35°-30° since it would not be useful for domestic tasks. For a
tank water temperature of 50°C, the contribution would be less than 10%. For 70°C,
it would only be about 5%.
Therefore, power delivered to the water was conservatively estimated by assuming it
was equal to 105% (5% extra) of the amount contributed by steam phase change
during operation of the system. Effective power was then this amount moderated by
a temperature-dependent steam energy transfer efficiency, ηS, less tank losses:
( ) ktan_lossin_steamseff_water PP.P −⋅⋅≅ 051η (6.9)
An approximation to tank losses was made by assuming only conduction losses
occurring via the insulation to the surroundings and in a radial direction. This
enabled the use of equation 4.35 for multilayered cylindrical structures.
[ ]⎪⎪⎩
⎪⎪⎨
⎧
≡
<=
=
etemperaturoffunctionT
ionapproximat
ionapproximat
ss
ndeff_ss
sts
ηη
ηη
η
21
11
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( ) ( )ambiw
T
T_insT
Tktan_loss TT
DtDln
lP −⋅
⎟⎟⎠
⎞⎜⎜⎝
⎛ +
⋅⋅=
2
2 κπ (6.10)
DT is the diameter of the water tank proper, tins_T is the thickness of the insulation and
lT is the height of the tank. The assumption was that the temperature of the internal
tank wall was equal to the water temperature: Tiw = Twater_tank. Since the water was
heated from the bottom, Twater_tank was taken as the maximum recorded temperature
of the water.
A second approximation, which was more accurate with the experimental results,
included the top and bottom areas of the tank as well. The value of lT was augmented
to reflect the augmented area. In this case equation 6.10 becomes:
( )( ) ( )ambktan_water
T
T_insT
TTktan_loss TT
DtDln
DlP −⋅
⎟⎟⎠
⎞⎜⎜⎝
⎛ +
+⋅⋅=
2
22 κπ (6.11)
Alternatively, the tank may be modelled as a cylinder of area Atank and the losses
found by the experimental determination of an overall heat loss coefficient, Utank,
using the following equation:
( )ambktan_waterktanktanktan_loss TTAUP −⋅⋅= (6.12)
The disadvantage of this method is that it is specific to the tank used, while the
previous method, in principle, can be adapted to any cylindrical tank.
Solution process
The net heat gained by the water was predicted from equations 6.8, 6.9 and 6.11:
( ) ( )( ) ( )ambktan_water
T
T_insT
TTpipe_lossVcond_totseff_water TT
DtDln
DlPLV.P −⋅
⎟⎟⎠
⎞⎜⎜⎝
⎛ +
+⋅⋅−−⋅⋅⋅⋅≅
2
22051
κπρη & (6.13)
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6.4.4 Summary of solution process for the entire system
Solving for the collector meant
determining output power as steam
production. Solution for the collector
included Sun-Earth geometry, energy
collection and heat transfer dynamics.
Solving for the transfer line meant
calculating the effective steam power
coming into the storage tank heat
exchanger as useful steam after transfer
losses. An experimental (conservative)
value of 150 W was used.
Solving for the storage tank meant
obtaining effective power transferred
and retained in the water by useful
steam. Solution included sensible heat
contributions and approximation to
losses from an augmented cylinder.
Collector simulation results are given in section 6.6.1. The efficiency was assessed
versus concentrator reflectance and absorber emittance (Figures 6.39 and 6.40).
Steam production was assessed versus concentration ratios and an optimal figure was
found for different absorber emittance values (Figure 6.43).
Results for the storage tank in section 6.6.4 show the increase in losses with
increasing water temperatures, with a maximum power loss estimated at
(100 ± 11) W. The higher accuracy in tank loss calculation for the modified
relationship of equation 6.11 was acknowledged.
Collector
Inputs:
Outputs:
Solution’s algorithm
for CPC panel
(figure 6.24)
Transfer line
Inputs: Psteam_coll
Outputs: Psteam_intank
Water storage tank
Inputs: Psteam_intank
Outputs: Pwater_eff
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6.5 Experimental work: prototype and system construction
The system designed was composed of the following elements:
• Solar collector panels for steam production with top cover
• Roof reservoir tank providing the water for steam conversion
• Conveyance system (tubes and pipes)
• Storage tank
• Heat exchanger
• Condensate receptacle
All three prototypes constructed were based on the same design principles. The
difference lay in materials chosen for construction of boilers and reflectors and
variations in the number of CPC structures per collector. The reservoir tank, the top
cover, the conveyance system, the hot water tank and the heat exchanger were
practically identical in all three.
6.5.1 System components
The CPC reflector
The criteria for construction of the CPC shape was based on the following:
- Collection times of 4 hours, meaning an acceptance half-angle of 30°
- Theoretical maximum concentration factor of 2
- Truncation to obtain a low height profile, comparable to flat plate collectors
- Vertical and horizontal fin profiles
The shapes of the reflectors were obtained from the parametric equations for the CPC
as given in chapter 3 and Appendix C. The absorber fins considered were 5 cm wide,
giving a surface of 10 cm2 per cm length. The aperture of the collector, therefore,
would be 20 cm wide in order to obtain the maximum concentration of 2 for these
circumstances. However, truncation was done at approximately a third of the total
height (8 cm), leaving the CPC structure with an aperture of 16 cm. An example of
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the actual horizontal fin profile used is given in Figure 6.10. The concentration factor
was reduced to 1.6 by this change with a slight increase in collection times.
Figure 6.10 Truncated CPC profile used (scale 1:3)
Absorber-boilers
The absorber boilers were a combination of copper fins, 50 mm wide, 1.8 m - 2.25 m
long and 0.07 mm thick, with copper tubes of 4.5 mm ID soldered on top (Figure
6.11).
Figure 6.11 Schematic of the fin and tube copper absorber
Soft soldering with a lead-tin alloy was used to attach tubes to fins in all but one of
the modules constructed (the exception being a brazed array for the second
prototype). The fin & tube arrangement was soldered or brazed to header and footer
pipes making up absorber-boiler modules (Figure 6.12). Each module had return
pipes at each side for convenient return of hot water bubbled-up into the header pipe
by the boiling process. If this water was not removed from the header pipe it would
interfere with and hinder steam delivery down the transfer line. The footer pipe was
connected to the bottom of the reservoir tank, which held the water that was gravity
fed to the boilers. All prototypes were blackened. The first and second prototype
2θa
Soft SolderTube
Fin
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modules were spray-painted black. For increased efficiency, a spectral selective paint
(Solkote™) was used for the second prototype and a spectral selective self-adhesive
material (Maxorb™) was used for the third prototype.
Figure 6.12 Absorber-boiler array of 7 fins & tubes connected to header/footer tubes and
return water pipes prior to blackening (2nd prototype)
An upper limit measure of fin efficiency was estimated based on standard heat
transfer relationships for flat plate collectors92F
93, owing to the similarity between the
straight rectangular fin-and-tube profile of flat plates and the CPC absorber profile:
⎟⎟⎠
⎞⎜⎜⎝
⎛ −⋅
⋅
⎥⎥⎦
⎤
⎢⎢⎣
⎡
⎟⎟⎠
⎞⎜⎜⎝
⎛ −⋅
⋅=
2
2
tubefin
fin
tubefin
fin
fin Dwt
U
Dwt
Utanh
κ
κη
(6.14)
Where: U = total heat loss coefficient from the panel in W/m2·°C
κ = 385 W/m·°C, the thermal conductivity of copper
tfin = 0.07 mm, thickness of the copper fins
wfin = 50 mm, width of copper fins
Dtube = 4.5 mm, diameter of absorber tubules
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For conservative purposes, a U-value of 8 W/m2·°C for the CPC panel was used,
which is above typical values for single cover flat plates93F
94. For these conditions, the
fin efficiency from equation 6.14 is above 94%, and so little thermal penalty was
expected by this design.
The small diameter for the boiler tubes was chosen on the need for expedite steam
creation. A small volume of water would be readily converted into steam, since it
was desirable to reduce as much as possible operation downtime arising from a
reduced solar input on days of partial cloudiness and other transient effects. For an
input of 820 W (from Table 6.5) on the array of Figure 6.12, each absorber-boiler
section will receive about 295 W. For a panel optical efficiency of 70%, about 205 W
of heat will be delivered to the water in each tubule. Assuming 90% of this heat is
converted into steam (185 W) the time taken to heat up all the water in the tubules
(about 30 cc) up to 100 °C and then vaporise it, is between 6 to 7 minutes, with a
mass flow rate of about sg
121 . This will depend on whether the panel has been
operating in steady-state mode or not. This also means that a steam flow rate around
scm3140 and a steam velocity of about 8.5 s
m could be expected. Under the most
favourable conditions and best prototype design, a steam flow rate close to 0.75 sL
(± 10%) was observed.
Roof reservoir tank
The reservoir tank was constructed of rolled and brazed galvanised iron sheeting. At
2 m long and 0.12 m in diameter, this reservoir was able to hold more than 20 L of
water (Figure 6.13). It was housed in a rectangular enclosure, made of the same sheet
metal, insulated with polyurethane foam and fibreglass wool. Copper pipes were
attached at each end of the tank. The bottom was connected to the footer pipes,
feeding the boiler array directly with cold water. The top was connected to the
transfer line for pressure equalisation throughout the system allowing the water to
flow freely into the boilers.
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Figure 6.13 Reservoir tank (from final prototype)
The connection to the transfer line was done with a smaller diameter pipe in order to
reduce as much as possible any steam condensation in the tank. As steam was
produced throughout the day, water levels in the absorber-boiler array and water tank
decreased. The fact that the tubes acted as “bubblers” enhanced the flow and mixture
of hot and cold water and kept recirculation happening with reduced water levels. As
long as the self-pumping mechanism worked well and the system was properly
primed from the beginning, a water level of 30% the total capacity of the tank was
not considered problematic in terms of the likelihood of having hot spots and high
stagnation temperatures. This was evidenced in preliminary rig tests of early
absorber-boiler modules.
Hot water tank with heat exchanger coil
The water tank used was a Saxon Copperflow™ 200 L domestic hot water tank
manufactured by Peter Sachs Ind. The tank itself is made of copper sheeting which
has been rolled and brazed together into a cylinder, then sealed top and bottom with
copper covers. It is contained in a BHP Colorbond steel case into which polyurethane
is injected to provide insulation (except for the top and bottom covers that use
polystyrene). The tank is factory fitted with a lengthy heat exchange copper coil and
an electric heating element. The coil is connected to the cold water inlet and to the
hot water outlet.
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The tank used in this system had the heating element removed and replaced by a
single copper pipe loop of 12.5 mm ID for heat exchanger from condensing steam.
The upper end of the heat exchanger was connected to the downward steam pipe.
The bottom end was connected to the condensate receptacle (Figure 6.14). As heat
transfer to the water in the tank from the phase change of steam was very efficient,
the length of the looped tube required was about 1 m. In order to recover as much
heat as possible from the hot water condensate a near horizontal loop was used.
Figure 6.14 Hot water tank
The final setup consisted of a 7 m long copper
transfer line running from the roof of a two
storey house to the ground level
Figure 6.15 Insulated vapour transfer line
(trajectory indicated by red arrows)
(a) Exchanger coil used (red) (b) Input and output ports for steam and condensate.
(c) Properly insulated and protected tank
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6.5.2 First prototype collector panel
The initial prototype (Figure 6.16) consisted of 4 modules, each module made up of
3 CPC absorber boiler structures with vertical fins. The boiler arrays were 1.8 m in
length. The reservoir tank was located to the left of the collector. A non-return loop
was placed at the bottom of this tank to prevent hot water in the footer tube from
thermosiphoning into the reservoir.
a) Single module on test rig b) 1st prototype
Figure 6.16 CPC modules and 1st prototype
The CPC profile was provided by mould forming of polyurethane foam. The mould
was made out of wood shaped to the vertical fin profile configuration of the CPC
(Figure 6.17). Two different materials were used for the reflectors. One was an
anodised and polished aluminium sheet of 0.5 mm which exhibited a mirror quality;
Anocoil™. This was used in three modules. For the remaining module, a 0.2 mm
thick polished aluminium roll sheet was used. Both were bent to shape and fixed onto
the mould before casting of the modules.
Figure 6.17 Vertical fin profile CPC mould before and after aluminium lining
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The absorbers were spray-painted with flat black paint and the modules covered with
3 mm UV resistant polycarbonate sheeting of 0.9 transmisivity. Four modules were
paralleled together by joining header and footer tubes and connecting the assembly to
the transfer line.
For this prototype, a second header tube was used to connect all modules and
reservoir tank to the downward transfer line (Figure 6.18)
Figure 6.18 Header tube of the 1st prototype and transfer line connection
Insulation for all piping was provided by foamed elastomeric nitrile rubber sleeve
tubing, Armaflex™, of 25mm OD (thick), 12.7 mm ID and thermal conductivity of
0.039 W/m2·°C at 45°C.
The entire assembly was set on a purpose built wooden structure with a tilt angle of
30° ± 3° and faced east for its entire operation. East facing was chosen as this
maximised solar input at the trial site and for the duration of the testing (summer).
Performance of this prototype was predicted from the mathematical model based on
the heat transfer modes discussed in previous section. There was good agreement
between experimental and numerical results (as detailed in section 6.6.1).
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6.5.3 Second prototype
To improve on the manufacturing process and cost-effectiveness of the collector, the
following changes were proposed and implemented in a second prototype:
• Increase module dimensions from 3-CPC to 7-CPC cavities.
• Replace relatively expensive reflector materials with low-cost reflector materials
• Replace vertical fin & tube configuration for a horizontal profile
• Layer the absorber boiler with a spectrally selective paint for increased efficiency
• Replace mould forming method by precision-cut polyurethane blocks.
• Increase aperture area of the entire collector system (2 modules)
• Encase modules in galvanised and robust metal enclosures
• Use brazing instead of soft-soldering
The end result was a double module collector arrangement of 5 m2 collection area
with a central reservoir tank (Figure 6.19).
Figure 6.19 Double-panel 2nd prototype with reservoir tank in the centre
Each module comprised seven absorbers (at 0.16 m spacing) 2.25 m long, assembled
in parallel and also attached to header and footer pipes, now included as an integral
part of the modules. Both modules had 2 copper return pipes. One of the modules
was brazed in an attempt to achieve better rigidity and have a system less prone to
leaks. Total effective area of each module was about 2.5 m2.
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Both assemblies were spray-coated with a solar selective paint of 0.9 absorptance in
the solar spectral range and a minimum achievable emissivity of 0.22 in the thermal
range (SolkoteTM Hi/Sorb-II selective solar coating). The spray painting was carried
out by a spray painting company so it was not possible to closely monitor the surface
thickness of the coating, which was a crucial aspect in the proper selective
functioning of the surface. The fins and tubes were identical in dimensions and
construction to the previous prototype, except for their increased length (2.25 m as
opposed to 1.8 m)
The process of fabricating the modules in this case was quite different. The
insulation and support structure for the boiler assemblies was obtained from
polyurethane foam blocks precision-cut to the required profile; length, width and
thickness. This was done by computer guided machinery provided by an industrial
application’s company (ReMax Pty Ltd). The CPC profile that eventuated was of
good precision and reproducibility, although about 1 mm extra depth was carved
from the intended mathematical shape. The polyurethane CPC structures were
painted to improve surface stability and improve reflector material adhesion. The
reflective material used was an aluminium coated paper (SisalationTM), fixed to the
profiles using a two-part self-curing epoxy resin (Araldite®). The cusp of the profiles
was reduced by about 5 mm so that the absorbers would not be directly in contact
with the reflectors and minimise heat losses via conduction. The modules were
placed in a galvanised iron sheet metal enclosure (Figure 6.20) and the absorber-
boiler arrays placed in position on top and in line with the axis of the CPC reflectors.
Figure 6.20 7-CPC module structure with reflective lining in metal case
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This was done for protection, stability and ease of use during transportation and
operation. Insulating and reflective polyurethane end pieces were placed at both ends
of the modules and polyurethane foam was mixed and poured into the side areas to
provide insulation for the return pipes and to secure the CPC profile in the container.
A cover of 3 mm clear polycarbonate with the edges bent up to provide a water
barrier was placed over the assembly and secured in place with galvanised sheet side
and end sections.
The modules were placed on a metal frame and oriented due north with a tilt angle of
approximately 30°. The transfer line was a 15 m long 12.7 mm OD copper tubing
with 19 mm foam rubber insulation. The system was located at the premises of the
industry partner, Peter Sachs Ind. Pty. Ltd.
6.5.4 Third prototype
The results from the second prototype revealed problems associated with the design
and operation of the unit. Even though lower costs were achieved in its fabrication,
the degraded performance clearly made it unsuitable for the objectives of this study.
Therefore, a third and last prototype was constructed, including the modifications for
improved performance from first prototype, correcting the issues of poor
performance for the second prototype, and adding the following changes:
• Use of spectrally selective nickel chrome surface on the absorber-boilers
• Use of highly reflective silver surface for the CPCs
• Replacement of rigid return pipes for flexible hoses
A module identical to the second prototype, was produced and tested (Figure 6.21).
Every copper fin and tube was layered with thin self-adhesive metal strips of
blackened nickel foil (Maxorb®) of very high absorptance in the solar spectrum
(α > 0.9) and low-emittance in the thermal spectrum (ε < 0.11) (Figure 6.22). All fins
were cover-protected after layering until the array panel was assembled.
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Figure 6.21 Single-module 3rd prototype with reservoir tank to the right
The CPC reflectors used were 0.5 mm thick acrylic sheets with a highly reflective
metallised backing (Silverlux™, ρ > 0.9), bent to the profile shape and glued on with
fast setting epoxy adhesive (Araldite®) (Figure 6.21). The CPC polyurethane module
was painted beforehand for improved strength and material adhesion. Interestingly,
the thickness of the reflector laminates seemed to partially compensate for the extra
depth that was cut-off from the structure as mentioned before.
a) Fin & tube prior to assembly b) Back side of array and lining of last fin
Figure 6.22 Fin and tube copper array before and during maxorb layering
It was realised that for return pipes it would be better to have flexible high
temperature tubing instead of rigid copper tubes. This would avoid expansion stress
between return tubes and absorber tubules, which could create vacuum leak points
affecting system performance. The third prototype therefore used high-temperature
(automotive) rubber hoses for return pipes, eliminating this problem.
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Figure 6.23 CPC structure with reflector material Silverlux™ (still covered with protective
foil) and maxorb-lined boiler array
The casing of the module, polycarbonate cover and water reservoir tank were
identical to the previous prototype and the entire module was placed in the same test
site as for the first prototype with a north-east orientation.
This prototype had the best performance, being almost twice as efficient as the first
prototype and was the concluding unit in the study of a SHWS incorporating passive
downward vapour phase transport. All numerical and experimental results are given
in the next section.
Figure 6.24 Steam production from 3rd prototype
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Figure 6.25 Collection and orientation layout for 3rd prototype showing collector and
reservoir on the roof and the storage tank at ground level
Figure 6.24 shows the panel in operation producing abundant steam. Figure 6.25
shows the panel in its final location and orientation, connected to the water tank via
the insulated transfer line.
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6.6 Results and discussion
6.6.1 Modelling results
The mathematical model was implemented using MATLAB™ and allowed for
performance prediction of CPC panels and the system as a whole. It assessed
radiation collection for any position, latitude, date and time as per Table 2.2 and
incorporated the algorithm for simulation of the heat transfer dynamics (Figure 6.8).
The modelling relationships were based on the simplified heat transfer modes of
Table 6.8 and Table E1. Temperatures and heat losses were obtained as well as
energy production and efficiency of the system for variations in input data
parameters (irradiance values, optical characteristics, etc.).
The design of the second prototype was made with the results obtained by this
process with further improvements carried on to the third prototype.
The efficiency plots of the following figures are the model predictions for the CPC
panel. Efficiencies were later estimated for each prototype by measuring the rate of
steam condensate produced during panel operation (section 6.6.2). The plots are
based on the well-known Hottel-Whillier-Bliss formulation for the derivation of solar
collector efficiencies94-94F95F
96 from which the efficiency equation for the CPC boiler can
be deduced:
( )⎥⎥⎦
⎤
⎢⎢⎣
⎡ −⋅−⋅==
GTTU
'FG
A/Q ambAcpcLAu
0ηη (6.15)
Qu is the useful heat collected, η0 = τC·Rcpc·αA, is the optical efficiency of the CPC, in
this case the product of cover transmittance, concentrator reflectance and absorber-
boiler absorptance. cpcLU = UL/C the collector heat loss coefficient (to the
surroundings) modified by the geometrical concentration ratio, C, (equation 3.2). F’
is the collector efficiency factor, a measure of the effectiveness of heat transfer from
the absorber to the fluid (the other quantities have been defined in previous sections).
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Since these collectors are intended for water boiling, they will not operate unless
TA ≥ 100°C. This means that the maximum efficiency obtainable will always be
below F’η0. In the plots, an upper limit for efficiency under near-extreme conditions
was chosen (e.g., Tamb ≅ 34°C, G ≅ 1100 W/m2):
⎥⎥⎦
⎤
⎢⎢⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛⋅−⋅≈
503
0cpcLmax U'F ηη (6.16)
Figure 6.26 Performance plots for variations in CPC wall reflectance
An important change between the first and second prototypes was the change in
reflector material (Figure 6.26), which was assessed concurrently with the
construction of the latter. The efficiency and reflectance are directly proportional, as
expected, since more radiation reaching the absorber means more energy available to
produce steam. From the plots above it is seen that reflectance changes of +0.1
equate to changes between 14%-35% in CPC efficiencies. The differences are higher
for lower reflectance values, suggesting that small changes can have a significant
effect in efficiency and must be taken seriously (as it was seen for the second
prototype results – Figure 6.45).
0.06 0.065 0.07 0.075 0.08 0.085 0.09 0.095 0.1 0.105 0.11 0.115 0.12 0.125 0.13 0.135 0.14 0.145 0.150
0.05 0.1
0.15 0.2
0.25 0.3
0.35
0.4 0.45 0.5
0.55 0.6
0.65 0.7
Efficiency curves for different CPC reflectance and irradiance values
(Ta - Tamb) / G [K·m²/W]
Effic
ienc
ies
Irradiance range = 600 - 1000 W/m²
Ta - Tamb (steady state) = 80 °C
Optical efficiency range = 0.47 - 0.81
Irradiance range = 600 - 1000 W/m²
Ta - Tamb (steady state) = 80 °C
Optical efficiency range = 0.47 - 0.81
Reflectance 0.55 0.65 0.75 0.85 0.95
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Figure 6.27 Performance plots for single- and double-cover collector models
0.06 0.065 0.07 0.075 0.08 0.085 0.09 0.095 0.1 0.105 0.11 0.115 0.12 0.125 0.13 0.135 0.14 0.145 0.15 0
0.05 0.1
0.15 0.2
0.25
0.3 0.35 0.4
0.45 0.5
0.55 0.6
0.65 0.7
Efficiency curves for different absorber emmissivities and irradiance values
(Ta - Tamb) / G [K·m²/W]
Effic
ienc
ies
Irradiance range = 600 - 1000 W/m² Ta - Tamb (steady state) = 80 °C Optical efficiency = 0.65 (External model from A Rabl - see text)
Irradiance range = 600 - 1000 W/m² Ta - Tamb (steady state) = 80 °C Optical efficiency = 0.65 (External model from A Rabl - see text)
SINGLE COVER SYSTEM
Emittance ( ε ) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Rabl, ε = 0.1 Rabl, ε = 0.9
0.06 0.065 0.07 0.075 0.08 0.085 0.09 0.095 0.1 0.105 0.11 0.115 0.12 0.125 0.13 0.135 0.14 0.145 0.15 0
0.05 0.1
0.15 0.2
0.25 0.3
0.35
0.4 0.45 0.5
0.55 0.6
0.65 0.7
Efficiency curves for different absorber emmissivities and irradiance values
(Ta - Tamb) / G [K·m²/W]
Effic
ienc
ies
Irradiance range = 600 - 1000 W/m² Ta - Tamb (steady state) = 80 °C Optical efficiency = 0.65
DOUBLE COVER SYSTEM
Emittance ( ε ) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
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Initially, with the intended construction of the first prototype it was thought that a
single cover system would be ideal and suffice for the objectives of the project. The
use of a double cover was later investigated for efficiency evaluation by absorber
emittance comparison (Figure 6.27). Also, predicted efficiency of the system is
directly proportional to the emittance of the absorber. This is true for both single and
double cover systems and was expected, since less radiation emitted by the absorber
means lower losses.
The other important observation is that for absorber emittance values below
approximately 0.4, the double cover system with a sheath surrounding the absorber
appeared to be less efficient than the single cover one. This showed that a simpler
and possibly lower cost CPC system could be devised by appropriate engineering of
the absorber-boiler in this area. Double cover systems have been proposed77,96F
97 for
reduction of losses in solar heating, therefore, it was considered during construction
of the second and third prototypes. However, due to the expected low emittance
values of the absorbers for these prototypes (less than 0.4), no double-cover or sheath
was used.
Efficiency results in the previous figures were compared to the work done by Rabl35
for similar panel set-up and conditions employed in this study:
- CPC panels of 1.6 concentration ratio
- Wind speed of 4.5 m/s
- Selective (ε = 0.1) and non-selective (ε = 0.9) absorber surfaces
- Tamb = Tsky = 10°C
- Optical efficiency of 0.65
Despite the simplified approach of this study’s prediction model, the efficiencies for
the single cover system were in moderate agreement with Rabl’s results. The model
developed predicted higher efficiencies for lower irradiance values and vice-versa.
For high emittance (ε = 0.9) and irradiance values above 800 W/m2, the models
differed by less than 20%. For low emittance (ε = 0.1) and irradiances over
600 W/m2, the models differed by less than 15% (Figure 6.27).
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An optical concentration ratio of 1.6 (without truncation) equates to an acceptance
half-angle of about 38.7°. This means that collection times would ideally take just
over 5 hours and for a north facing panel, collection would start roughly at 9:30 am
and finish close to 2:30 pm. The maximum irradiance values at start and finish times
with optimum tilt angle and clear sky conditions would rarely reach 800 W/m2 in
subtropical latitudes peaking around 1000 W/m2 around noon. For a truncated CPC
with a reduced geometrical concentration ratio from 2 to 1.6 (as was the case with all
prototypes) the situation is different. Truncation will reduce the available power
input compared to the full-size scenario (Figure 6.10) with a slight increase in
collection times that will result in low radiation gains (Figure C2).
For low radiation gains the system would not operate, so in reality, it was expected to
behave very similarly to a full-size CPC arrangement with a reduced power input due
to geometrical reduction of the aperture. This meant that collection times resulting in
effective system operation would be close to the collection times expected for a non-
truncated concentrator. The experimental work confirmed this.
Total effective volume of water converted to steam over an entire operation cycle
was predicted to be between 6 L to 12 L for a 4 m2 collection area and an average
irradiance value of 880 W/m2 (Figure 6.28). Again, production is higher for lower
emittance values, as expected. The pre-boil time seen as nil production of steam at
the beginning of operation does not account for heat capacity effects of the elements.
In reality this time would be longer as the system heats up completely and
approaches thermal equilibrium.
From these results and from equations 6.9 and 6.13 it was possible to estimate the
requirements for the design of CPC collector panels based on hot water needs. For
instance, to supply the energy target of 30 MJ to 200 L of water, the amount of steam
necessary to transfer this energy would have to be more than 13 L, after taking into
consideration heat losses and steam/water heat exchange efficiencies. There are
different ways of achieving this:
- Increasing the collection area
- Using a higher reflectance material for the CPC
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- Using a lower emittance surface for the absorbers together with high absorptance
- A combination of the above-
In commercial design it is then a matter of optimising these, and other factors, to
produce the optimum ‘high-performance/cost-effective’ ratio.
Figure 6.28 Total steam production for a typical CPC panel over 5 hours
There is also an optimum concentration ratio for different absorber emittances and
the model allowed to determine which concentration ratio would yield maximum
steam power production (Figures 6.29 and 6.30)
The horizontal line in Figure 6.29 (pink) represents the average power for optimum
concentration, which would deliver the largest amount of energy to the water for the
parameters selected (latitude, tilt, etc). The optimum in this case was 1.7 and steam
production would last close to 5 hours: from about 9:36 am to 2:24 pm (cyan curve,
indicated with arrow). By integrating over time, total steam energy could be found
0 25 50 75 100 125 150 175 200 225 250 275 3000
2
4
6
8
10
12
14
Heating time of absorber (min)
Volu
me
of w
ater
vap
ouris
ed (L
)
Steam production vs. heating time of absorber
Irradiance (fixed) = 880 W/m² Concentration ratio = 1.6 Collection area = 4.032 m² Ambient/sky temperature = 20° C
EMITTANCE (ε) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
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for each concentration curve. The highest value obtained of about 1542 W·h or
5.55 MJ, was for this concentration. The values are strongly dependent on the
emissive and absorptive properties of the collection medium. The figures above were
obtained for high emittance and high absorptance.
Figure 6.29 Steam power produced for various CPC concentration ratios
The plots of Figure 6.30 are an extension of Figures 6.28 and 6.29 considering how
steam energy produced by the CPC panel varies with absorber emittance and
concentration. Steam output varies markedly with the emittance of the absorbing
surface. It is seen that for high emittance values (ε ≥ 0.7), concentration ratios
between 1.5 and 2 appear to yield very similar results with no more than 3%
difference. As the emittance of the surface is lower, the optimum concentration
decreases.
These results depend on the geographical location and date and positioning of the
collectors. The plots of Figures 6.28, 6.29 and 6.30 were obtained for latitude -27.5°,
autumn equinox (21st March) with the collector facing north and tilted to the latitude
angle (maximising energy collection).
6 7 8 9 10 11 12 13 14 15 16 17 18 0
50
100
150
200
250
300
350
400
450
500
550
600
650
700
750
800
850
900
950
1000
Solartime
Pow
er p
er u
nit a
rea
(W/m
²)
Steam power production over a day for different concentration ratios
Absorber emittance/absorptance = 0.9 / 0.95
OPTIMUM CONCENTRATION RATIO = 1.7
Steam production energy ~ 1542 W·h
Average Power ~ 321 W
Azimuth = 0°
Latitude = -27.5° Tilt = 27.5°
Tamb = 20°
Concentration (angle)
C = 1 (Ø = 90°) C = 1.4 (Ø = 45.6°) C = 1.6 (Ø = 38.7°) C = 1.7 (Ø = 36°) C = 1.8 (Ø = 33.7°) C = 2 (Ø = 30°) C = 2.5 (Ø = 23.6°) C = 3 (Ø = 19.5°) C = 5 (Ø = 11.5°) C = 11 (Ø = 5.22°) Average power Irradiance profile
OptimumOptimum
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Figure 6.30 Daily steam energy produced for various CPC concentration and emittance values
The results of Figure 6.30 could be used as a design tool in the selection of optimal
characteristics for the SHWS given the requirements for domestic hot water. For
seasonal and panel orientation changes, several plots would be required for a more
comprehensive assessment.
The energy target of 30 MJ is about 8.4 kWh. Thus, referring to Figure 6.30 it would
appear that the minimum collector area required is 4.5 m2 for a solar selective
absorber ε = 0.4 with concentration in the range 1.3-1.8. In reality, it will be higher
than this since these are results for steam power output from the panel, without
considering transfer line losses, steam heat transfer efficiency (ηS) in the exchanger
and tank losses.
Additionally, Figure 6.30 does not consider truncation for the CPC. In this study the
collection aperture for 2× concentration was truncated to 80% the original value. An
80% power output was then used as an empirical lower limit to the real output.
1 1.5 1.7 2 2.5 3 3.5 4 4.5 5 5.5 60
500
1000
1500
2000
2500
Concentration ratio
Stea
m e
nerg
y pe
r uni
t are
a pe
r day
(W·h
/m2 ·d
ay)
Steam energy per unit area vs. concentration ratios
EMITTANCE (ε) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
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Therefore, as a design tool, these results would still require adjustment for:
- Truncation of the CPC
- Pipeline losses, which were taken as 150 W (section 6.4.2)
- ηs values (section 6.4.3)
- Tank losses (section 6.4.3)
6.6.2 Experimental results from prototypes
6.6.2.1 First Prototype (Figure 6.31)
Figure 6.31 Efficiency results for the 1st CPC prototype
For efficiencies above 20%, experimental data for this prototype and results from
Rabl’s numerical study were in very close agreement, with differences being smaller
than 3%. The differences between the model prediction from this study (blue curve)
for the same data and same efficiencies were under 13%.
0.07 0.075 0.08 0.085 0.09 0.095 0.1 0.105 0.11 0.115 0.12 0.125 0 0.025 0.05
0.075 0.1
0.125 0.15
0.175 0.2
0.225 0.25
0.275 0.3
0.325 0.35
0.375 0.4
(Ta - Tsky) / G [K·m²/W]
Effic
ienc
ies
Efficiency curves comparisons for 1st prototype
HIGH EMMITTANCE ( ε = 0.9) Model prediction Results from A Rabl* Results from 1 s t prototype
R > 0.99 P < 10-11
ΔF’η0 = 0.03
ΔF’UL = 0.3
(Eq. 6.30)GT..exp
Δ⋅−= 76880η
cpc
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For irradiance values above 840 W/m2, the efficiencies of the collector were above
25%. To supply 30 MJ/day to the water in a 4-hour period, an average power of
delivery of about 2100 W is required (Table 6.2). The aperture area of this panel was
about 3.5 m2 (4 modules of 1.8 m × 0.49 m each). For an average irradiance of
880 W/m2 (Table 6.2) and considering associated heat losses in the system, to able to
deliver close to 2100 W to the water a SHWS incorporating the design of this first
prototype would require a minimum of 3 panels.
6.6.2.2 Second Prototype (Figure 6.32)
Figure 6.32 Efficiency results for the 2nd CPC prototype
The disappointing performance of this prototype was most probably due to the
overestimation of the true optical efficiency of the system:
- Use of lower average reflectance material for the CPC reflectors (Sisalation™)
- Overestimation of the actual reflector values since the reflectance of the material
was not well characterised after application
0.07 0.075 0.08 0.085 0.09 0.095 0.1 0.105 0.11 0.115 0.12 0.125 0.13 0.135 0.140
0.025 0.05
0.075 0.1
0.125 0.15
0.175 0.2
0.225 0.25
0.275 0.3
0.325 0.35
0.375 0.4
(Ta - Tsky) / G [K·m²/W]
Effic
ienc
ies
Efficiency curves comparisons for 2nd prototype HIGH EMMITTANCE (ε = 0.9) Model prediction Results from A Rabl* Results from 2 n d prototype
(Eq. 6.30)GT..exp
Δ⋅−= 64570η
R > 0.98 p < 0.003
ΔF’η0 = 0.04
ΔF’UL = 0.5cpc
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- Underestimation of the emittance of the absorber-boilers since the Solkote™
solar selective surface was not well characterised after application
- Suspected steam leaks in the system
- Insufficient insulation used for transfer piping
The nominal value for solar reflectivity of the Sisalation product is about 0.82. It is
possible that the average reflectance of the CPC structure was well below this value
due to handling in the process of adhesion. It is noticeable from the photographs that
the CPC reflectors presented visible defects, such as crevices and bumps (Figures
6.19-6.21). Also, due to surface damage during soldering, brazing and inadequacies
of surface cleaning of the copper substrate, it is possible that the emissivity was
higher than the suggested range (0.28-0.49). The experimental determination of
system optical efficiency seems, therefore, necessary, and could be incorporated as
part of future prototype development. A suitable method is discussed in section 6.7.
Since top-up water was often required in the reservoir tank during operation, it is
probable that there was a leak in the system. Any escape of steam would have
lowered the measured collector efficiency.
6.6.2.3 Third Prototype (Figure 6.33)
The third prototype exhibited the best performance with over 50% efficiency for the
higher irradiance values (over 800 W/m2). The improved performance was attributed
mainly to the high attention to detail and improved fabrication process. In particular:
- Absorber-boiler array layout and soldering
- Application of a high quality selective surface
- Use of highly reflective material as CPC reflector
- Use of flexible return pipes as part of the boiler array
Results were close to model predictions for surface emittance below 0.3. Numerical
predictions from Rabl’s work were similar as well, although the experimental results
were higher, on average. Rabl’s model slightly underestimated the measured results
for low irradiance values while the model of this project produced an overestimation.
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Figure 6.33 Efficiency results for the 3rd CPC prototype
Despite the improvements, the system presented inaccuracies and other defects:
- The alignment of tubes and fins in the centreline focus of the CPC
- The layering of the fins with the selective surface product
- The actual CPC profile (shape)
- The adhesion of the reflector material to the CPC walls.
Additionally, the system suffered mechanical and thermal stress prior to operation at
the designated test site. It was observed after several weeks of operation that the
self-pumped mechanism was progressively diminishing which inevitably required a
manual refilling of the reservoir from time to time.
Taking all this into account, and the fact that a simple simulation model was used,
the results obtained from the third prototype were in very good agreement with both
numerical models. It is concluded that this system had an excellent performance.
0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.180
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
(Ta - Tsky) / G [K·m²/W]
Effic
ienc
ies
Efficiency curves comparisons for 3rd prototype
LOW EMMITTANCE ( ε = 0.1) Model prediction ε = 0.1 Model prediction ε = 0.2 Model prediction ε = 0.3 Results from A Rabl* Results from 3rd prototype
R > 0.96 p < 10-5
ΔF’η0 = 0.03
ΔF’UL = 0.3
(Eq. 6.30)GT..exp
Δ⋅−= 54570η
cpc
GT.. exp
Δ ⋅ − = 92 77 0 η
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126
6.6.3 Comparison of the 3 prototypes (Figure 6.34)
Figure 6.34 Prototypes performance comparison
The average efficiencies for temperature differences (Tabs - Tamb) = (80 ± 2)°C and
irradiance values of 800 and 1000 W/m2 are given in Table 6.11.
Table 6.11 Efficiency prediction for all prototypes
ESTIMATED EFFICIENCY % Prototype
(for 800 W/m2) (for 1000 W/m2) 1st 20 ± 5 34 ± 5 2nd 12 ± 2.5 21 ± 5 3rd 47 ± 10 54 ± 5
The last prototype clearly outperformed the other two, with much higher efficiencies
and in 3 out of 4 cases, more than double the values for the first and second ones.
Comparison of efficiency parameters (Table 6.12) also shows this superiority and the
fact that it compares very well next to other collector types77.
0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
(Ta - Tsky) / G [K·m²/W]
Effic
ienc
ies
Efficiency curves comparison between all prototypes Results from A Rabl, ε = 0.1 Results from A Rabl, ε = 0.9 Results from 1 s t prototype Results from 2 d d prototype Results from 3 r d prototype
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Table 6.12 Collector efficiency parameters
Efficiency parameters Collector
F’η0 F’ULcpc
7F
* 1st Prototype 0.88 ± 0.03 6.7 ± 0.3 2nd Prototype 0.57 ± 0.04 4.5 ± 0.5 3rd Prototype 0.77 ± 0.03 2.9 ± 0.3
CPC with inverted ‘V’ receiver 0.74 4.0 Flat plate with non-selective surface 0.75 8.0
Flat plate with selective surface 0.75 5.0 Evacuated tube 0.6 1.2
6.6.4 Water tank
Assessment of water tank temperature variations was done over a continuous period
of 6 days and 5 nights for the calculation of heat losses from the tank water.
Figure 6.35 Water tank temperature for no-load conditions over 6 consecutive clear days
* Note that for a flat plate, where C =1, L
cpcL UU =
Water tank temperature vs. time for daily operation
0 5
10 15 20 25 30 35 40 45 50 55 60 65 70 75
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140
Time (h)
Tem
pera
ture
(°C
)
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Figure 6.35 shows a typical set of temperature results obtained from the SHWS using
the last prototype operating for about 4 hours each day (i.e., 1 panel system). The
average irradiance on the system was fairly similar for all 6 days. The daily energy
gain was similar in all cases and revealed what could be expected for hot water
production from a system of this type with a single panel (Table 6.13). The losses
were higher for higher tank temperatures (more pronounced negative slopes)
doubling by the third day. Even though there was a tendency for slightly higher
associated cooling times overnight as days went by, the differences were not
significant (less than 5%). The differences between daily temperature gain of the
water were within ±1° C, which for the amount of tank water, equated to about
±0.8 MJ of energy gain. Given the fact that overnight heat losses increased steadily
for consecutive days, it would appear that the average steam efficiency, ηs_eff, did not
vary significantly even at water temperatures of 68° C (albeit a slight decrease, see
section 6.4.3). Environmental conditions were basically the same for the duration of
this analysis on water tank energy gain and losses, which gave a good indication of
the performance of the tank in this regard.
Table 6.13 Energy collection and heat losses for the water in the tank
Period Energy_IN Power_IN Max. Temp.
Cooling time Q-loss U-loss
(MJ) (W/m2) (°C) (h) (W) (W/m2·°C) Day 1-2 12.61 ± 1.18 876 ± 104 30.9 ± 0.5 18.9 ± 0.1 37 ± 11 1.3 ± 0.4 Day 2-3 12.21 ± 1.17 848 ± 103 43.1 ± 0.5 19.1 ± 0.1 59 ± 11 1.1 ± 0.2 Day 3-4 12.53 ± 1.18 870 ± 103 53.8 ± 0.5 19.4 ± 0.1 77 ± 11 1.1 ± 0.2 Day 4-5 11.42 ± 1.17 793 ± 101 61.2 ± 0.5 19.3 ± 0.1 92 ± 11 1.1 ± 0.2 Day 5-6 12.13 ± 1.17 843 ± 103 68.5 ± 0.5 19.8 ± 0.1 100 ± 11 1.0 ± 0.1 Average 12.2 ± 1.2 846 ± 12% - - - -
The theoretical calculations for tank losses based on the initial approximation of
equation 6.10 underestimated the experimental results by 20% to 36% and it was
believed that the losses through the top and bottom sections of the tank were partly
responsible for this, given the fact that this simplification is only valid when
lT >> DT. This prompted the use of equation 6.11, which resulted in a more accurate
loss assessment with errors ranging from –14% to +8%.
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129
It is important to note that there was very
little insulation on the bottom of the tank.
Better insulation is warranted, since losses of
about 100W over a 19-20 hour period
amount to high overall energy losses. Albeit
being under cover, the outdoor and relatively
exposed positioning of the tank (Figure 6.36)
most probably contributed to higher heat
losses than what could have been obtained if
it had been better sheltered and/or kept
indoors.
Figure 6.36 Hot water storage tank, transfer
pipe and condensate receptacle
6.7 Conclusions and discussion
6.7.1 Performance of the downward vapour heat transport SHWS
The development of a fully functional vapour downward heat transport solar hot
water system revealed that the self-pumped approach is a viable option in providing
domestic hot water. The system was operated separately with each of 3 different
concentrator-boiler collector panels designs. In the case of the last collector
prototype, it was seen that efficiencies over 40% were achievable, which makes it
possible to provide the entire hot water needs for a dwelling by proper sizing of the
system. Great attention to detail, better construction skills and better quality products
were the reasons for improved performance.
The system using the last prototype (2.5 m2 panel) was able to deliver an average of
12 MJ to the water in the tank, operating for about 4 hours each day (9:30 am –
1:30 pm) over a 6-day period during winter. Average power delivered to the water
store was 846 ± 100 W.
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130
Simulation predictions
The results of Figure 6.33 for the last prototype revealed very high panel efficiencies.
For an average measured irradiance over the panel of about 850 W and ambient
temperatures between 15 °C to 20 °C, an efficiency of 49% would yield close to
1050 W output average steam power. Truncation effects were included in these
calculations.
From Figure 6.30, for emittance values, ε, between 0.1 and 0.3 and concentration
ratios between 1.7× and 2×, the simulation model predicted an average steam power
output from the CPC panel, PS_avg, of about 1300 W for daily operation.
The plots of Figure 6.30 were repeated including the effects of truncation and pipe
losses for a realistic comparison with experimental results (Table 6.13). For
emittance values between 0.3-0.1, and for pipe (transfer line) losses ranging from
zero to 150 W, the model now predicted the results shown in Table 6.14.
Table 6.14 Prediction of average system steam power for truncation effects and different pipe losses from the plots of Figure 6.30
Pipe losses (W) PS_avg (W) 0 1100 50 1040 100 1000 150 960
The slightly higher results (+50 W) compared to the predictions from the plots of
Figure 6.33 were attributed to a more accurate time-integration calculation over the
full operation cycle of the collector.
From the experimental results, the average power gained by the water in the tank,
water_effP , was close to 850 W. The model predicted average output steam power from
the panel, panel_outP , close to 1100 W for the same operating conditions. Assuming
low tank losses, loss_tankP , of 30 W during the day and average pipeline losses,
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131
loss_pipeP , of 100 W, it was possible to determine an effective steam heat transfer
exchanger efficiency, ηs_eff, for daily operation and assess the capabilities of a
multipanel system.
Combining equations 6.8 and 6.9 and rearranging for efficiency:
( )[ ]pipe_lossout_panel
ktan_losseff_watereff_s PP.
PP
−⋅
+≅
051η (6.17)
Substituting the proposed values in equation 6.17 gave 840.eff_s ≅η
The remaining 16% steam power that apparently does not go into the water is
assumed to be a result of the experimental error in the measurements, the
assumptions and simplifications of sensible heat contribution (section 6.4.3) and the
characteristics of the condenser coil. Despite the fact that a near horizontal loop was
used to recover as much sensible heat as possible, this actual design and the diameter
of the pipe probably did not favour a speedy heat transfer from the flowing
downward steam as initially thought. Hence, a fraction of the steam power could
have ended in the condensate receptacle, with little sensible heat being collected.
This would warrant a proper design analysis of the heat exchanger tube, possibly
increasing pipe diameter and/or length. Another reason for the reduced steam transfer
efficiency could also be an overestimation of the average steam power given by the
numerical model. Additional temperature measurements close to the coil (and maybe
the use of heat flux sensors) and temperature determination of the condensate would
shed more light into any possible heat being unaccounted for.
Nevertheless, a second panel added to the system should be able to deliver an
additional 950 W of average power to the water. It could be thought of as if the first
panel were supplying close to 850 W (after allowing for pipe and tank losses) and the
second one were supplying close to its full effective steam output of around 1100 W,
reduced by the steam transfer efficiency. This is easily verifiable from equation 6.13
setting the pipeline and tank losses to zero.
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132
Duplicating the panel arrangement in the system to a tytal of 5 m2 collection area
would increase daily energy delivery to over 25 MJ.
It is estimated that increasing the area of each panel by 20% to 3 m2 would surpass
the daily average requirement of 30 MJ for domestic hot water. For year-round
performance, it is possible the values would be higher, since these calculations are
based on winter measurements for a non-optimal panel orientation.
6.7.2 Elements construction and materials used
The construction process and materials used were very much improved in the
development of the last prototype. All panels, however, encountered a few problems
during and after fabrication.
CPC profile design and reflective material layout
Polyurethane foam appeared to be the best material for CPC insulation and structural
support, despite the disadvantages associated with brittleness and high cost. For the
different reflector materials used in each prototype, the best performance was
obtained from the highest reflectivity element (Silverlux™) for the third prototype.
All reflectors exhibited shifting, misalignment and deformations during construction
and to some degree during operation. The first prototype modules appeared to have
fewer problems in this regard since they were made by mould forming with the
reflectors already in place. In contrast, the second and third prototypes had their CPC
profile determined by the foam structure with the reflectors later glued on top.
Absorber-boiler copper array and roof reservoir
The copper array of fins, tubules and pipes was very successful in boiling water at a
fast rate and producing useful steam. It was, however, difficult to assemble and
manipulate and relatively expensive to produce. Its effectiveness was dependent on
the accuracy of the line-focus alignment of the boilers within the CPC cavities, the
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Chapter 6 - Solar hot water system with passive downward vapour phase heat transport
133
reflectance of the CPC walls and the quality of the black coating used on the fins to
maximise absorption and minimise emission.
The best performance was obtained for the third prototype, which operated for two
years until it was dismantled. The reservoir tank was operated for the second year
with the use of a timed electric pump that took about four minutes each day to pump
up 20 L of water from the condensate receptacle and refill the reservoir.
The prototype arrays were found to be prone to leaks. The self-pumped mechanism
worked flawlessly only in the first prototype after leaks where identified and repaired
on some modules. For the second prototype, the soft-soldered panel was certainly a
suspect for leaks as well as the reservoir tank. For the third prototype, leaks occurred
after a month of operation. Both second and third prototypes experienced a decline in
operation of the self-pumped recharging mechanism over time.
The water reservoir tanks constructed showed signs of rusting with the water
progressively turning brown over months of operation of the units. Dismantling of
the first and second prototypes confirmed this.
From continued operation of the third prototype during clear sky conditions it was
found that the water tank, under no-load, reached a stagnation temperature of
(84 ± 2) °C (Figure 6.37).
At this water temperature, and for ambient temperatures between 15–30 °C, the
losses from the tank were around 110-130 W. At this point, the losses were equal to
the gains, so there was no effective power delivered to the water, i.e, 0Pwater_eff =
and abundant steam was seen flowing into the condensate receptacle.
As demonstrated by the results of Figure 6.37, the system had a self-regulating
mechanism for dumping excessive heat.
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134
Figure 6.37 Water tank temperature for no-load conditions over 12 consecutive days showing stagnation water temperature
6.7.3 Model predictions compared with experimental results.
The results from the model allowed a satisfactory characterisation of the SHWS as a
whole. From the calculation of energy collection (for date, time and location),
together with a simplified analytical approach for heat transfer (for collector panels,
transfer pipe, exchanger and tank losses) the model was able to predict performance
to a reasonable accuracy, despite the relatively high experimental errors (±10% of
effective average power delivered to the water in the tank over a day). The model
was, therefore, useful as an indicator of how a SHWS incorporating downward
vapour phase transport would operate. It was also useful in predicting how different
parameters affect system performance, enabling optimisation with a lesser need for
continuous prototype construction and testing.
The simplifications would also explain the linearity of the model and overestimation
of efficiencies for low irradiance values, when compared to Rabl’s model for similar
CPC concentrations and when compared with experimental results.
Water tank temperature vs. time for daily operation
0 4 8
12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92
0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 Time (h)
Tem
pera
ture
(°C
)
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135
The experimental determination of panel optical efficiency would allow for a more
reliable verification of the thermal modelling and to better assess discrepancies such
as those encountered with the second prototype. To this end, a simple method that
could be applied to each prototype in future development is the following:
- Obtain the efficiency curve of the prototype by measuring water temperature rise
(not steam production) as water of known flow rates is pumped through. The
resulting curve will be similar to those of Figure 6.34
- Fit the data obtained to an expression of the form of equation 6.15
- The resulting maximum efficiency (y-axis intercept from this fit) occurs when
there is virtually no temperature increase in the water, therefore no heat losses. In
these conditions, the amount of heat absorbed by the water is purely determined
by the optical efficiency. Therefore, this value is an estimate of the optical
efficiency8F
*.
Economics
The excellent performance of the third prototype did, however, carry the
disadvantage of higher costs. Certainly, the use of a much better reflector (specular
silver), a high performance selective surface (Maxorb™) and the degree of attention
to detail in its fabrication came at an increased price. It was then determined that by
automating the design process in the construction of the absorber boiler and given the
current costs of the materials used, a unit of this type would be comparable in cost to
the higher end SHWS models currently available in the market. More on the
economics of this system is given in chapter 8, but it can be said that this particular
high-efficiency prototype requires additional work and re-engineering from a
fabrication and material usage perspective in order to make it a competitive product
with mainstream units.
* Actual determination of solar panel efficiency from standardised industrial tests is much more involved. See Australian Standard AS 2535.1(1999) for further reference.involved.
Chapter 7 - Air-to-water heat transfer solar hot water
system with heat exchanger-water tank
coupling 7.1 Introduction
The air heater SHWS is composed of five sections:
• Collector panel that heats air
• Pipes that transport the air to and from the panel
• Heat exchanger: where the air exchanges heat with the water in the storage tank
• An insulated, large capacity water tank, coupled to the heat exchanger
• A centrifugal fan blower to mobilise the air around the system
This system relies on the heating of air in flat collection panels. The hot air is
delivered to the heat exchanger for heat transfer to the water. Hot water in the
exchanger drives a thermosiphon between the exchanger and the water tank. The
output air from the exchanger is either discarded or recycled back into the panel
since the system can operate, and was evaluated, in open and closed loop modes.
7.1.1 Basic design for the construction and operation of the air-to-water heat
exchanger-coupled tank SHWS
To meet the proposed daily target of Table 1.2, the following assumptions and
considerations were made for system design (Table 7.1, Figure 7.1):
Table 7.1 Assumed efficiencies for basic system components
Elements required Efficiencies9F
* Air-to-water heat exchanger 50% or higher
Collector panel 60% or higher TOTAL SYSTEM ~30% or higher
* Efficiencies assumed for a minimum required airflow rate of 60 L/s at 50°C, or 0.065 kg/s
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137
Assumed airflow rate for
efficiencies of table 7.1
Φv = 60 L/s or kg/s 0.065 =m&
Cair @ 50°C = 1007 J/kg·°C
Figure 7.1 Sketch for the air-to-water heat exchanger-coupled tank SHWS
Preliminary tests with the heat exchanger used showed that efficiencies above 50%
could be obtained at airflow rates of 60 L/s and water flow rates of about 10 cc/s.
For design purposes, since the panel had a 90° collection half-angle, the system
could be expected to operate for about 6 hours in winter and about 8 hours in
summer. For 6 hours of operation:
Table 7.2 Assumed energy and power requirements for 6-hour operation
Required daily energy in the water (from Table 1.2): 25 – 30 MJ Required average power into water: 1160 – 1400 WRequired average power input to the exchanger: 2320 – 2800 WRequired average power into system: 3900 – 4700 W
The airflow rate should be sufficiently high to draw enough power from the collector
and carry it into the exchanger. To satisfy power requirements the following scenario
was assumed for airflow rates of 60 L/s and water flow rates of 10 cc/s:
Given Parameters
Collector input
Initial air temperature, To = 30 °C
+
Using: TCmP air Δ⋅⋅= & Eq. 4.64
Collector panel
Water tank
Heat exchanger
(Optional: return pipe)
Fan/blower
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138
For operation in closed-loop mode:
- the optional return pipe is used
- the exhaust air is fed back into the panel
- input air temperature will rise
Finally, the sizing of the collector panel would be dependent on the required average
power input to the system over a 6 hour period (3900 – 4700 W) and the average
irradiance during operation.
Required collector output
Power to be gained by air = 2320 – 2800 W
Expected air temperature = 65°C – 73°C
Required exchanger input
Power carried by air at entry point = 2100 – 2500 W
Expected air temperature = 61°C – 68°C
Hot tank water
Average power going in the water = 1050 – 1250 W
Energy gained over 6 hours = 22.7 – 27 MJ
Output air temperature
Tair_out ≈ 40 - 45°C
Collector input
Tair_in > To
Back to:
Less than 10% losses from air pipes
Exchanger efficiency 50%
Closed-loop operation
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139
Table 7.3 Average irradiance for minimum absorber area required during OPEN LOOP operation mode
Average irradiance over 6 hours: 770 W/m2 Absorber area required: ~6.0 m2
For lower input air temperatures a larger absorber area would be required. For
example, if input air temperatures were 10 °C (winter), air would have to be heated
by about 60°C in order to obtain the required collector output air temperature (about
70°C). The required average power input to the exchanger, from Table 7.2, would
then become 3900 W and the required average power into the system 6500 W. For
the same average irradiance of Table 7.3, this would require an absorber area of
about 8.4 m2. This is, however, considering open loop operation, where ambient air
is drawn into the panel and warmer air is discarded at the exhaust of the exchanger.
For closed-loop operation the system cannot be simply characterised as for the
preceding situation. In this case, the input air temperature would rise as the air is
heated and recycled. If irradiance values were constant, this rise would halt when
equilibrium was reached and the heat gains and losses would be the same. Since
irradiance values are constantly changing, this dynamic cannot be so easily
estimated. In any case, this configuration would be expected to have a better
performance prospect and was the option of choice since:
- The closed system is not subject to foreign contamination/hindrance, therefore…
- Internal maintenance (panel heating element, pipes, exchanger) is reduced
- Higher temperatures are achievable and better use is made of the energy available
- Smaller panel collection area required
- A return pipeline is not a significant additional cost
- The disadvantages related to a longer pipeline are outweighed by the benefits
For the closed loop mode a rough estimate of panel area required could be made by
considering that the return pipe would also produce near to 10% power drop in the
recycled air. This means that most of the power lost from the exhaust air in open loop
mode (~50% of the total at exchanger input) would go back into the system.
Considering this, the panel area for closed loop operation could be much smaller
(Table 7.4).
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140
Table 7.4 Average irradiance for minimum absorber area required during CLOSED LOOP operation mode
Average irradiance over 6 hours: 770 W/m2 Absorber area required: ~3.0 m2
It is possible that in closed loop mode, very high air temperatures (above 100°C)
would be obtainable, in which case a heat dumping mechanism would have to be
contemplated. The return pipe could be engineered for such purpose.
Also, in both open and closed loop modes with no air circulation, high stagnation
temperatures would set in the panel, requiring some stagnation control mechanism.
The actual large-scale collector prototype constructed was 3.6 m × 1.2 m, with an
effective absorber area of 3.25 m × 1.14 m, or 3.7 m2.
The novel developments in this system were related to the engineering of the
collector panels and the heat exchanger/exchanger-tank coupling.
7.2 Types of solar air heating panels
Flat plate collection systems are the means by which most domestic SHWS are
operated. Although extensive research has gone into the fabrication and improvement
of these panels for the transport of liquid fluid, not as much has been done when air
is the transport fluid. This is because solar air heating systems (SAHS) have mainly
been used for space heating97F
98-98F99F
100 and food dehydration and drying applications100F
101-101F102F103F
104.
Air type collectors have similar components as water type ones. They are composed
of: glazing, absorber, flow channels (manifolds, etc) and a container with insulation.
The crucial development in a collector of this type is the design of the absorber.
Different geometrical approaches for absorber-heaters have been tested and
documented. Examples are given next according to the absorber type used.
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Group A: Air heating panels using flat absorbers
Figure 7.2 Longitudinal view for 3 different air-heating flat-plate solar panels
The collectors in this group (Figure 7.2) use the same type of absorber, but the fluid
flow is different in all of them and removes heat in a different way. Type A(a) is the
simplest arrangement where the heat absorber is in contact with the back insulating
material and the fluid flows over it. In type A(b) the absorber is placed at a certain
distance from the back and the fluid flows under it. This arrangement produces lower
convection losses to the top cover. In type A(c) the fluid flows over and under the
absorber and is capable of delivering more energy to the air under certain
circumstances. Type A(d) is similar to type A(b), where the absorber has protrusions;
fins or baffles that increase turbulence, increasing heat transfer to the fluid.
Group B: Air heating panels using corrugated & finned absorbers
Figure 7.3 Transverse view for 2 different air-heating solar panels with multi-channel
absorber plates
In type B(a) (above) the absorber has a series of channels through which the fluid
flows. Type B(b) is a triangular shaped absorber with fluid also flowing between the
channels. For the latter, fluid can flow below or above, or both below and above the
absorber. This configuration is designed to reduce the losses due to radiation and at
the same time increase turbulence and heat transfer.
For all the preceding collectors, the materials used as absorbers are commonly
aluminium and steel sheets, formed into the desired shapes.
Vf →
a) Conventional single channel panel
Vf1 →
Vf2 →
c) Double-channel panelb) & d) Single channel panel with modified top
Vf →
(Optional: protrusions/ribs)
a) Multi-channel absorber panel
Vf ⊗ ⊗ ⊗
b) Triangular shaped multi-channel absorber panel
Vf1
Vf2⊗ ⊗ ⊗
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142
Group C: Air heating panels using alternative absorbing media
Type C(a) collector absorbers (Figure 7.4) are made of a series of overlapped glass
plates creating narrow channels over the entire depth of the flow chamber through
which fluid flows. A part of the plates have been blackened so that the fluid in its
entirety is heated while traversing these narrow passages.
Figure 7.4 Longitudinal view for 2 different air-heating flat-plate solar panels using
alternative absorber type
Type C(b) is the so-called metal matrix collector. As its name implies, this collector
has a matrix-like metal structure through which the fluid flows as if it were being
forced through a wire mesh. Other variations in collector design include the use of
double-glazing and various absorber corrugation shapes.
Of the air heating solar applications and studies available, a small proportion refer to
the generation of domestic hot water by making use of solar air heating panels.
A means for obtaining domestic hot water from the use of a totally passive SHWS
incorporating collectors with a similar construction to those of type C(a) above is
described in a US Patent dated to the early 1950s4. The system referred to employs
natural air convection in a closed loop circuit, where hot air is driven upward towards
the tank that contains the water to be heated. It is a close-coupled system. Another
patented system designed in the 1970s104F
105 describes a SAHS for domestic water
heating employing a collector panel, which is crossed by a forced airflow fed by an
electrical fan. Heat is exchanged with an internally located water container. Both
systems have the option of using the hot air for other purposes, not just for hot water
generation (eg. space heating). A third system, proposed in 1987 105F
106, describes
another passive SAHS for domestic water production. The heat collection method in
this case is by open convection air trapping in a purpose-built black box. By clever
engineering, hot air is carried to the water tank for production of hot water.
a) Overlapped glass plates absorber panel
Vf →
b) Metal-matrix absorber panel
Vf
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143
Other theoretical and experimental developments have shown that SHWS using
air-heating collectors can be a viable, inexpensive, solution for domestic hot water
needs. For example, the study of a SAHS prototype based on air recirculation across
an air/water heat exchanger revealed that collector panel areas of 8 m2 were adequate
for this purpose106F
107. Another study of a system, adapted for Indian climates,
employing commercially available plastic air heating collectors and an air/water heat
exchanger, concluded that the use of plastic panels as a replacement for conventional
all-metal air heater panels in SHWS, is better suited for domestic hot water supply107F
108.
Other studies have provided simulation prediction models that describe collector
panel efficiencies and overall system performance108F
109,109F
110 and techno-economic
analyses for maximising hot water production and minimising costs110F
111.
Since solar hot air can be used for a variety of purposes, research has had strong
concentration on the development and engineering of collector panels themselves,
without necessarily creating an entire solar heating system for a specific purpose.
Some of these developments, which are of direct interest to this study, are explored
in the following section.
7.3 Heat transfer
Heat transfer assessment was done for all the elements of the system; the panels, the
piping, the heat exchanger, the fan-motor and the storage tank. Additionally, a
thermohydraulic assessment was done, since the overall performance was
conditioned by the fluid resistance posed by each of those elements.
The intended design for the SAH considered the following characteristics:
- Readily available building materials
- Inexpensive
- Easy to manufacture
- Easy to handle, install and maintain (if required)
- Durable
- Acceptable performance
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7.3.1 Air heating collector panel
In this study, a flat panel was considered the most suitable collector device, owing to
its geometrical properties; ease of manufacture and ease of integration into building
architecture, as well as offering typical all-day solar energy collection times.
Of the three kinds of flat absorber collectors, type A(c) has been considered as
offering a better performance under most conditions111F
112-112F113F114F
115.
In solar engineering, collector types B have received a lot of attention, with many
different absorber shapes studied and tested. These have included corrugated,
roughened, finned and channeled absorbers. There are many studies of the design,
modelling and experimental and simulated performance for this kind of
absorber115F
116-116F117F118F119F120F121F122F123F124F125F
126. Amongst them, it is worth noting the development of the so-called
“Vee” corrugated or V-corrugated (V-type) absorber, where the plate has V-shaped
creases or folds, resembling triangular channels. Several studies105-109,113 have
suggested their superiority over conventional flat plates under a variety of conditions.
The use of channels, roughened plates, and fins and baffles has also been regarded as
a better substitution for flat plate types111,126F
127.
A study comparing five different collector designs127F
128 with single glazing suggested
no particular advantage in using a V-corrugated absorber in place of conventional
flat absorbers. The best performance was obtained by the use of an undulated duct as
a fluid flow channel.
Studies of the effect of collector aspect ratio (length/width) on different types of
collector panels have also suggested that thermal performance is improved by
modifying the geometrical characteristics of these panels104,128F
129-129F130F
131.
From the literature, it seems that non-flat plate absorbers outperform the
conventional ones in most cases. However, there is nothing conclusive other than
what pertains to very specific, localised and custom-tailored conditions of
experimentation and setup.
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The first air collector prototype of this study was built with the V-corrugated
absorber profile (Figure 7.5). The heat transfer dynamics of such system is explained
in detail in the following pages. The construction process and materials used is given
in subsequent sections.
Figure 7.5 Transverse view of 1st prototype with a V-shaped absorber panel and triangular fins
Detailed explanation of the modelling development of the collector is necessary since
this represents the foundation over which any prediction of heat transfer dynamics
can be claimed. As such, the following pages examine and explain:
- The energy exchange between the elements within the collector and between the
collector and its surroundings
- The heat transfer modes associated with the above
- The relationships that lead to realistic modelling
- A mathematical formulation for convenient expression and manipulation of these
relationships (thermal networks)
- The evolution of the thermodynamic system and an algorithm for determining the
required parameters in performance prediction (temperatures and efficiencies)
The heat transfer modes for triangular and flat profile collectors with air flowing over
and under the absorbers are similar and are depicted in Figure 7.6
In the heat transfer analysis several assumptions were made:
1. The system is air tight (no leaks)
2. Heat capacity effects of cover, absorber and back plate are negligible
3. Temperature of the elements varies only in the direction of fluid flow
4. Each panel can be considered as made up of small transversal sections of the
whole that have been joined together. Temperatures of the elements of each
section can be considered uniform.
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Figure 7.6 Heat transfer modes for a) double channel flat and b) V-shaped absorber
configurations
7.3.2 Collector panel energy balance equations and relationships for heat
transfer modes
The energy balance equations for heat exchanged due to convection, conduction and
radiation for the absorber panels of Figure 7.6 follow (refer to nomenclature page for
description of parameters and subscripts):
For upper side of top cover (C1)
( ) ( ) ( ) ( )skyCCSambCCACCC TThrTThcTThrhcI −⋅+−⋅=−⋅++⋅ 11122121α (7.1)
For lower side of top cover (C2)
( ) ( ) ( ) ( )122121212122 CCCfCfCabC
ababCC TThrhcTThcTT
AA
hrI −⋅+=−⋅+−⋅+⋅⋅ ατ (7.2)
For fluid flow above absorber (f1)
( ) ( ) ( ) ( ) ( )111212111 inoutpCfCCCffababababf TTCmTTdxwhcTTdxwhc −⋅+−⋅⋅⋅=−⋅⋅⋅ & (7.3)
a) Longitudinal view of a double-channel absorber panel
Qair1
Qair2
I
I·τ
I·τ 2
hcabf1
hcf2B
hcf1C2
hcabf2
hc21
hcCA
hrabC2
hrabB
hrCS
hr21
I
I·τ
I·τ 2
hcabf1
hcf2B
hcf1C2
hcabf2
hc21
hcCA
hrabC2
hrabB
hrCS
hr21
Qair2 ⊗
Qair2 ⊗ Qair1
⊗
b) Transverse view of a multi-channel triangular absorber panel
ϑ
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147
where: dxab = dxC = dx = element surface length
wab = width of absorber
wC = width of collector
(7.4)
(7.5)
(7.6)
(7.7)
(7.8)
( ) ( ) ( ) ( ) ( )111212111 2 infpCfCCCffababababf TTCmTTdxwhcTTdxwhc −⋅+−⋅⋅⋅=−⋅⋅⋅ & (7.9)
( ) ( ) ( )dx·w
TTCmTThcTThcC
ifpCfCffababf12 111212111 ⋅−⋅+−⋅=−⋅Ω⋅ & (7.10)
For heat absorber (ab)
( ) ( ) ( ) ( )2211222
fabC
ababffab
C
ababfBab
C
ababBCab
C
ababCab TT
AAhcTT
AAhcTT
AAhrTT
AAhrI −⋅⋅+−⋅⋅+−⋅⋅+−⋅⋅=⋅⋅ ατ (7.11)
For fluid flow below absorber (f2)
( ) ( ) ( )dx·w
TTCmTThcTThcC
ifpBfBffababf12 2222222 ⋅−⋅+−⋅=−⋅Ω⋅ & (7.12)
For bottom back (B)
( ) ( ) ( )ambBBSBfBfBabc
ababB TThTThcTT
AAhr −⋅=−⋅+−⋅⋅ 22 (7.13)
(7.14)
(7.15)
( )
( )dx·w
TTCmQ
dx·wTTCmQ
Cifpair
Cifpair
12
12
2222
1111
⋅−⋅=
⋅−⋅=
&
&
Ω=
=⋅
2
2
1θ
θ
sin
wsinw Cab
( )
( ) ( )1111
111
111
2
2
2
infinout
infout
finout
TTTT
TTT
TTT
−=−
−=
=+
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The energy equations for the flat plate collector of Figure 7.6a are derived as a
special case of the previous, by noting that Aab = AC and that if θ = 180° Ω = 1.
Table 7.5 Heat transfer modelling parameters for thermal network of Figure 7.7
Parameters Description
Temperatures: Tamb Ambient Tc1 Top cover – upper side Tc2 Top cover – lower side Tf1 Air in upper channel Tab Absorber Tf2 Air in lower channel TB Bottom of panel
Thermal resistors: (RT = 1/A·hT) RQ1sky RQ1A
RQ1 Radiation & Convection Cover → Ambient
RQ2 Radiation & Convection* Cover → Cover R1 Radiation Absorber → Cover
Rf1C2 Convection Upper channel → Cover
Rabf1 Convection Absorber → Upper channel
Rabf2 Convection Absorber → Lower channel
Rf2B Convection Lower channel → bottom R2 Radiation Absorber → bottom RB Conduction & Convection Back → Ambient
Heat flow: QC1 Heat absorbed by upper side of cover QC2 Heat absorbed by lower side of cover QL Total heat losses from absorber to cover QR1 Radiation losses from absorber to lower side of cover Qair1 Useful heat carried away by air flowing in upper channel Qf1 Heat lost from absorber to air flowing in upper channel Qab Attenuated solar energy reaching absorber Qf2 Heat lost from absorber to air flowing in lower channel
Qair2 Useful heat carried away by air flowing in lower channel QR2 Radiation losses from absorber to bottom of panel Ql Heat losses from bottom and sides of panel
* It is later seen that there is no convection, but rather conduction, inside cover space
}
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149
To solve the energy equations and find the temperatures of each element and the
temperature of the air exiting the collector the thermal resistance network
formulation explained in chapter 4 and used in chapter 6 was used here as well. An
explanation of the parameters for the heat network for this model (Figure 7.7) is
given in Table 7.5:
Figure 7.7 Thermal resistance network for absorber panel configurations of Figure 7.6
The expressions and calculations of radiation and heat transfer coefficients were
taken from various sources as referred to in chapter 4 and are given in Appendix F.
Solution process
The iterative procedure mentioned in chapter 4 and used in the SHWS of chapter 6
was employed here as well. The solutions algorithm followed a very similar structure
with the difference that the air heater panel was divided into several transverse
sections (typically 20), where width >> length, and the iteration process was done for
each (refer to Figure 6.16 for a flowchart description):
For each section (j-th section):
1- Input air temperature10F
*, ambient and sky temperatures were known.
2- Temperatures were assumed for each of the elements (cover, airflow, etc)
3- Heat transfer coefficients and thermal resistances were found.
4- Energy balance equations were solved simultaneously.
5- New element temperatures, new_jiT , were found.
6- Old temperatures were replaced by new ones and steps 2-5 were repeated.
* For an open loop system, the input air temperature for the first section is always the ambient temperature. For a closed loop system it is the air temperature at the end of the return pipe.
QR1→
Tf2 Tb Tamb Tab
Tf1
TC2TC1 Tamb
Qab
QL + QC2 →
Ql ←
← QR2
Qair2 Qair1
QC2 QC1 R2
RB Rf2B Rabf2 Rabf1 Rf1C2
R1
RQ2
RQ1sky
RQ1A
← Qf2 Qf1→
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150
7- Output air temperature, out_jairT , obtained when: o010.TT old_j
inew_j
i ≈− .
8- The process was repeated for the next section where: in_jair
out_jair TT 1+=
9- The temperature of the air exiting the collector was found from the last section.
The solution process was implemented using MATLAB™. Numerical results are
shown in Figures 7.22 through 7.37. Typical numerical values for a panel with the
absorber profile of Figure 7.6a are given in Table 7.6.
7.3.3 Conveyance system energy balance equations and relationships for heat
transfer modes (pipes and bends)
Heat was lost to the environment from the associated conveyance system. Heat
travelled from the hot air to the walls of the pipe, from there to the insulation and
then git was taken away by convection air currents that enveloped the pipe.
Convection from the outside of the insulated pipes was the main mechanism of heat
loss in this case. Radiation losses were not considered since the insulation was also a
highly reflective material, thus reducing radiation emission.
Energy balance equations were established again with the help of the corresponding
thermal resistance network of Figure 7.8. The calculations are given in Appendix F.
Figure 7.8 Pipe section / schematic for air pipe heat loses to the environment
The energy balance equations for the pipe are:
Tw out Tamb
Tw_in
T1 T0 Q0 →
↑ Q0_loss
Q1 →
Q0_eff
Vf →
Q0_eff
Twin Tf TambTwout≈ 0
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151
( ) ( ) ( ) ( )ambpoutworat
ambop TTCmTTAln
LTTCm −⋅⋅=−⋅⋅⋅⋅
−−⋅⋅ − 12 κπ (7.16)
( ) ( ) ( )amboutw'
cvoutworat
TTAhTTAln
L−⋅⋅=−⋅
⋅⋅⋅−−
κπ2 (7.17)
From Equation 7.17, Tw-out was found, substituted in Equation 7.16 and T1 was also
found. This was the output temperature of the pipe section. With these two
parameters, power lost from the pipe and power conveyed by the pipe at its outlet
was determined. This way, the temperature drop in the circulation pipes for open and
closed loop modes were found.
The heat transfer coefficient, hcv, was dependent on the dominant convection modes
operating at any one time (free or forced convection) and further influenced by the
position of the pipe itself, ie. vertical, horizontal or a combination.
The maximum value for this coefficient (Equation 4.16) was (conservatively) taken
as: [ ] maxforced
cfree
cVfree
cHcv h,h,hh =
The heat transfer coefficients were determined by the use of relationships 4.1, 4.7
and 4.13-4.15, as given in chapter 4 (where the characteristic length, L, was equal to
the diameter of the pipe, Dp).
Solution process
The entire pipe was divided into many “slices”, or transverse sections, and the
balance equations were solved for each of them. The output temperature of one slice
was the input temperature for the next and so on.
Equation 7.16 can be solved deterministically, but not Equation 7.17. Since the
Nusselt number for the outer convective currents was dependent on the temperature
of the fluid, when Equation 7.17 was solved for Tw-out, the resultant equation was
implicit in form. This required Tw-out to be found via iteration. For each section of the
pipe, a series of iterations were done to determine Tw-out and from there T1. Eventually
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152
all T1 temperatures were found for all slices, where the last slice gave the output air
temperature of the pipe.
For typical conditions and experimental setup (4.1 m pipe length of 90 mm diameter,
5 mm insulation thickness, 60 L/s airflow, 20°C ambient temperature, air
temperature of 70°C at pipe entrance) the predicted temperature drop was 5.5°C and
the power loss was 361 W, with an average heat loss coefficient over the length of
the pipe from insulation to the ambient of 5.8 W/m2°C
7.3.4 Heat exchanger energy considerations and power gain in the water
Due to the inherent complexities of the thermal behaviour of a compact heat
exchanger and to the dynamic nature of this situation, the losses and gains in this
particular case study were determined with the aid of experimental measurements.
There was one balance equation for this case:
xoutwaterinxoutxlosswaterinxin PPPPPP ______ +≈++= (7.18)
The exchanger was well insulated so the loss from the exchanger was considered
small enough to be neglected in the expression for the power going into the water. To
predict overall system performance it was necessary to determine power gained by
the water in the thermosiphon process and how much power was returned to the
system (air recycling) or discarded to the ambient via the air exiting the exchanger
(open loop mode). It was therefore necessary to be able to predict:
- water flow rates
- output water temperature from the exchanger
- output air temperature from the exchanger
Pin_x = Power carried by the air at exchanger input
Pout_x = Power carried by the air at exchanger output
Pin_water = Power gained by the water in the exchanger
Ploss_x = Power losses from the exchanger
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153
Water flow dynamics of the heat exchanger-water tank thermosiphon circuit is quite
complex and is determined by many factors: input/output temperatures of air and
water entering and exiting the exchanger, water column density in the tank, hydraulic
resistance of connection pipes and exchanger itself. There is no direct,
straightforward, approach to be used in this case. In fact, it is very dependent on the
specifics of the elements used to create the thermosiphon effect, making it very
difficult to develop a general solutions method. However, experimentally it was
found that water flow rates were no larger than 10.5 cc/sec with temperatures
peaking at 62°C. For a pipe diameter of 12.7 mm, these conditions would produce
Reynolds numbers below the transition value of 2000. Assuming then that the flow
was laminar, flow rate was calculated by using Poisseuille’s equation for laminar
flow in straight pipes. The method used is loosely based on the original formulation
developed for thermosiphon assessment in a SHWS 131F
132 and further exploration and
developments of other studies132F
133,133F
134 on the topic.
The thermosiphon was driven by the
density differences between hot and cold
water columns. From Equation 5.30 and
noting that Δp =ρ·g·h (see Figure 7.9):
(7.19)
Figure 7.9 Thermosiphon and hot water stratification for the SHWS heat exchanger and tank
Water density is a function of temperature and for the operational temperature range
of the thermosiphon system (0°C-70°C) it can be approximated to a quadratic
equation with very good accuracy (< 0.2%). Water viscosity is also dependent on
temperature and can be approximated reasonably well to a 3rd order polynomial
(< 5.5%). See appendix G for details on these approximations.
As hot water entered the top of the tank, the cold column height progressively
diminished. Due to the physical setup of the thermosiphon loop (Figure 7.9) about 31
of the total water of the tank lay above the hot water entry point. If there had been no
( )l
)hh(g)(r nv ⋅⋅
−⋅⋅−⋅⋅=Φ
ηρρπ
810
4
Thot
Tcold
Hot air
Cold air
lh=h hn
ρ1
ρ0
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154
water mixing and little conduction, the height and temperature for the cold water
column would have remained relatively unchanged at the initial stages. For (upper
value) water flow rates of 11 cc/s in a tank containing 190 L, this would have lasted
approximately 1½ hours.
Therefore, as an approximation to the water flow equation, hn ≈ 0. Since h = lh
(length of the thermosiphon pipe):
ηπ
ηρρπ
⋅⋅−⋅⋅⋅
=⋅
⋅−⋅⋅≈=Φ
88
21
20
410
4 g)TT(Crg)(rmwflow & (7.20)
ηπ
⋅
⋅−⋅⋅⋅≈
8
224 g)TT(Crm water_outwater_in
w& (7.21)
Where C = -0.004 is a quadratic constant in the density formula approximation and
η≡η[T], as given by Equations G5 and G4, respectively (Appendix G). Tin_water and
Tout_water represent the exchanger input and output water temperatures, respectively.
Power delivered to the water was (from Equation 4.49):
( )water_inwater_outwwwater_in TTCmP −⋅⋅= & (7.22)
Substituting for water flow from Equation 7.21:
( ) ( )η
π⋅
−⋅−⋅⋅⋅⋅⋅=
8
224water_outwater_inwater_inwater_outw
water_in
TTTTCgCrP (7.23)
All parameters in Equation 7.23 were known or easily determined, with the
exception of Tout_water. An expression for Tout_water as a function of other known
parameters was found from the exchanger effectiveness, which was determined
following the effectiveness-NTU method described in chapter 4.
Temperature measurements of the exchanger showed water output temperatures lay
between the air input and air output temperatures, so for simplicity and as a first
approximation it was assumed that the exchanger was operating as if in counterflow
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155
mode (as explained in chapter 4). The output water flow from the exchanger was
experimentally inferred to be no more than 11 c/s and the temperature no higher than
62 °C. The airflow was fixed at a semi-constant 60 L/s (0.065 kg/s) with air input
temperatures close to 75 °C for irradiance levels over 900 W/m2. Given these
conditions, the fluid with minimum value of heat capacity was the water:
( ) CW
watcm o& 46< , whereas ( ) CW
aircm o& 60> .
The relationship for effectiveness (Equation 4.56b) under these considerations was:
water_inx_in
water_inwater_out
TTTT
−
−=ε (7.24)
Tout_water was then determined since Tin_x, Tin_water and ε were known:
( ) water_inx_inwater_out TTT ⋅−+⋅= εε 1 (7.25)
Since the effectiveness was determined experimentally ( 730.≅ε & 0.69 for open and
closed loop modes, respectively - section 7.6.2), the following expressions for output
water temperatures were used:
Open loop operation → water_inx_inwater_out T.T.T ⋅+⋅= 270730 (7.26a)
Closed loop operation → water_inx_inwater_out T.T.T ⋅+⋅= 310690 (7.26b)
By substituting these equations into Equation 7.23, power delivered to the water was
found. Since the air power going into the exchanger, x_inP , was known, the power
carried out by the air exiting the exchanger, x_outP , was also determined. From this
value, the output air temperature was found.
It is important to note that exchanger effectiveness is not constant and varies as
conditions for fluid flow and temperatures vary. This calculation was done as a first
order approximation based on the assumptions mentioned earlier. A detailed
justification for using a constant effectiveness is given in section 7.6.5
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156
Solution process
This was a straightforward process where Equations 7.26, 7.21, 7.23 and 7.18 were
solved to obtain:
Output water temperature from exchanger, Tout_water ↓
Flow rate of water in the thermosiphon, wm&
↓ Power delivered to the water, Pin_water
↓ Output power and air temperature from exchanger, x_outP & Tout_x
The power and air temperature at the input of the exchanger were required and were
determined from the calculations for pipe losses of the previous section.
It is also important to note that the radius of the pipe used in the calculation of water
flow rate was an “effective” radius and not the actual radius of the vertical pipe.
Effective radius values were determined from experimental correlations
(Figures 7.39, 7.40, 7.46 and 7.47). The reason being that the flow path of the water
was a combination of the vertical pipe, the input and output points from the water
tank which were, in fact, reduction ports and the large number of narrow water
channels in the heat exchanger. As a result, an effective radius was obtained.
7.3.5 Centrifugal Fan-Motor
Temperature losses across the motor while recycling the air back into the collector
panel were evident during the experimental work. Heat losses in the motor were
essentially from convective air currents to the surroundings and radiation.
A simple approach in determining these losses had the motor modelled as a metal
cylinder allowing convenient determination of internal air temperature and power
drop. An overall heat loss coefficient, Umot, was determined from experimental
results and applied for all cases.
The energy balance equation was:
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157
mot_outmot_lossmot_in PPP += (7.27)
(7.28a)
(7.28b)
Amot was simply the area of the motor exposed to the environment. Assuming a
cylindrical geometry, this was:
( )motmotmot
mot lDDA 22
+⋅⋅
=π (7.29)
Dmot and lmot were the diameter and length (or width in this case), respectively.
Since the motor was a relatively small object, the internal temperature was
approximated as:
2mot_outmot_in
mot
TTT
+= (7.30)
Equating and rearranging Equations 7.28 for the output air temperature and
substituting expression 7.30:
⎟⎠⎞
⎜⎝⎛ ⋅
+⋅
⋅⋅+⋅⎟⎠⎞
⎜⎝⎛ ⋅
−⋅=
2
2motmot
airair
ambmotmotmot_inmotmot
airair
mot_out AUCm
TAUTAUCmT
&
&
(7.31)
Once Tout_mot was known, mot_lossP and mot_outP were found.
Solution process
The temperature input to the motor, Tin_mot, was the temperature output from the
exchanger, Tout_x, which had been found from the previous section. The overall heat
loss, Umot, was found experimentally. The ambient temperature was known. With
these values Tout_mot was found from Equation 7.31. By knowing Tout_mot, the
temperature and power drop in the return pipe were calculated using the process
described in section 7.3.3 for pipes and bends.
( )
( )⎪⎩
⎪⎨
⎧
−⋅⋅
−⋅⋅=
ambmotmotmot
mot_outmot_inairair
mot_loss
TTAU
TTCmP
&
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158
7.3.6 Water Tank heat gains and losses
The process for determining energy gain and losses for the tank of this SHWS was
similar to the one employed for the previous system of chapter 6, although simpler.
In fact, the same tank was used but without the internal heat exchange copper pipe
loop. Energy gains and losses were given by the energy gain of the water flowing
inside the compact heat exchanger and from the losses from the tank, respectively11F
#.
The power delivered to the water, Pin_water, was determined as explained in
section 7.3.4, Equation 7.23. The heat losses were found via the method explained in
section 6.4.3:
( ) ( )ambktan_water
T
T_insT
*T
ktan_loss TT
DtDln
lP −⋅
⎟⎟⎠
⎞⎜⎜⎝
⎛ +
⋅⋅=
2
2 κπ (6.27)
Where DT , tins_T and lT are the diameter of the water tank, the thickness of the
insulation and the augmented height of the tank12F , respectively.
Finally: ktan_losswater_ineff_water PPP −= (7.32)
from eq. 7.23 from eq. 6.27
Solution process
Equation 7.32 was solved from Equations 7.23 and 6.27. For conservative purposes,
Twater_tank was equated to the maximum temperature of the water, Tout_water 13F
♦. Results
for effective power gained by the water are given in section 7.6.2.
# There are also energy losses from the thermosiphon pipe, which can be initially neglected assuming the pipes are insulated and present a very small surface contact area with the exterior.
Refer to section 6.4.3 for more information on the assessment of water tank heat losses.
♦ A more realistic approach would probably be: ( ) 2x_inwater_outktan_water TTT +=
*
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7.3.7 Summary of solution process for the entire system
Solving for the collector meant determining the power carried by the output air. Solution included solar energy collection and heat transfer dynamics.
Solving for the downward transfer line meant
determining the effective air power going in
the exchanger after pipe losses. Losses
determined from pipe convection currents.
Solving for the heat exchanger and water tank meant determining thermosiphon output water temperature and power, exchanger output air temperature and power, tank losses and effective power delivered to the water. Solution involved the thermohydraulic assessment of the thermosiphon, the exchanger effectiveness and convective air losses from the tank.
Solving for the fan-blower meant determining motor body losses and output air temperature and power. Solution included experimental assessment of an overall heat loss coefficient and cylindrical geometry approximation of the motor.
Solving for the return transfer line meant determining the input air temperature and power to the panel. Solution as for the downward transfer line.
Collector Panel Inputs: Outputs:
Solution’s algorithm for air heating panel
(page 187)
Inputs: outpanel_airT
Outputs: Tin_x , Pin_x
Downward Transfer Line
Inputs: Tout_x , Pout_x
Outputs: Ploss_mot , Tout_mot , Ploss_mot
Fan-Blower Motor
Tout_water , Tout_x Ploss_tank
Pin_water , Pout_x Pwater_eff
Tin_x , Tin_water Tout_water
Pin_x Pin_water
Heat Exchanger Water Tank
Inputs:
Outputs:
Inputs: Tout_mot , Ploss_mot
Outputs: inpanel_airT , in
panel_airP
Return Transfer Line
(Only for closed loop operation)
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During closed loop mode operation, the temperatures of all elements involved
increased progressively up to an equilibrium point. From there on, variations
happened due to the changing irradiance values. From a numerical perspective, this
equilibrium was reached when the input temperature of the collector panels remained
constant after several calculations for the entire loop.
All experimental and numerical results pertaining to the solution process above are
given in section 7.6.
7.4 Thermohydraulic assessment of airflow
Pressure drops in all the elements of the system strongly affect performance of the
fan-blower so it was necessary to evaluate thermohydraulic performance in order to
find the pumping/blowing power required and determine overall system
performance. Evaluation was based on the determination of head losses and minor
losses and finally the effective efficiency as explained in chapter 5.
7.4.1 Pressure losses
Head losses
The expression for head loss for each straight pipe section, hfi, was given by
Equation 5.16 and was dependent on:
- Pipe geometry (diameter, length, area)
- Airflow rate
- Kinematic viscosity of the air, ν
These head losses were related to the pipes that transported the air from the collector
output to the exchanger and in the case of closed loop operation, from the output of
the motor back to the collector input.
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Minor losses
Calculation of minor losses was dependent on the number of fittings, valves and
other obstacles that affected the flow in any way. Therefore, in order to find these
losses it is necessary to know how many attachments of this nature were part of the
conveyance/piping system.
The minor head losses for fittings, bends and other elements are given by
Equation 5.22 and was dependent on:
- Pipe geometry (diameter, length, area)
- Airflow rate
- Loss coefficients (K-values) which are function of the geometry of the element
The “minor” losses, on occasions, can account for higher pressure losses than major
head losses. This may happen in systems containing relatively short straight pipe
sections and many contributing elements. Furthermore, the use of unconventional
devices, such as heat exchangers and collector panels, will accentuate this.
Total losses, HTOT, were the combination of all losses, major and minor, as given by
Equation 5.26.
The kinematic viscosity, ν, being temperature dependent, was a dynamic figure that
changed with changing air temperatures affecting head loss calculations. However,
since the interest lay in the performance of the system after reaching thermal
equilibrium and air temperatures did not vary greatly in the pipe sections, the
kinematic viscosity remained reasonably constant. Head losses, therefore, varied to
some extent in each pipe reaching a maximum value once in thermal equilibrium.
The results for pressure loss in the pipes allowed for performance evaluation. The
pumping power required to countervail the hydraulic losses and maintain a desired
flow rate is given by Equations 5.2 and 5.29:
TOTvmot HgCP ⋅⋅⋅Φ⋅= ρ (7.33)
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Solution process
This was a fairly straightforward procedure in concept. It involved:
- Determination of K-values
- Calculation of minor losses
- Calculation of major losses
- Determination of total head loss, or pressure loss, in the system
- Calculation of net pumping power required
The desired flow rate, which was fixed, enabled calculation of all heat and pressure
losses and the corresponding net power required.
The determination of the K-values, in general, is not a trivial matter. For standard
pipe bends and fittings, tabulated values are available in the literature. However, for
unconventional elements, even empirical equations are seldom available.
For the heat exchanger and collector panel and a few other elements (such as
reduction/expansion joints), K-values were obtained by correlation with experimental
data obtained from the SAHS itself. The procedure for determination of pipe losses is
given in section 7.3.3. Experimental and numerical results are shown in section 7.6.3
7.5 Experimental work: construction details
The system contained:
• Air heating solar collector panel
• Air conveyance system
• Heat exchanging mechanism
• Hot water storage tank
• Fan/motor air blower
The major focus of work was the design of an appropriate solar collector and heat
exchanger subsystem.
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7.5.1 System components
Collector Panels
1. First prototype
The design of the collector panels involved the construction of two prototypes. The
first one (Figures 7.10 and 7.11) was done to test a V-corrugated absorber
configuration with fins with the expectation that it would offer higher heat transfers
than conventional and more easily constructible flat-type absorbers (as mentioned
and modelled in sections 7.2 and 7.3, respectively).
The body was made out of 29 mm thick high-density polystyrene (32 kg/m3) sheets
serving also as insulation. The cover was a section of a Twinwall™ double-sided
polycarbonate sheet with internal slats used for protection and glazing purposes.
Figure 7.10 V-corrugated absorber panel with fins and polystyrene housing
Figure 7.11 1st prototype air heater absorber panel with air diffuser sections and double cover
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The actual absorber shape was made out of aluminium sheeting (0.1 mm) which was
bent and cut to obtain the profile and fins desired. It was sprayed on the upper side
with a flat black paint. The entire absorber was fixed to a 6 mm thick medium
density fibreboard (MDF) sheet for ease of handling and stability, which was then
dropped into the polystyrene casing (Figure 7.11)
The internal dimensions of this prototype were 173 cm × 45 cm × 6 cm. Entrance
and exit ports were made out of polyvinyl chloride (PVC) pipe reduction/expansion
fittings to accommodate PVC pipes of 90 mm external diameter (OD). Two 6 cm
buffering zones with diffusers were set at the extremes of the panel to allow for a
more uniform heat transfer and mixing of the air throughout the panel and to reduce
low impedance pathways that could encourage the formation of hot or cold zones.
Seven thermocouples were placed at different
locations on the absorber to monitor
temperature variations. The prototype was set
on a tilted movable frame and exposed to
sunlight with the fan blowing into it
(Figure 7.12). Operation over several days and
for different airflow rates was intended as the
means for assessing performance and
determining the suitability of the absorber
profile chosen in order to construct a larger
scale prototype.
Figure 7.12 1st prototype air heater panel
on movable tilted base
Flow rates where produced by varying the applied voltage to the motor (Figure 7.13)
and were initially determined by the use of a hot wire anemometer and later by a
large cylindrical tunnel-bag of transparent and flexible polyethelene sheet, 5.15 m ×
0.59 m (Figure 7.14).
Thermocouple
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Figure 7.13 1st prototype on work bench with fan blower and variable power supply
a) Anemometer b) Cylindrical air bag
Figure 7.14 Devices used in the determination of airflow rates
Anemometer readings of air velocity were taken at the inlet port of the motor. These
were correlated with results for airflow obtained with the tunnel-bag. It was soon
realised that the anemometer was an unreliable tool for this purpose due to the
following reasons:
- Small variations in the position of the unit’s probe in the pipes produced major
variations in recorded values.
- Limited scale for the application: maximum velocity that could be resolved was
about 10 m/s
- Temperature limited up to 50° C with errors increasing with increasing
temperatures (which made it unusable for the closed loop system)
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Results obtained with the air bag were considered more accurate, reproducible (±5%)
and generally more reliable and that is why the anemometer was not used initially.
Construction of the unit was closely followed by simulation modelling according to
the theory described earlier, which showed good agreement between experimental
and numerical results. After due consideration from these and other modelling results
it was decided that a double cover absorber-in-the-middle panel with airflow over
and under it (Figure 7.2c) was the best option for a large-scale unit.
2 Second prototype
The second prototype was essentially a larger version of the previous one with the
following features and differences:
• External dimensions: 120 cm × 360 cm
• Double cover Twinwall™ polycarbonate sheeting
• Polystyrene case which doubled as insulation
• Flat aluminium absorber placed at midpoint height in the airflow chamber
The second prototype (Figure 7.15) was divided into two equal sections, thus
doubling the length of travel of the air. Buffer sections with diffusers at the input and
output of the panel were also provided. A buffer section of about 20 cm was located
opposite to the input and output ports for reducing friction flow losses and to
accommodate a stagnation temperature control mechanism.
Figure 7.15 2nd prototype large scale air heater panel on tilt-adjustable frame
IN
OUT
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167
Actual construction of the heat absorber involved joining several flat sections of
aluminium sheeting shaped to the required profile. A total of 24 absorber sections
were made, sprayed with flat black paint and joined to compose an entire effective
absorber area of 3.7 m2 (57 cm × 650 cm).
The bottom of the collector panel was laid out with 26 plywood strips of 1 cm ×
57 cm × 0.6 cm, glued and evenly spaced out as a “bed” for affixing the absorber
sections (Figure 7.16). The absorbers where firmly fastened with nails, leaving upper
and lower airflow paths of the same dimensions.
Figure 7.16 Absorber panel profile and panel construction
An aluminium frame with 4 different tilt angle options was built to accommodate this
prototype. Measurements of air input and output temperatures were taken over
several weeks for varying irradiance values. The panel was later coupled with the
heat exchanger, water tank and associated piping and operated in open loop and
closed loop (air recycling) mode.
Stagnation temperature problems with the prototypes were foreseen before their
construction and certainly evidenced during their operation. The main drawback in
this regard was the temperature limit for structural stability of polystyrene, which is
80 °C134F
135. Under operation, even in closed-loop mode and at high flow rates (>60 L/s)
internal temperatures could actually go beyond the critical value. This issue has been
considered and discussed in section 7.7
b) Absorber sheet layering a) Cross-sectional profile of flow chamber
Absorber sections
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Heat Exchanger
The heat exchanging mechanism was essentially a small and compact cross-flow heat
exchanger of high surface area per unit volume, typical of those used in the
automotive industry (Appendix H). The use of a readily available, mass-produced,
proven and robust compact heat exchanger, easy to use and integrate as a part of a
system, would be ideal for the purpose of a low cost, low maintenance SHWS
incorporating air as the heating fluid. Suitability would be a matter of assessing
whether the unit delivered the required power into the water or not.
The exchanger chosen (Figure 7.17a) contained a copper core 160 cm × 160 cm ×
49 cm with upper and lower header tanks. Thin flat vertical tubes ran parallel to each
other from one tank to the other. An array of V-corrugated metal sheeting with small
triangular fins interspersed between each tube made up for the rest of the unit.
Figure 7.17 Heat exchanger employed in the SHWS
The exchanger was cased in a wooden box with two openings at the bottom and top
for the input and output water pipes (Figure 7.17b) respectively, and two more
(larger) openings at the sides for the input and output air ports. Some modifications
were effected to the unit in order to provide an opening at its bottom. Pipe fittings
were fixed to these ports. The compact size can be ascertained from Figure 7.17a.
b) Exchanger inside casing and fan/blower motor attached towater tank
a) Compact heat exchanger
Back side
Front side
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The exchanger was tested for varying air and water flow rates. Water flow rates were
provided and determined by a garden hose attached to a conventional tap valve and a
measuring cylinder. Hot air and varying airflow rates were provided by hot air
blowers.
Water Tank
The water tank used for the SAHS was the same described in chapter 6. In addition
to the input and output ports used for steam entry and condensate collection in the
system of chapter 6, there were three more access ports fitted with ball valves and
spaced evenly within 60 cm from the bottom of the tank (Figure 7.18).
Figure 7.18 Hot water tank and heat exchanger
A tube was taken from the lower of these points to the water input of the heat
exchanger, which delivered cold water from the bottom of the tank. Hot water
emerging from the top of the exchanger headed towards the upper input port. Via a
natural thermosiphon process. It is therefore noted that this tank was operating as a
storage/displacement unit, where thermal stratification was established from top to
bottom and with the intention of extracting and using the water being heated.
Valves
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A small opening was made at the top side of the inner copper tank so that water
temperature profiles could be measured. This was done by attaching a thermocouple
to a (1 m) wooden ruler and measuring temperatures in the tank at fixed depth
positions every 5 cm. Cold and hot water temperatures were determined by fixing
thermocouples to the water input and output pipes of the heat exchanger.
Centrifugal fan/blower motor
The fan used was also sourced from the automotive industry with a nominal
operating voltage of 13.5 V and a maximum 120 W power consumption at a flow
rate of 93 L/s (Appendix H).
Figure 7.19 Upper view of centrifugal fan-blower attached to heat exchanger
The main requirement for a fan of this type was the delivery of required flow rates
despite pressure drops in the pipes. This meant selecting a unit with sufficient net
power consumption. The centrifugal fan used was able to deliver flow rates as high
as 63 L/s when operating below its nominal voltage while connected to the system in
closed loop mode. It was considered adequate for the purpose of the project.
The fan was operated by the use of two variable voltage power supplies connected in
parallel. It was used in the first prototype to determine performance under irradiation
for several flow rates. A fixed range of 2, 4, 6, 8, 10 and 12 volts was used to vary
the flow rate. In this case, air was drawn from the surroundings and pumped into the
prototype (as seen in Figure 7.12)
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When used with the second prototype, the inlet opening of the fan was always
connected to the exit port of the heat exchanger (Figure 7.19). When operating in
closed loop mode, the outlet was connected to the return pipe driving the air back
into the collector.
Pipes, bends and fittings
Piecing together the collector panel, the heat exchanger and the fan finally formed
the complete system. This was done with standard PVC stormwater pipes of 86 mm
ID and 90 mm OD and several elbow and joining fittings.
A few images of the system operating in open loop mode are given in Figure 7.20.
Figure 7.20 2nd prototype air heater panel & SHWS in operation
As explained in the introduction, it was the closed loop mode the most favourable
mode of operation for a variety of reasons, among which are:
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- Protection from external contamination and much less maintenance required
- Higher temperatures achievable and a more efficient system
- Smaller panel collection area required due to higher efficiency
In this operation mode, the airflow trajectory from the output of the fan/blower to the
output of the exchanger was about 18.1 m, divided in the following way:
• 9.6 m straight pipe sections (4) + 0.2 m straight section joiners
• 7 m panel compartment (including airflow turn-around at the third buffer zone)
• 0.85 m elbow fittings (10)
• 0.26 m heat exchanger compartment
• 0.2 m reduction/expansion fittings (4)
Holes were made at different points in the pipes to check for air temperatures, air
velocities and pressure drops. Air temperatures where measured with a thermocouple
by introducing the sensing tip up to the mid point of flow in the tubes. Temperatures
in the straight sections of the tube had up to a ±1.5°C variation.
Air velocities were determined in the beginning by placing the anemometer
measuring probe also at midpoint distance within the outward and return pipes, and
far from fittings that could introduce undesirable effects and produce inaccurate
results. The tunnel-bag was later used by opening the loop at the point of entry of the
collector and placing it on the return pipe.
For this system, the minor losses were the major contributors to total pressure drop.
This was due to the relatively short straight pipe sections compared to the quantity of
the other hydraulic resistive elements.
Experimental measurements of static pressure at various points in the system were
taken with a piezometer/nozzle arrangement, coupled with a differential water
manometer using atmospheric pressure as a reference point (Figure 7.21). Results
showed that the major frictional losses were due to the collector panel and the heat
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exchanger and how correlation with calculated K-values may have indicated the
presence of large errors in pressure drop measurements (Table 7.5).
Figure 7.21 Measurement of pressure drop in mm H2O gauge across a pipe section
Reflective insulation (Astrofoil™) was provided around the pipe connecting the
output of the collector to the input of the exchanger. The insulation consisted of two
layers of aluminium foil laminated to the outsides of a sheet of heavy-duty 5 mm
thick polyethylene air-bubble cushioning. The high reflectivity and trapped air spaces
between the foil surfaces made this material a very good insulator. It was also
weatherproof, ideally suited for outdoor applications like this one.
a) No air flow (Φv = 0) b) Turbulent air flow (Φv >10 L/s)
Attachment producing pressure losses
2h1 2h2
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7.6 Results
7.6.1 First prototype
Typical experimental and numerical results for this prototype are outlined below.
Five different scenarios were studied for four different profiles:
• Single and double cover collector with absorber at back (Figure 7.2a)
• Double cover collector with absorber in the middle (Figure 7.2c)
• Double cover collector with V-corrugated absorber (Figure 7.3b)
• Double cover collector with V-corrugated absorber, with added fins
These profiles were studied for different conditions to determine which one would
offer an overall optimum performance, from its construction to its ongoing operation.
It was decided to construct the V-corrugated profile with fins with ongoing
development of the modelling. The decision was based on the idea that high
turbulence in the collector would relate to higher heat transfer to the air.
Experimental results for this prototype showed that there was close agreement with
the numerical data (Figures 7.22 – 7.23 and Table 7.6). From the modelling it also
seemed that very similar performances could be obtained between the two
V-corrugated absorber profiles (with and without fins) and the profile for the
absorber that divided the chamber into upper and lower halves. The remaining
profiles with the absorber at the back did not perform as well. Assuming then that the
model predicted well the experimental results, it was believed that in a practical
situation the corrugated absorber profile (with and without fins) and the flat
absorber-in-middle profile would behave very similarly. With this in mind,
additional analyses were performed.
A numerical analysis was undertaken to determine whether the dimensions of the
fins were a significant factor in the performance of a full-scale collector for low and
high input air temperatures. In the prototype, the maximum possible triangular fin
length (fin height) that could be made was 30 mm. Results suggested that it was
possible for relatively small irregularities in the V-corrugated profile (~1 mm) to
produce noticeable differences in output temperatures (figs 7.24 – 7.27).
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Figure 7.22 Output air temperature vs. airflow rate for different panel configurations
Figure 7.23 Collector efficiency vs. airflow rate for different panel configurations
0 10 20 30 40 50 60 70 80 90 100 11020
30
40
50
60
70
80
90
100
110
120
Air flow rate (L/s)
Out
put t
empe
ratu
re (°
C)
Output temperature vs. flow rate for air exiting collector panel
Irradiance = 941 W/m²
Ambient temperature = 20 °C
Input temperature = 20 °C
Collector length = 1.55 m
V-corrugation V-corrugation with finsSimple single cover Simple double cover Complex double coverExp. results
0 10 20 30 40 50 60 70 80 90 100 110 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Air flow rate (L/s)
Col
lect
or e
ffici
ency
Efficiency of the collector vs. flow rate for air exiting the collector
V-corrugation V-corrugation with finsSimple single cover Simple double cover Complex double coverExp. results
Irradiance = 941 W/m²
Ambient temperature = 18.5 °C
Input temperature = 19 °C
Collector length = 1.55 m
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Table 7.6 Numerical results for the complex double cover profile of Figure 7.22 for various airflow rates (Figure 7.6a absorber profile)
Airflow rates (Φ) (L/s) Calculated and given parameters 10 20 30 40
Absorber length 1.55 m Absorber width 0.45 m
Optical efficiency 0.73 Average irradiance 941 W/m2
Wind speed 5 m/s Tamb (also Tin) 20 ° C
Temperatures at exit point of panel ° C
Tc1 27.7 25.4 24.1 23.3
Tc2 45.0 38.1 34.2 31.7
Tf1=Tf 51.8 38.5 33.1 30.1
Tab 100.9 77.1 64.3 56.4
Tf2=Tf 51.8 38.5 33.1 30.1
TB 73.5 60.2 52.3 47.1
Heat transfer coefficients W/m2·°C
hQ1* 14.0 16.4 19.2 22.2
hQ2 11.4 10.4 10.0 9.8
hrabC2 8.5 7.1 6.5 6.1
hcf1C2 4.7 7.5 10.2 12.8
hcabf1 4.7 7.5 10.2 12.8
hcabf2 4.7 7.5 10.2 12.8
hcf2B 4.7 7.5 10.2 12.8
hrabB 0.8 0.7 0.7 0.6
hB 2.2 2.2 2.2 2.2
Total heat loss W/m2·°C
UL 4.3 2.9 1.8 0.8
Experimental results for the V-corrugated absorber prototype (Figure 7.22) Airflow rates (L/s) 11.3 ± 0.4 17.6 ± 0.7 23.1 ± 1.0 27.6 ± 1.2 31.3 ± 1.5
Tf (°C) 48.2 ± 0.4 41.2 ± 0.4 36.5 ± 0.4 33.6 ± 0.5 30.2 ± 1.5 * The radiation heat transfer coefficient in h1 is referenced to the ambient temperature.
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The convection heat transfer from the absorber to the air flowing in the channels,
hcabf1 & hcabf2, is similar (is described by the same set of equations). The same
applies for the transfer between the flowing air and lower side of the top cover,
hcf1C2, and the transfer between the air and the bottom of the panel, hcf2B. These
quantities were calculated for the double-channel flat absorber profile configuration
(Figure 7.6a) as a special case of the more complex situation of heat transfer from
corrugated and finned triangular channels explained in chapter 4. The calculations
were adapted to reflect no corrugation or roughness in the channels, with an absorber
area equal to the panel aperture area. These transfer coefficients are the decisive
factors in determining useful heat. More energy is delivered to the air stream for
higher flow rates, since more heat is removed from the absorber. Conversely, less
heat is lost, so the total heat loss, UL, decreases with increasing flow rates. This can
also be seen as lower heat transfer coefficients for radiation emitted by the absorber,
hrabC2 and hrabB, and a lower figure for the combined conduction and radiation that
occurs from the lower to the upper side of the top cover, hQ2. It is important to note
that the heat transfer coefficient, hQ1, associated with the losses from the top cover is
not really an indicator of actual physical heat loss from that element. It contains the
heat transfer coefficient for forced and free convection from the cover to the ambient,
hcCA (which, incidentally, does not vary much with varying airflow rates inside the
panel). However, its radiation loss component has been referenced to the ambient
temperature instead of the sky temperature. This is done for ease of calculation of the
thermal network (section 4.2.3) and its increase with increasing airflow rates is
because of the large quotient that results as the cover temperature, TC1, approaches
the ambient temperature, Tamb (see Equation 4.42). The actual radiation transfer
coefficient from cover to sky, hrCS, decreases with increasing airflow rates.
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Figure 7.24 Output air temperature vs. airflow rate for finned V-corrugated absorbers for an input air temperature of 20°C
Figure 7.25 Efficiency vs. airflow rate for a V-corrugated absorber of various fin lengths
0 10 20 30 40 50 60 70 80 90 100 110 60
70
80
90
100
110
120
130
140
Air flow rate (L/s)
Out
put t
empe
ratu
re (°
C)
Output air temperature vs. flow rate for a V-corrugated absorber panel
Irradiance = 900 W/m² Ambient temperature = 20 °C
Input temperature = 20 °C Collector length = 6.5 m
No fins 0.1 mm fins0.5 mm fins
1 mm fins5 mm fins
10 mm fins30 mm fins
0 10 20 30 40 50 60 70 80 90 100 110 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Air flow rate (L/s)
Col
lect
or e
ffici
ency
Efficiency of the V-corrugated absorber panel vs. air flow rate
No fins 0.1 mm fins 0.5 mm fins
1 mm fins5 mm fins
10 mm fins30 mm fins
Irradiance = 900 W/m² Ambient temperature = 20 °C
Input temperature = 20 °C Collector length = 6.5 m
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Figure 7.26 Output air temperature vs. airflow rate for finned V-corrugated absorbers for
an input air temperature of 60°C
Figure 7.27 Efficiency vs. airflow rate for a V-corrugated absorber of various fin lengths
0 10 20 30 40 50 60 70 80 90 100 11085
90
95
100
105
110
115
120
125
130
135
140
Air flow rate (L/s)
Out
put t
empe
ratu
re (°
C)
Output temperature vs. flow rate for air exiting collector panel
Irradiance = 900 W/m² Ambient temperature = 20 °C Input temperature = 60 °C Collector length = 6.5 m
No fins 0.1 mm fins 0.5 mm fins
1 mm fins 5 mm fins
10 mm fins 30 mm fins
0 10 20 30 40 50 60 70 80 90 100 1100
0.1
0.2
0.3
0.4
0.5
0.6
Air flow rate (L/s)
Col
lect
or e
ffici
ency
Efficiency of the V-corrugated absorber panel vs. air flow rate
Irradiance = 900 W/m² Ambient temperature = 20 °C Input temperature = 60 °C Collector length = 6.5
No fins 0.1 mm fins 0.5 mm fins
1 mm fins 5 mm fins
10 mm fins 30 mm fins
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Chapter 7 - Air-to-water heat transfer solar hot water system with heat exchanger-water tank coupling
180
Another analysis was done comparing all profiles for a full-size model (Figures 7.28
– 7.33). For different input temperatures there was little variation in the relative
performance of the V-corrugated profiles. The higher the input temperature and the
higher the flow rates, the smaller the difference in the collector output air
temperature and efficiency. For airflow rates above 60 L/s, the performance of both
profiles was equivalent from an operational point of view (with temperature
differences below 1.5°C). For this range of airflow rates and for medium-high and
high input temperatures, the profile for the absorber in the middle of the chamber
also showed a good performance, with temperature differences of less than 3.5°C
when compared with the other two.
This profile was considered the overall optimal for inclusion in the final full-scale
prototype, since it was much easier, faster and more reliable to manufacture and the
difference in performance could be easily compensated by increasing the length of
the collector allowing for a larger area and more input solar power.
Figure 7.28 Output air temperature vs. airflow rate for input air at 20°C and different
panel configurations
110 0 10 20 30 40 50 60 70 80 90 100
40
50
60
70
80
90
100
110
120
130
Air flow rate
Out
put t
empe
ratu
re (°
C)
Output temperature vs. flow rate for air exiting collector panel
V-corrugation V-corrugation with fins Simple single cover Simple double cover Complex double cover
Irradiance = 900 W/m² Ambient temperature = 20 °C
Input temperature = 20 °C Collector length = 6.5 m
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Chapter 7 - Air-to-water heat transfer solar hot water system with heat exchanger-water tank coupling
181
Figure 7.29 Efficiency vs. airflow rate for input air at 20°C and different panel
configurations
Figure 7.30 Output air temperature vs. airflow rate for input air at 40°C and different
panel configurations
0 10 20 30 40 50 60 70 80 90 100 1100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Air flow rate (L/s)
Col
lect
or e
ffici
ency
Efficiency of the V-corrugated collector vs. flow rate
V-corrugation V-corrugation with finsSimple single cover Simple double cover Complex double cover
Irradiance = 900 W/m²
Ambient temperature = 20 °C
Input temperature = 20 °C
Collector length = 6.5 m
0 10 20 30 40 50 60 70 80 90 100 11050
60
70
80
90
100
110
120
130
Air flow rate (L/s)
Out
put t
empe
ratu
re (°
C)
Output temperature vs. flow rate for air exiting collector panel
V-corrugation V-corrugation with finsSimple single cover Simple double cover Complex double cover
Irradiance = 900 W/m²
Ambient temperature = 20 °C
Input temperature = 40 °C
Collector length = 6.5 m
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Chapter 7 - Air-to-water heat transfer solar hot water system with heat exchanger-water tank coupling
182
Figure 7.31 Efficiency vs. airflow rate for input air at 40°C and different panel configurations
Figure 7.32 Output air temperature vs. airflow rate for input air at 60°C and different
panel configurations
20 30 40 50 60 70 80 90 100 110 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Air flow rate (L/s)
Col
lect
or e
ffici
ency
Efficiency of the V-corrugated collector vs. flow rate
V-corrugation V-corrugation with fins Simple single cover Simple double cover Complex double cover
Irradiance = 900 W/m²
Ambient temperature = 20 °C
Input temperature = 40 °C
Collector length = 6.5 m
0 10
0 10 20 30 40 50 60 70 80 90 100 110
70
80
90
100
110
120
130
Air flow rate (L/s)
Out
put t
empe
ratu
re (°
C)
Output temperature vs. flow rate for air exiting collector panel
V-corrugation V-corrugation with fins Simple single cover Simple double cover Complex double cover
Irradiance = 900 W/m²
Ambient temperature = 20 °C
Input temperature = 60 °C
Collector length = 6.5 m
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Chapter 7 - Air-to-water heat transfer solar hot water system with heat exchanger-water tank coupling
183
Figure 7.33 Efficiency vs. airflow rate for input air at 60°C and different panel configurations
Another analysis was done to determine the efficacy of the dimensions chosen for the
second prototype, namely, the ratio of the internal height of the collector, D, over the
length, L. This is known as the D/L ratio and is a parameter used in the assessment
of system efficiency113. Due to manufacturing and system constraints owing to
readily available materials, the height of the air chamber in the collector was to be 60
mm. The shortest collector length that could eventuate would be 6.4 m. With these
dimensions, D/L = 0.0094.
The result of the numerical analysis, Figures 7.34 - 7.37 show that for the profile
chosen and for mid to high input air temperatures, values of D/L below 0.0044 have
negligible effect on the efficiency and operation of the collector. The closest figure to
the design value of 0.0094 is 0.0088, which offers only slightly reduced performance
from the optimum (less than 1.5°C). It is estimated that if this design ratio is used it
would give less than 3°C output temperatures from the optimum. This is not
significant enough to require a redesign of the prototype system. In actual fact, the
D/L ratio that eventuated from the second prototype construction was 0.05/6.6 =
0.0076. The second prototype is discussed next.
0 10 20 30 40 50 60 70 80 90 100 110 0
0.1
0.2
0.3
0.4
0.5
0.6
Air flow rate (L/s)
Col
lect
or e
ffici
ency
Efficiency of the V-corrugated collector vs. flow rate
V-corrugation V-corrugation with finsSimple single cover Simple double coverComplex double cover
Irradiance = 900 W/m²
Ambient temperature = 20 °C
Input temperature = 60 °C
Collector length = 6.5 m
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Chapter 7 - Air-to-water heat transfer solar hot water system with heat exchanger-water tank coupling
184
Figure 7.34 Variation of the ouput air temperature for 20°C input air based on different
D/L ratios
Figure 7.35 Efficiency air temperature for 20 °C input air temperatures based on different
D/L ratios
0 10 20 30 40 50 60 70 80 90 100 110 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Air flow rate (L/s)
Col
lect
or e
ffici
ency
Efficiency of collector panel vs. flow rate for various D/L ratios – Low input air temperatures
Irradiance = 900 W/m²
Ambient temperature = 20 °C
Input temperature = 20 °C Collector length = 6.5 m Collector width = 0.57 m
0.00025 0.00055 0.0011 0.0022 0.0044 0.0088 0.0176 0.0352 0.0704 0.1408 0.2816
D/L
Output temperature vs. flow rate for air exiting collector panel forvarious D/L ratios – Low input air temperatures
0 10 20 30 40 50 60 70 80 90 100 110
30
40
50
60
70
80
90
100
110
120
130
Air flow rate (L/s)
Out
put t
empe
ratu
re (°
C)
Irradiance = 900 W/m² Ambient temperature = 20 °C Input temperature = 20 °C Collector length = 6.5 m Collector width = 0.57 m
0.00025 0.00055 0.00110.00220.00440.00880.01760.03520.07040.14080.2816
D/L
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Chapter 7 - Air-to-water heat transfer solar hot water system with heat exchanger-water tank coupling
185
Figure 7.36 Variation of the ouput air temperature for 40°C input air based on different
D/L ratios
Figure 7.37 Efficiency air temperature for 40 °C input air temperatures based on different D/L
ratios
0 10 20 30 40 50 60 70 80 90 100 110 40
50
60
70
80
90
100
110
120
130
Air flow rate (L/s)
Out
put t
empe
ratu
re (°
C)
Output temperature vs. flow rate for air exiting collector panel for various D/L ratios – High input air temperatures
Irradiance = 900 W/m²
Ambient temperature = 20 °C
Input temperature = 40 °C Collector length = 6.5 m Collector width = 0.57 m
0.00025 0.00055 0.0011 0.0022 0.0044 0.0088 0.0176 0.0352 0.0704 0.1408 0.2816
D/L
0 10 20 30 40 50 60 70 80 90 100 1100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Air flow rate (L/s)
Col
lect
or e
ffici
ency
Efficiency of collector panel vs. flow rate for various D/L ratios –High input air temperatures
Irradiance = 900 W/m²
Ambient temperature = 20
Input temperature = 40 °C Collector length = 6.5 m Collector width = 0.57 m
0.000250.000550.00110.00220.00440.00880.01760.03520.07040.14080.2816
D/L
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Chapter 7 - Air-to-water heat transfer solar hot water system with heat exchanger-water tank coupling
186
7.6.2 Second prototype
Temperatures at all the relevant points in the system were obtained during operation
in open and closed loop modes. This enabled estimation of power delivered to the
water, Pin_water, and its comparison with model results, constituting the decisive
figure in performance assessment. Experimental data and numerical results are given
in sections 7.6.2.1 and 7.6.2.2 for the open and closed loop modes, respectively.
Performance prediction process
The solution process for numerical prediction of Pin_water (Equation 7.23) was
explained in section 7.3.4. It required the following parameters:
- Heat loss coefficients of the system
- The exchanger effectiveness
- The effective radius of the thermosiphon coupling
Heat loss coefficients were calculated as in section 7.2. The exchanger effectiveness
was determined from Equation 7.24 and was found from the relevant input and
output temperatures, Tin_x, Tin_w, Tout_water, that were measured during system
operation. Two different values, ε = 0.73 and ε = 0.69, were obtained for open and
closed loop modes, respectively (Figures 7.39 and 7.46). (Subsequent direct
measurements on the isolated exchanger gave similar results, section 7.6.5).
The remaining parameter, the effective radius of the thermosiphon loop, was used as
a parameter to fit the experimental data. From the theory of section 7.3.4, the power
delivered to the water, Pin_water, versus Tout_water could be calculated (Equation 7.23).
The results for open and closed loop operation are given in Figures 7.40 and 7.47,
respectively. Experimental findings for Pin_water versus Tout_water were plotted on the
same graphs revealing two different radii values, r = 3 mm and r = 3.75 mm, for each
mode. (Subsequent direct measurements on the isolated exchanger gave similar
results, section 7.6.4).
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Chapter 7 - Air-to-water heat transfer solar hot water system with heat exchanger-water tank coupling
187
Knowing the heat loss coefficients, the exchanger effectiveness and the effective
thermosiphon radius, Equations 7.18, 7.21, 7.23 and 7.26 were used to predict system
temperatures over a wide range of input irradiance. The predicted temperatures
versus the measured temperatures are shown in Figures 7.38 and 7.41 for open loop
mode and in Figures 7.45 and 7.48 for closed loop mode. Within the limited range of
irradiance available for measurement it is seen that the theory predicted the system
temperatures reasonably well (to within 7% of experimental results).
7.6.2.1 Open loop operation mode
The airflow rate measured was (61 ± 4) L/s. All relevant temperatures and numerical
predictions in Figure 7.38 corresponded to measurements taken for a typical run.
Figure 7.38 Experimental and numerical temperature variations vs. time of the day for the
elements of the 2nd prototype air heater panel and SHWS in open loop mode
Temperatures for 2nd prototype air heater panel & SHWS elements vs. time OPEN LOOP OPERATION
Time of the day
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
9:36 9:56 10:16 10:36 10:56 11:16 11:36 11:57 12:17 12:37
Tem
pera
ture
s (°
C)
12:57
Collector length = 6.5 m
Collector width = 0.57 m
Effective radius = 3 mm
Tin_col
Tout_col
Tin_w
Tout_w
Tin_exch
Tout_exch
Tout_exch_NUM
Tout_w_NUM
Tin_exch_NUM
Tout_col_NUM
Tamb
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Chapter 7 - Air-to-water heat transfer solar hot water system with heat exchanger-water tank coupling
188
The rise in air temperature was about 40 °C – 45 °C and it dropped in the exchanger
by 11 °C – 18 °C. Assuming the entire power drop in the exchanger got transferred
to the water, no more than 40% of the gain from the collector was used.
The numerical temperature predictions were slightly lower at early stages of system
operation and slightly higher at later stages (this is explained later when numerical
predictions over a wider range of irradiances are presented).
Power delivered to the air was about 2900 W for an air mass flow rate of about
0.066 kg/s. Taking 970 W as a representative average irradiance during operation,
the average input power to the collector was about 3600 W. A quick estimation of
the efficiencies gave 80% for the collector and just under 33% for the entire system.
Heat exchanger effectiveness
The effectiveness was calculated by plotting the temperature differences ratio of
Equation 7.24 (Figure 7.39). An initial approximation of a linear fit to the data
yielded a constant exchanger effectiveness of 0.73 ± 0.04.
Figure 7.39 Experimental results and numerical fit for determination of exchanger
effectiveness (eq. 7.24) for an airflow rate of 61 L/s in open loop mode
Exchanger effectiveness plot for input and output fluid temperatures OPEN LOOP OPERATION
0 2 4 6 8
10 12 14 16 18 20 22 24 26 28 30 32 34 36
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50
Tin_x – Tin_water (°C)
T out
_wat
er -
T in_
wat
er (°
C)
Air flow rate = 61 L/s y = 0.726x Y-error
X-error
R = 0.81
p < 0.0001
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Chapter 7 - Air-to-water heat transfer solar hot water system with heat exchanger-water tank coupling
189
The results are quite removed from the origin and there is no previous knowledge of
the variation of the effectiveness with the ratios of the varying fluid temperatures.
Therefore, the simple assumption of linear behaviour with zero intercept is very
naïve, to say the least. Calculating the effectiveness by using the average ratio of the
temperature differences would be more appropriate. It was found, however, that the
result for effectiveness in both cases was basically the same (0.726) and so the
simplification of a linear fit was kept.
Effective thermosiphon radius
Comparison between experimental and theoretical values of power delivered to the
water versus output water temperature showed that a radius of (3.0 ± 0.4) mm fitted
the data reasonably well (Figure 7.40)
Figure 7.40 Experimental measurements and numerical predictions for power delivered to
the water vs. exchanger output air temperature for various thermosiphon pipe
radii (eq. 7.22) and for an airflow of 61 L/s in open loop operation
0 10 20 30 40 50 60 0
500
1000
1500
2000
2500
3000
Tout_water (°C)
Pow
er d
eliv
ered
to w
ater
(W)
Power delivered to the water vs. output water temperature for various pipe radii OPEN LOOP OPERATION
70
RADIUS
2 mm 3 mm 4 mm 5 mm 6 mm
+
Ambient temperature = 30 °C
Collector input air temperature = 31.5 °C
Exchanger input water temperature = 23.8 °C
Collector length = 6.5 m
Irradiance = 1007 W/m²
Airflow = 61 L/s
Exp. data
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Chapter 7 - Air-to-water heat transfer solar hot water system with heat exchanger-water tank coupling
190
Average values for the temperatures and the irradiance were used as input parameters
for the model to produce the curves of Figure 7.40.
Temperature predictions
It was now possible to predict all system temperatures since the required parameters
were known. A plot of theoretical temperatures for a full range of irradiance values
(Figure 7.41) revealed that almost all temperatures increased with increasing
irradiance, except for the output exchanger air temperature that reached a maximum
at around 980 W/m2 and then dropped off. This seemed to indicate that at these high
irradiance values, the water flow rate was high enough to allow a higher power
transfer between the air entering the exchanger and the thermosiphon loop, therefore
lowering the output air temperature.
Figure 7.41 Experimental temperature variations and numerical predictions over a wide
range of irradiance values for the 2nd SHWS prototype in open loop mode
0 100 200 300 400 500 600 700 800 900 1000 1100 1200 20
25
30
35
40
45
50
55
60
65
70
75
80
Irradiance (W/m2)
Tem
pera
ture
(°C
)
Temperatures for 2nd prototype heater panel & SHWS elements vs. irradiance OPEN LOOP OPERATION
Tamb
Tin_col
Tout_col
Tin_exch
Tout_exch
Tin_water
Tout water
Collector length = 6.5 m
Collector width = 0.57 m
90
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Chapter 7 - Air-to-water heat transfer solar hot water system with heat exchanger-water tank coupling
191
This phenomenon was not observed experimentally, basically because of the narrow
range of irradiance values available.
Similar to the results from Figure 7.38, these plots showed that the experimental
results were less than predicted at the start and higher than predicted at the end. This
was surely an indication of thermal inertia of the system as evidenced in other
studies135F
136. Dynamic effects due to the thermal mass of the system were not included
in the steady state theory developed in section 7.2. This effect was more clearly seen
and more accurately represented in Figure 7.38, since the numerical values for those
plots were computed for actual values of ambient temperature, Tamb, input water
temperature, Tin_water, and input panel air temperature, Tin_col, for every set of
measurements. In contrast, the curves of Figure 7.41 were produced from fixed
values for these temperatures and so the differences appear more pronounced when
they are not. It is clear (Figure 7.41) that Tin_water, Tin_col and Tamb were not constant.
The limited irradiance range of operation restricted the correlation between the
model and experimental data. Measurements at lower irradiance values would have
been useful in the validation of the numerical simulation process. The solar window
for the SHWS was restricted, allowing operation from 9 am until 2 pm. However, it
is also noted that effective operation of the system would only occur for relatively
high irradiance values and even though the actual experimental range was a narrow
one, a wider irradiance range would only be useful for values above 700 W/m2,
which would happen between the expected operation times of the day (section 7.1).
Another interesting fact was that output air temperatures from the collector were
always slightly higher than numerical predictions (Figure 7.42). Since the actual
absorber profile was not smooth, imperfections and protrusions as small as 1 mm on
the surface could act as if they were “mini-fins” inducing a heightened turbulence
and contributing to the higher temperatures (Figures 7.24 and 7.26). Also, since the
real profile (Figure 7.16a) was more like a multi-channel absorber, a higher energy
exchange with the air would be expected. The wooden strips covering the bottom of
the collector, besides reducing the height by about 5 mm from the original design,
thus reducing the D/L ratio and increasing performance, (Figures 7.34 and 7.36)
might have contributed with an increase in turbulence as air flowed over them.
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Chapter 7 - Air-to-water heat transfer solar hot water system with heat exchanger-water tank coupling
192
Figure 7.42 Experimental and numerical output air temperature variations for the 2nd
prototype air heater panel vs. time of the day in open loop mode
Power calculations
The power delivered to the water carried a high associated uncertainty due to the
uncertainty variations of all temperatures and the simplifications in the modelling of
the exchanger. Numerical and experimental results are given in Figure 7.43
Since a lossless exchanger was assumed, the calculated power delivered to the water
was equated to the power drop of the air in the exchanger. For open loop operation in
this particular case (3 hours of operation) this was:
Pin_water_exp: (996 ± 220) W
Pin_water_num: 923 W
With an average irradiance of (970 ± 40) W/m2 and an absorber area of 3.7 m2, total
system efficiency was about 27%, with variations between 20% to 34% due to the
high associated uncertainties. Numerical prediction gave (25 ± 1)%
Collector panel output air temperature vs. time OPEN LOOP OPERATION
60
62
64
66
68
70
72
74
76
78
80
82
9:36 9:50 10:04 10:19 10:33 10:48 11:02 11:16 11:31 11:45 12:00 12:14 12:28
Time of the day
Tem
pera
ture
(°C
)
Tout_col_NUM-RAW
Tout_col_NUM+2°
Tout_col_EXP
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Chapter 7 - Air-to-water heat transfer solar hot water system with heat exchanger-water tank coupling
193
Figure 7.43 Experimental results and numerical prediction for power delivered to the water
vs. time of the day for open loop operation and for 61 L/s airflow
Water tank temperature profile
Subsequent runs with the system operating in closed loop mode included
measurements of the temperature profile of the water in the tank after a day’s
operation. These results were used to better determine the average power delivered to
the water. Since this was not implemented during the early stages of open loop
operation, special runs were done afterwards specifically to have a set of results that
would be representative of the dynamics and power delivered to the water in this
configuration mode. The results given in Figure 7.44 are for one such run where the
temperature profile was measured after 1.5 hours of system operation.
Power delivered to water vs. time – OPEN LOOP OPERATION
Pow
er (W
)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
1500
9:36 9:50 10:04 10:19 10:33 10:48 11:02 11:16 11:31 11:45 12:00 12:14 12:28
Pin_wat_NUM
Pin_wat_EXP
Time of the day
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Chapter 7 - Air-to-water heat transfer solar hot water system with heat exchanger-water tank coupling
194
Figure 7.44 Temperature measurements for a vertical profile of the water in the storage
tank for open loop operation of the system and for 61 L/s airflow
The plot above shows obvious signs of thermal stratification with a transitional
region extending down and ending at about the centre of the tank. The assumption of
an unchanging cold water column was therefore not true. However, it was a good
starting point for the determination of an otherwise very difficult calculation.
After measuring the depth profile, the water in the tank was mixed thoroughly and a
final average temperature of 30 °C was obtained. From this Figure, and for 1.5 hours
of heating 190 L of water, it was determined that the average power delivered to the
water during operation of the system, Pin_water_exp, was: (1070 ± 150) W. Incidentally,
this figure was very close to the power measured in the open loop system operation
as shown in Figure 7.43. Despite the fact that the tank temperature profile was taken
for a different data collection time it was reasonable to expect a similar result since
operating and environmental conditions for both runs were similar.
Temperature depth profile for hot water in the tank OPEN LOOP OPERATION
20 21 22
23 24 25 26 27 28
29 30 31 32 33
34 35 36 37 38 39
40 41 42
0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84
Tank height (cm)
Tem
pera
ture
(°C
)
Mixed
Unmixed
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Chapter 7 - Air-to-water heat transfer solar hot water system with heat exchanger-water tank coupling
195
7.6.2.2 Closed loop operation mode
The airflow rate measured was (63 ± 4) L/s. All relevant temperatures and numerical
predictions in Figure 7.45 corresponded to measurements taken for a typical run.
Figure 7.45 Experimental and numerical temperature variations vs. time of the day for the
elements of the 2nd prototype air heater panel and SHWS in closed loop mode
The rise in air temperature was lower than for the open loop mode, about
35 °C - 37 °C, but the drop in the exchanger was higher: about 20 °C - 23 °C. This
meant that about 60% of the power in the air was transferred to the water. For
approximately 0.069 kg/s mass airflow rate, the power delivered to the air was about
2500 W. Taking 890 W as a representative average irradiance during operation, the
average input power to the collector was about 3300 W and the efficiency of the
entire system about 45%. The higher efficiency compared to the open loop
configuration was due to the larger heat transfer in the exchanger.
Temperatures for 2nd prototype heater panel & SHWS elements vs. time CLOSED LOOP OPERATION
Time of the day
Tem
pera
ture
s (°
C)
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
9:36 9:50 10:04 10:19 10:33 10:48 11:02 11:16 11:31 11:46 12:01
Collector length = 6.5 m
Collector width = 0.57 m
Radius = 3.75 mm
Tin_col
Tout_col
Tin_w
Tin_exch
Tout_exch
Tout_w_NUM
Tin_exch_NUM
Tout_col_NUM
Tamb
Tout_w
Tout_exch_NUM
Tin_col_NUM
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Chapter 7 - Air-to-water heat transfer solar hot water system with heat exchanger-water tank coupling
196
Heat exchanger effectiveness
The effectiveness was calculated by plotting the temperature differences ratio of
Equation 7.24 (Figure 7.46). A linear fit to the data yielded a constant exchanger
effectiveness of 0.69 ± 0.04, lower than for the open loop mode.
Figure 7.46 Experimental results and numerical fits for determination of exchanger
effectiveness (Equation 7.24) for an airflow rate of 63 L/s in open loop mode
Similar to the effectiveness calculation in open loop mode, the average ratio of the
temperature differences was compared to the slope value from the linear fit and the
results were practically the same (less than 0.1% difference).
Effective thermosiphon radius
Comparison between experimental and theoretical values of power delivered to the
water versus output water temperature showed that a radius of (3.75 ± 0.4) mm fitted
the data reasonably well (Figure 7.47).
y = 0.691x
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
38
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52
Exchanger effectiveness plot for input and output fluid temperatures CLOSED LOOP OPERATION
Tin_x – Tin_water (°C)
T out
_wat
er -
T in_
wat
er (°
C)
Air flow rate = 63 L/s
X-error
Y-error
R = 0.775p < 0.0014
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Chapter 7 - Air-to-water heat transfer solar hot water system with heat exchanger-water tank coupling
197
Figure 7.47 Experimental measurements and numerical predictions for power delivered to
the water vs. exchanger output air temperature for varius thermosiphon pipe
radi (eq. 7.56) and for an airflow of 63 L/s in closed loop operation
Average values for the temperatures and the irradiance were used as input parameters
for the model to produce the curves of Figure 7.47.
Temperature predictions
Since the air temperature input of the collector changed with time, the output
collector and exchanger air temperatures and the output water temperature increased
in a non-linear fashion (Figure 7.48), as opposed to the linearity observed in the open
loop system (Figure 7.42).
Temperature (°C)
Pow
er d
eliv
ered
to w
ater
(W)
Power delivered to water vs. exchanger output water temperaturefor various pipe radii – CLOSED LOOP OPERATION
0 5 10 15 20 25 30 35 40 45 50 55 60 650
250
500
750
1000
1250
1500
1750
2000
2250
2500
3000
70
2750
Ambient temperature = 21 °C
Collector input air temperature = 30.9 °C
Exchanger input water temperature = 15.6
Collector length = 6.5 m
Irradiance = 883 W/m²
Airflow = 63 L/s
RADIUS
2 mm 3 mm 3.75 mm 4 mm 5 mm
+ Exp. data
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Chapter 7 - Air-to-water heat transfer solar hot water system with heat exchanger-water tank coupling
198
Figure 7.48 Experimental temperature variations and numerical predictions over a wide
range of irradiance values for the 2nd SHWS prototype in closed loop mode
Similar to the open loop configuration, all temperatures increased with increasing
irradiance with the exception of the output exchanger air temperature, which reached
a maximum and then dropped off. Additionally, and since the system was operating
with air recycling, the collector input air temperature experienced the same thing.
The effects of thermal inertia were also seen for this operation mode (Figures 7.45
and 7.48) for the exchanger input, exchanger output and collector input air
temperatures. Collector output air temperatures were also consistently higher than
model predictions (2 °C - 3°C).
Irradiance (W/m2)
Tem
pera
ture
(°C
) Temperatures for 2nd prototype heater panel & SHWS elements vs. irradiance
CLOSED LOOP OPERATION
0 100 200 300 400 500 600 700 800 900 1000 1100 1200
10
15
20
25
30
35
40
45
50
55
60
65
70
75
0
5
Tamb
Tin_col
Tout_col
Tin_exch
Tout_exch
Tin_water
Tout_water
Radius = 3.75 mm
Collector length = 6.5 m
Collector width = 0.57 m
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199
Power calculations
The results for power in the water versus time of the day during system operation
were higher compared to the open loop mode (Figure 7.49) and this was due to the
higher heat transference in the exchanger.
Figure 7.49 Experimental results and numerical prediction for power delivered to the water
vs. time of the day for 63 L/s airflow in closed loop mode
For 1.8 hours of operation, the results for power delivered to the water were:
Pin_water_exp: (1430 ± 200) W
Pin_water_num: 1300 W
For an average irradiance of (890 ± 40) W/m2 and an absorber area of 3.7 m2, total
system efficiency was about 40% or more which is higher than the value of 27%
found for the open loop system.
Pow
er (W
)
Power delivered to water vs. time CLOSED LOOP OPERATION
Time of the day
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
1500
1600
1700
1800
1900
9:36 9:43 9:50 9:57 10:04 10:12 10:19 10:26 10:33 10:40 10:48 10:55 11:02 11:09 11:16 11:24 11:31
Pin_wat_NUM Pin_wat_EXP
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200
Water tank temperature profile
The temperature profile of the water was measured after operation and there was also
evidence of thermal stratification in the tank with a transitional region extending
downwards by ⅔ the length of the tank (Figure 7.50).
Figure 7.50 Temperatre measurements for a vertical profile of the water in the storage tank
for 63 L/s airflow in closed loop mode
The water in the tank was mixed twice to arrive at a uniform temperature. The final
average value obtained was 23.6°C. After 1.8 hours of operation and heating 190 L
of water, the average power delivered to the water was: (1121 ± 200) W. This value
was lower than the numerical predictions and experimental data given in Figure 7.49.
System efficiency in this case was about 34%, still higher than in open loop mode.
The results for the closed loop system showed that it delivered more power than the
previous configuration.
Temperature depth profile for hot water in tank CLOSED LOOP OPERATION
Tem
pera
ture
(°C
)
Tank height (cm)
14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41
0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80
Mixed
Unmixed
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201
7.6.3 Determination of head loss and pressure drops in the system
Values for pipe losses in the whole system were determined both numerically and
experimentally. This was done for the closed-loop configuration, since it was the
configuration of choice for continuous operation.
A schematic of the system showing the resistive elements and pressure drop
measurement points is given in Figure 7.51. The experimental and numerical data is
given in Table 7.7 as well as the K-values for each element.
Figure 7.51 Schematic of conveyance infrastructure: pipes, elbows, fittings and other elements
The numerical calculations for pressure loss in the system were based on the theory
outlined in chapter 5, which was applied to all elements except for the heat
exchanger. Pressure measurements were taken in accordance with the description and
setup of Figure 7.21. The fan blower, used always in its medium setting, (refer to
Appendix H) was capable of producing flow rates in excess of 90 L/s when operating
against no static pressure. In closed loop operation, flow rates above 60 L/s were
obtainable. With these rates it was possible to achieve the daily hot water energy
requirements of 30 MJ (Table 1.2).
L
M J
A
B
C
D E
F
G H
I
K fan/blower
1
2
3
4 5
6
7
8
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202
Table 7.7 Theoretical and experimental pipeline pressure drops
Pressure drop (Pa) Element type & ID
(Figure 7.51) Description Loss Value Calculated
Exp. (± 20)
A1 15° Kf_15 = 0.06 0.4 P2 - P1 Elbow fittings
A2 90° Kf_90 = 1.2 7.2 Straight pipe LAB A to B – join 0.2 m 1.3 42
B1 15° Kf_15 = 0.06 0.4 Elbow fittings
B2 45° Kf_45 = 0.3 1.9
11.2
P3 - P2 Straight pipe LRET B to C – join 5.1 m 33
34
C1 22.5° Kf_22.5 = 0.1 0.6 P4 - P3 Elbow fittings C2 90° Kf_90 = 1.2 7.2 58
Straight pipe LCD C to D – join 0.2 m 1.3 9.1
Reduction fitting D Collector input Kfr = 0.01 0.08 P5 - P4 Sudden
expansion E Collector inlet Kxc = 0.8 6.5
Other element F Collector panel Km ≈ 3 0.5 108 Sudden
contraction G Collector outlet Kcc = 13.7 111
Expansion fitting H Collector output Kfx = 0.02 0.16
118
I1 45° Kf_45 = 0.3 1.9 P6 - P5 Elbow fittings
I2 15° Kf_15 = 0.06 0.4 2.3 6
P7 - P6 Straight pipe LOUT I to J – join 4.1 m 26.5
26
Elbow fitting J 45° Kf_45 = 0.3 1.9 P8 - P7
Combination Fitting K1 X-changer input Kxi = 0.9 5.2
Sudden expansion K2 X-changer inlet Kxm = 0.6 3.6 72
Other element L X-changer body Kp ≈ 70 ~22 Sudden
contraction M1 X-changer outlet Kcm = 4.7 28
Combination Fitting M2 X-changer output Kco = 0.9 5.2
~66
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The motor was never operated at its maximum voltage rating and it functioned
continuously for many hours with no apparent deterioration. Based on current and
voltage measurements, it had an average power consumption of less than 80 W, and
was able to provide the required airflow rates for this study. In a commercial
application, the call would be for a 240 VAC motor with the same physical criteria
design for this centrifugal blower, unless the system were to be used as a stand-alone
system, in which case photovoltaic panels would be used.
The results in Table 7.7 show that for an airflow rate of 63 L/s, the major losses were
due to the collector panel assembly, which included the reduction and expansion
fittings for the entrance and exit ports, and the heat exchanger. Pressure drop
calculations for straight pipe sections correlated fairly accurately with the
measurements at the different points, despite the large associated error (±20 Pa).
Correlations for the minor losses, however, indicated the presence of unaccounted
resistance factors, systematic errors, or both. It is important to note that elbow
fittings and joiners used were forced on to the straight pipe in order to obtain the
airflow pathway that the test site allowed with the hardware available at the time.
Therefore, actual airflow bends where not smooth, experiencing sharp entering and
exiting effects into and from these fittings. Even though all elbow bends were
considered as rough mitre-type bends, with sharp angles, the additional resistance
measured indicated something else was happening. Measurements with errors as high
as 100% (and higher) are not useful in practice, nevertheless the technique allowed
determining two things: the elements producing the largest pressure drops and the
possibility of determining theoretically the pressure drops for given airflow rates.
Another source of error was attributed to the measurement process, which besides
having a large uncertainty, was dependent on the actual positioning of the measuring
nozzle in the pipeline (Figure 7.19). It is possible that pressure drops were masked
and/or enhanced by the mere fact of taking measurements close to those elements
producing minor losses and by the depth at which the nozzle was inserted into the
pipes (about 10 mm). This could also explain the better correlation for head losses
from the straight pipes, where the effect of a fully developed flow would have been
prevalent. The largest discrepancy was observed for the measurement between points
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204
3 and 4; the bend of the return pipe and the input to the collector. The airflow at the
entrance was confronted by a slight contraction and then suddenly by an expansion
into the collector chamber area, which could have artificially raised the expected
pressure drop between the points in question.
It is noted that the largest minor losses occurred for sudden contraction fittings,
especially from the collector exit where the airflow cross-sectional area suddenly
reduced to about 15% of its value (from about 0.034 m2 to 0.005 m2).
Of particular importance are the unconventional resistance elements: the panel and
the heat exchanger, for which the K-values were estimated. The panel proper (F),
without the input and output attachments, actually posed a relatively low resistance
due to its large cross-sectional area. Its effect was approximated to that of two 90°
degree mitre bends with an extra pressure loss at the back buffer zone where the
airflow bend actually occurred (K ≈ 1.5 x 2). The K-value assigned to the heat
exchanger was worked out from the experimental results. Since discrepancies where
found for minor losses, it is possible that the resistance posed by the exchanger was
lower than the estimation.
Finally, the so-called “combination” fittings (K1 and M2) used for the heat exchanger
were actually a special type of fitting (Figures 7.15 and 7.17). K1, for instance,
produced a partial expansion of the airflow into a relatively small space followed
immediately by a contraction into the actual exchanger chamber opening, or inlet
(where an expansion then took place as indicated by K2). The effect of M2 was the
opposite. These K-values were conservatively estimated assuming twice the value of
an expansion-contraction or (contraction-expansion) effect (K ≈ 0.45 x 2).
Since the airflow rate was 0.063 m3/s and the pressure losses in the system were
about 346 Pa, the estimated power required to overcome these losses (from
Equation 5.29) was about 22 W. Total pump efficiency was then no less than 27%
and about 58 W were consumed as part of the electro-mechanical conversion process
for airflow generation. The air pump is not very efficient. However, if these power
losses are compared with a power gain from the system of about 1000 W of hot
water, they represent less than 6% of the total, which is not a major loss. It is
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205
important to note that these are worst-case scenarios, since actual motor power
measurements were not taken (80 W is an upper bound value) and the efficiency
could be higher. Also, more than 1000 W of heat into the water is expected, on
average, for daily operation as discussed in the previous section. It would appear then
that improving on motor design to increase efficiency might not be significantly
useful. More detailed assessment of power consumption is required. Keeping with
the objectives of this project, going for a higher motor efficiency could be pursued if
it is possible to source a readily available, mass produced, alternative (eg. improved
and inexpensive successor model). Compared with the power consumption of
non-solar hot water systems, this represents an insignificant loss, considering for
instance, that a typical electrical hot water system with a 160 L tank consumes about
2400 W. On the other hand, domestic solar hot water split systems that use a pump to
simulate a natural thermosiphon operation, consume less than 20 W and do not
operate continuously as the fan-motor does. Compared to these, the fan-motor is in
clear disadvantage, but putting it all in context and referring again to non-solar
systems and the project’s objectives of low-cost and ease of implementation, a
fan-blower motor efficiency of about 27 % is acceptable.
Overall, the results showed that it was possible to predetermine the hydraulic
resistance offered by a SHWS of this nature for proper sizing of the motor and
eventually finding overall efficiency.
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206
7.6.4 Thermosiphon effective radius and linear fluid flow approximation
From the results for open and closed loop operation of the SHWS, two different
effective radii, 3 mm and 3.75 mm, were determined for the thermosiphon loop. This
represents a difference of 20%. The discrepancy could be explained from the high
associated uncertainties of the measurements and the simplifications used in the
analysis of the thermosiphon process, especially the assumption of a constant
effectiveness for the heat exchanger and a constant hot water column of water
driving the flow. A more detailed analysis of the relationship between water flow and
pressure drop in the exchanger was carried out in order to assess the usefulness of the
Poiseuille equation and infer a more accurate effective radius (if possible).
The experimental setup is shown in Figure 7.52 and the method consisted in the
determination of pressure drops across the exchanger for known water flow rates. A
similar approach to that of air pressure drops was done, with manometer readings in
mmH20 before and after the flow entered the exchanger. A hose was connected to the
input of the exchanger and tap water allowed to flow from 1.7 cc/s up to 46 cc/s.
Actual flow rates were determined by measuring collected fluid volume over time.
The results are shown in Figure 7.53.
Figure 7.52 Pressure drop measurement setup for water flow in the heat exchanger
Δh
Heat Exchanger
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207
Figure 7.53 Experimental measurements for pressure drops vs. water flow rates in the heat
exchanger and equation fits showing a linear response below 12 cc/s
The results showed a linear response range for flow rates below 12 cc/s. This
supported the assumption made in section 7.3.4 of laminar flow under 10.5 cc/s
allowing the application of Poiseuille’s equation for flow rates under this range.
The linear fit to the points below 12 cc/s in Figure 7.53 has a high correlation
coefficient, being well approximated by an equation with zero intercept from which
the effective thermosiphon radius of the heat exchanger could be easily determined.
This assumption of linearity, however, was based on a thermosiphon radius equal to
twice the size of the calculated effective radius for the exchanger. A reduction in pipe
size would imply a reduction in the laminar flow threshold as well. For the effective
thermosiphon pipe radius (Table 7.8) and from Equation 5.18 for the Reynolds
number, this would indicate that laminar flow would be observable for flow rates
under 6 cc/s. In actual fact, and as given by the results above, fluid flow appeared to
depart from its laminar nature in the vicinity of 11 cc/s.
From Poisseuille’s equation for laminar flow (Equation 5.30):
Pressure drop vs. water flow rate for the heat exchanger
P2 = 0.168·Φ2 + 4.785·Φ
R2 = 0.998
p < 0.014
0
50
100
150
200
250
300
350
400
450
500
550
600
0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48
Flow rate (cc/s)
Pres
sure
(Pa)
Linear flow range (< 12 cc/s)Entire flow range
P1 = 6.094·Φ
R = 0.982
p < 0.001
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208
( )fitlinearofslopear
lPL=
⋅⋅⋅
=Φ 4
8π
η (7.34)
There was excellent agreement between the calculated radius from Equation 7.34
with the value obtained from open loop operation, as shown in Table 7.8. It was also
seen that there was deviation from closed loop operation.
Table 7.8 Comparison of different values for the thermosiphon effective radius
Experimental process Effective radius (mm)
Thermosiphon process established under whole system operation in OPEN LOOP MODE (section 7.6.2.1) 3.0 ± 0.4
Thermosiphon process established under whole system operation in CLOSED LOOP MODE (section 7.6.2.2) 3.75 ± 0.4
Forced water flow under exchanger operation only (this section) 2.9 ± 0.4
The results for closed loop operation were larger than the calculation for independent
testing of the heat exchanger by about 23%. Despite the differences, the results from
the plot of Figure 7.53 were very useful, as they seemed to validate those results
obtained during open and closed loop modes. It is noteworthy that during whole
system operation, a larger pipe section was considered in the calculation of effective
thermosiphon radius and was attached to entry/exit ports of the tank that also posed
hydraulic resistance (not to mention the effects of entrant and exit losses for the fluid
as it cycles in and out the tank). This would have invariably affected the result;
specifically since the water column driving the thermosiphon was deemed constant
throughout operation and equated to the pipe section length. In actual fact, given that
other simplifications and high associated uncertainties would also account for
variations in effective radius calculation, the results obtained and compared in
Table 7.8 were in general good agreement with each other and were consistent with
the experimental work carried out earlier.
Above 12 cc/s the behaviour was clearly non-linear and Equation 7.34 was no longer
applicable. However, the 2nd order polynomial approximation for pressure drops for
this particular system was able to predict results with moderate accuracy. It is
possible it could be used in other circumstances for overall pressure drop calculations
if fluid flow were modified for active operation and water flow rates were known.
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209
7.6.5 Exploring exchanger effectiveness variation under system operation
The numerical results and calculations inferred during open and closed loop
operation of the SHWS for many system parameters were obtained from several
assumptions and simplifications of the analytical theory. Of particular importance
was the determination of the following parameters:
• The thermosiphon output water temperature
• The water flow rate
• The power delivered to the hot water tank
• The exchanger output air temperature
• The effective thermosiphon radius
One such assumption was that the exchanger effectiveness remained constant
throughout operation (section 7.3.4). It is well known that exchanger effectiveness is
not constant and will vary with varying input fluid temperatures and flow rates. As a
first approximation, however, it appeared satisfactory and allowed a simple approach
to the numerical prediction of the above parameters. The values obtained were within
expected ranges and correlated reasonably well with experimental measurements. An
additional investigation was done in an attempt to more closely characterise the
exchanger effectiveness.
The experimental setup this time required the operation of the exchanger with known
water and airflow rates and known water and air temperatures. Hot air was blown
into the exchanger at different flow rates from two hair dryers connected to a mixing
box and tap water was delivered to the exchanger at a range of different flow rates.
Water flow rates were determined by measuring volume collected over time. Airflow
rates were determined, not with the use of the air tunnel-bag, but with the
anemometer. For this purpose a better, more comprehensive, calibration was
performed as it was clear from the early stages of development of the project that the
anemometer provided unreliable results in most cases (section 7.5.1). The calibration
procedure is given in Appendix I.
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210
It was explained in section 7.3.4 that the water was the fluid undergoing the
maximum temperature change available in the exchanger at all times, allowing a
simpler expression to be used when calculating exchanger effectiveness. However, if
standard operating conditions were to change (eg. low irradiance levels, different
airflow rates), this would no longer be so, in which case the general expression for
effectiveness would need to be used (Equation 4.57) with careful consideration on its
application and with the inconveniences that it presents in the determination of other
parameters of interest (section 4.5).
Since the purpose of the simulation was performance prediction, a different
expression, labelled ‘modified effectiveness’, replaced the standard effectiveness
relationship to unequivocally determine the output water temperature, Tout_water,
which was the key parameter in the determination of power:
( )( )water_inx_inairair
water_inwater_outww
water_inx_in
x_outx_in'
TTCm
TTCmTTTT
−⋅⋅
−⋅⋅=
−−
=&
&ε (4.58)
Experimental determination of flow rates and temperatures for water and air were
carried out in two sets of measurements and for two different airflow rates. The
results showed an exponential variation of ε' with increasing water flow rates
(Figure 7.54).
For very low water flow rates ( 0≈wm& ) heat transfer was negligible so there was
virtually no change in airflow temperature, i.e., Tin_x ≅ Tout_x, therefore ε’ ≅ 0. When
water flow rates were very high ( ∞→wm& ) the water temperature in the exchanger
did not change appreciably and Tout_water ≈ Tin_water. Depending on how good the heat
transfer from the collector fluid was, Tout_x would approach Tin_water but would never
be equal to it. Therefore, ε’ < 1 at all times. The variation of ε’ with wm& was fitted
reasonably well to an exponential expression (Figure7.54).
Different fit expressions were required for different airflow rates. However, the
variation of ε’ with the quotient airairww CmCm && was well approximated by a single
exponential fit for both airflow rates as given by Equation 7.35 (Figure 7.55).
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211
Figure 7.54 Experimental measurements for the modified effectiveness vs. water flow rates in the heat exchanger and exponential equation fits to the data
Figure 7.55 Experimental measurements for the modified effectiveness vs. ‘ Cm ⋅& ’ product quotient between water and air. An exponential equation fits the data well.
Modified effectiveness vs. water flow rate
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Water flow rate (cc/s)
Mod
ified
effe
ctiv
enes
s ( ε
')
y = 1- e-0.2062x
R = 0.98
p < 0.0001
y = 1- e-0.1158x
R = 0.983
p < 0.001
Tamb = 25 °C
1.0
44 L/s 63 L/s
airm&
Modified effectiveness vs. aaww CmCm ⋅⋅ &&
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3
Mod
ified
effe
fctiv
enes
s ( ε
')
Tamb = 25 °C
y = 1-e-0.9089x
R = 0.964
p < 0.0011
44 L/s 63 L/s
airm&
aaww CmCm ⋅⋅ &&
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212
From Figure 7.55: aa
ww
CmCm.
' e ⋅⋅
⋅−
−= &
&90890
1ε (7.35)
Figure 7.56 Predicted values for modified effectiveness vs. water flow rate from the
exponential expression of Equation 4.74
The exponential expression for effectiveness was able to reproduce the experimental
results for two different airflow rates up to ±13% accuracy (Figure 7.56).
In the calculation of power delivered to the water (section 7.3.4), the temperature of
the water leaving the exchanger was calculated by assuming a constant effectiveness.
The output temperature of the water was used to determine water flow rate. The
power in the water was then found from its flow rate and temperature rise. The use of
the mathematical fit shown before for the modified effectiveness would have been
better suited for these calculations since it implicitly takes into account the variable
nature of the exchanger effectiveness for varying fluid flow and temperature
conditions. Therefore, the modified effectiveness, ε’, could better characterise the
dynamics of heat transfer in the heat exchanger. From Equations 4.58 and 7.35:
( )( ) ( )water_inwater_out
airair
wwwater_inx_in
water_inx_inCmCm
.
TTCmCm
TT
TTe airair
ww
−⋅⋅⋅
−−
−=⋅
⋅⋅
&
&&
&90890
(7.36)
Prediction of modified effectiveness vs. water flow rate
Water flow rate (cc/s)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Mod
ified
effe
ctiv
enes
s ( ε
')
19.7 W/°C 28.4 W/°C
airair Cm ⋅&
Tamb = 25 °C
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213
This equation has two unknowns: wm& and Tout_water, which must be determined in
order to calculate the power delivered to the water, Pin_water. The water flow rate is
also given by Poisseuille’s equation and is dependent on Tout_water:
ηπ
⋅
⋅−⋅⋅⋅≈
8
224 g)TT(Crm water_outwater_in
w& (7.21)
By substituting Equation 7.21 into 7.36, the resultant relationship is a function only
of Tout_water and even though implicit in form, it can be solved by an iteration process,
such as the one applied in the solution of Equation 7.17 for air temperatures in the
pipe. Once the output water temperature is known it can be substituted in Equation
7.21 to find wm& and ultimately the power delivered to the water, Pin_water. Additional
experimental data would be required to verify this expression for low water flow
rates and various airflow rates. This could be a point for further work.
From the modified effectiveness a direct correspondence with actual exchanger
effectiveness was obtained by recalling Equation 4.57 and noticing that:
⎪⎭
⎪⎬⎫
⎪⎩
⎪⎨⎧
=⋅⋅
aa
wwCmCm
','max&
&εεε (7.37)
The effectiveness was then plotted versus water flow rates by using the relationship
for ε’ from Equation 7.35 and Equation 7.37 (Figure 7.57).
It is seen that exchanger effectiveness is certainly variable for different water flow
rates and airflow rates. For comparison, the two different effectiveness values used
for the open and closed loop configurations, and their uncertainties, are shown as a
constant band in Figure 7.57. These results were useful in the assessment of the
assumed validity of these constant effectiveness values. The first assumption made
was that the water was the fluid undergoing the maximum heat transfer at all times,
so only the right hand expression of Equation 4.57 for the effectiveness was used
(which is Equation 7.24). For the conditions of operation where airflow rates were
above 60 L/s and water flow rates below 10 cc/s, the plot shows that this was indeed
the case. Furthermore, for water flow rates between 6 cc/s and 14 cc/s, the
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Chapter 7 - Air-to-water heat transfer solar hot water system with heat exchanger-water tank coupling
214
effectiveness values were all contained within the experimental band. The
effectiveness was more sensitive to changes in water flow rates and since airflow
rates were quasi-constant with no more than 5% variations, the experimental
uncertainty for effectiveness was attributed only to variations in water flow rate
during operation. Given that the SHWS operated under environmental conditions that
also remained relatively unchanged, no major variations in water flow rates were
expected anyway. This restricted even further the possible excursion of the
effectiveness values to a narrower range. Experimentally, the values determined for
effectiveness in each configuration mode (0.73 and 0.69) carried an uncertainty of
6% and also differed by the same amount.
Figure 7.57 Variation of exchanger efficiency vs. water flow rate obtained from the
experimental fit for modified effectivness
Given the above, the use of a constant effectiveness to calculate power delivered to
the water during operation of the SHWS in this study appeared justifiable.
Heat exchanger effectiveness vs. water flow rate
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 Water flow rate (cc/s)
Effe
ctiv
enes
s (ε
)
Experimental ε range
= 63 L/s am& = 44 L/s am&
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215
According to the model, from Equations 7.25 and 7.23 it can be seen that if the
effectiveness is higher, the temperature of the water coming out of the exchanger will
be higher and so will the power delivered to the water. A more appropriate heat
exchanger for the system would be one as compact as the unit used, but with a higher
effectiveness. It would then be a matter of selecting such a unit by estimating
effectiveness values from manufacturer technical specifications for input and output
fluid temperatures14F
*. Additionally, the pressure drop introduced in the air circulation
system by the better unit should ideally be less than the existent one, or at least
should not offset the possible extra power gain in the water by demanding an even
higher motor power expenditure. This is also possible to estimate from the
fan-blower motor specifications required and used in conjunction with these compact
exchangers (since they are originally designed for automotive applications).
There appears to be another modelling approach136F
137 for natural convection heat
exchangers that may offer additional simplicity and accuracy compared to the model
presented here. In this other method, compact heat exchangers are characterised by
two relationships:
- The pressure difference (or pressure head) driving the thermosiphon versus the
mass flow rate of the fluid: Δp vs wm&
- The modified effectiveness versus the mass flow rate: ε’ vs wm&
A correspondence can then be made between thermosiphon pressure difference and
the modified effectiveness, which in turn would allow determination of the output
water, Tout_water (from Equation 7.25), and the power delivered to the tank water.
Pressure and heat transfer characteristics are unique for every exchanger so the
pressure difference required for different water flow rates must be determined
experimentally. The pressure head can be inferred from water temperature profiles of
the tank water and natural convection loop by using the relationship between the
temperature and density (Equation G7 – Appendix G). This method therefore
requires knowledge of water temperature profiles of the thermosiphon.
* Developing a custom-tailored solution would not be in line with the objectives of low cost and
readily available materials for system construction.
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216
Most of the assumptions and limitations of the model used in the project are due to
the characterisation of the convection loop flow as being laminar, so that the water
flow rate could be determined only from the input water and air temperatures to the
exchanger. For future work this alternate modelling is worth exploring with the
determination of possible relationships between pressure differences in the
thermosiphon loop and the input and output water temperatures. Computational fluid
dynamics can also be employed for a purely numerical simulation from first
principles.
7.7 Discussion
7.7.1 Air heater system elements
Collector panel
The air heating panel was designed for all day collection, as is the case with
conventional flat plate collectors. The panels were aimed at being a very low cost
alternative and did not have the complexities of the previous system (concentrating
devices, metal pipes, etc) having a thin aluminium sheet for absorber a polystyrene
body and polycarbonate cover. Ambient air was the transfer fluid and even small air
leaks would not present a problem during operation of the device137F
138 so the system
did not require leak-proof joints.
Stagnation temperature issues and robustness of collector panel structure.
During operation of open and closed loop modes, airflow rates above 61 L/s were
capable of delivering close to the required power into the water, but were not high
enough to keep collector air temperatures below 80 °C at all times. Under no airflow,
temperatures could easily reach 100 °C and beyond, melting the polystyrene walls,
dividers and air diffusers very quickly (1 min). At higher temperatures (> 120 °C) it
could also damage the polycarbonate cover.
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Polystyrene is a very easy material to work with due to its manageability and low
weight and depending on its density it can provide excellent structural support as
well as excellent thermal insulation. It is also relatively inexpensive when compared
with other standard building materials (eg., polyurethane, wood). Despite its benefits,
it has two main drawbacks. One is the fact that its softness makes it prone to wear
and tear from exposure to physical impact. Were the material used by itself in an
open external environment such as a rooftop, it could be easily damaged by the local
wildlife (eg. possums, birds) or environmental perturbations (eg, hail storms). The
second and most significant disadvantage is the material’s low operational
temperature range. Above 80°C, the polystyrene cell structure starts to degrade. After
prolonged use at relatively high temperatures it becomes rigid and brittle. It is
affected by UV radiation which makes it turn yellow and fragile in a similar fashion
as with high temperatures, so if it were to be exposed to continuous sunlight it would
require some sort of protection. Protection from the elements and environmental
threats could be provided by using an adequate casing structure (metal sheeting,
plastics or even layering the exterior of the collector with some type of rugged paint).
However, the temperature issue cannot be easily solved.
This presented a very serious limitation to temperature operation of the device.
Temperatures in the vicinity of the polystyrene foam could not be allowed to go
beyond 80 °C for a sustained period or the structure would start to melt. Therefore,
air was not allowed to stagnate to high temperatures inside the collector when in full
sunlight so a reflective aluminium paper cover was used at all times on top of the
panel when the system was not operating.
Besides affecting the collector itself, pipe fittings and pipe sections at the entrance
and exit of the collector, would also suffer since the highest operational temperature
for the plastic piping used is 70°C under no pressure (PVC).
Considerable thought was given to the implementation of a temperature control
mechanism from the very beginning and this is why the collector was built with a
large 20 cm buffer zone as described earlier. Initially, a passive control mechanism
was considered whereby two hatches would open (via a bimetallic strip) when the
temperatures reached the undesired value. This would allow ambient air to flow in
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218
the collector reducing the temperature. To assess whether natural convection
established in this manner would be sufficient, the buffer zone included two openings
on each side of the collector that could be left open or closed at will. It was soon
realised that natural convection via these hatches would not be enough to lower the
temperature of the air inside the panel to safe levels.
A second, active, control mechanism was considered using one or more axial fans to
produce the current flow required. In this case, a thermostat and associated electronic
and electromechanical devices would be required to carry on the opening and closing
of the hatches. Power would have to be available for this system to work, so the idea
of using a stand-alone low-powered solar panel was considered. Even though high
flow rates would be needed, the mechanism would only act against the internal
pressure offered by the collector and not the rest of the system. It was believed that
small fans would be able to deliver the necessary flow rate. This idea was also
discarded after a few tests since it became obvious that the added complexity of such
mechanism would not only be a disadvantage in terms of the added amount of
potential failing elements but also would increase the cost of production excessively.
A satisfactory solution to the high temperature hindrance of the system remains open.
The situation is similar with the use of PVC stormwater pipe as the air transfer
medium. A few ideas on how to tackle these problems have been suggested in
chapter 9. In any case, it is concluded that polystyrene is not suitable as a
body/insulation material per se, so if this were to be the intention, then it is
mandatory to consider a temperature control mechanism as well.
Conveyance system, heat exchanger and fan/blower motor
The stormwater PVC piping used was inexpensive, accessible and weather resistant
although a high-temperature material offering the same advantages should be used
for commercial deployment. It was a useful exercise to explore the hydraulic
resistance posed by the system allowing proper determination of motor power
requirements and overall efficiency, providing a simple method for obtaining these.
The maximum temperature drops observed for the air in the pipe was between 5-6°C.
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219
The compact heat exchanger and blower motor used not only proved adequate for the
tasks at hand but being readily available and mass produced items further improved
the cost-effective quality of this system.
Water tank
The water temperature depth profiles measured inside the tank provided a more
direct way for comparison and assessment of temperatures and power delivered to
the water with numerical predictions. It was convenient to modify the same tank used
in the vapour transport system for use with the heat exchanger of this system.
Uncertainties and Inaccuracies:
All temperature measurements had large associated errors and the actual accuracy of
the digital thermometer used was no better than ±0.7°C. Therefore, the results for
power into the water carried a large associated error as well.
The temperature measurements for air exiting the collector were the most difficult to
obtain due to the variability of the temperature measured across the transverse
section of the pipe. Air temperatures at the output of the collector had variations from
65 °C up to 85 °C when the collector was receiving maximum power input.
It is thought that there were three main reasons behind this:
- The air temperature in the collector is higher under the absorber and higher than
model predictions
- Despite having the diffuser, air mixing at the end of the collector did not happen,
allowing a very distinct temperature gradient to exist at the point of exit.
- The abrupt and non-symmetrical expansion of the air at the exit point leaved an
upper, “cold “, section of the transfer pipe with much lower temperatures than the
bottom, extending and maintaining the temperature gradient. However, uniform
mixing occurred farther down the pipe.
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220
Temperatures taken along the pipe were used to determine the average collector
output temperature that would result from uniform air mixing. Still, variations
recorded were between 1°-3° depending on the points of measurement. Turbulence
and the length of the pipe might not allow for these variations to be lower, meaning
that these uncertainties might be unavoidable.
Hot and cold water temperature measurements where taken by placing the
thermocouple on the surface of the uninsulated thermosiphon copper pipes. These
pipes represented a very small surface area and since power losses would be very
small it saved the inconvenience of using insulation on them.
Airflow measurements
For the closed-loop mode, once the system was “opened”, the effect of minor losses
due to the sudden presence of an entrance and exit increased the overall pressure
resistance of the piping and reduced the flow rate. An indirect approach to quantify
this effect was devised with a one-off correlation between anemometer and air bag.
The anemometer was left in a fixed position in the middle of the outer flow pipe and
velocity readings correlated for open and closed loop modes with and without the use
of the air bag. The problem with off-scale readings of the anemometer for the closed
loop mode was solved by positioning the probe against the airflow in a way that
reduced its sensitivity. By knowing the correspondence between air-bag volume flow
measurements and anemometer readings for the open loop, figures for closed loop
were inferred when the piping was opened later on. The higher pressure drop (lower
airflow) for the open loop configuration was evident.
The more accurate calibration done during the second characterisation of the heat
exchanger determined that two calibration factors had to be applied to the raw
anemometer readings in order to obtain a more realistic value of the airflow in the
pipes (Appendix I). However, the fact that its operation is limited to low
temperatures and that it cannot resolve air velocities higher than 10 m/s makes it
unsuitable in the study of these SHWS.
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221
7.7.2 Economics
The system incorporating the air heater panel, even though not passive and requiring
the use of an electric fan/blower motor, was inexpensive compared to the previous
passive system. The reason lay in the materials used. This system had an inexpensive
body/insulation structure, very light and easy to work with. It also had very little
metal, since the heat absorber element was a very thin sheet of aluminium. The
conveyance system was made of plastic stormwater pipes in contrast with more
expensive copper pipes. This not only reduced material costs, but also eased
fabrication costs. By design, it was a system that could be “pieced together” from
readily available parts.
The trade-off, of course, was its active nature and a projected increase in
maintenance, particularly for the motor, and the need of an ‘on/off’ control
mechanism operating the system during useful hours of the day. The stagnation
temperature problem also remains a hurdle to overcome, while the passive system
has no problems in this regard (as long as the self-pumped mechanism works
appropriately). More on the economics of this system is given in chapter 8
7.7.3 Model prediction results
Collector panel
Results for the collector panel revealed that the model underpredicted the output air
temperature, typically by 2°C - 3°C. The obvious suggestion for this would be
inaccuracies of the model, which approximated the absorber profile as if it were a flat
absorber in the middle of the collector chamber with air flowing over and under it
(Figure 7.2c) instead of a series of absorber channels where the air went through and
over them (Figure 7.3a). At the time of construction it was not believed that the
differences between the model and actual absorber profile would result in
temperature differences as high as those observed. On closer look, it could be a
significant factor. However, at this point in time there is no assurance that a more
accurate profile model would explain the differences.
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222
The results of collector output air temperatures indicated that there was a vertical
temperature gradient in the outcoming air and that the temperature was much higher
for the air flowing through the channels than above the absorber. The model used did
not explain this, with temperature predictions for the air under the absorber being
only slightly higher. This indicated that mixing by means of the diffuser and buffer
zone at the end of the collector was not occurring. It also seemed intuitively correct
since the air flowing closer to the bottom of the collector was in contact with a larger
surface from which it could extract heat. It is also true that radiation losses from the
upper side of the absorber were higher than from the inside of the channels, where
the heat was “trapped” and air flowing through them could extract more heat. The
approximate model used could not account for these facts.
Heat exchanger
A similar situation occurred in the modelling of the heat exchanger and
thermosiphon process where assumptions and simplifications such as laminar flow,
an unchanging cold water thermosiphon column and constant exchanger
effectiveness limited the accuracy of calculations. However, as an initial
approximation to the actual thermodynamic behaviour, the modelling for the heat
exchanger was satisfactory.
The use of a ‘modified’ effectiveness as a way to better characterise the exchanger
and provide more accurate modelling showed how output water temperature and
power delivered to the water could be calculated without the need to assume a
constant effectiveness or to use two different effectiveness expressions. Assessment
for more widely variable operating conditions, including low and high irradiance
values, would require the use of a ‘modified’ effectiveness.
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223
7.8 Conclusions
The air heater panel SHWS that was designed and constructed proved to be a
cost-effective system capable of delivering the power needed to satisfy hot water
demands for a 4-person household (30 MJ/day) if properly sized. Based on
experimental and theoretical modelling, the large scale flat-plate absorber-in-the-
middle profile (Figure 7.2c) was the best alternative for this purpose.
With air recycling (closed loop mode), an absorber area of 3.7 m2 was able to deliver
over 1100 W into the water for an average irradiance of 900 W/m2. For 6 hours of
daily operation (9:00 am – 3:00 pm), this meant no less than 23.7 MJ gained by the
water. Higher energies would be obtained by upscaling the area of the absorber. It is
estimated that for an area of 4.8 m2 or greater, the daily average requirement of
30 MJ would be comfortably met.
Results also showed that the average efficiency of the SAHS in closed loop mode
was 33%, although the large associated uncertainties put it between 27%-40%.
Chapter 8 - Economic analysis The purpose of this chapter is to provide a general idea of the costing incurred in the
fabrication of the hot water systems developed and their feasibility as potential
commercial products. It is not intended as a comprehensive techno-economic
analysis, requiring additional knowledge of engineering and manufacturing
processes, marketing strategies, current market energy consumption trends and other
commercial and social related issues. Such an analysis is beyond the scope of this
study.
The systems proposed and costed as more realistic commercial options include
modifications, additions and improvements to the systems developed in this study.
Further explanation and details of proposed changes and improvements for future
work are given in chapter 9.
The elements for each system are outlined in Tables 8.1 and 8.2 in the next pages.
Costing is intended for the materials only, however, as most of it is retail pricing,
some labour costs and profit margins are embedded in them. This also means that the
costs are upper bound figures and it is expected that the total system manufacturing
prices would be less if mass-produced (probably by 15-20% and maybe more).
Detailed added labour costs and profit gains are not particularly discussed here since
it would be all too speculative, but as a general indication they can be classed in the
following way:
⎩⎨⎧ Assembly
- Labour costs Transportation
Installation ⎩⎨⎧ Factory
- Profit gains Distributor
Reseller
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Chapter 8 - Economic analysis
225
8.1 SWHS with passive downward vapour phase heat transport
This is the most labour intensive system of the two developed. The reason being that
the absorber heater element of the panels, being made entirely of copper, required
extensive work and attention to detail, particularly with the application of the solar
selective surface.
The 3rd prototype panel constructed for the system was the most efficient and is the
one referred to here. The panel itself cost about AUD$1400 in materials, for a 2.9 m2
panel aperture and absorber collection area of 2.5 m2. The entire system cost about
AUD$2300, including the vapour transfer line, the insulation and a 200 L water tank
with an internal heat exchanger coil. Costs for a two-panel system would be around
AUD$3700. However, to satisfy the nominal requirement of 30 MJ/day of power
delivered to the water, a 16% increase in absorber area for each panel is required.
With this in mind the total costing is expected to rise beyond $4100 and considering
it is basically for the materials the system must be better costed to become a
competitive option.
The elements and pricing for a proposed, high-efficiency, commercially orientated
unit is given in Table 8.1. The pricing is substantially lower than the previous figures
and the overall cost is comparable to high-end domestic SHWS that retail around
$4500.
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Chapter 8 - Economic analysis
226
Table 8.1 Projected costing for the first system developed15F
*
Elements/Materials Cost (AUD$) Quantities Total
(AUD$)
ZincAlume® casing $16/m2 6 m2 $96 Aluminium reflectors (anodised, 0.3 mm thick) $16/m2 5.5 m2 $88
Cellulose fibre insulation $200/m3 < 0.18 m3 $36 Polycarbonate cover (6 mm thick, Twinwall)
$38/m2 3.6 m2 $137
Boiler tubules (6.4 mm OD) $5.6/m 16.1 m $90
Boiler fins (0.55 mm thick) $5.9/m 15.8 m $93
Header pipes (44.5 mm OD) $41/m 2.4 m $99
Joiners/tubes - Various $20
Abs
orbe
r-bo
iler
mat
rix
Rubber hose $10/m 4 m $40 Maxorb™ selective surface adhesive film $60/m2 2 m2 $120
CO
NC
EN
TR
AT
ING
PA
NE
L
Accessories $120 Assortment $120
TOTAL for 1 panel - 3.6 m2
$939
Copper coil pipe (12.7 mm OD) $6/m 8 m $48
Pipe fittings and joints $5 4 $20
Insulation $7/m 8 m $56
TR
AN
SFE
R
LIN
E
Aluminium tape (roll) $20 3 $60
TOTAL for transfer line $184
Plastic reservoir tank (high temperature)
(refer to text) 20 L $155
Water tank w/electrical booster and heat exchange coil (240 L) $565 1 $565
Condensate collection tank and related accessories (20 L) $40 1 $40
Other accessories $80 Assortment $80
Grand TOTAL for a 2-panel system $2902
* High-efficiency system based on the 3rd prototype panel
Wholesale/trade pricing, including tax
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Chapter 8 - Economic analysis
227
A cost of about $2900 is obtained for the two-panel system and for materials only.
Since this is a very labour intensive system, automation in its fabrication is crucial to
reduce costs. A more detailed look with suggestions for future work improvements is
given in chapter 9, but a brief look into the reason for the elements chosen will allow
for better understanding of the costing done.
The anodised aluminium reflector concentrators are to be produced as a single metal
element formed out from an industrial rolling process with the profile shape desired.
The reflector then goes into the case made out from the zincalume sheet. This leaves
empty space between them, which is filled up with cellulose fibre insulation. On top
goes the absorber-boiler matrix and the system is covered with polycarbonate
double-sheet. The insulation proposed is blown into the empty cavities and is very
economical compared with other expensive and/or labour intensive options (eg.
injected polyurethane). The water reservoir tank is ideally a high-temperature
resistant plastic tank that will not have the problem of rusting and corroding as the
zincalume™ tank had. The price has been inferred from the cost of lower
temperature-graded plastic tanks, assuming the cost for the one desired would be four
times higher.
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Chapter 8 - Economic analysis
228
8.2 SHWS incorporating an air heater collector panel and heat
exchanger-water tank coupling
The air heater collector panel system cost about AUD$1500 to put together from the
building materials and for a 4.3 m2 panel, an absorber collection area of 3.7 m2 and a
200 L water tank. The cost was much less than for the previous system, however, it
did not consider a stagnation temperature control mechanism, or the robustness
required for outdoor exposure, which is necessary for unattended operation in a
domestic environment. Additionally, for 30 MJ/day of power delivered to the water,
a minimum absorber collection area of 4.8 m2 is needed. Automatic operation of the
system was not considered either and would most probably require electronic control
circuitry.
With this in consideration, the costing for a proposed system of this type is given in
the following table where it is seen that total costs for the elements and materials is
still within a reasonable, competitive, range. A tentative solution to the temperature
limitation problem is included by considering a collector structure moulded from
fibreglass reinforced plastic and insulated with cellulose fibre. High density
polyethylene (HDPE) pipes and joints are considered instead of PVC.
This system may offer the possibility of retrofitting to existing conventional domestic
tank units. It would basically depend on the water tank providing extra ports where a
thermosiphon circuit can be attached (some tanks include draining/purging outlets
and other suitable ports)
In this case, installation costs might be higher, especially if modifications to the tank
are required, but the extra expense for a new tank is spared.
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Chapter 8 - Economic analysis
229
Table 8.2 Projected costing for the second system developed
Elements/Materials Cost (AUD$) Quantities Total
(AUD$)
Fibreglass reinforced plastic hollow body
(refer to text) 1 $245
Cellulose fibre insulation $200/m3 < 0.19 m3 $37 Polycarbonate cover (6 mm thick, Twinwall)
$38/m2 5.5 m2 $210
Aluminium absorber (0.1 mm thick)
$2/m2 8 m2 $16
Black paint spray (can) $7 10 $70
AIR
HE
AT
ER
PA
NE
L
Fasteners and washers $0.4 40 pairs $16
TOTAL for 1 panel - 5.5 m2
$594
HDPE pipes (90 mm OD)
$7/m 15 m $105
Pipe fittings and joints $10 8 $80 Insulation $11/m2 4.2 m2 $47
TR
AN
SFE
R
LIN
E
Aluminium tape (roll) $20 2 $40
TOTAL for pipes $272
Air-to-water heat exchanger $135 1 $135 Fan/blower motor (13.5 VDC, 9 A)
$230 1 $230
Power supply (12 VDC, 150 W)
$80 $80
Electronic control mechanism $50 Various $50 Other accessories $50 Assortment $50 Water tank w/electrical booster (240 L) $550 1 $550
Grand TOTAL for a 1-panel system $1961
This proposed commercial option is under $2000 and could come down by $300, or
more when mass-produced. The fibreglass body structure for the panel would
eliminate the high temperature and fragility problems of polystyrene. The figure
quoted in the table has been inferred from the costs of fibreglass reinforced plastic
Wholesale/trade pricing, including tax
Novel approaches to the design of domestic solar hot water systems
Chapter 8 - Economic analysis
230
panels used for glazing and roofing applications. The electronics include the on/off
control mechanism and associated wiring. The ‘other accessories’ include the
insulation of the thermosiphon loop, the wooden case for the heat exchanger and
miscellaneous bits and pieces.
Another possible change is the use of an AC blower motor that would eliminate the
need for a DC power supply, reducing capital costs and running/maintenance costs.
Overall economic appraisal for both systems
Assessment of an accurate final market price for these SHWS is not possible at this
stage, but an approximate indication based on the previous discussion can be given.
For some SHWS the compounded labour and profit price increase (excluding
installation) can reasonably be up to 60%16F
* the manufacturing prices (and probably
not much higher). The current rebate and renewable energy certificate schemes
offered by the state and federal governments, respectively, encourage the adoption of
this technology and these systems would certainly benefit from it, where savings of
up to $1500 on the purchase price are possible (refer to chapter 1).
The following table shows tentative “ballpark” sale prices for the systems assuming a
15% decrease in the costing prices and then a 60% increase from labour and profits:
Table 8.3 Tentative sale prices for commercial versions of the SHWS
SHWS Sale price(AUD$)
After government discount schemes17F
# 1st: Vapour transport $3950 $2450 - $3200 2nd: Hot air transport $2670 $1170 - $1920
* Information obtained from relevant sources in the industry. # $750 from state rebate scheme and up to $750 from energy certificates, depending on location
Novel approaches to the design of domestic solar hot water systems
Chapter 8 - Economic analysis
231
Installation costs can range between $250-$500. They would be less compared to
installation of conventional units, since there is no need to hoist the tank up on the
roof and reinforce the roof.
The second system is clearly more economical and for that reason probably better
suited for near-future commercial deployment. It has clear advantages over the first
one, such as making use of more readily available materials, not being affected by air
leaks, easier to handle and install. The first system, although more detailed and
expensive, is comparable in cost to high-end units on the market and with additional
improvements could become a viable alternative by offering something that no other
system can offer: a remotely coupled, and passive, domestic SHWS of minimal
maintenance.
These prices, however, might still be high and not competitive enough for market
penetration amongst current solar units. Only additional research and in-depth
costing will clarify this. Nevertheless, the general conclusions obtained from this
study and the figures shown here are encouraging. It is believed that additional work
on these systems, each for different reasons, holds potential for a domestic solar hot
water option that will increase adoption of the technology.
Chapter 9 - General discussion, conclusions and avenues
for future work The main objective of this research project was the development of alternate
solutions for domestic solar hot water systems in subtropical latitudes that would
deliver comparable performance to mainstream units and have a few advantages over
them, the major one being a reduced cost. Inexpensive domestic SHWS would
encourage and increase their market penetration and as a consequence it would have
other positive benefits (e.g., reduction in greenhouse gas emissions). The main thrust
of this study has been the production and demonstration of a complete solar hot
water system that can be manufactured inexpensively by combining readily available
materials in a smart and innovative way. To this end two different systems were
designed, built and tested.
The first system concentrated solar energy on a copper absorber-boiler array of fins
and tubes to produce steam from water supplied from a small water reservoir tank.
This steam was the heat transfer fluid that moved downward into a heat exchange
pipe within a ground level water tank, heating the water, condensing and falling into
a containment unit. The operation was entirely passive, since the condensate was
pulled up due to the partial vacuum that occurred after system cooling. Three
collector panel prototypes were built.
The second system used an air heater panel. Air was circulated in open and closed
loop configuration circuits by means of a fan/blower motor, and forced across a
compact heat exchanger coupled to the water tank. This produced a natural
thermosiphon flow heating the water. Two collector panel prototypes were built.
In order to predict performance and characterise the systems, an analytical modelling
approach was followed by simulating heat transfer modes for all the elements of the
systems (using MATLAB™). Heat gains and losses for all elements of the systems
were calculated under normal environmental conditions and system setup, such as,
geographical location, dates and times of the year, collector panel layouts and
orientation.
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Chapter 9 - General discussion, conclusions and avenues for future work
233
The systems developed show potential in satisfying the objective of alternate, low
cost domestic solar hot water systems. Although additional study and research is
required in order to bring these systems to a point of commercial maturity, the
research has shown it is possible to produce SHWS with cost effective and efficient
materials, where not all of them require exclusive manufacturing processes, but can
be “off-the-shelf” type of devices in many cases. This was more so for the second
system developed. In the case of the first system, a viable economic option is
proposed for some of the elements, basically the concentrator reflector and
structure/body of the panels.
Experimental results from the operation of the systems were compared with the
simulation predictions and found to be in reasonable agreement. The analytical
approach used for characterisation of the elements of the system is useful for both
design and system prediction under varied environmental conditions, geometrical
construction and physical properties of the materials involved.
A brief discussion and concluding remarks for each system, with references to
hypothetical future work, is given next.
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9.1 SHWS with passive downward vapour phase heat transport The design of a solar hot water system incorporating downward vapour phase heat
transport was successful, operating in self-pumped mode where water was converted
to steam and delivered down a transfer line providing over 12 MJ/day of effective
energy for domestic hot water, during the winter season. The system used a single
panel configuration (2.5 m2). During early afternoon hours, the collected condensate
was returned back into the panel assembly and reservoir tank, recharging the system,
leaving it ready for operation for the following day.
Three prototype panels were constructed, with the last panel having efficiencies
between 30% and 53% for an irradiance range of about 500-930 W/m2 and providing
the best performance in the SHWS. Radiant energy to hot water energy conversion
efficiencies over 40% were obtained above 700 W/m2.
The system is able to supply the recommended daily energy target of 30 MJ for
domestic hot water by increasing total panel area to about 5.8 m2.
System performance was predicted by the development of an analytical simulation
program that took into account solar energy collection and calculated effective
energy gained by the water based on date, time, geographical position, orientation of
the panels and heat transfer modes between elements. Numerical and experimental
results were in close agreement, and it is concluded that the model was (and is)
useful for investigation and design purposes of systems of this kind. Optical and
geometrical parameters (e.g., absorber emittance, reflectance of CPC walls,
concentration ratios) can be varied and optimised for different geographical and
layout conditions for maximum energy collection.
Compared with other collector panels, having a symmetrical and truncated CPC
profile is an advantage over more complex geometries and the use of evacuated tubes
from a fabrication point of view and is viable for building integration in a similar
way to flat plates. This self-pumped system can cope with steam production and the
reclaiming of the condensate so there is no need for consideration of non-renewable
fluids and/or fluids with hazardous properties that would require system sealing
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235
(such as ethanol). Since the system operates at atmospheric pressure and is open to
the atmosphere at the condensate receptacle tank, there is no need for high-pressure
relief valves that would be necessary otherwise.
The efficiency gains relative to systems with conventional selective surface flat plate
collectors are not very significant. Therefore the advantages lie in the economic
benefits obtainable by exchanging absorber area with reflector area (increased
concentration) and by placing the water store on the ground rather than on the roof
while retaining a passive nature.
Avenues for improvement include modifications and/or use of different materials for:
Structure
- CPC Insulation
Reflectors
- Numerical simulation model
- Absorber-boiler array
- Water reservoir tank
- Hot water tank insulation and heat exchange coil
- Condensate receptacle
- Panel adjustments in situ
Numerical simulation model
The program can be enhanced to include a way of determining the optimum
orientation for year-round energy collection of a CPC, based on geographical and
placement constraints. The analytical approach can also be improved by including
more realistic simulations like multiple ray reflections, better account of truncation
effects and more accurate heat transfer modes between elements. Also, atmospheric
modelling of attenuation can be revised and updated with more accurate
relationships, and even account for regional conditions, if available.
⎩⎨⎧
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CPC structure, insulation and reflectors
The polyurethane material used in the second and third prototype panels was very
convenient since it had a three-fold purpose: structural support, insulation and CPC
profile shaping. It was also capable of resisting temperatures up to 140°C. The
problem was its fragility and elevated cost in terms of the material itself and the
processes involved in its creation and use for prototyping. If stagnation temperatures
in the panels over 140°C are allowed, the material would not be able to endure it. It
is also not biodegradable.
The reflector material used in the third prototype was Silverlux™; expensive and
difficult to integrate in the CPC profile. It offered the highest reflectance, though.
Other materials could be used with the possibility of reducing manufacturing costs.
The structural support and shape may be given by a metal sheet rolling process,
where thin polished aluminium sheets are fed into a machine that gives them the
CPC profile required in an automated fashion. This option could also serve as the
reflecting media.
Mould-formed hollow fibreglass CPC panel structures would also be another
alternative that could then be injection-filled with expanding polyurethane, making it
also an automated process and subject to mass production. The reflector material
would then have to be added on to the fibreglass. High reflectance aluminium tape
and metalised plastics (as with the Silverlux™ used) are two options. A metal box,
similar to the one used (also from zincalume™ sheets) to house the entire panel
elements would be satisfactory.
For insulation, other materials could be used, such as glasswool. Polyester batts are
another option, although it is flammable and non-biodegradable. Cellulose fibre
thermal insulation, made out of pulverised recycled news print and used for roof
insulation, is an inexpensive option that can be applied as an amalgamated powder,
filling up completely the space where it is put. It has excellent insulation and
fire-resistant properties as well as being biodegradable.
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237
There is also evidence that insulation of CPC collector panels in a plywood box has a
small effect (10% improvement) in the reduction of back heat losses compared to
dead air space behind the reflectors138F
139. As long as the reflectors are properly isolated
(physically) from the rest of the structure, it is possible that actual insulation is only
required for the header and return pipes of the panel.
Absorber-boiler array
The heat collection array for every panel was made entirely of copper tubes, pipes
and fins. The actual absorber-boiler represented a very small section of all the copper
mass used. One area of improvement in this regard would be to retain the copper fin
and tubes for heat collection and substitute header and footer pipes, return pipes and
joints by less expensive materials, such as galvanised steel pipes. High temperature
plastic header and footer pipes in a hybrid plastic-metal boiler array could be a
possibility as long as leak-proof joints are feasible. On the other hand, the advantage
of having the entire array made of copper is two-fold:
- it is a very ductile material, easy to work with
- it does not rust (although it will corrode, given the “right” conditions)
The array elements should all be brazed together, forming a much stronger bond than
soft solder can provide. This will certainly minimise vacuum leaks caused by weak
joints. It is noted that for the last prototype, the return pipes were substituted by
high-temperature rubber hosing (section 6.5.4). This should be a standard feature of
construction for any future developments.
It is desirable to have fins with indentations in the middle, as a mild centreline
depression over the entire length, so that the boiler tubes can be easily located and
soldered/brazed onto the fins. This is possible to achieve by a press mould
specifically designed for this purpose at the point of fabrication of the fins. Such
pressing could create a small circular indentation (or even a V-shaped groove)
enough to serve as a rest-point for the tubes and facilitate soldering.
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Water reservoir tank
There was rusting of the interior and input/output junction points of the reservoir
tanks. The reasons for this were the materials chosen for the tank (zincalume™). The
use of a high-temperature plastic tank (e.g. glass reinforced polyester) would
eliminate rusting and corroding. For a SHWS of this kind operating continuously in a
domestic environment, it is necessary to use demineralised water and replenish it as
it evaporates from the condensate collection tank. This would also protect eventual
scaling of the copper absorber-boiler arrays.
Hot water tank, insulation and heat exchange coil
The first area of improvement with the tank is the insulation, since there was little on
the bottom. Ideally, the tank should be located in an easily accessible place.
The heat exchange coil used was a single copper pipe loop located at the bottom of
the tank (Figures 6.14 and 9.1a). It was short since very efficient steam heat transfer
to the water was expected for low water temperatures and it was nearly horizontal in
order to capture most of the sensible heat from the condensate before it was collected
in the receptacle. In the end, however, it appeared that even though heat transfer was
high, it was not as efficient as initially thought. Also, since the condensate was to be
pulled back into the panel assembly and reservoir tank, it was not desirable to have
this cold condensate in contact with the hot water on its way back so that there would
be minimal heat loss from the reclaim action.
However, this arrangement does not provide as efficient hot water volume per
draw-off as that of a stratified tank. The reason is that under stratification more
energy (more hot water) is available at the point of collection. In the current
situation, mixing of the water disperses the energy and lowers the temperature. A
vertical heat exchanger (Figure 9.1b) will produce this stratification with a steep
temperature gradient and is a worthwhile pursuit, especially if the system is not
relying on the self-pumped mechanism for recharge, but includes a return pipe to the
panels, where condensate is delivered with the use of a small pump.
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239
Figure 9.1 Original near-horizontal heat exchanger and proposed vertical arrangement
for hot water stratification
A decision to make is whether the tank will be of the storage/displacement type, able
to withstand mains pressure, or of the heat exchange type where water is drawn via a
copper coil connected to the mains water supply and immersed in an all-copper hot
water tank. The first type is what is commonly used in commercial solar hot water
systems. One of the main reasons for this is that the heat exchange tank requires a
higher temperature in the water (about 10°C higher) to be able to provide the same
energy/day at draw-off point. For every litre of hot water in contact with the coil, an
additional 0.0413 MJ are required. For a 200 L system this equates to about 8.3 MJ
extra and this would necessitate an increase in collector panel absorber area with the
consequent increase in cost. However, a mains pressure tank is a more expensive
option, so a closer look into this issue is warranted.
Condensate receptacle
The condensate receptacle tank should not be insulated as it serves as a heat dump. It
is closed, but not airtight since it should always be at atmospheric pressure. Ideally it
would be transparent so that the level of water remaining after continued evaporation
is easily determined. It could also include a simple electronic monitoring mechanism
to detect low-levels of water and alert the user accordingly. If a condensate return
TAVG
Downcoming steam
Condensate receptacle
Cold
Hot
Exchange coil
a) Horizontal exchange coil
Downcoming steam
Condensate receptacle
Thot
Tcold
Condensate
return pipe
Cold
Hot
Pump
Exchange coil
b) Vertical exchange coil
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Chapter 9 - General discussion, conclusions and avenues for future work
240
pipe is used with a pump (Figure 9.1b), the pump can be connected to a simple mains
timer switch and operated for a few minutes everyday, long enough to recharge the
system. A self-priming diaphragm pump (as the one used) is recommended. The
return pipe would not require any insulation.
Panel adjustments
Maximising energy collection during seasonal changes will improve performance.
Once the panel is given the desired azimuth, tilt and twist angles and the orientation
is fixed, the use of the additional ρ-rotation, which is a rotation of the panel structure
about its normal (in that final position), could improve performance (section 6.3). It
is probably useful to explore incorporating into the panel base a mechanism to allow
movement of the panel in this way. Together with the adequate simulation/modelling
study, a series of predetermined ρ angles applied seasonally could optimise year
round collection. On the other hand, the financial and added complexity implications
(eg. maintenance) of this idea might prove too costly to justify it.
Economics
The last prototype, which was the most efficient, resulted in relatively high
production costs, comparable to high-end conventional SHWS. The main reasons for
this were the amount of metal (copper) and the high quality reflector and selective
surface used. Automating the production of metallic concentrators/reflectors could be
the answer to reduced costs.
There are established techniques in the fabrication of high performance CPC
collectors, with companies around the world providing products of good repute. The
merit of this study in proposing an alternate method to those already available lies
precisely in the search of a cost-effective solution that produces reasonable results by
integrating existing technologies without the need to create specialised processes.
The one issue that remains as the most contentious in this goal of integration and low
cost production is the use and type of a selective surface material.
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241
9.2 SHWS with an air heater collector panel and heat exchanger-
water tank coupling
The design and operation of the air heater panel solar hot water system demonstrated
that a low cost solution for domestic SHWS can be made from readily available
materials. The system operating with air recycling under a reduced solar window of
2.5 hours over summer and spring delivered, on average, over 1100 W into the water.
Over a 6-hour period this would represent an energy gain in excess of 23 MJ (for a
3.7 m2 absorber panel).
Two air panel prototypes were built, the second one being a full-scale unit, for which
efficiencies of up to 33% for the entire system where obtained under air recycling
operation (closed loop configuration) and average irradiance values of 900 W/m2.
By adequately increasing the area of the panel (about 30%) this system can deliver
the minimum daily recommended domestic hot water power of 30 MJ.
System performance was also predicted by analytical modelling translated into a
series of computer programs developed in MATLAB™. The basic code was the
same between the two systems, although the air panel heater system had a more
comprehensive development in the consideration of the different heat transfer modes,
owing also to the fact that more elements were involved. Part of this included a first
approximation in the characterisation of the heat exchanger coupled to the water tank
and responsible for the thermosiphon process. Experimental results and model
predictions were close enough to declare the analytical model useful in system
design and performance prediction. As with the vapour transport system, virtually all
relevant environmental and system parameters were user adjustable.
The system was clearly much more cost effective that its predecessor, however, it did
remain with several unresolved issues specifically, the integrity of the panel under air
stagnation situations. The main aspects to be explored and improved if the system
were to be developed further require a re-evaluation of the material used and/or the
addition of a temperature control system.
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242
Air heater panel
The high stagnation temperature of the system was the most compelling reason to
discard the use of polystyrene as the main material in a hypothetical future
construction of air heater panels of this kind. The (unsuccessful) testing of a couple
of temperature control mechanisms showed that the risks and added complexities
involved in implementing and operating such mechanisms might defeat the purpose
of the project: the cost effectiveness and simpleness intended in the original design.
If a single cover polycarbonate sheet is used, the losses due to top convection will be
higher forcing a lower air temperature inside the collector. It might be possible this
way to achieve the necessary gain-loss balance ratio by which temperatures inside
the collector will never reach 80 °C (provided the motor is in operation). On the
other hand, increased heat losses will result in a reduced efficiency for the collector,
which may be too low for the unit to deliver the necessary power into the water.
Controlling the losses might also be a matter of redesigning the thickness of the walls
of the collector. Since structural stability and robustness depend in great measure on
the amount of polystyrene used, this is not an attractive option. In any case, this is
only a palliative solution since it does not take care of the stagnation problem.
The idea of using a different material as the body/structure of the panel seems like
the most viable option to solve this problem. Additionally, the higher the
temperatures allowed, the higher the power the air can carry away and this might
allow designs of large panels or multipanel systems in series with each other.
In the following page is a comparative chart (Table 9.1) showing the properties of
several materials, their advantages and disadvantages for insulation and/or structural
support. It is not intended as a comprehensive collation of all qualifying physical and
chemical properties and commercial indicators of performance. Rather, its purpose is
to provide a glimpse of a few common building materials available “off-the-shelf”
that could be used for the construction of a solar air heater collector panel.
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243
able 9.1Proposed materials for construction of the solar air hinsulation, body
Tem
pera
ture
L
imit
(°C
)
80
130
80
140
350
200
50
? 350
120 - - - - 70
90
Wea
ther
re
sist
ance
Fair
Fair
Fair
Poor
Hig
h
Poor
Poor
Fair
Hig
h
Hig
h
Fair
Fair
Hig
h
Hig
h
Hig
h
Hig
h
Fire
to
xici
ty
Fair
Fair
Fair
Fair
Nil
Nil
Fair
Low
Low
Hig
h
Nil
Nil
Nil
Nil
Fair
Fair
Fire
ha
zard
Hig
h
Low
Hig
h
Low
Nil
Nil
Hig
h
Low
Nil
Hig
h
Nil
Nil
Nil
Nil
Low
Low
Ade
quat
e fo
r st
ruct
ural
su
ppor
t Po
or
No
Yes
Poor
No
No
Yes
No
Yes
Yes
Yes
Yes
Yes
Yes
- -
Ade
quat
e fo
r in
sula
tion
Yes
Yes
Yes
Yes
Yes
Yes
Poor
Yes
Poor
No
No
No
No
No
No
No
Den
sity
(k
g/m
3 )
15
32
32
36
10
30
> 40
0
100 - - - - - - - -
Rel
ativ
e co
st
Low
Low
Fair
Hig
h
Low
Low
Hig
h
Hig
h
Fair
Hig
h
Low
Fair
Hig
h
Hig
h
Low
Low
MA
TE
RIA
L
Poly
styr
ene
foam
Poly
prop
ylen
e fo
am
Poly
styr
ene
foam
– X
Plyu
reth
ane
foam
Gla
ss w
ool
Cel
lulo
se fi
bre
(CFI
)
Woo
d
Cor
k
Fibr
egla
ss
Hig
h te
mp.
pla
stic
s
Zinc
allo
y st
eel
Gal
vani
sed
stee
l
Stai
nles
s ste
el
Alu
min
ium
PVC
Poly
ehty
lene
(HD
PE)
Tab
le 9
.1
Prop
osed
mat
eria
ls fo
r co
nstr
uctio
n of
the
sola
r ai
r he
ater
pan
el: i
nsul
atio
n, b
ody
stru
ctur
e an
d ou
ter
casi
ng
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Chapter 9 - General discussion, conclusions and avenues for future work
244
With the (functionally limited) exception of polystyrene, none of these materials are
capable of providing good insulation and structural stability simultaneously.
Possibly the best way to obtain the desired collector panel would be to combine the
rigidity of materials such as fibreglass composites or zinc alloy steel (Zincalume™)
with Glasswool sheets, polypropylene foam or cellulose fibre insulation. This would
eliminate the high temperature vulnerability problem that polystyrene faces with a
lightweight, easy to use, relatively inexpensive, safe, weather resistant, robust
combination of materials. Production would be a two step process since the casing of
the collector must first be made and then filled with the appropriate insulation. A
mould would be required to produce a fibreglass casing. If metal sheets were used,
then the shape could be rolled out or machine-pressed. Once the infrastructure is in
place, collector production becomes a routine process.
However, the double cover used (Twinwall®) does not tolerate temperatures above
120°C without sustaining damage so it might have to receive special attention and
maybe consideration given to an alternate cover material. This could also take care of
the warping that arose from its flexibility and high temperature gradient from the
glazing. On the other hand, this polycarbonate top cover is a cheaper alternative
compared to glass, it is easier to handle and easier to work with and carries a 10 year
warranty against loss of light transmission and a 5 year warranty against breakage
caused by hailstones up to 25 mm in diameter. It is also guaranteed UV resistant.
Another option might be to use polystyrene in conjunction with another material. For
example, a large polystyrene collector body with an oversized internal chamber can
be layered with 10 mm corkboard internally and on the top sides of the collector
walls. With this arrangement it might be possible to have very high internal air
temperatures, but the polystyrene being safely insulated by the pre-layered material.
The external polystyrene might then be painted for added robustness and general
protection. This might offer an even more cost-effective solution.
The PVC stormwater pipes would have to be changed to another piping system that
would allow higher air temperatures to be carried continuously, day after day,
without degradation of the material and also be suitable for outdoor use. The material
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245
of choice would be high density polyethylene (HDPE) that can be obtained in the
form of pipes, tubes, fittings and bends as a consumer product and slightly more
expensive than PVC piping. It is also UV resistant. Finally, the insulation used for
the conveyance system would remain the same (Astrofoil™) or a similar product that
minimised both radiation and heat conduction losses and suitable for outdoor use.
Air and water flow measurements
Anemometer readings for airflow calculations were unreliable since they were
strongly dependent on the position of the probe inside the pipes, were limited in scale
(60 L/s max) and were limited to low temperature operation (50°C). Measurements
with the airbag were much more reliable and accurate (within ±5% variations),
although particularly invasive for the closed-loop mode since the piping had to be
opened up to attach the bag. A future improvement on the measurement of air
velocity and determination of airflow rates would be the use of several, more
sophisticated, flow rate meters of little invasiveness left permanently in the piping
system at different spots.
Water flow rates could not be measured due to lack of equipment and time
constraints of the project. A tiny digital water flow rate meter could be used in the
thermosiphon pipe providing instantaneous measurement of water flow rate.
Measurements of irradiance where done with a thermopile that had errors of up to
3%. An improvement here would be to have a more accurate probe and associated
meter. This is an expensive improvement and probably not warranted.
A major improvement in the measurement of all parameters would be to affix all
measuring probes permanently (or semi-permanently) at different places in the
system and couple them with a data logging mechanism.
Additionally, a way of automating daily operation is required. A very simple solution
would be to use a timer-operated relay that would give power to the motor between
predetermined hours of the day (e.g 6:00 am to 6:00 pm). Adjustments would have to
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246
be done for peak summer periods where longer operation times are required and
winter periods where shorter times are sufficient. This solution, however, would have
the motor operating during overcast days and is therefore not an optimum one. A
better option for operation only when enough sunlight is available would be having
the relay switched on when a predetermined light threshold is detected. A
photovoltaic cell or a light sensitive resistor mounted on the panel frame and some
extra circuitry would probably be adequate for this.
An improvement or change in the pressure drop measuring technique for the pipe
system would allow more accurate assessment of the hydraulic resistance and a more
accurate selection of the required pumping power from the fan/blower motor.
Seasonal performance:
The system was tested during early spring and summer seasons. The collector was
tilted at about 30° and North-East orientated such that the global irradiance measured
on the top cover during operation was roughly between 700-1000 W/m2. During the
winter season, physical constraints of the test site restricted operation of the system.
An extension to the study of the effect of winter conditions can certainly be carried
out both numerically and experimentally. The numerical curves shown have been
produced with this in mind, giving an indication of how the system would perform
with a reduced irradiance for open and closed loop operations. The main factor
affecting the operation during seasonal change are the solar position and the ambient
temperature. Besides the reduced irradiance on the collector, during winter,
temperatures drop considerably meaning that losses are increased. It is easy to
simulate this situation numerically and expect to get a reasonably close result to
experimental measurements.
For the characterisation of the air heater prototype system, this extra investigation
would have to be done and the findings on operability during winter; tilt angles and
other recommendations and observations, would be part of the outcome. It would be
ideal to have a system requiring minimal maintenance where, among other things,
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247
the collector panel could be set up to maximise solar contribution during winter and
left like that for all times (e.g., north facing with a tilt angle around 45°).
Numerical simulation model
As it was seen, the modelling of a collector with an absorber plate in the middle of
the chamber and airflow above and below under-predicted the experimental results
obtained from the prototype developed. Instead, the model used for more turbulent
flow (corrugation and fins) gave better results. In actual fact, the absorber-in-middle
model was an approximation to the real scenario which consisted of a series of
absorber channels and the airflow going through and over them (Figure 7.3a).
Modelling for this type of collector would improve the overall modelling scheme. It
would determine if additional investigation in heat transfer aspects were still required
in case the results still did not approximate reasonably well experimental findings.
The model would be more versatile if it took into account tilt and azimuth angles of
the collector and real-time change of irradiance over a day of operation. This was
incorporated into the model prediction for the SHWS. The benefit here would be a
closed solution to performance under real circumstances, from morning to afternoon,
for clear skies with known ambient, cold water temperatures and airflow rates.
The heat exchanger modelling done could be further improved by taking into account
that the temperature and height of the cold water column will change quite drastically
over a full day’s operation (6 hours or more). There is also dependency of the
effectiveness and the efficiency of the exchanger with airflow rates and temperatures.
Including this dynamic behaviour will certainly produce more realistic results.
This would require monitoring the changes in the cold water column, thermosiphon
water flow and water temperatures for a set of known input air power values into the
collector. Measurement of water flow rates would require the least invasive
technique possible, since any material inside the thermosiphon pipe will create
resistance and affect the flow. It is suggested that some type of magnetic flow, or
ultrasonic, transducer could be used although this might be a costly application. Also,
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exploring other modelling techniques for the characterisation of heat exchangers is
worth considering (such as the alternate method discussed in chapter 7).
Similar to the suggested improvements for the collector, more extensive temperature
depth profile measurements would enable a better experimental evaluation of the
actual temperature gradients in the tank and assessment of the energy gained by the
water. This could be done by placing several temperature probes in strategic places,
including the thermosiphon pipes and the inside of the exchanger. Measurements
would then be recorded at real time by a data logging system.
Physical improvement and large scale systems
Besides the high temperature issue requiring changes to the materials used for
prototyping, other changes of the actual design can provide increased performance.
A higher power output can be obtained by reducing the height of the air chamber in
the collector since the efficiency increases for decreasing D/L ratios (Figures 7.35
and 7.37). For the same collector length of 6.5 m, it appears that a chamber height of
30 mm (instead of 50 mm) would certainly mean higher collector efficiency and
more power available. A reduction in height implies less material, therefore more
economical. A flatter collector would be less conspicuous and more appealing from
an architectural point of view. However, it would also mean increased pressure
losses, so careful assessment would be required to determine if the gain would be
sufficiently higher than the losses to justify doing it. Other, more practical, problems
might also arise, like the difficulty of finding appropriate reduction and expansion
fittings adequate to the reduced size of the collector.
Pipe sizes are an important factor as well. Larger pipe diameters imply higher heat
losses but lower pressure losses and vice-versa. Therefore, there is a trade-off
between these two figures and there will be an optimum size for a given airflow rate.
Bends and fittings account for minor losses, which can be quite substantial if care is
not taken in having smooth air-passage trajectories and gradual expansions and
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249
reductions. A deeper exploration into the piping layout and the different connections,
in conjunction with the optimum pipe size, might result in a noticeable decrease in
pressure drops and the system requiring less pumping power or achieving higher
flow rates (and more power transferred as a result).
It was assumed that the efficiency of the exchanger is very high in relation to the
power gained by the water and this might not be the case so better insulation for the
heat exchanger would be another area of improvement.
The possibility of using this system for industrial applications is also feasible and
would imply rescaling of the collector panels and a careful study of the hydraulic
resistance of the transfer pipes and high temperatures issues.
Final words
Both systems developed satisfied the aims and objectives of the project to different
degrees. The vapour transport system has an advantage over the air heating system in
its passive nature. While the air heating system still requires investigation into the
temperature limitation problem, this is not so with the vapour system. Stagnation in
the concentrator panels would be a consequence of the self-pumped mechanism not
working properly, where the reservoir tank would run dry. It is very easy to
determine if this is happening and correct the problem before it is allowed to
continue for an extended period. Under day-after-day operation as evidenced with
the first prototype, this will never happen. Even in the event of this problem ocurring,
localised high temperatures around 200 °C in the vicinity of the absorber boilers
would not be a problem for a brazed structure with the selective surface used. The
top cover would probably require additional assessment under the potential of high
temperatures, but metal reflectors would not be affected by elevated heat inside the
concentrator cavity. On the other hand, the air heater was clearly much easier to
fabricate and much more cost-effective. It is also easier to manipulate, install and
service. Provided the temperature limitation problem is solved, these advantages
might make a future commercial deployment more feasible over the first one.
Appendix A – Mathematical relationships and calculations
in solar geometry and CPC orientation A1 Panel orientation
The qualitative process described in Chapter 2 for orientating and positioning of the
CPC plane involves rotations about preselected axes. These can be accomplished by
3×3 rotation matrices applied to the unit vectors that define the orientation of the
panel (VN) and position of the CPC (VP). The azimuth rotation is a rotation about the
z-axis, while the tilt and twist rotations about the transverse and longitudinal axes of
the plane are actually rotations about the x- and y-axis, conveniently chosen to obtain
the same outcome.
Step 0: Defining unit vectors and matrices
VNpol = (1, 90°, 0) – vector normal to the CPC plane
VPpol = (1, 0, 90°) – vector parallel to the plane and normal to the CPC line-axis
(refer to Figures 2.5 - 2.7)
These vectors can be transformed into their Cartesian form (VN,VP) in order to apply
the rotations required:
( )ϕθ ,,VV mpolar =
( )θϕθϕθ sinV,coscosV,sincosVV mmmcart ⋅⋅⋅⋅⋅= (A.1)
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡−=
xx
xx
cossinsincosX
θθθθ
00
001 – rotation about the x-axis (A.2)
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
−=
yy
yy
cossin
sincosY
θθ
θθ
0010
0 – rotation about the y-axis (A.3)
Novel approaches to the design of domestic solar hot water systems
Appendix A – Mathematical relationships and calculations in solar geometry and CPC orientation
252
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡ −=
10000
xz
zz
cossinsincos
Z θθθθ
– rotation about the z-axis (A.4)
For a rotation θu about an arbitrary vector, ( )w,v,uVU = :
( ) ( ) ( )( ) ( ) ( )( ) ( ) ( ) ⎥
⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
−⋅+−⋅⋅+⋅−⋅⋅+⋅−−⋅⋅+⋅−⋅+−⋅⋅+⋅−⋅⋅+⋅−⋅⋅+⋅−−⋅+
=
uuuuuu
uuuuuu
uuuuuu
coswcoscoswvsinucoswusinvcoswvsinucosvcoscosvusinwcoswusinvcosvusinwcosucos
Uθθθθθθ
θθθθθθθθθθθθ
111111111
2
2
2
(A.5)
Step 1: Applying azimuth, tilt and twist rotations to the CPC panel
For illustration purposes, only vector VN will be used. The same applies for VP.
a) Order of the rotations: azimuth tilt twist:
These operations are equivalent to applying first a rotation in the y-axis, then in the
x-axis and finally in the z-axis.
NN VYXZ'V ∗∗∗= (A.6)
b) Order of the rotations: azimuth twist tilt:
These operations are equivalent to applying first a rotation in the x-axis, then in the
y-axis and finally in the z-axis.
NN VXYZ'V ∗∗∗= (A.7)
The resulting vectors are then transformed back into their polar form to obtain the
effective azimuth and tilt angles that redefine the position of the CPC plane.
( )eff'effN ,,V ϕθ1= (A.8)
The actual tilt angle of the panel is: 'effeff θθ −°= 90 (A.9)
Novel approaches to the design of domestic solar hot water systems
Appendix A – Mathematical relationships and calculations in solar geometry and CPC orientation
253
Step 2: Applying ρ-rotation about the normal to the panel
In section 2.5 it was mentioned that rotations about this angle would not affect the
orientation of the panel, but would change the position of the CPC. It would
therefore be necessary to calculate the new position and this could be done by
applying the rotation matrix of Equation A.5 to vector VP’.
'VU'V PP ∗= δρ (A.10)
Step 3: Determining incidence angle, θinc, on the plane of the CPC panel
The cosine of the incidence angle for direct solar radiation on flat tilted surfaces may
be obtained by one of the following expressions139F
140:
SeffeffSeffeff
Seffeffeffeffinc
hsinsinsincoscoshcossininscos
coshcoscoscoscossincossincossinsincos
⋅⋅⋅+⋅⋅⋅⋅+
⋅⋅⋅+⋅⋅⋅−⋅⋅=
ϕθδϕθφδ
θφδϕθφδθφδθ (A.11a)
( )effSeffzeffzinc cossinsincoscoscos ϕϕθθθθθ −⋅+⋅= (A.11b)
Since the incidence angle will change throughout the day, the final objective is to
determine when this angle will fall within the admittance criterion of the CPC, which
will then indicate energy collection times.
Step 4: Determining solar azimuth, ϕS , altitude, α, and zenith, θz, angles, and
other quantities of interest.
The parameters of Eqs. A.11 have been defined in Table 2.1. Of interest are the
declination, δ, solar altitude and zenith angles, α and θz, solar azimuth angle,ϕs, and
the hour angle, hs. These can be found from different relationships available in the
solar literature, with the later-developed algorithms22 appearing to be the most
accurate and simple to use.
It was also mentioned in Chapter 2 that the solar altitude angle could be determined
from Equation A.11a by considering a flat horizontal surface (θeff = 0°). The
resulting angle in this case is the zenith angle, where α = 90-θz.
Novel approaches to the design of domestic solar hot water systems
Appendix A – Mathematical relationships and calculations in solar geometry and CPC orientation
254
Step 5: Collection angle, θc and collection times are found
From the solar azimuth and altitude angles, solar vectors, VS, for each position of the
sun from dawn to dusk can be obtained (and converted to Cartesian coordinates). To
determine collection times, it was mentioned in Chapter 2 that the collection angle,
θc, must be found. It was also said that this is the angle between the projection of the
solar vector on the transverse plane perpendicular to the panel, VST, and the vector
normal to the surface, VN’, as seen in Figure 2.9. The vector VST therefore has
components on the axes that contain VN’ and VP’. These components are VSP’ and
VSN’, respectively.
It is easy to see that: 'V
'Vtan
SN
SP
c =θ (A.19)
Vectors VSP’ and VSN’ are also the direct projections of the solar vector, VS, on the
said axes via the angles θSP and θSN, respectively. These angles can be obtained from
the scalar product between Vs and VP’, and, Vs and VN’. So one way of determining
the collection angle is the following:
1) Projection angles between VS, and VN’ and VP’ are found:
(A.20)
(A.21)
2) Vector components VSN’ and VSP’ are found:
(A.22)
(A.23)
SNSNNSNS coscos'VV'VV θθ =⋅⋅=•1
1
SPSPPSPS coscos'VV'VV θθ =⋅⋅=•
SNSNSSN coscosV'V θθ =⋅=
SPSPSSP coscosV'V θθ =⋅=
Novel approaches to the design of domestic solar hot water systems
Appendix A – Mathematical relationships and calculations in solar geometry and CPC orientation
255
3) The collection angle is found from these components
'VV'VV
coscos
'V
'Vtan
NS
PS
SN
SP
SN
SP
c•
•===
θθθ (A.24)
⎟⎟⎠
⎞⎜⎜⎝
⎛
••
= −
'VV'VVtan
NS
PSc
1θ (A.25)
Since these are unit vectors, and their coordinates are known, the collection angle can
be readily found. Finally, calculation of irradiance during collection times is done:
If Collection Occurs
Irradiance –Gcb (from Eq. 2.9)
ac θθ ≤ catm cosG θτ ⋅⋅0
ac θθ > 0
The process outlined here was implemented in a MATLAB™ program as part of the
development of this project. A summary of the input and output data for the program
is given in Table A1.
Table A1 Input/Output data for solar geometry modelling program
INPUT DATA OUTPUT DATA
General parameters Internal calculations
• CPC geometrical data (aperture, etc) • CPC optical data (reflectance, etc) • Geographical data (latitude, etc) • Date and time
• Atmospheric attenuation • Effective azimuth and tilt angles • Angle of incidence • Solar azimuth and altitude angles • Energy on collector plane over a day• Collection times
User-defined panel layout Graphs and plots • Azimuth, tilt and twist angles • ρ-rotation (ρ angle)
• Irradiance profile • Collection times
Appendix B – Etendué invariant and optical concentration B1 The etendué invariant and upper limit for concentration
Consider a very general optical system bounded by homogeneous media of different
refractive indices (n and n’ ) (Figure B1).
Figure B1 General optical system and the étendue invariant
P represents the origin of an incident ray on the system from the input media.
P’ is the end point of the same ray after emerging at the output media.
The incident and emerging ray segments are specified in each media by:
- Coordinates P(x,y,z) and P’(x’,y’,z’)
- Direction cosines (L,M,N) and (L’,M’,N’)
The positions of the origins and the directions of the axes for the cartesian
coordinates of each medium are arbitrary. Small spatial displacements for each ray
are, therefore, given by differential increments dx, dy, dx’ and dy’. Similarly, small
changes in angular direction are given by dL, dM, dL’ and dM’. There is then a
two-dimensional spatial displacement for the position of the rays given by the
differential areas dx·dy, dx’·dy’ and of angular extent dL·dM, dL’·dM’ (Figure B2).
The expression for étendue invariance is given by:
n2·dx·dy·dL·dM, = n’2·dx’·dy’·dL’·dM’ (B.1)
P
n
P’
n’
x
y
z
x'
y'
z'
Novel approaches to the design of domestic solar hot water systems
Appendix B – Etendué invariant and optical concentration
257
Figure B2 The étendue for a general optical system (measure of angular displacement
shown for y-coordinate)
Integrating B.1 over the spatial and angular variables allows determination of optical
relationships between input and output rays that depend on the collection and exit
angles and the input and output aperture dimensions.
Consideration is now given to a 2D concentrating system of input and output
apertures 2w and 2w’, and acceptance and exit angles 2θ and 2θ’ (Figure B3).
Figure B3 Two dimensional concentrator of acceptance angle 2θ and output angular
range 2θ’
Since this is a 2D system with rays varying in position and angular displacement
only in the y-coordinate (no x component), the étendue expression of Equation B.1
reduces to:
n·dy·dM, = n’·dy’ ·dM’ (B.2)
In other words, concentration only occurs in the y-dimension. The origin of the
cartesian axes, being arbitrary, is conveniently located about the axis of the system.
This way, the spatial position, y, varies over ±w, which is the extent of the input
aperture. The angular displacement, M, which is the direction cosine for the rays in
P
dy
dx
dM
2θ
2θ
2w 2w’
2θ’
n n' z
y
Novel approaches to the design of domestic solar hot water systems
Appendix B – Etendué invariant and optical concentration
258
the y-direction, varies over the angular collection range ±θ. A similar argument
applies to rays emerging in the output media.
In the system, θsinry ⋅= , where r is the magnitude of the vector representing the
incident ray. Therefore, θsinM = and θθ dcosdM ⋅= .
The integral for the étendue relationship is then:
∫∫∫∫−−−−
⋅⋅⋅=⋅⋅⋅'
'
'
'
w
w
''''w
w
dcosdyndcosdyn ϕϕϕϕθ
θ
θ
θ
(B.3)
( ) ( ) ( ) ( )''' sinwnsinwn θθ ⋅⋅⋅⋅=⋅⋅⋅⋅ 2222 (B.4)
''' sinwnsinwn θθ ⋅⋅=⋅⋅ (B.5)
Relating this to the previous definition of concentration (Equation 3.3)
θθ
sinnsinn
wwC
''
' ⋅⋅
== (B.6)
For fixed values of n and n’, and for any input acceptance angle, θ, the maximum
concentration will be obtained when 2πθ =' , the maximum emergence angle. The
expression for maximum concentration for a 2D system is given by:
θsinwwC '
Dmax
12 == (B.7)
For a 3D system with axisymmetric properties and circular entrance and exit
apertures, w in Equation B.7 becomes the aperture radius, a, and the maximum
concentration is given by (Equations 3.4 and 3.7):
223
⎥⎦
⎤⎢⎣
⎡⋅
=⎟⎠⎞
⎜⎝⎛=
θsinnn
aaC
'
'D
max (B.8)
Appendix C – Mathematical formulation for the design of
the CPC shape and the horizontal fin profile C.1 The CPC reflector shape
Figure C1 Construction of the CPC profile
In Figure C1, the CPC segment (black) is represented as the plot of the function for
that profile in the Cartesian coordinate system with origin O. The polar form equation
for the parabola allows calculation of the vector magnitude for each point on the
segment and to later determine the equivalent (x,y) pair for easy plotting and
representation.
(C.1)
Equation C.1 is later parameterised into the corresponding x and y coordinates to
achieve this. It is therefore necessary to determine the focal length, f, of the parabola
P’ P
θ
2w’
θ
ϕ
2w
L
R r
f
y
x
O
Q
O
( )⎟⎠⎞
⎜⎝⎛
=−
⋅=
21
22 ϕϕ sin
fcos
fr
Novel approaches to the design of domestic solar hot water systems
Appendix C - Mathematical formulation for the design of the CPC shape and horizontal fin profile
260
that generates the segment of interest. As discussed in Chapter 3, this is a parabola
with focal point at P’, vertex O and axis as defined in Figure C1,
with: ⎥⎦⎤
⎢⎣⎡ +∈ θπθϕ
22 ,
Focal point calculation
To find f, the known value of 'wr ⋅=+=
22
θπ
ϑ is used and substituted in Equation C.1:
⎟⎠⎞
⎜⎝⎛ +−
⋅=⋅=
+=θπθ
πϑ
21
222 cos
fwr ' (C.2)
( )θsinwf ' +⋅= 1 (C.3)
Concentration ratio
Firstly: ( )( )
θθ
θθϑ 221
212
sinsinw
cosfQ'Pr
' +⋅=
−⋅
=== (C.4)
Then: ( ) '''
' wsinw
sinsinwsinQ'Pww +=
+⋅=⋅=+
θθθθ 1 (C.5)
Which takes it back to the theoretical maximum for concentration:
Csinw
wsinww '
'
==⇒=θθ
1 (C.6)
Concentrator length (or height)
( ) ( ) θθθ
θθθθθϑ cotww
sincos
sinsinwcosQ'PsinrL '
'
⋅+=⎟⎟⎠
⎞⎜⎜⎝
⎛⋅
+⋅=⋅=⋅= =
12 (C.7)
The x and y coordinates for every point on ( ) 'wsinrx −−⋅= θϕ (C.8)
the concentrator’s surface are given by: ( )θϕ −⋅= cosry (C.9) {
Novel approaches to the design of domestic solar hot water systems
Appendix C - Mathematical formulation for the design of the CPC shape and horizontal fin profile
261
The x-coordinate has been biased due to the selection of the origin in the middle of
the exit aperture, while all values of r originate from P’, located at -w’ from the
origin. The angles have also been biased due to a similar argument, since the axis of
the parabola is tilted by -θ° from the coordinate axes. Plotting Equations C.8 and C.9
will result in the CPC profile shape of Figure 3.10 for the right side reflector wall. A
mirror image about the axis (-x,y) will yield the second segment. This procedure can
be readily employed to fabricate concentrators with plane absorber shapes. The
construction of the horizontal absorber profile of Figure 3.7b, used for the second
and third prototypes is detailed below.
For many convex absorbers (eg. circular cross-section absorbers) obtaining the
required CPC shape can be done via an extension of the edge-ray principle, by
stating that extreme rays at the aperture of the collector must be tangent to the
absorber after one reflection. For plane absorbers, it can be seen that this reduces to
focusing to a single point as already discussed. Its application is more demanding for
absorbers other than plane absorbers however, since it requires specifying and
solving a set of differential equations that characterise the concentrator profile18F
*.
C.1.1 Truncation
In practical applications, the CPC profile is often truncated to reduce size and cost.
The penalty for doing so is small, since the upper half of the reflector in a full-sized
CPC is nearly parallel to the optical axis and has very little contribution to
concentration. The reflector area can be reduced by about 50% without any
significant loss in concentration and even though some rays outside the acceptance
angle can reach the absorber, the resulting gain in radiation at the absorber is very
small 140F
141,141F
142 (Figure C2).
* In the case of 3D problems, the application of this principle is more limited. Other, more general methods of design have to be applied to assure that ideal concentration is reached.
Novel approaches to the design of domestic solar hot water systems
Appendix C - Mathematical formulation for the design of the CPC shape and horizontal fin profile
262
Figure C2 Comparison of the fraction of radiation incident on the aperture of a CPC for
different CPC scenarios (assuming perfect reflectivity)
C.2 The horizontal absorber CPC profile
This section describes the detailed construction of the profile of choice for the
concentrators used in the 2nd and 3rd prototypes for the SHWS (Figure 3.7b).
The profile of the compound parabolic sections for this CPC is shown in Figure C3.
Figure C3 Compound parabolic profile for the horizontal absorber concentrator
3
2
1
P’
SS’
R’ R
Q’ Q
O
A’
B’
C’
x
θ
ϕ3 θ
ϕ1
ϕ2
P
1.0
0.5
ΔΔ
+θ -θ +θ’-θ’
Full CPC
Full CPC with angular surface error Δ Truncated CPC
Novel approaches to the design of domestic solar hot water systems
Appendix C - Mathematical formulation for the design of the CPC shape and horizontal fin profile
263
Following the edge-ray principle, 3 different sections are identified for this profile.
Since the system is a mirror image about its axis, consideration is only given to one
side and then the treatment can be duplicated for the other
C.2.1 Sections of the CPC profile
Section 1: Below the absorber where there is no direct illumination from
extreme rays
This section is made up by curve OS (blue). An involute of the absorber drawn from O
to S and centred at P will result in an arc of a circle.
Section 2: Below the absorber level where direct illumination from extreme
rays is available
This section is defined by curve SR (green). Extreme rays falling on this segment
must be focused on the edge, P, of the absorber. In this case it can be seen that SR is
part of a parabola with focus at P and axis Q’PS
Section 3: Above the absorber level
This section is given by curve RQ (brown). In this case, extreme rays must be
focused on edge, P’, of the absorber. Again, a parabolic section will satisfy this
condition, with a parabola with focus at P’ and axis A’P’B’, parallel to Q’PS.
Similar arguments apply to the construction of the other half of the CPC.
C.2.2 Mathematical formulation of the CPC profile
The origin of the coordinate system is located at the centre of the absorber, O. All
Cartesian equations for the different sections are referred to these coordinates.
Section 1: Arc of a circle with centre at P and radius OP
The equations for this segment are straightforward, noting that the x and y
components are the projections of the radius on each coordinate axis.
Novel approaches to the design of domestic solar hot water systems
Appendix C - Mathematical formulation for the design of the CPC shape and horizontal fin profile
264
ϕcoswwx ''S ⋅−=1 (C.10)
ϕsinwy 'S ⋅−=1 (C.11)
The coordinates are biased according to the displacement from the origin of the
system (at O) since the vector that defines that arc originates from P.
Section 2: Section of parabola with focus at P, focal length PS and axis Q’PS
The parametric equations are determined from the polar equation for the parabola,
( )ϕcosfr
−⋅
=1
2 (C.12)
The focal distance is required, which is given by segment PS. Note that this is the
radius of the arc from section 1.
So the equation for the parabola is:
( )ϕcoswrS −
⋅=
12
2 (C.13)
And the x and y components are then:
( ) wsinrx SS +−⋅= θϕ22 (C.14)
( )θϕ −⋅= cosry SS 22 (C.15)
Bias is only in the x coordinate since the origin for the calculation of rS2 is displaced
+w from the origin of the system.
Section 3: Section of parabola with focus at P’, focal length P’C’ and axis A’P’B’
The focal length for this section is the distance P’C’ which is calculated in the
following way:
Data: ⎥⎦⎤
⎢⎣⎡ +∈ θθπϕ 2
2,
Rearranging Equation B.1:
( )2
1 ϕcosrf −⋅= (B.16)
⎩⎨⎧Data:
⎥⎦
⎤⎢⎣
⎡+∈ θπϕ
20,
'woP =
⎩⎨⎧
Data: 'wPSf ==
⎥⎦
⎤⎢⎣
⎡+∈ θππϕ
22 ,
Novel approaches to the design of domestic solar hot water systems
Appendix C - Mathematical formulation for the design of the CPC shape and horizontal fin profile
265
Also: PRPPr ' +=+θπ
2
, with P'P = 2w and θθπ sin
w
cos
fPR S
+⋅
=⎟⎠
⎞⎜⎝
⎛+−
⋅=
12
21
2 2
Substituting in Equation 3.27 and solving for f:
( )θsinwf 'S +⋅= 23 (C.17)
Finally: ( )ϕ
θcos
sinwr'
S −+⋅⋅
=1
223 (C.18)
With x and y components given by:
( ) wsinrx SS −−⋅= θϕ33 (C.19)
( )θϕ −⋅= cosry SS 33 (C.20)
Bias is now –w in the x coordinate.
Plotting the parameteric equations for these sections will result in the profile shape of
Figure C3 for positive x-values (right hand side). The rest of the profile is obtained
by reflection of these values
C.2.3 Truncation
Truncation was implemented in the
design by limiting the length of
section 3 of the CPC in accordance
with a reduced input aperture
dimension
The final shape of the horizontal CPC
profile is shown, to scale, in Figure C4
the solid black section. The truncated
sections are given by the dotted curves.
Figure C4 Truncated CPC
2θ
Appendix D – Heat transfer parameters and pipe friction Many different parameters have been used in the heat transfer
modelling of both the SHWS developed in this study. The following
relationships and definitions complement the theory developed in
Chapter 4
D1 – Convection transfer and quantities of interest (section 4.2.1)
( )
t
fluidsurface
Pr
LTTgGr
αν
νβ
=
⋅−⋅⋅= 2
3
( )
( )2D
1D
.
.
tfff
LTgPrGrRaαν
β⋅
⋅Δ⋅⋅=⋅=
3
(D.3)
Where: g = 9.8 m/s2
T1
=β
ν = kinematic viscosity (m2/s)
αt = thermal diffusivity (m2/s)
The Prandtl number, Pr, expresses the relative magnitudes of diffusion of
momentum (ν) and diffusion of heat (αt) in a fluid as convection is established. The
subscript f indicates that the properties of Equations D.1 and D.3 are evaluated at the
film temperature, Tf:
( )2
fluidsurfacef
TTT
+= (D.4)
Thus: f
f T1
=→ ββ , ν → νf and ftt αα →
Novel approaches to the design of domestic solar hot water systems
Appendix D – Heat transfer parameters and pipe friction
267
It is advisable to use the film temperature since the properties of the fluid may vary
considerably between surface and free-stream conditions. The characteristic length,
L, in this case is the ratio of the surface area over the perimeter: PAL = .
For a horizontal arbitrary tilted plate (section 4.2.1.1) the parameters used are:
(4.9)
(D.5)
(D.6)
(D.7)
(D.8)
(D.9)
(D.10)
The characteristic length for this case is also: PAL = .
In forced convection over flat plates (section 4.2.1.2), the Reynolds number is given
by:
(D.11)
Where: =mv mean fluid velocity (m/s)
ρf = mass density (kg/m3)
μf = dynamic viscosity (kg/m·s)
x = distance from leading edge of plate (m)
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛+
=
T
lH
HNu.ln
.Nu411
41
418350 Hl
T RaC.Nu H θ⋅⋅=
( ) 94
169
49201
6710
⎥⎦⎤
⎢⎣⎡ +
=
Pr.
.Cl
( )αν
βθθ ⋅
⋅Δ⋅⋅=
30 LTcos,gRa maxH
31
HtHtH RaCNu θ⋅=
⎟⎟⎠
⎞⎜⎜⎝
⎛⋅+
⋅+⋅=
Pr.Pr..CtH 0101
010701140
( ) 1011010
lHtHH NuNuNu +=
νμρ xvxv m
f
mfx
⋅=
⋅⋅=Re
Novel approaches to the design of domestic solar hot water systems
Appendix D – Heat transfer parameters and pipe friction
268
D2 – Pipe friction and the Moody diagram
The characteristic length for convection arising from fluid flow in ducts is called the
Hydraulic Diameter, Dh, which is defined as:
d
dh P
AD ⋅= 4 (D.12)
Where Ad is the flow cross-sectional area and Pd is the wetted perimeter of the duct.
A friction factor that accounts for the frictional resistance in pipes is defined in its
general form as:
2v
f 2m
w
⋅=
ρτ (D.13)
Where: τw = wall shear stress (kg/m·s2)
The relationship for friction used in this study was:
( )[ ] 2
7781750−
⋅= Reln.f (D.14)
The Moody diagram142F
143 that is presented next shows the relationship between friction
and the Reynolds number and how friction is affected by the nature of the flow
(whether its laminar, transitional or turbulent) and by the pipe roughness and
diameter.
The curves in Figure D1 are the result of plotting the implicit equation known as the
Colebrook equation for friction143F
144:
⎥⎥⎦
⎤
⎢⎢⎣
⎡
⋅+
⋅⋅−=
D.fRe.log
f 7351221 ε (D.15)
Where the quantities Re, ε and D have been defined in Chapters 4 and 5.
Novel approaches to the design of domestic solar hot water systems
Appendix D – Heat transfer parameters and pipe friction
269
Figu
re D
1 Fr
ictio
n fa
ctor
s fo
r vs
. Rey
nold
s nu
mbe
r fo
r va
riou
s pi
pe r
ough
ness
and
dia
met
er r
atio
s an
dfo
r la
min
ar, t
rans
ition
al a
nd tu
rbul
ent f
low
Novel approaches to the design of domestic solar hot water systems
Appendix D – Heat transfer parameters and pipe friction
270
For very large Reynolds numbers, the first term in brackets in Equation D.15 is very
small and the resulting equation is that for complete turbulent flow. For smooth pipes
(ε ≈ 0), the second term in brackets is negligible and the result for friction is an
implicit form of f. Similar results are obtainable by the use of Equation D.14 (the
expression used in this study).
The Moody diagram and Equation D.15 are amply referred to in heat transfer, fluid
mechanics and hydraulics literature for pipe system design and fluid flow studies.
Appendix E – Analytical expressions for the heat transfer
dynamics of the CPC panel SHWS E1 – Convection and radiation heat transfer relationships for the
elements of the CPC collector panel system
The expressions used for heat transfer in the determination of power gain and losses
from the CPC panel described in Chapter 6 were based on the simplified heat
exchange modelling between elements, given by Table E1, and the sources and
theory provided in Chapter 4. All relationships refer to the concepts and process
explained in section 6.4.
Table E1 Modelling relationships
Heat transfer modes Configurations used for modelling
Convection Radiation Absorber-Sheath Absorber-Sheath
Two concentric cylinders Sheath - Cover Sheath – Cover
Flat horizontal plate Cover-Surroundings -
Small object in large enclosure - Cover-Sky
1. Convection and radiation from top cover to the environment (hcCA & hrCS)
Convection:
To calculate hcCA, expressions for forced and free convection from the panel open to
the atmosphere were used. To be conservative, the maximum of these two was
selected.
• Free convection calculation:
From Equations 4.7, 4.8 and C1-C4: PA
RaChc
mfCA
CAfree
κ⋅⋅= (E.1)
Novel approaches to the design of domestic solar hot water systems
Appendix E - Analytical expressions for the heat transfer dynamics of the CPC panel SHWS
272
CCA and m are dependent on the Rayleigh number, Raf, evaluated at the film
temperature Tf. A and P are the area and perimeter of the cover, respectively and κ is
the thermal conductivity of the air.
• Forced convection calculation:
From Equations 4.7, 4.10, 4.11 and D.1-D.4:
lRePr.
hc xCAforced
κ⋅⋅⋅=
21
316640
(E.2)
Pr and Re are the Prandtl and Reynolds number, respectively and l is the length of
the cover (which was basically the same as the length of the collector panel).
The final result for convection heat transfer coefficient from the top cover to the
environment, hcCA, was:
[ ] maxCAforcedCAfreeCA hc,hchc = (E.3)
Radiation:
From Equations 4.28, 4.29:
( )( )ambC
skyCcCS TT
TThr
−
−⋅=
44
εσ (E.4)
The equivalent thermal resistance for both convection and radiation heat transfer
from the top cover to the surroundings and to the sky was (from Equation 4.36):
⎥⎦
⎤⎢⎣
⎡+
⋅=CSCA
C hrhcAcR 11 (E.5)
Novel approaches to the design of domestic solar hot water systems
Appendix E - Analytical expressions for the heat transfer dynamics of the CPC panel SHWS
273
1 Convection and radiation between sheath and top cover (hcFC & hrFC)
Heat transfer modes between the sheath and CPC cavity with top cover were
modelled assuming a similar behaviour to heat transfer between concentric cylinders.
Convection:
From Equations 4.21, 4.22:
⎟⎠⎞
⎜⎝⎛⋅
⋅⋅=
FF
nFC
CFC
rrlnr
RaCkhV
δ (E.6)
CFC and n are dependent on the Rayleigh number, Raf. rF and rV are the “effective”
radii for the sheath and CPC cavity, respectively. In the modelling process and
numerical simulation, rV = 0.11m and rF = 0.05 m.
The thermal resistance for this heat transfer mode was (from Equation 4.36):
FCFCFC hcA
R⋅
=1 (E.7)
Radiation:
For radiation transfer, it was assumed that all radiation emanating from the sheath
eventually ended up on the cover (FFC = 1).
From Equation 4.34:
( ) ( )
C
F
C
C
f
CFCFFC
AA
TTTThr⋅
−+
+⋅+⋅=
εε
ε
σ11
22
(E.8)
AF and AC represent the areas of sheath and top cover, respectively.
Novel approaches to the design of domestic solar hot water systems
Appendix E - Analytical expressions for the heat transfer dynamics of the CPC panel SHWS
274
The thermal resistance for this heat transfer mode was (from Equation 4.36):
FCFFCR hrA
R⋅
=1 (E.9)
The equivalent thermal resistance for convection and radiation modes from the
sheath to the top cover, RF, was:
⎥⎦
⎤⎢⎣
⎡+
⋅=FCFCF
F hrhcAR 11 (E.10)
3. Convection and radiation between absorber and sheath (hcAF & hrAF)
Interaction between these two elements was also modelled like two concentric
cylinders exchanging heat. The previous equations are also applied in this case.
Convection:
As for 6.9: ⎟⎠⎞
⎜⎝⎛⋅
⋅⋅=
A
FA
nCF
CabF
rrlnr
RaCkh δ (E.11)
The value for rA was obtained from the original area of the absorber by equating this
value to the area of the modelled cylinder of equal radius:
πWrA = (E.12)
It is noted that this sheath had an oval cross-section because it was a tight fit to the
shape of the absorber-boilers (Figure 6.22).
The thermal resistance for this heat transfer mode was (from Equation 4.36):
AFACAF hcA
R⋅
=1 (E.13)
Novel approaches to the design of domestic solar hot water systems
Appendix E - Analytical expressions for the heat transfer dynamics of the CPC panel SHWS
275
Radiation:
As for 6.11: ( ) ( )
AFA
TTTThrA
F
F
A
FAFAabF
⋅−
+
+⋅+⋅=
εε
ε
σ11
22
(E.14)
The equivalent thermal resistance for this heat transfer mode is (from Equation 4.36):
abFARAF hrA
R⋅
=1 (E.15)
The equivalent thermal resistance for convection and radiation heat transfer from the
absorber to the sheath, RA, was:
⎥⎦
⎤⎢⎣
⎡
+⋅=
AFAFAA hrhcA
R 11 (E.16)
Appendix F – Analytical expressions for the heat transfer
dynamics of the air heater panel SHWS
F1 – Convection, conduction and radiation relationships for heat
exchange between the elements of the air heater SHWS
All expressions used for heat transfer assessment in the SHWS incorporating the air
heater panel are based on the modelling and construction setup described in
chapter 7. The sources used were given and explained in chapter 4.
1. Convection and radiation coefficients from upper side of cover to the
environment (hcCA & hrCS)
Convection coefficient:
To calculate hcCA, expressions for forced and free convection for a horizontal panel
of arbitrary tilt open to the atmosphere were used and the maximum value between
them selected as a conservative measure.
• Free convection calculation
From Equations 4.14, and D.5-D.10:
( )A
PNuNuhchc lHtH
HAfreeQ⋅⋅+
==κ
θ
1011010
1 (F.1)
10tHNu and 10
lHNu are empirical relationships dependent on the Rayleigh and Prandtl
numbers, as well as the tilt angle, θ. A and P are the area and perimeter of the top
cover, respectively. κ is the thermal conductivity of the air.
Novel approaches to the design of domestic solar hot water systems
Appendix F - Analytical expressions for the heat transfer dynamics of the air heater panel SHWS
277
• Forced convection calculation
From Equations 4.7, 4.10,4.11 and D.1-D.4:
lRePr.
hc xAforcedQ
κ⋅⋅⋅=
21
316640
1 (F.2)
Pr and Re are the Prandtl and Reynolds number, respectively and l is the length of
the cover (which was basically the same length of the collector panel).
The final result for convection heat transfer coefficient from the top cover to the
environment, hcQ1A, was:
[ ] maxAforcedQAfreeQAQ hc,hchc 111 = (F.3)
Radiation coefficient:
From Equation 4.29:
( )( )ambC
skyCcskyQ TT
TThr
−
−⋅=
1
441
1 εσ (F.4)
The equivalent thermal resistance for both convection and radiation heat transfer
from the top cover to the surroundings and to the sky was (from Equation 4.36):
⎥⎥⎦
⎤
⎢⎢⎣
⎡
+⋅=
skyQAQCQ hrhcA
R11
111 (F.5)
2. Convection and radiation coefficients from lower side to upper side of cover
(hc21 & hr21)
Convection and radiation relationships between flat plates with tilt angles between 0°
and 75° were used in this case, considering also possible convection suppression (or
enhancement) due to the slats present in the collector’s double cover.
Novel approaches to the design of domestic solar hot water systems
Appendix F - Analytical expressions for the heat transfer dynamics of the air heater panel SHWS
278
Convection coefficient:
From Equations 4.17, 4.19, 4.20, D.3:
(F.6a)
(F.6b)
Where a tilt angle, θ, of 45° for the panel was used for simplicity and to be
conservative. The ‘+’ superscript of the brackets means that non-zero values are to be
taken.
If Ra < 2415, Nuno_slats = 1, there would have been no convection between the plates
and the slats had no effect. Instead, heat transfer would have been via conduction
through the air space. This can be seen from Equation 4.7, which reduces Equation
4.6 to Equation 4.1; that of pure conduction heat transfer:
←=⇒⋅= LkhL
kNuh TT
1
conduction heat transfer coefficient
Note that if Nuno_slats > 1, the ratio from Equation 7.21a above is independent of the
Rayleigh number and the slats may actually enhance convection by up to 50%.
The average temperature of the air between the plates was above 30 °C at all
operational times, since the temperatures of the air exiting the panel were close to
75 °C. It was estimated that the temperature difference, ΔT, between the upper and
lower sides of the cover would rarely reach 40°C. The interplate distance, HS, was
6 mm.
With these values and from Equation D.3, an upper limit value for the Rayleigh
number was found:
slats_noNu44444444 344444444 21
↓
[ ][ ]
⎪⎪⎪⎪
⎩
⎪⎪⎪⎪
⎨
⎧
=⎥⎦⎤
⎢⎣⎡ −⋅+⎥
⎦
⎤⎢⎣
⎡−⋅⎥
⎦
⎤⎢⎣
⎡−⋅+
>⎪⎭
⎪⎬⎫
⎪⎩
⎪⎨⎧
⎥⎦⎤
⎢⎣⎡ −⋅+⎥
⎦
⎤⎢⎣
⎡−⋅⎥
⎦
⎤⎢⎣
⎡−⋅+⋅
⋅
⋅
=++
++
1105024151236814411
110502415123681441111070
1160
31
31
280
280
slats_no
slats_no
max.
max.
slats
NuifRa.RaRa
.
NuifRa.RaRa
.,Ra.
,Ra.
Nu
Novel approaches to the design of domestic solar hot water systems
Appendix F - Analytical expressions for the heat transfer dynamics of the air heater panel SHWS
279
<→⋅
⋅Δ⋅⋅= max
t
Sf RaHTgRa
ανβ 3
800
Therefore, the Nusselt number was always unity and there was no convection arising
between the plates.
Radiation coefficient:
Radiation was calculated by approximation from the formula for radiation exchange
between two infinite parallel plates
From Equation 4.32:
( ) ( )12
2122
21
21−
+⋅+⋅=
C
CCCC TTTThrε
σ (F.7)
The equivalent thermal resistor for these heat transfer modes was:
( )21212
1hrhcAc
RQ +⋅= (F.8)
3. Convection coefficient from airflow in upper channel to lower side of cover
(hcf1C2)
The heat transfer mode in this case was approximated by that of air flowing in a
triangular duct.
From Equations 4.23, 4.24, D.14:
[ ] 21
70240036021
21
71
92211 Cf_smooth..
h
CfCf NuPrRe.
Dhc ⋅
⎭⎬⎫
⎩⎨⎧ ⋅⋅+⋅= −κ
(F.9)
Novel approaches to the design of domestic solar hot water systems
Appendix F - Analytical expressions for the heat transfer dynamics of the air heater panel SHWS
280
The corrugation parameters that defined the dimensions and layout of the fins in the
channels are the following: αr = 90°, pr = 0.09 m, dr = Dh, er = 0.02 m. These values
were used in Equation 4.24 and the result is given in Equation 7.24.
Nusmooth was determined from Equation 4.23 and was dependent on the Reynolds and
Prandtl numbers. It was also dependent on the friction factor.
( )( ) ( )18712071
83
22
1−⋅⋅+
⋅⋅=
Prf..PrRefNusmooth (F.10)
The equivalent thermal resistor for this heat transfer mode was:
( )2121
1
CfCCf hcA
R⋅
= (F.11)
Note that this was the same relationship for:
- Convection heat transfer between fluid in lower channel to back of collector
- Convection heat transfer between absorber and fluid in upper and lower channels
However, also note that BfabfabfCf hchchchc 22121 ≠≠≠ in the most general sense,
because the thermal conductivity, κ, is dependent on the temperatures of the heat
exchanging elements.
4. Radiation coefficient from absorber to lower side of cover (hrabC2)
The area of the V-corrugated absorber, Aab, was larger than that of the collector
aperture, AC.
From Equations 4.4 and 4.34:
( ) ( )
2
222
2
2 11C
ab
C
C
ab
CabCababC
AA
TTTThr⋅
−+
+⋅+⋅=
εε
ε
σ (F.12)
Novel approaches to the design of domestic solar hot water systems
Appendix F - Analytical expressions for the heat transfer dynamics of the air heater panel SHWS
281
The equivalent thermal resistor for this heat transfer mode was:
( )21
1
abCab hrAR
⋅= (F.13)
A radiation shape factor, F12 = 1, was used. In reality, F12 < 1. It can be readily seen,
since the corrugated nature of the absorber necessarily meant that part of the
radiation emitted was re-absorbed, so not all the radiation reached the bottom side of
the cover.
5. Convection coefficient from absorber to airflow in upper channel (hcabf1)
As for Equation 7.24:
[ ] 1
7024003601
1
71
92211 abf_smooth..
h
abfabf NuPrRe.
Dhc ⋅
⎭⎬⎫
⎩⎨⎧ ⋅⋅+⋅= −κ
(F.14)
The equivalent thermal resistor for this heat transfer mode was:
( )1
11
abfab
abfhcA
Rc⋅
= (F.15)
6. Convection coefficient from absorber to airflow in lower channel (hcabf2)
As for Equation 7.28:
[ ] 2
7024003602
2
71
92211 abf_smooth..
h
abfabf NuPrRe.
Dhc ⋅
⎭⎬⎫
⎩⎨⎧ ⋅⋅+⋅= −κ
(F.16)
The equivalent thermal resistor for this heat transfer mode was:
( )2
21
abfab
abfhcA
Rc⋅
= (F.17)
Novel approaches to the design of domestic solar hot water systems
Appendix F - Analytical expressions for the heat transfer dynamics of the air heater panel SHWS
282
7. Radiation coefficient from absorber to back cover (hrabB)
As for Equation 7.26
( ) ( )
B
ab
B
B
ab
BabBababB
AA
TTTThr⋅
−+
+⋅+⋅=
εε
ε
σ11
22
(F.18)
The equivalent thermal resistor for this heat transfer mode was:
( )abBab hrAR
⋅=
12 (F.19)
8. Convection coefficient from airflow in lower channel to back cover (hcf2B)
As for Equation 7.24:
[ ] Bf_smooth..
h
BfBf NuPrRe.
Dhc 2
7024003602
2
71
92211 ⋅⎭⎬⎫
⎩⎨⎧ ⋅⋅+⋅= −κ
(F.20)
The equivalent thermal resistor for this heat transfer mode was:
( )BfC
BfhcA
R2
21
⋅= (F.21)
9. Conduction coefficient from back cover (hB) and the sides (he) of the
collector to the environment
A total conduction loss was calculated as a combination of back losses and side
losses in the following way:
• Losses from the back
Novel approaches to the design of domestic solar hot water systems
Appendix F - Analytical expressions for the heat transfer dynamics of the air heater panel SHWS
283
B
BB x
hΔ
=κ (F.22)
BxΔ = thickness of insulation
• Losses from the sides
These losses were estimated by assuming one-dimensional heat flow around the
perimeter of the collector and referencing them to the collector aperture area93:
( ) TAhAhQ eeCBeB_loss_total Δ⋅⋅+⋅=+ (F.23)
( )C
CS
e
e
C
e
e
e'e wl
wlHxA
Ax
h⋅
+⋅⋅⋅
Δ=⋅
Δ=
2κκ (F.24)
(F.25)
(F.26)
( )C
CS
e
e
b
b
wlwlH
xxhB
⋅+⋅⋅
⋅Δ
+Δ
=2κκ (F.27)
If κe = κB (same material) and Δxe = ΔxB (same thickness), then:
( )⎥⎦
⎤⎢⎣
⎡
⋅+⋅⋅
+⋅Δ
=C
CS
wlwlH
xhB 21κ (F.28)
The equivalent thermal resistor for this heat transfer mode was:
( )eBB AA
xR+⋅
Δ=
κ (F.29)
( ) TAhh C'eB Δ⋅⋅+
TAchB Δ⋅⋅
wC = collector width
44 344 21
Novel approaches to the design of domestic solar hot water systems
Appendix F - Analytical expressions for the heat transfer dynamics of the air heater panel SHWS
284
F2 – Equations and calculations for heat loss in the pipe system of
the air heater SHWS
From the design rationale of section 7.1.1, (airflow rates of 60 L/s at 50°C, air
temperatures above 30°C) and for a pipe diameter of about 90 mm and from
Equation D.11 for the Reynolds number, airflow should always be turbulent (even if
it were to drop to a tenth of its value, i.e., 6 L/s => Re > 4400).
Considering this and since the downpipe to the exchanger was surrounded by a very
good insulator, it was assumed that the temperature of the internal wall, Twin, was
close to the temperature of the fluid, Tf. Therefore, Tf ≅ Twin.
Energy available at the end of a pipe section is given by Q1 (Figure 7.8):
1QQQQ effolossoo ==− −− (F.30)
From Equation 4.35, conduction losses through the walls of a long cylinder are:
( )ooutw
o
outwo
o
outwlosso TT
rrln
LT
rrln
LQ −⋅⎟⎠⎞
⎜⎝⎛
⋅⋅⋅=Δ⋅
⎟⎠⎞
⎜⎝⎛
⋅⋅⋅= −
−−−
κπκπ 22 (F.31)
Furthermore, Qo-loss, is dissipated in the environment mainly by convective currents:
( )outwamb'
cv''
cvo
o
outwlosso TTAhTAhT
rrln
LQ −−
− −⋅⋅=Δ⋅⋅=Δ⋅⎟⎠⎞
⎜⎝⎛
⋅⋅⋅=
κπ2 (F.32)
Where: o
outw'
rat rr
DD
AAA −=
+==
ς2 ; =ς thickness of the insulation
Finally, the resultant energy balance equations are:
( ) ( ) ( ) ( )ambpoutworat
ambop TTCmTTAln
LTTCm −⋅⋅=−⋅⋅⋅⋅
−−⋅⋅ − 12 κπ (F.33)
( ) ( ) ( )amboutw'
cvoutworat
TTAhTTAln
L−⋅⋅=−⋅
⋅⋅⋅−−
κπ2 (F.34)
Appendix G – Polynomial approximations of select
physical properties of air and water G1 - Approximations used in the application of heat transfer theory
for analysis and performance prediction of the SHWS
developed in this study.
In the development of the passive downward vapour phase transport SHWS
(Chapter 6) the numerical simulations and performance prediction of the heat transfer
theory developed required the use of the thermal conductivity, κ, kinematic viscosity,
ν, and thermal diffusivity, αt, for air of varying temperatures within the CPC cavity.
Likewise, the development of the solar air heater panel and associated SHWS
(Chapter 7) also required these quantities to be known, plus the specific heat and
density for the air flowing through the system. Additionally, it required a way of
determining the density and kinematic viscosity of the water in the thermosiphon
loop for varying temperatures.
Numerical calculation of these quantities was done in the programs developed by
approximating accepted values from data tables available in the literature to adequate
polynomial equations.
In this regard, the variation of thermal diffusivity, kinematic viscosity and thermal
conductivity for air vs. temperature were well approximated by linear fits with no
more than 2.5% deviation. The specific heat and density required 2nd order
polynomial fits giving errors below 0.2%. Water density versus temperature was
also approximated by a 2nd order polynomial with excellent results, also giving errors
below 0.2%. Water viscosity required a 3rd order polynomial fit in order for errors to
be below 6% in the range of operating temperatures of the system. Refer to the
tables and plots that follow.
All “accepted” tabulated values are taken from Holman (refer to bibliography).
Novel approaches to the design of domestic solar hot water systems
Appendix G - Polynomial approximations of select physical properties of air and water
286
Table G1 Thermal diffusivity and kinematic viscosity for air at atmospheric
pressure
Temperature Thermal diffusivity, αt Kinematic viscosity, ν (K) (°C) (m2·s-1·10-5) (m2·s-1·10-5)
Fit Fit
250 -23 1.568 1.532 1.131 1.105 300 27 2.216 2.267 1.569 1.595 350 77 2.983 3.002 2.076 2.085 400 127 3.760 3.737 2.590 2.575
Error (max) 2.3% 2.4%
Table G2 Thermal conductivity, specific heat and density for air at
atmospheric pressure
Temperature Thermal conductivity, κ Specific heat, Cp Density, ρ (K) (°C) (W·m-1·°C-1) (kJ·kg-1·°C-1) (kg·m-3)
Fit Fit Fit
250 -23 0.02227 0.02225 1.0053 1.0048 1.4128 1.4137 300 27 0.02624 0.02605 1.0057 1.0058 1.1774 1.1761 350 77 0.03003 0.02985 1.0090 1.0087 0.9980 0.9985 400 127 0.03365 0.03365 1.0140 1.0136 0.8826 0.8809 Error (max) 0.8% 0.05% 0.2%
Fit equations: 57 1087110471 −− ⋅+⋅⋅= .T.airα (G1)
58 1033110809 −− ⋅+⋅⋅= .T.airν (G2)
25 1040210607 −− ⋅+⋅⋅= .T.airκ (G3)
00511071104 527 .T.TCairp +⋅⋅+⋅⋅= −− (G4)
297110841021 325 .T.T.air +⋅⋅−⋅⋅= −−ρ (G5)
Novel approaches to the design of domestic solar hot water systems
Appendix G - Polynomial approximations of select physical properties of air and water
287
(a)
(b)
Figure G1 Plots of the linear fits for thermal diffusivity, kinematic viscosity and thermal conductivity of air vs. temperature
Thermal conductivity of air vs. temperature
y = 7.6E-05x + 2.4E-02
R = 0.9995
0.021
0.023
0.025
0.027
0.029
0.031
0.033
0.035
-40 -20 0 20 40 60 80 100 120 140
Temperature (°C)
Ther
mal
con
duct
ivity
(W/m
·°C
)
Temperature (K)
Physical properties of air vs. temperature
1.00
1.25
1.50
1.75
2.00
2.25
2.50
2.75
3.00
3.25
3.50
3.75
4.00
-30 -20 -10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140
Kin
emat
ic v
isco
sity
& T
herm
al d
iffus
ivity
(m2 /s
)·10-5
y = 1.469E-07x - 2.142E-05
R = 0.9991
y = 9.768E-08x - 1.333E-05
R = 0.9993
Kinematic viscosity
Thermal diffusivity
Novel approaches to the design of domestic solar hot water systems
Appendix G - Polynomial approximations of select physical properties of air and water
288
(a)
(b)
Figure G2 Plots of polynomial fits for specific heat and density of air vs. temperature
Specific heat of air vs. temperature
y = 4E-07x2 + 1.7E-05x + 1.005 R = 0.9985
1.004
1.005
1.006
1.007
1.008
1.009
1.01
1.011
1.012
1.013
1.014
1.015
1.016
-40 -20 0 20 40 60 80 100 120 140 Temperature (°C)
Spe
cific
Hea
t (kJ
/kg·
°C)
y = 1.2E-05x2 - 4.8E-03x + 1.297 R > 0.9995
0.85
0.90
0.95
1.00
1.05
1.10
1.15
1.20
1.25
1.30
1.35
1.40
1.45
-30 -20 -10 0 10 20 30 40 50 60 70 80 90 100 110 120 130
Density of air vs. temperature
Temperature (°C)
Den
sity
(Kg/
m3 )
Novel approaches to the design of domestic solar hot water systems
Appendix G - Polynomial approximations of select physical properties of air and water
289
Table G3 Selected properties for water at atmospheric temperature
Temp. Dynamic viscosity, η Density, ρ (°C) (kg/m·s)·10-4 (kg/m-3)
Fit Fit
0 17.9 17.6 999.8 998.0 4.44 15.5 15.6 999.8 997.9 10 13.1 13.3 999.2 997.6
15.56 11.2 11.4 998.6 997.0 21.11 9.80 9.85 997.4 996.2 26.67 8.60 8.53 995.8 995.2 32.22 7.65 7.44 994.9 993.8 37.78 6.82 6.56 993 992.3 43.33 6.16 5.87 990 990.5 48.89 5.62 5.32 988.8 988.4 54.44 5.13 4.89 985.7 986.1
60 4.71 4.56 983.3 983.6 65.55 4.30 4.28 980.3 980.8 71.11 4.01 4.04 977.3 977.8 76.67 3.72 3.79 973.7 974.5 82.22 3.47 3.52 970.2 971.0 87.78 3.27 3.19 966.7 967.2 93.33 3.06 2.76 963.2 963.2 Error (max)
5.5% 0.2%
Fit equations: 0017601085410261092 52739 .T.T.T.wat +⋅⋅−⋅⋅+⋅⋅−= −−−η (G6)
9980040 2 +⋅−= T.watρ (G7)
Novel approaches to the design of domestic solar hot water systems
Appendix G - Polynomial approximations of select physical properties of air and water
290
(a)
(b)
Figure G3 Plots of the polynomial fits for selected physical properties of air vs. temperature
Water density vs. temperature
y = -0.004x2 + 998
960
965
970
975
980
985
990
995
1000
1005
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
Temperature (°C)
Den
sity
(kg/
m3 )
Water viscosity vs. temperature
0
0.0002
0.0004
0.0006
0.0008
0.0010
0.0012
0.0014
0.0016
0.0018
0.0020
0 10 20 30 40 50 60 70 80 90 100 Temperature (°C)
Vis
cosi
ty (k
g/m
·s)
y = -2.90E-09x3 + 6.20E-07x2 - 4.85E-05x + 1.76E-03
Appendix H – Air/water heat exchanger and fan-blower
motor H1 – Compact heat exchanger (heater core) used in the air-to-water
heat exchanger-water tank coupled SHWS
The heat exchanger core used is fabricated for cabin air heating of motor cars,
specifically: Toyota Corona vehicles from 1983 through 1996, Nissan model 200B
and Toyota Camry ST141.
Table H1 Specifications for the heat exchanger core
Manufacturer Denso Pty Ltd – 0Hwww.denso.com.au Part No. ND803 (also HTR 803.N8T) Body construction Copper core Heater core dimensions 160cm × 160cm × 49cm Top header dimensions 160cm × 59cm Bottom header dimensions 160cm × 59cm
Figure H1 Picture-schematic of original heater core used as a heat exchanger
Novel approaches to the design of domestic solar hot water systems
Appendix H - Air/water heat exchanger and fan/blower motor
292
H2 – Centrifugal fan-blower motor used in the air-to-water
heat exchanger-water tank coupled SHWS
This unit is used as a source of pressurised air for ventilation and heating systems,
particularly for cabin heating of buses and trucks.
Table H2 Specifications of the fan/blower motor
Manufacturer Torin Fans & Blowers Pty Ltd
Model No. H30730 Nominal voltage 13.5 Volts DC
Low 65 Medium 93 Nominal airflow –
free discharge (L/s) High 130 Low 5.2 Medium 9 Nominal current
(A) High 16.8 A 106 × 106
Dimensions (mm) B 90
Figure H2 Picture-schematic of the fan/blower
B
A
Appendix I – Anemometer calibration
I1 – Two-step calibration process for accurate anemometer readings For the final study of variations in exchanger effectiveness with changing
temperatures and flow rates of the fluids (section 7.5.2) the anemometer was used to
determine airflow rates. Since its operation was deemed unreliable at the early
stages of the project, a more comprehensive look into the anemometer readings and
more accurate calibration with known airflow rates was obtained.
The calibration was done in a two step process:
1- First the velocity profile for airflow across the transverse area of the pipes was
measured. Readings of air speed were taken at different distances from the wall
of the pipe. A polynomial expression was fitted to the experimental data
(Figure I1) and an average flow rate was determined by integration over the
transverse area of the pipe. The ratio between this average and the value
obtained from the peak reading at the centre of the pipe resulted in a primary
calibration factor, cal1. Since experimental measurements were taken with the
anemometer in the centre of the pipe, this calibration allowed for a more accurate
account of the (real) average airflow speed. The result, however, required
another calibration against known air speed values since there was no way of
knowing if the absolute readings of the anemometer were accurate or not.
2- The anemometer was then fixed to the outer edge of a rotary clothesline (Hills
Hoist) of 2.6 m radius, which was rotated at a constant pace for different periods.
The tangential speed at its periphery was easily determined from the number of
turns it was given over the period of measurement. Several runs were made for
increasing air speeds and the results were compared with the values for airflow
speed obtained from the anemometer. A linear correlation between the data was
obtained and from there a secondary calibration factor, cal2 (Figure I2).
Novel approaches to the design of domestic solar hot water systems
Appendix I – Anemometer calibration
294
Figure I1 Speed profile for airflow in the pipes vs. transverse distance and polynomial fit
The ratio of the average flow rate to the maximum flow rate obtained from the peak
speed measured at the centre of the pipe gives the first calibration factor.
From Equation 5.19: pipepeak_airpeak_air Areav ⋅=Φ (I.1)
Where: sL
sm
peak_airpipe
sm
peak_air.
m.Area
v290290
1085
53
23 =≈Φ⇒⎪⎭
⎪⎬⎫
⋅=
=−
From the polynomial fit: [ ] 5080010 24 +⋅−⋅−= r.r.vs
m)r( (I.2)
The average flow rate is found by integrating over the area:
drrv )r(
.
air ⋅⋅⋅=Φ ∫ π234
0 (I.3)
sL.
sm.rr.r.
.
air 118018101050403010 3
4
34
0
246 =≈×⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛⎥⎦
⎤⎢⎣
⎡⋅+⋅−⋅−⋅=Φ −π
6201 .calpeak_air
air ≈Φ
Φ= (I.4)
Transverse speed profile of airflow in the pipe system
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
-5 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Distance from the centre of the pipe (cm)
Air
spee
d (m
/s)
y = -0.01x4 - 0.08x2 + 5 R2 > 0.99
Pipe radius = 4.3 cm
Novel approaches to the design of domestic solar hot water systems
Appendix I – Anemometer calibration
295
Figure I2 Correlation between anemometer readings and known air speed values
showing a strong linear fit to the data.
The linear fit to the data allows a more accurate determination of real airflow speeds
from the anemometer:
250650 .v.v anem_airreal_air −⋅≅ (I.5)
The second calibration factor is the ratio of the two airflow speeds:
anem_airanem_air
real_air
v..
vv
cal 2506502 −== (I.6)
This factor is not static and should be built into the calculations for each anemometer
reading. However, for simplicity, it is possible to use a constant value provided
airflow rates do not change much. For the calculations of section 7.5.2, where two
different airflow rates were used (10.8 m/s and 7.5 m/s), a constant calibration factor
of 0.62 was applied
Calibration curve for anemometer against known airflow speeds
y = 0.65x - 0.25
R2 > 0.99
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5
Anemometer readings (m/s)
Acc
urat
e ai
r spe
ed m
easu
rem
ents
(m/s
)
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