Numerical analysis of a minichannel solar collector for CO ...€¦ · tracking. Solar collectors vary in performance depending on their design. One key issue that remains a subject

Numerical analysis of a minichannel solar collector for CO2-based Rankine cycle applications

G. Diaz School of Engineering, University of California, USA

Abstract

The combined effects of increasing energy consumption, higher fuel prices, and green-house-related climate change are challenging universities and industry to develop more efficient and sustainable ways to produce power, heating, and cooling for industrial, commercial, and residential applications. The utilization of renewable energy sources is receiving considerable attention as a non-resource-depleting approach that reduces the emissions of pollutants and green-house gases to the atmosphere. Solar thermal systems have the capacity to provide heat in a sustainable way for a variety of applications due to the relatively large range of temperatures that different collector configurations can attain. Non-imaging-optics based compound parabolic concentrating reflectors combined with evacuated-tube collectors can operate at 200oC at efficiencies near 50% without the need for tracking. In addition, a trend towards natural working fluids to reduce the effects of global warming and ozone-layer depletion has sparked the proposal of several refrigeration and combined cooling, heating and power cycles using CO2. This paper analyzes the performance of a minichannel-based evacuated-tube solar collector operating with supercritical CO2 suitable for solar-driven Rankine cycle applications. Keywords: minichannel, solar collector, Rankine cycle, cogeneration.

1 Introduction

The fluctuating costs of fuel prices, the increasing demand for energy, and the evident signs of climate change have fostered the development of technologies that utilize renewable energy sources, use more environmentally-friendly

Energy and Sustainability II 23

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working fluids, utilize low-grade heat sources, and/or have higher energy efficiencies than the more traditional thermal applications. At the legislative level, some states have taken strong action to increase energy efficiency and power generation from renewable energy sources, and to promote the utilization of combined heat and power (CHP) and combined cooling, heating, and power (CCHP) systems. For instance, the California Air Resources Board is planning to increase CHP electricity production by 30,000 GWh by 2020. An important part of a CHP system is the power-generating cycle. In this respect, power cycles that utilize low-grade heat sources such as waste heat or heat from evacuated-tube solar collectors, have been proposed by several researchers. Organic Rankine cycles [1–2] have been proposed but they tend to use working fluids such as isobutane, propane, benzene, or toluene that are either flammable or toxic. Kalina cycles [3] utilize an ammonia/water mixture and consist of extensive internal heat recovery to improve efficiency in thermal power cycles. Although ammonia is a natural working fluid with zero ozone depleting and global warming potentials, it is toxic. Thus, one alternative natural working fluid for power generating cycle or CHP applications corresponds to CO2 [4–7]. Minichannels have successfully been utilized in heat exchangers by the residential air conditioning industry due to their improved performance and compact size compared to round-tube and fin heat exchangers [8, 9]. Minichannel tubes are classified with respect to their hydraulic diameter which covers the range between 200m and 3mm [8]. This technology will allow a reduction of 4.2 quadrillion Btus of electric energy consumption, between 2006 and 2030, and a decrease of 33 million metric tons in carbon emissions [10]. Non-imaging-optics based compound parabolic concentrating (CPC) reflectors [11] combined with evacuated-tube collectors have been shown to operate at temperatures near 200oC with efficiencies of 50% without the need of tracking. Solar collectors vary in performance depending on their design. One key issue that remains a subject of intense research relates to effectively transferring the heat obtained from the sun to the working fluid. Minichannel-based evacuated tube solar collectors have been proposed to improve the efficiency of the collector [12]. This paper analyzes the performance of an evacuated-tube solar collector utilizing minichannel tubes for a solar-driven Rankine cycle producing electric power and hot water.

2 Transcritical cycle

In recent years there has been a trend towards utilizing more environmentally friendly working fluids in air conditioning and low-grade power generating cycles. Carbon dioxide, water, air, hydrocarbons, and ammonia constitute a set of the natural working fluids that provides an environmentally friendly option to reduce ozone depletion and green-house-gas emissions. Table 1 shows a comparison of properties of commonly used working fluids, where global warming potential (GWP) is an index that relates the potency of a greenhouse gas relative to the emission of CO2 over a 100-year period.

24 Energy and Sustainability II



Table 1: Working fluid property comparison [13].

ODP/ GWP

FLAMMABLE/ TOXIC

REFRIG. CAPACITY

(kJ/m3) R-744 0/1 N/N 22545 R-12 1/8500 N/N 2734 R-22 0.05/1700 N/N 4356

R-134 0/1300 N/N 2868 R-407C 0/1600 N/N 4029 R-410A 0/1900 N/N 6763 R-717 0/0 Y/Y 4382 R-290 0/3 Y/N 3907

Carbon dioxide, R-744, has a higher volumetric capacity, higher heat transfer coefficients, and it is readily available which makes it low cost. One drawback is that it requires higher operating pressures. Its ODP and GWP compare favourably with other commonly used working fluids.

3 Minichannel solar collector

A variety of solar collectors available in the market serve different purposes depending on their optimal operating temperature. Absorber surfaces, flat-plate collectors, evacuated-plate collectors, evacuated-tube collectors, and external or internal concentrator with evacuated-tube collector are some of the different options available today. The most common evacuated-tube collectors include a U-tube, a concentric-pipe, or a heat pipe attached to a metal absorber that has a selective coating applied on its external surface. In these designs, heat transfer from the metal absorber to the working fluid encounters several thermal resistances. Heat flows from the absorber to the working fluid by conduction through the absorber fin. Cost reduction results in the absorber thickness being very thin, usually less than a millimetre, creating a resistance to the flow of heat. Also, the absorber is usually wrapped around the pipe carrying the working fluid and ultrasonic-welding is utilized at discrete points to attach the absorber fin to the pipe. Poor contact is obtained at points where the fin is not welded to the pipe. Figure 1a shows a schematic of a counter-flow evacuated-tube solar collector. A minichannel tube can have a similar free flow area as a round-tube but a much larger wetted perimeter. The port dimensions, shown in fig. 1b, tend to be small so that pressure-drop needs to be considered in performance analyses [12]. In solar collectors, the path of the heat transfer involves less thermal resistances than in absorber/round-tube designs. Also, the large wetted perimeter combined with the excellent heat transfer properties of CO2 reduce the amount of working fluid needed inside the collector. Charge minimization is an important safety advantage of minichannel tubes that operate at the high pressures required by CO2.




Figure 1: Schematic of evacuated-tube solar collectors. (a) Absorber/round-tube counter-flow design. (b) Minichannel solar collector.

4 Model description

In the following subsections we derive the models for the minichannel-based solar collector and the Rankine cycle operating with CO2.

4.1 Solar collector

The radiation heat transfer coefficient between the tube and the glass is given by

g

g

g

Ae

A D

DAgrh

1)(

1

1,

To model the heat transfer to the fluid using minichannels, we need to consider the resistance from the external tube surface to the fluid.

RT 0 twall

kCuP0L

1

0Atoth f

where twall is the tube wall thickness, PO is the tube perimeter, and surface efficiency is given by

0 1 (NAfin

Atot

)(1 fin )

Mini-channels Selective coating

Evacuated glass tube

Absorber

Fluid

(a) (b)

Evacuated glass tube




where N is the number of webs inside the tube, Afin is the cross sectional area of the fin, Atot is the total heat transfer area inside the tube, and the fin efficiency is given by

2/

)2/tanh(

finf

finffin Lm

Lm

where mf =(hf P/(kCuAfin))1/2, P is the perimeter of the fin, and Lfin corresponds to

half of the length of the tube webs. The energy balance at the glass becomes

0)())()(( 44,

44 gbAgrAeskyggairsgge TThATTTThGA

(1) An energy balance at the external tube surface gives

QTThGA gbAgrsgA

gAAe

))(

)1(1( 44

,

(2)

where

0T

fb

R

TTQ

(3)

where Tb and Tf are the tube and fluid temperatures, respectively.

4.2 Solar-powered Rankine cycle

The solar-driven Rankine cycle for heat and electric power generation, shown if fig. 2, is modelled using thermodynamic relations.

HeatExchanger

CondenserTurbine

Pump

Twin

Twout

TwHW

a

b

Wp

Wt

c

d e

Solar collectors

Figure 2: Solar-powered Rankine cycle.

The power generated by the expander and the power used by the pump are modelled as:

W

t m

(hc hd ) (4)




W

p m

(hb ha ) (5) where

)( cdstcd hhhh , (6)

pabsab hhhh /)( (7)

The isentropic efficiencies of the expander and pump have been considered as ηt = 0.7 and ηp = 0.85, respectively. The heat added to the working fluid at the solar collectors is calculated as:

Q

m

(hc hb ) (8) The heating of water at the heat exchanger and condenser are modelled as:

)()( outW

HWWpWedPH TTcmhhm

w (9)

)()( inW

outWpWaePH TTcmhhm

w (10)

The efficiency () of the CHP system is obtained as:

QWW ptCHP /)( (11)

5 Numerical simulations

Numerical simulations were obtained using the Engineering Equation Solver (EES) software [15] that includes the thermophysical properties of carbon dioxide. The parameters used for the simulations, including the specifications of the evacuated-tube solar collector, are described in table 2 [12].

5.1 Evacuated-tube solar collector

The evacuated-tube solar collector is subdivided in sections along the length and eqns. (1) to (3) are utilized to obtain the performance of a single collector. Figure 3 shows the outlet temperature of the CO2 (solid line) as well as the

Table 2: Parameters used for the simulations.

Property Value Dimension Value Glass tube length 1,640mm External tube perimeter 183 mm Glass external diameter

65 mm Wetted tube perimeter 240 mm

Glass internal diameter

56 mm α selective coating 0.90

Tube major 88 mm ε selective coating 0.1 Tube minor 3.58 mm Solar irradiation 1000 W/m2 Tube wall 0.7 mm ηt 0.7 Web thickness 0.7 mm ηp 0.85 Number of webs 21 Inlet water temperature 17oC Free flow area 1.6x10-5 mm2




0 0.01 0.02 0.03 0.04 0.050

45

90

135

180

225

0.49

0.5

0.51

0.52

0.53

0.54

0.55

0.56

0.57

mass flow rate [kg/s]

To

ut [

oC

]

effi

cien

c y

Figure 3: Tout and efficiency versus mass flow rate for a single solar collector at Tin = 160 (oC).

50 85 120 155 190 2250

50

100

150

200

250

0.4

0.45

0.5

0.55

0.6

0.65

0.7

Tin [oC]

To

ut [

oC

]

effi

cien

cy

Figure 4: Tout and efficiency versus mass flow rate for a single solar collector at mass flow rate of 0.01(kg/s).

efficiency (dashed line) of the minichannel solar collector as a function of mass flow rate for a fixed inlet CO2 temperature of 160 (oC). It is observed that there is no significant gain in efficiency of the collector with mass flow rates higher than 0.02 (kg/s). The outlet temperature of CO2, Tout, remains above 200 (oC) at very low flow rates but it levels off approximately at 164 (oC) as the mass flow rate is increased. Figure 4 shows the performance of a single collector in terms of outlet CO2

temperature and collector efficiency as a function of inlet temperature for a fixed mass flow rate of 0.01 kg/s. The outlet temperature of the working fluid increases linearly with respect to Tin while the efficiency displays a nonlinear behaviour. It is observed that the collector operates at nearly 50% of efficiency




at 190 (oC). This is assuming the use of a non-tracking external compound parabolic concentrator designed using non-imaging optics [16].

5.2 Rankine cycle operation

We combined the model of the minichannel evacuated-tube solar collector with eqns. (4) to (11) that describe the performance of the Rankine cycle. The heat obtained at the collectors in eqn. (3) corresponds to the heat added to the Rankine cycle in eqn. (8). Twenty squared meters of collector area are utilized for the simulations. In order to increase the outlet temperature of the CO2, the collectors are connected in a combination of series and parallel configuration. Figure 5 shows the performance of two collectors connected in series operating at a pressure at state (b) of 13 (MPa). No significant gain in collector efficiency is obtained with mass flow rates higher than 0.002 (kg/s).

0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004 0.0045 0.00550

85

120

155

190

225

0.62

0.63

0.64

0.65

0.66

0.67

0.68

0.69

0.7


To

ut [

oC

]

colle

cto

r ef

fici

ency

Figure 5: Collector performance in Rankine cycle as a function of mass flow rate at Pb = 13(MPa). The figure shows the results for two collectors connected in series.

Figure 6 shows the outlet temperature of the hot water TwHW and the

efficiency of the Rankine cycle as a function of mass flow rate. It is seen that the maximum efficiency of the Rankine cycle does not correspond to the maximum efficiency of the solar collector. The efficiency of the Rankine cycle decreases with higher mass flow rate mainly because the work of the pump increases at a higher rate than the work of the turbine. The change in the outlet water temperature is not significant, remaining near 30 (oC) for a water flow rate of 0.2 (kg/s). Figures 7 and 8 show the effect of changing the operating pressure of the solar collector in the Rankine cycle at a constant mass flow rate of CO2 of 0.002 (kg/s). The efficiency of the collector in the Rankine cycle decreases only




slightly with increasing operating pressure. On the other hand, outlet collector temperature of the CO2 increases significantly with pressure. Figure 8 shows an increase in Rankine-cycle efficiency with increasing solar-collector operating pressure and a small decrease in Tw

HW with increasing pressure at the collector. The results indicate that an optimization process needs to be performed to obtain the optimum operating point for efficiency of the solar collectors and overall Rankine cycle.

0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004 0.0045 0.00528.5

29

29.5

30

30.5

31

31.5

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08


Tw

HW

[o

C]

Eff

icie

ncy

(R

anki

ne

cycl

e)

Figure 6: Rankine cycle efficiency P collector = 13 MPa. The figure shows the results for two collectors connected in series.

9500 10000 10500 11000 11500 12000 12500 13000 13500 1400075

80

85

90

95

100

105

0.68

0.682

0.684

0.686

0.688

0.69

0.692

0.694

0.696

0.698

PCO2 [kPa]

To

ut [

oC

]

effi

cien

cy

Figure 7: Tout and efficiency versus pressure at the collector in Rankine cycle for a fixed mass flow rate of 0.002 (kg/s). The figure shows the results for two collectors connected in series.




Figure 9 shows a schematic of the pressure-enthalpy diagram for an arbitrarily chosen solar collector pressure of 13 (MPa) and a mass flow rate of 0.0015 (kg/s). The solar collectors outlet CO2 temperature reaches 145 (oC) and Tw

HW reaches 30 (oC) with a water flow rate of 0.2 (kg/s). It is noted that the carbon dioxide temperature at the exit of the turbine corresponds to 86 (oC). Thus, for residential or small commercial applications that require less amount of water at higher temperature, there is still the potential to increase Tw

HW.

9500 10000 10500 11000 11500 12000 12500 13000 13500 1400030.2

30.3

30.4

30.5

30.6

30.7

30.8

30.9

0.035

0.04

0.045

0.05

0.055

0.06

0.065

PCO2 [kPa]

Tw

HW

[o

C]

e ffi

cien

cy (

Ran

kin

e cy

cle)

Figure 8: TwHW and Rankine-cycle efficiency versus pressure at the collector

for a fixed mass flow rate of 0.002 (kg/s). The figure shows the results for two collectors connected in series.

0

2

4

6

8

10

12

14

16

0 100 200 300 400 500 600 700 800

Enthalpy [kJ/kg]

Pre

ss

ure

[M

Pa

10oC

20oC

0oC

80oC 120oC 160oC 200oC

a

b c

de

Figure 9: Pressure-Enthalpy diagram of the solar powered Rankine cycle.




6 Conclusions

The thermal analysis of a minichannel-based evacuated-tube solar collector has been performed. The numerical model developed has been combined with the model of a Rankine cycle operating with carbon dioxide. The results show that parameters such as mass flow rate and operating pressure at the solar collector have a significant influence in the performance of the solar collector as well as the overall Rankine cycle.

References

[1] Hung, T.C., Waste heat recovery from organic Rankine cycle using dry fluids. Energy Conversion and Management, 42, pp. 539-553, 2001.

[2] Vijayaraghavan, S. & Goswami, D.Y., Organic working fluids for a combined power and cooling cycle, Journal of Energy Resources Technology. 127, pp. 125-130, 2005.

[3] Kalina, A.I., Combined cycle and waste-heat recovery power systems based on a novel thermodynamic energy cycle utilizing low-temperature heat for power generation, ASME Paper; 83-JPGC-GT-3. 1983

[4] Zhang, X.R., Yamaguchi, H., Fujima, K., Enomoto, M. & Sawada, N., A feasibility study of CO2-based ranking cycle powered by solar energy. JSME International Journal; Series B, 48(3), pp. 540-547, 2005.

[5] Yamaguchi, H., Zhang, X.R., Fujima, K., Enomoto, M. & Sawada, N. Solar energy powered Rankine cycle using supercritical CO2. Applied Thermal Engineering, 26, pp. 2345-2354, 2006.

[6] Chen, Y., Pridasawas, W. & Lundqvist, P. Low-grade heat source utilization by carbon dioxide transcritical power cycle. Proceedings of ASME-JSME Thermal Engineering Summer Heat Transfer Conference, Vancouver, BC; HT2007-32774, pp. 1-7, 2007.

[7] Diaz, G., Performance Improvement of a CO2 Combined Cooling, Heating, and Power Cycle Using Solar Thermal Collectors. Proceedings of SOLAR, San Diego, CA, Paper # 0238, pp. 1-6, 2008.

[8] Steinke, M.E. & Kandlikar, S.G., Single-phase heat transfer enhancement techniques in microchannel and minichannel flows. Proceedings of Microchannels and Minichannels ASME Conference, ICMM2004-2328, pp. 141–148, 2004.

[9] Yun, R., Kim, Y., and Park, C., Numerical analysis on a microchannel evaporator designed for CO2 air-conditioning systems. Applied Thermal Engineering, 27, pp. 1320-1326, 2007.

[10] Air conditioning efficiency standards: seer 12 vs. seer 13. Environmental and energy study institute report, 2001. http://www.eesi.org/030602_ SEER_13

[11] Winston, R., Principles of solar concentrators of a novel design. Solar Energy, 20, pp. 59-67, 1974.




[12] Diaz, G., Performance Analysis and Design Optimization of a Minichannel Evacuated-tube Solar Collector. Proceedings of ASME IMECE, Paper # IMECE2008-67858, Boston, MA, Nov. 2008.

[13] Kim, M-H, Pettersen, J., Bullard, C.W., Fundamental process and system design issues in CO2 vapour compression systems, Progress in Energy and Combustion Science; 30, pp. 119-174, 2004.

[14] Rahman, F., Al-Zakri, A.S., Rahman, M.A.A., Two-dimensional mathematical model of evacuated tubular solar collector. ASME Journal of Solar Energy Engineering, 106, pp. 341-346, 1984.

[15] Klein, S.A. Engineering Equation Solver. Madison, WI, F-Chart Software. [16] Winston, R., Minano, J.C., Benitez, P.G. Nonimaging optics. Elsevier

Academic Press, 2005.




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Numerical analysis of a minichannel solar collector for CO ...€¦ · tracking. Solar collectors vary in performance depending on their design. One key issue that remains a subject