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I Theoretical Simulation of Solar Chimney Asst.Prof. Dr. Hani Aziz Ameen Dr. Kayser Aziz Ameen Dies and Tools Eng. Dept. Dept. of Power Eng. Technical College – Baghdad College of Engineering University Of Baghdad Keywords: thermodynamics, s olar chimney, power plant , turbine, collector Abstract The objective of this study was to evaluate the solar chimney performance theoretically. A mathematical model was developed to estimate the effects following parameter (height of chimney, floor diameter, height of air inlet, height of turbine and efficiency of deck (collector)) on the power output and it found that when increasing the floor diameter and when increasing the height of chimney, obtained increasing the power output, but the effect of height of air inlet on the power output. The results showed that when increase the height of air inlet this lead to decreasing in power output. The effect of position of turbine is less than others parameters, when increasing the height of turbine that lead to little increasing in power output. Finally the effect of efficiency of deck or collector, when increasing the efficiency of deck that leads to increasing in power output. Nomenclature A surface area, m 2 c D chimney wall thickness coefficient c p specific heat at constant pressure, J/(kg K) D diameter, m E energy, W g o gravitational acceleration, m/s 2 H height or altitude, m H e height of air inlet, m H T height of turbine, m Theoretical Simulation of Solar Chimney Dr.Hani Aziz Ameen PDF created with pdfFactory Pro trial version www.pdffactory.com

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I

Theoretical Simulation of Solar Chimney Asst.Prof. Dr. Hani Aziz Ameen Dr. Kayser Aziz Ameen Dies and Tools Eng. Dept. Dept. of Power Eng. Technical College – Baghdad College of Engineering

University Of Baghdad Keywords: thermodynamics, solar chimney, power plant , turbine, collector Abstract

The objective of this study was to evaluate the solar chimney

performance theoretically. A mathematical model was developed to

estimate the effects following parameter (height of chimney, floor

diameter, height of air inlet, height of turbine and efficiency of deck

(collector)) on the power output and it found that when increasing the

floor diameter and when increasing the height of chimney, obtained

increasing the power output, but the effect of height of air inlet on the

power output. The results showed that when increase the height of air

inlet this lead to decreasing in power output. The effect of position of

turbine is less than others parameters, when increasing the height of

turbine that lead to little increasing in power output. Finally the effect of

efficiency of deck or collector, when increasing the efficiency of deck

that leads to increasing in power output.

Nomenclature A surface area, m2 cD chimney wall thickness coefficient cp specific heat at constant pressure, J/(kg K) D diameter, m E energy, W go gravitational acceleration, m/s2 H height or altitude, m He height of air inlet, m HT height of turbine, m

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h convective heat transfer coefficient, W/(m2 K) K thermal conductivity W/(m K) M air mass flow rate, kg/s Nu Nusselt number P power, W Pr Prandtl number P absolute static pressure, Pa R 287.04 J/(kg K), individual gas constant (for air) Re Reynolds number S solar radiosity, W/m2 SCPP solar chimney power plant T absolute temperature, K v flow velocity, m/s

Greek α Absorptivity β angle, deg ε emissivity ϕ view factor η efficiency ηT internal efficiency of turbine ν kinematic viscosity coefficient, m2/s ρ density, kg/m3 σ = 5.6693 × 10−8 W/(m2K4): Boltzmann constant for black

radiation τ Transmissivity Subscripts a Air ch chimney d Deck eff effective f Floor P turbine power Q Heat sky Sky T turbine x, y different surface o environment 1, 2, 3 localities shown in Figure 2-1

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1-1 Introduction A solar updraft tower power plant – sometimes also called 'solar

chimney' or just ‘solar tower’ – is a solar thermal power plant utilizing a

combination of solar air collector and central updraft tube to generate a

solar induced convective flow which drives pressure staged turbines to

generate electricity.

Sensible technology for the wide use of renewable energy must be

simple and reliable, accessible to the technologically less developed

countries that are sunny and often have limited raw materials resources. It

should not need cooling water and it should be based on environmentally

sound production from renewable or recyclable materials[1].

A technology of solar chimney power generation is not new in

power generation sector, world over as shown in figure (1-1) . The Sun’s

radiation heats a large body of air, which is then forced by buoyancy

forces to move as a hot wind through large turbines to generate electrical

energy. Solar chimney power plants, with an output of 5-200 MW,

require a transparent roof several kilo meters in diameter, and the tube has

to be as high as possible to achieve a large output. With the use of

materials of better absorbing radiation, both the diameter of the base of

the chimney as well as its height may be substantially reduced. On this

basis, solar chimney plants are appropriate on land with no natural

vegetation, such as desert regions [2].

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Figure (1-1) Solar Chimney

The solar tower meets these conditions. Economic appraisals based

on experience and knowledge gathered so far have shown that large scale

solar towers are capable of generating electricity at costs comparable to

those of conventional power plants. This is reason enough to further

develop this form of solar energy utilization, up to large, economically

viable units. In a future energy economy, solar towers could thus help

assure the economic and environmentally benign provision of electricity

in sunny regions.

1-2 History Review The solar updraft tower’s three essential elements – solar air

collector, chimney/tower, and wind turbines - have been familiar for

centuries. Their combination to generate electricity has already been

described in 1931 by Günther,. Then at (1983, 1984) Haaf gives test

results and a theoretical description of the solar tower prototype in

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Manzanares, Spain with an output from 50 to 200 MW. For Australia, a

200 MW solar tower project is currently being developed. Conditions in

Australia are very favorable for this type of solar thermal power plant:

Insulation levels are high, there are large suitably flat areas of land

available, demand for electricity increases, and the government’s

Mandatory Renewable Energy Target (MRET), requires the sourcing of

9,500 gig watt hours of extra renewable electricity per year by 2010

through to 2020[1].

1-3 Advantages and Disadvantages of Solar Chimneys

Advantages of solar chimneys are: • solar chimney power stations are particularly suitable for generating

electricity in deserts and sun-rich wasteland,

• it provides electricity 24 hour a day from solar energy alone,

• no fuel is needed; it needs no cooling water and is suitable in extreme

drying regions,

• it is particularly reliable and a little trouble-prone compared with other

power plants,

• the materials concrete, glass and steel necessary for the building of solar

chimney power stations are everywhere in sufficient quantities, and

• no ecological harm and no consumption of resources. Disadvantages are:

• some estimates say that the cost of generating electricity from a solar

chimney is five time higher than produced by gas turbine; although fuel

is not required, solar chimneys have a very high capital cost.

• The structure itself is massive and requires a lot of engineering expertise

and materials to construct[3].

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1-4 The Characteristics of This Solar Chimney The characteristics of this solar chimney power plant are listed

below[4].

• Efficient solar radiation use. The hot air collector used in the system,

can absorb both direct and diffused radiation. Thus the solar chimney

can operate on both clear and overcast days. The other major large-scale

solar thermal power plants, which are often driven by high temperature

steam generated from solar concentrators, can only use direct radiation.

• Free dual functions, natural energy storage, and greenhouse effect. The

collector pro-vides storage for natural energy, as the ground under the

transparent cover can absorb some of the radiated energy during the day

and releases it in the collector at night. Thus solar chimneys also

produce a significant amount of electricity at night. The collector it-self

can also be used as a greenhouse, which will benefit agriculture

production accordingly.

• Low operation cost. Unlike conventional power stations, and also other

solar. Thermal type power stations, solar chimneys do not need cooling

water. This is a key ad-vantage in northwestern China where there have

already been problems with drinking water.

• Low construction cost. The building materials needed for solar

chimneys, mainly concrete and transparent materials are available

everywhere in sufficient quantities. Particularly important is that no

investment in a high-tech manufacturing plant is needed, as both wind

turbine and solar collectors are well developed industrial products.

1-5 Functional Principle The solar tower’s principle is shown in figure (1-1). Air is heated

by solar radiation under a low circular transparent or translucent roof

open at the periphery; the roof and the natural ground below it form a

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solar air collector. In the middle of the roof is a vertical tower with large

air inlets at its base. The joint between the roof and the tower base is

airtight. As hot air is lighter than cold air it rises up the tower. Suction

from the tower then draws in more hot air from the collector, and cold air

comes in from the outer perimeter. Continuous 24 hours operation can be

achieved by placing tight water-filled tubes or bags under the roof. The

water heats up during day-time and releases its heat at night. These tubes

are filled only once, no further water is needed. Thus solar radiation

causes a constant updraft in the tower. The energy contained in the

updraft is converted into mechanical energy by pressure-staged turbines

at the base of the tower, and into electrical energy by conventional

generators[1].

1-6 The Maintenance of Solar Chimney In terms of operation and maintenance, solar updraft towers and

solar panels are the easiest plants to run. Neither requires any consumable

input. Both are very resistant to environmental exposure. Solar panels

have no moving parts, and a broken unit can simply be wired out of a

system. The one delicate part of a solar updraft tower, the turbine, is

protected from the worst environmental effects at the base of the

chimney. The rest of the plant also has very low failure rates.

Glass panels from the collector are relatively easily replaceable by

local materials, and the plant can function acceptably with a low number

of missing panels. Because of these infrequent failure and minimal input

requirements, neither type of plant requires the attentions of a group of

service personnel. While it is desirable to have a full time maintenance

staff, these plants could be tended very infrequently.

The low maintenance requirements may also be an important factor

in the decision to construct solar updraft towers in remote communities.

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Specialty replacement parts are not required for these plants; basic

maintenance of the collector can be performed by those skilled in

construction labor. The feathering turbine of a solar updraft tower is the

only complex, actively controlled part in the system, but the turbine can

function with the blades set at a fixed angle with a reduction in efficiency.

In general, solar updraft towers are very robust.

On the other hand power towers share many of the same issues as

trough plants; water use for evaporative cooling, maintenance costs for

cleaning and operating the mirrors, and the inability to operate in cloudy

conditions. Additionally, power towers have the disadvantage that they

typically have to be built as large units, as opposed to many other solar

technologies[2].

1-7 The Aims of Study High solar radiation and ambient temperature, and large desert in

Iraq are excellent conditions to install efficiently solar chimney power

plants there. Therefore this research aimed to develop a validated

mathematical model of solar chimney. It is proposed to improve the

performance of solar chimney under effects of various parameters. The

mathematical simulation of the solar chimney has been developed

including all its performance parameters, dimensions (of deck (collector),

chimney, etc). The mathematical model has been used to predict the

performance of the solar chimney power plant.

2-1 Theoretical Analysis of Solar Chimney Analysis of a solar chimney power plant (SCPP) is presented in

this chapter. The SCPP is typical of many possible examples of power

plants driven by solar radiation. The overall process of power generation

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in the SCPP is very complex. Up to the present date, only selected aspects

have been studied. The present study attempts to develop an analysis of

the total SCPP process. The complexity of such a thermodynamic object

forces many simplifying assumptions.

Although not easy to prove, it is supposed that the proposed

mathematical thermodynamic model has enough information to determine

the effects of varying input parameters on the SCPP output parameters,

especially determining the trends for these effects.

The proposed model involves some magnitudes that, although they

do not precisely determine a real situation (e.g., the effective temperature

of a surface or the average convective coefficients of heat transfer), they

must, however, not be assumed constant, i.e. they have a certain freedom

to vary and respond to show their approximate values and trends of

variation(5).

2-2 Description of the solar chimney model A typical SCPP consists of a circular greenhouse-type collector

with a tall chimney at its center. Air flowing radially inward under the

collector deck is heated from the collector floor and deck, and enters the

chimney through a turbine.

Figure (2-1) depicts an example of an SCPP selected for the

present study. Draft-driven environmental air (point 0) enters the

collector through the gap of height He. The collector floor of diameter

(Df) is under the transparent deck, which declines appropriately to ensure

the constant radial cross-sectional area for the radially directed flow of

the air. The collector floor preheats air from state 0 to state 1 (state 1

prevails in the zone denoted by a dashed line). The preheated air (state 1)

then expands in the turbine to state 2. The turbine inlet and outlet

diameters are D1 and D2, respectively. The height of the turbine is HT (H1

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+ HT = H2). Expanded air leaves the SCPP (at point 3) through the

chimney at height H3. For the established geometrical parameters of the

collector– turbine–chimney system, and for the constant thermodynamic

input data such as solar radiation intensity and environment parameters,

the system spontaneously self-models itself in response to the actual

situation. This means that the buoyancy effect determines the flow rate of

air through the system as well as all the air parameters, temperature, and

pressure along the path of the air flow[5].

Figure (2-1). Scheme of the considered SCPP[5]

2-3 The Main Assumption for the simplified the model of SCPP[5] 1- The floor has no heat loss to the soil. It is perfectly insulated and is

perfectly black (emissivity εf = 1). Thus, there is no solar energy

reflected from the floor. It is worth noting that a further

simplification, not applied in the present consideration, could be

the assumption that the floor material be of almost infinitely large

conductivity, which then could motivate the assumption of a

constant temperature of the floor in the entire collector.

2- The deck material is prepared in such away that it is almost

perfectly transparent for solar radiation (transmissivity τ = 0.95)

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and the remaining part (5%) of solar radiation arriving at the deck

is reflected. However, the deck material absorbs perfectly

(absorptivity α = 1) any low-temperature radiation, e.g., from the

floor. Thus, consideration of multi-reflected radiation fluxes is

simplified. In addition, the deck is thin enough that heat conducted

through the deck occurs at a zero temperature gradient. The

properties of the deck are assumed so as to better expose the effect

of trapping solar radiation energy within the collector.

3- Chimney material is perfectly black. The chimney wall is thin, thus

there is no temperature gradient along the wall thickness and both

sides of the chimney (inner and outer) have the same temperature

constant along the chimney height.

4- Air is considered to be an ideal gas, the parameters for which fulfill

the state equation p = ρ × R × T, and the specific heat is assumed to

be constant (i.e., average, not varying with temperature).

5- Air is almost perfectly transparent for radiation (transmissivity τa ≈

1 and emissivity εa ≈ 0). Air can exchange heat only by convection

or conduction.

6- Air flow in the entire SCPP is frictionless. The relative air pressure

drop rT during expansion inside a turbine is estimated differently

by many authors. The drop is considered in the range from 0.66 to

0.97 “for maximum fluid power, the optimum ratio” rT = 2/3.

7- Using average values of gravitational acceleration and air density

along the height H3

8- The momentum conservation equation for the air flow within the

collector is derived as:

p0 − p1 = ρa1w 21

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where ρa1 and w 21 are the density and flow velocity, respectively, of air at

point 1.

9- In order to obtain the fair comparison basis, assume the

environment temperature T0 = 288.14 K, (15◦C), and environment

pressure p0 = 101.235 kPa.

2-4 Calculation the pressure inside the SCPP[5] According to the assumption (9), the environment pressure ( p0)

equal (101.235 kPa) and temperature environment (To) equal (15°C).And

according the assumption (8), it can find the value of pressure in point

(1).

p1 = p0 − ρa1w 21 (2-1)

According the assumption (7), it can be find the pressure in point (3)

30330

03 22H

ggpp o ρρ ++

−= (2-2)

Where the following approximations, used by [5], were applied :

g3 = g0 - 3.086*10-6*H3

ρ3=ρ0 - 9.973*10-5*H3 (2-3)

Where : p0= 101.235 kPa

g0 = gravitational acceleration = 9.81 m/s2

According the assumption (6) the air flow in entire SCFF is

frictionless. The relative air pressure drop (rT).

32

31

21 ==−−

Trpppp

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( )3112 32 pppp −−= (2-4)

2-5 Calculation the density inside the SCPP[5]

According to the assumption (4), the environment density (ρ0) can

be calculated by Appling the ideal gas equation

po = ρo × R × To

o

oo RT

p=∴ρ (2-5)

Where :

R :- Gas Constant and equal = 287 kJ/kg.K

From assumption (4), and by using the perfect gas law in part (1),

p1 = ρ1 × R × Ta1 , and in environment part (o) po = ρo × R × To , and when

dividing the two equation obtain.

1

11

a

o

oo T

Tpp

ρρ = (2-6)

Calculation of density (ρ2) is based on the equation for the

isentropic expansion in a turbine, then the density in part (2) can be

obtain. 1

1

2

1

2

`1 −

=

− kk

k

pp

ρρ

(2-7)

Where : k :- specific heat ratio = 1.4

The density in part (3) can be calculated by using equation (2-3).

2-6 Calculation the velocity inside the SCPP[5]

To calculate the equivalent velocity of air inside each part of the

SCPP, using the Bernoulli equation (BE) with frictionless in each part.

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And the environment velocity is known and equal to zero (vo=0). Appling

BE between (o-1) obtain.

2

21

1

12

22z

gvp

zg

vpo

o

o

o ++=++γγ

−×=

1

11 2

γγpp

gvo

o (2-8)

Appling BE between (1-2) obtain.

To Hg

vpz

gvp

++=++22

22

2

221

1

1

γγ

−−×= T

o

o Hpp

gv2

22 2

γγ (2-9)

Appling BE between (2-3) obtain.

−−×= 3

3

33 2 H

ppgv

o

o

γγ (2-10)

2-7 Calculation the temperature inside the SCPP[5] The calculation of temperature depends upon the energy analysis is

based on energy conservation equation. The energies E are used in six

equations written successively for: floor surface, air in collector, collector

including floor, air, and deck), turbine, chimney, and chimney surface.

2-7-1 Calculation the air temperature inside the SCPP The energy calculations were carried out with additional

assumptions. The air temperature distribution in the collector (part (1))

was assumed to be linear and thus

Ta = (To + Ta1)/2.

Ta1= 2Ta – To (2-11)

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Calculation of temperature Ta2 (part (2)) is based on the equation

for the isentropic expansion in a turbine,

kk

pp

TT aa

1

1

212

= (2-12)

Based on additional calculations the air temperature drop in the

chimney (part (3)) can be estimated as proportional to the chimney

surface and inversely proportional to the air mass rate,

Ta2 − Ta3 = 0.154 × D2 × H3/m.

( )m

HDpp

TTTk

k

oaa32

1

23

154.02

1−

−= (2-13)

Where :-

Ta = effective air temperature

m = air mass flow rate, kg/s and equal = 112

14 avD ρπ

D1 = diameter of part (1)

D2 = diameter of part (2)

H3 = height of the chimney

To calculate the effective air temperature (Ta) write the energy

collector equation (the total energy sum of the enthalpy of the air, kinetic

energy ,and the potential energy in part (1) equal to the total energy sum

of the enthalpy of the air, kinetic energy, the potential energy in part (2),

and turbine power).

Ea1 + Ev1 + Ep1 = Ea2 + Ev2 + Ep2 + EP (2-14)

Where : -

Ea1 = m.cp.(Ta1 -To) = m.cp.(2Ta -2To) (2-15a)

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Ea2 = m.cp.(Ta2 -To) = m.cp.(Ta

kk

pp

1

1

2

-To) (2-15b)

Ev1 = m.2

21v

(2-15c)

Ev2 = m.2

22v

(2-15d)

Ep1 = ( ) ( )

−+−− 2

3113

314

2

14 261 a

aa

aa

am ρρ

ρ (2-15e)

Ep2 = ( ) ( )

−+−− 2

3213

324

2

24 261 aaa

aa

am ρρ

ρ (2-15f)

ρ1 is function to the effective air temperature (Ta)

a1 = constant and equal 9.7808 m/s2

a2 = constant and equal -3.086*10-6 1/s2

a3 = constant and equal 1.217 kg/m3

a4 = constant and equal -9.973*10-5 kg/m4

EP = turbine power = tchi pAV ∆332

Assume : KK = Ev2 + Ep2 + EP - Ev1 - Ep1

tp∆ : different pressure over the turbine

Sub. The equation of (2-15) into the equation (2-14), and

rearrangement obtain,

−+=

−−k

kk

k

ppT

mcKK

ppT o

pa

11

1

2

1

2

211

21 (2-16)

The equation (2-16) is a nonlinear equation because the density of

air in part (1) is function to effective air temperature.

To write the equation of effective temperature of the floor (Tf)

write the energy floor surface equation (The solar radiation arriving at

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the floor = convection heat from floor to air + energy exchanged by

radiation between floor and deck)

Esf = Efa + Efd (2-17)

The total solar energy received by the floor is :-

dfdsf SAE ετ= (2-18a)

The convection heat from floor to air is :-

( )affadfa TThAE −= (2-18b)

The energy exchanged by radiation between the floor and deck is

( )44dfdfd TTAE −= σ (2-18c)

Where :

τd = transmissivity of deck

εf = emissivity of floor =1

S = solar radiosity at the earth surface, W/m2

Ad = Area of deck = ( ) 4/21

2 DD f −×π

σ = 5.6693*10-8, W/(m2K4), Boltzmann constant for black radiation

hfa = convective heat transfer coefficient, W/(m2K)

Sub. Equation (2-18) into equation (2-17), and obtain the effective

temperature of the floor.

( ) afa

fddff T

hS

TTT +=−+ετ

σσ 431 (2-19)

To write the equation of effective temperature of the deck (Td)

write the energy equation of air in collector (convection heat from floor to

air + convection heat from deck to air equal to kinetic energies +

Enthalpy of the air + potential energy).

Efa + Eda = Ea1 + Ev1 + Ep1 (2-20)

Where :

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Eda = Ad.hda.(Td – Ta) (2-21)

K1 = Ea1 + Ev1 + Ep1

Sub. Equation (2-18b) and equation (2-21), obtain

++=+

fa

daa

fadd

fa

daf h

hThA

KThhT 11 (2-22)

To write the equation of temperature of the chimney (Tch), sky

(Tsky), and ground (Tgr), the energy equation collector

Esf = Ea1 + Ev1 + Ep1 + Edsky + Edo + Edch (2-23)

Where :

Edsky = energy exchanged by radiation between deck and sky

= ( )44skydddsky TTA −σϕ (2-24a)

Edch = energy exchanged by radiation between deck and chimney

= ( )44chdddch TTA −σϕ (2-24b)

Edo = convection heat from deck to atmosphere

= Ad.hdo(Td – To) (2-24c)

K2 = Ea1 + Ev1 + Ep1 – Esf

f

3

DH2 ,

90905.0 ×=

−= β

βϕchd (2-24d)

( )[ ] ( )2322

22

4HHDcDcD dchddfdch −=− πϕ

πϕ (2-24e)

dchdsky ϕϕ −=1 (2-24f)

chskychdchgr ϕϕϕ −−=1 (2-24g)

5.0=chgrϕ

Sub. Equation (2-24) into equation (2-23), obtain

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[ ] 4433chddchskyddskydddchdoddddskyd TATATAhATAT σϕσϕσϕσϕ −−++

odod ThAK += 2 (2-25)

The energy equation of chimney

Ea2 + Ev2 + Ep2 + Edch = Ea3 + Ev3 + Ep3 +Echo + Echsky + Echgr (2-26)

Where :

Echo = convection heat from chimney surface to atmosphere.

= Ach.hcho.(Tch – To) (2-27a)

Echsky = energy exchanged by radiation between chimney surface

and sky

= ( )44skychchchsky TTA −σϕ (2-27b)

Echgr = energy exchanged by radiation between chimney surface

and ground

= ( )44grchchchgr TTA −σϕ (2-27c)

( )232 HHDcA pch −×××= π = chimney surface area

K3 = Ea2 + Ev2 + Ep2 - Ea3 - Ev3 - Ep3

[ ] [ ]433skydchskyskychddchchchchgrchochch TATTATAhAT σϕϕσϕ −++

[ ] [ ] ochochgrchchgrgrdddchddchskyd ThAKTATTATAT +=+−+ 3333 σϕϕσϕ (2-28)

The energy equation of chimney surface

Each + Edch = Echo + Edsky + Echgr (2-29)

Where :-

Each = heat transferred from chimney air to the chimney surface

= ( ) ( )

+

−−

choaach Tm

HDppTThHHD

kk

32

1

2232

154.01221

1

π

= K4 - ( ) chachThHHD 232 −π

(2-30)

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Sub. Equation (2-30), (2-27a,b,c) and equation (2-24b) into

equation (2-29) get.

( )[ ]33232 chchchgrchochchddchachch TAhATAhHHDT σϕσϕπ +++−

[ ] [ ] [ ]3433grchchgrgrskyddskyskyddddchdddsky TATTATTTATA σϕσϕσϕσϕ +−−+

ochoch ThAK += 4 (2-31)

Rearrangement the equation (2-19), (2-22), (2-25),(2-28) and (2-

31)in matrix form we get

( )

( )

+++

+++

=

−+++−−−++−−−++

−+

ochoch

ochoch

odod

hh

ahAK

ahS

gr

sky

ch

d

f

grchchgrskyddskychchchgrchochchddchachdddchdddsky

grchchgrskydchskychddchchchchgrchochdddchddchsky

skyddskychddchdddchdoddddsky

fa

da

df

ThAKThAKThAK

TT

TTTTT

TATATAhATAhHHDTATATATATATAhATATA

TATATAhATAhh

TT

fa

da

fad

fa

fd

432

1

00

00

0001

000)1(

1

3333232

33

333333

3333

33ετ

σϕσϕσϕσϕπσϕσϕσϕσϕϕσϕϕσϕ

σϕσϕσϕσϕ

σσ

(2-32)

By using the iteration method (Newton Raphson methods) to solve

equation (2-32) and equation (2-16) as shown in Appendix (A), obtain the

all temperature in the SCPP. Where (h) is the respective coefficient the

coefficient (hach) is determine as :

2/ DkNuhach ×=

Where :

k :- thermal conductivity of air = 0.0267 ,W/(mK)

Nu :- Nusselt number = 4.08.0 PrRe023.0 ××

Pr :- Prandtl number for air = 0.7

Re :- Reynolds number = ν/22Dv

ν :- kinematic viscosity coefficient for air = 1.6×10-5 m2/s

In the similar way (hfa) is determined and it was assumed that (had = hfa).

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2-8 Calculation the Power Output of the SCPP[1] The fundamental dependencies and influence of the essential

parameters on power output of a solar tower are presented here in a

simplified form: Generally speaking, power output P of the solar tower

can be calculated as the solar input solar Q and multiplied by the

respective efficiencies of collector, tower and turbine(s):

turbchidsolarQP ηηη ⋅⋅⋅= (2-33)

Tower efficiency is given in reference [1].

opchi Tc

Hgo⋅⋅

= 3η (2-34)

chit

Pturb VAp

E∆

=η (2-35)

Where :

Qsolar = dfd SAετ

3-1 Results and Discussion The analytical method, which is expected to produce a solution of

SCPP in an analytical form (usually successful in a very simplified case).

Then, from the solution of the differential problem, ordinary solvable

equations can be obtained. Usually, the introduction of many simplifying

assumptions allows us to pass over the stage of formulating differential

equations and directly develop regular algebraic equations that can be

solved if the number of unknowns is not larger than the number of

derived equations. The present study belongs in this category.

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3-2 Reference case The computation using the presented model as follows.

The floor diameter is Df = 240 m, and the chimney height is H3 = 195m.

Other data are as follows :

S= 800 W/m2, k=1.4, hcho=7 W/(m2K)

Tgr=To CD=1.015 hdo=5 W/(m2K)

R= 287.04 J/(kgK) He=0.3 m HT= 1 m

The results computation can be show in Table (3-1). And in

Figures (3-1) and (3-2) respectively.

Table (3-1). The results of reference case

Power (W) Df (m) H3 (m) He (m) To (K) dη HT (m)

74434.98 240 195 0.3 288 100% 1

Figure (3-1). Distribution of the absolute pressure in the SCPP

98.5

99

99.5

100

100.5

101

101.5

0 1 2 3 4

Loaction along the air flow

Abs

olut

e pr

essu

re (k

Pa) Collector

Turbine

Chimney

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Figure (3-2). Distribution of the temperature in the SCPP 3-3 Effect of parameter on the power output

The results can be used to illustrate the tends of the output data in

response to changes in some input parameters. The effect of varying the

value of floor diameter on the power output as shown in Figure (3-3).

This figure illustrating when increase the floor diameter increase the

power output.

Figure (3-3). The effect of floor diameter on the power output

050

100

150200

250300

350

400450

To Tf Td Ta Tch Tgr

Temperature location in SCPP

Tem

pera

ture

(K)

40000

45000

50000

55000

60000

65000

70000

75000

80000

0 100 200 300

Diameter of floor (m)

Pow

er (W

)

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The effect of height chimney on the power output can be shown in

the Figure (3-4). The results shown that when increase the height of

chimney this lead to increase in power output. The decreasing in power as

shown which is results from the nonlinearity equation.

0

10000

20000

30000

40000

50000

60000

70000

80000

0 50 100 150 200 250

Height of chimney (m)

Pow

er (W

)

Figure (3-4). The effect of height of chimney on the power output

The effect of height of air inlet on the power output can be shown

in the Figure (3-5). The results shown that when increase the height of air

inlet this lead to decreasing in power output.

0

20000

40000

60000

80000

100000

120000

140000

160000

180000

200000

0 0.1 0.2 0.3 0.4

Height of air inlet (m)

Pow

er (W

)

Figure (3-5). The effect of height of air inlet on the power output

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The effect of position of turbine is less than others parameters as

shown in Figure (3-6), when increasing the height of turbine that lead to

little increasing in power output.

74000

74050

74100

74150

74200

74250

74300

74350

74400

74450

74500

0 0.5 1 1.5

Height of turbine (m)

Pow

er (W

)

Figure (3-6). The effect of height of turbine on the power output

The effect of efficiency of deck or collector is shown in Figure (3-

7), when increasing the efficiency of deck that lead to increasing in power

output.

0

10000

20000

30000

40000

50000

60000

70000

80000

0 0.5 1 1.5

efficiency of deck (collector)

Pow

er o

utpu

t (W

)

Figure (3-7). The effect of efficiency of deck on the power output

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4-1 Conclusions and Suggestions for Future Work This research includes a mathematical model of solar chimney, the

theoretical analysis solved by using Newton Raphson methods as shown

in Appendix (A) and this work focus on the effect of dimensional

parameters of SCPP on the power output of this SCPP.

4-2 Conclusions

1- When increasing the floor diameter, obtained increasing the power

output

2- The effect of height chimney on the power output. The results

when increasing the height of chimney this lead to increasing in

power output. The decreasing in power as shown which a result

from the nonlinearity equation is.

3- The effect of height of air inlet on the power output. The results

showed that when increase the height of air inlet this lead to

decreasing in power output.

4- The effect of position of turbine is less than others parameters,

when increasing the height of turbine that lead to little increasing in

power output.

5- The effect of efficiency of deck or collector, when increasing the

efficiency of deck that lead to increasing in power output.

4-3 Suggestions for future work 1- Study the effect of friction inside of collector and chimney on the

power output

2- Study the effect of type of floor (soil, rocket, etc) on the power

output

3- Study the effect of dust and fog on the environment and chimney

on the power output.

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4- Improve the ways to increase the power output of SCPP on the

night.

5- Improve the work of SCPP by using the geothermal.

Appendix – A – Solve the Non- Algebraic Equations A-1 Iteration Methods for Polynomial Approximation

In this appendix shows the details used to solve the polynomial

equation (2-16) by Newton Raphson methods. Perhaps the most widely

used of all root locating formulae is the Newton Raphson equation

(Figure (A-1)). If the initial guess at the root is Xi, a tangent can be

extended from the point (Xi , F(xi)).

Figure (A-1). Graphical depiction of the Newton Raphson method. A tangent to the function of Xi (that is F’(xi)) is extrapolated down to the X-

axis to provide an estimate of the root at Xi+1[6]

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The point where this tangent crosses the X-axis usually represents

an improved estimate of the root. In the Figure (A-1) the first derivative

at Xi is equivalent to the slope:-

1

0)()('+−

−=

ii

ii xx

xFxF (A-1)

Which can be rearranged to yield

)(')(

1i

iii xF

xFxx −=+ (A-2)

This formula can be repeatedly used to find improved

approximations to the real root XT.[6]

A-2 Newton’s Method For System of Non-Linear Equations

The iteration forms of this method have the general form[7].

KJJ

J

J

KPF

PF

PF

PF

PF

PF

PF

PF

PF

KJKJ PPPF

PPPFPPPF

P

PP

P

PP

J

JJJ

J

J

=

∂∂

∂∂

∂∂

∂∂

∂∂

∂∂

∂∂

∂∂

∂∂

+),......,,(

),......,,(),......,,(

21

212

211

1

2

1

1

2

1

21

2

2

2

1

2

1

2

1

1

1

M

M

M

OMM

OMM

OMM

LLL

LLL

M

M

M

M

M

M

(A-3)

Or on vector form

{PK+1} = {PK} – [J]-1{F(PJ)} (A-4)

Where F(PJ) is the vector represent the set of non-linear algebraic

equations need to solve (J equation), [J] is the Jacobean matrix of partial

derivatives for J equation defined as {F(PJ)} and J independent variables.

{PK+1}, {PK} is the vector represented the root of {F(PJ)} from iteration

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(K+1) and {PK} is the vector represent the roots of {F(PJ)} from iteration

K. Those methods are used to solve the sets of equations (equation (2-32)).

References

1- Jörg Schlaich, Rudolf Bergermann, Wolfgang Schiel, Gerhard

Weinrebe; “Design of Commercial Solar Updraft Tower Systems –

Utlilization of Solar Induced Convective Flows for Power

Generation”; Schlaich Bergermann und Partner (sbp gmbh),

Hohenzollernstr. 1,70178 Stuttgrat, Germany.

2- Mohammed Awwad Al-Dabbas; “A Performance Analysis of Solar

Chimney Thermal Power Systems”; Thermal Science Journal; Vol.

15, No. 3, pp. 619-642, 2011.

3- T. Z. Ming, W. Liu, Y. Pan; “Numerical Analysis of the Solar

Chimney Power Plant With Energy Storage Layer”, ISES World

Congress, Vol. 5, pp. 1800-1805, 2007.

4- Y. Dai, “Case Study of Solar Chimney Power Plants in

Northwestern Regions of China”, Renewable Energy Journal, Vol.

(28), No. (8), pp. 1295-1304, 2003.

5- Richard Petal; “Engineering Thermodynamics of Thermal

Radiation For Solar Power Utilization” ; The McGraw Hill Ltd.;

1st edition; 2010.

6- Steven C. Chapra and Raymond P. Canale; “Numerical Methods

for Engineers”; 2nd edition; McGraw hill Ltd.; 1989.

7- Richard L. Burden and Douglas Faires; “Numerical Analysis”; 3rd

edition; Prindle Weber and Schmidt Ltd; 1985.

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The Author

Dr. Hani Aziz Ameen , born in Iraq/Baghdad in 1971 was

awarded a degree of Ph.D. in Mechanical Engineering –

Applied Mechanics – in the University of Technology,

Iraq/Baghdad (1998). He has more than 50 published

research articles and he has an expert in the ANSYS software and finite

element analysis. He worked in several universities and colleges

(Technology University- AlNahrain University- Tikrit University –

Technical College AlMusaib). now he is an assistant professor in the

Technical College – Baghdad / Dies and Tools Engineering Department.

E-mail: [email protected]

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