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Performance of a flat-plate solarthermal collector using supercriticalcarbon dioxide as heat transfer fluidJahar Sarkara

a Department of Mechanical EngineeringIndian Institute ofTechnology (BHU), Varanasi, IndiaPublished online: 03 Sep 2013.

To cite this article: Jahar Sarkar (2013) Performance of a flat-plate solar thermal collector usingsupercritical carbon dioxide as heat transfer fluid, International Journal of Sustainable Energy, 32:6,531-543, DOI: 10.1080/14786451.2013.833205

To link to this article: http://dx.doi.org/10.1080/14786451.2013.833205

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International Journal of Sustainable Energy, 2013Vol. 32, No. 6, 531–543, http://dx.doi.org/10.1080/14786451.2013.833205

Performance of a flat-plate solar thermal collector usingsupercritical carbon dioxide as heat transfer fluid

Jahar Sarkar∗

Department of Mechanical Engineering, Indian Institute of Technology (BHU), Varanasi, India

(Received 20 March 2013; final version received 30 July 2013)

Energetic and exergetic performance analyses of flat-plate solar collector using supercritical CO2 have beendone in this study. To take care of the sharp change in thermophysical properties in near critical region,the discretisation technique has been used. Effects of zonal ambient temperature and solar radiation, fluidmass flow rate and collector geometry on heat transfer rate, collector efficiency, heat removal factor,irreversibility and second law efficiency are presented. The optimum operating pressure correlation hasbeen established to yield maximum heat transfer coefficient of CO2 for a certain operating temperature.Effect of metrological condition on heat transfer rate and collector efficiency is significant and that onheat removal factor is negligible. Improvement of heat transfer rate is more predominant than increase inirreversibility by using CO2. For the studied ranges, the maximum performance improvement of flat-platesolar collector by using CO2 as the heat transfer fluid was evaluated as 18%.

Keywords: supercritical carbon dioxide; flat-plate solar collector; modelling; thermal efficiency; exergeticperformance

Nomenclature

Ac collector surface area, m2

cp specific heat capacity, J/kg Kd tube diameter, mE exergy, WG mass velocity, kg/m2sh specific enthalpy, J/kgI incident solar radiation, W/m2

kp plate thermal conductivity, W/mKL length of the tube, mmf fluid mass flow rate, kg/snt number of tubesNu Nusselt numberp pressure, barQ heat transfer rate, WRe Reynolds numbers specific entropy, J/kg K

∗Email: js_iitkgp@yahoo.co.in

© 2013 Taylor & Francis

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t, T temperature, C, KTa ambient temperature, KTas apparent sun temperature, KUL heat loss coefficient, W/m2KW tube spacing, mx axial direction of tubeα heat transfer coefficient, W/m2Kα0τ0 transmittance–absorptance productδ plate thickness, m segmentμ fluid viscosity, Ns/m2

ρ fluid density, kg/m3

Subscriptsb properties at bulk temperaturef heat transfer fluidw properties at wall temperature

1. Introduction

The flat-plate solar collector is widely used nowadays to absorb and transfer solar energy foroperation in the low temperature range (up to 60C) or in the medium temperature range (up to100C).Applications of flat-plate solar collector include direct and indirect water heating systems,space heating and cooling, absorption and adsorption solar refrigerations, industrial process heatand solar desalination (Kalogirou 2004). Due to growing demand for higher energy density ofthermal system, nowadays it is essential to improve the performance of solar collector, which canbe achieved by several possible ways, such as change/improvement of materials, heat transferfluid and design. Choice of working fluid is dependent on several factors and the heat transferproperty is one of them; good heat transfer property of fluid makes the system more efficient aswell as compact. Good quality water, if available easily, is an ideal heat transfer fluid and ethyleneglycol/water, propylene glycol/water, silicone oil and air are some alternatives (Kalogirou 2004;Yohanis et al. 2012). Recently, alumina–water and carbon nanotube–water nanofluids have beenproposed as heat transfer fluids in flat-plate solar collector (Yousefi, Shojaeizadeh, et al. 2012;Yousefi, Veysi, et al. 2012).

Carbon dioxide is one of the natural working fluids, which has several advantages, such aszero ozone depletion potential, zero effective global warming potential, non-flammability, non-toxicity, compatibility with normal lubricants and common machine construction materials, easyavailability and very low price. Furthermore, CO2 gives superior heat transfer properties for nearcritical operation. Carbon dioxide has been used successfully as a working fluid in refrigerationand heat pump cycles (Sarkar, Bhattacharyya, and Ramgopal 2009). It has also been proposedas working fluid in Brayton power cycle (Sarkar 2009; Sarkar and Bhattacharyya 2009) andRankine power cycle (Yamaguchi et al. 2006). Zhang and his co-workers (Yamaguchi et al. 2006;Zhang et al. 2006; Zhang, Yamaguchi, and Uneno 2007; Zhang and Yamaguchi 2008) proposedCO2 as a working fluid in solar-energy-powered transcritical Rankine cycle using evacuated tubesolar collector, and theoretically and experimentally analysed the performances for combinedproduction of electricity and thermal energy. The annually averaged collector efficiency wasfound to be above 60.0% in the case of supercritical CO2 as working fluid, which is much higherthan that of water-based solar collector. They have also investigated an optimal arrangement ofthe solar collectors to get the best performance with regarding to the aims of power productionand heat utilisation (Niu et al. 2013). Solar energy has been used as a heat source for supercritical

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International Journal of Sustainable Energy 533

CO2 Brayton cycle also (Garg, Kumar, and Srinivasan 2013; Singh et al. 2013a, 2013b). Sunet al. (2012) have used supercritical CO2 Brayton cycle for hydrogen production. Palmer et al.(2013) patented supercritical carbon-dioxide power generating system and method to use bothhybrid fossil fuel and solar radiation as heat source. Wang et al. (2012) proposed transcriticalCO2 as working fluid in a new combined cooling, heating and power system driven by solarenergy. Delussu (2012) has done a qualitative thermo-fluid-dynamic analysis of a CO2 solar pipereceiver. Cau, Cocco, and Tola (2012) have done performance and cost assessment of integratedsolar-combined cycle systems using CO2 as heat transfer fluid in parabolic collector. Yamaguchiet al. (2010) used evacuated tube solar collector for water heating. However, to the best of theauthors’knowledge, the study on flat-plate solar collector using supercritical CO2 as a heat transferfluid is scarce in open literature.

In this study, the energetic as well as exergetic performance analyses of flat-plate solar collectorusing supercritical CO2 have been done and compared with water. To take care of the sharp changein thermophysical and transport properties in near critical region, the discretisation technique hasbeen used for simulation of solar collector. Effects of zonal ambient temperature and incidentsolar radiation, fluid mass flow rate and collector geometry on useful heat transfer rate, collectorefficiency, heat removal factor, irreversibility and second law efficiency are presented as well.

2. Mathematical modelling and simulation

Supercritical CO2 is proposed as a solar collector heat transfer fluid in indirect solar heatingsystem to take the advantage of excellent heat transfer properties of CO2 in near critical point.The possible layout and p–h diagram are shown in Figure 1. As shown, the liquid CO2 is heated tosupercritical fluid through flat-plate solar collector (process: 1–2), and then it is passed through thethermal storage system and cooled to liquid by using solar energy for heating of air, water or anyrequired fluids. The thermal storage system is used to reduce the temperature fluctuation occursdue to time varying radiation and to maintain a nearly constant temperature heating. A pump isused to maintain required pressure rise for flow through solar collector – heat exchanger system.As the main aim of this study to promote CO2 as solar collector working fluid, the performanceof collector using CO2 has been only studied. The collector has been modelled based on energyand exergy balances. It may be noted that properties of CO2 changes abruptly near the criticalpoint. To consider the lengthwise property variation, the solar collector has been discretised andmomentum and energy conservation equations have been applied to each segment. The followingassumptions have been made in the analysis:

(1) Both heat transfer and fluid flow are in steady state(2) There is uniform solar heat gain throughout collector surface(3) Heat loss occurs from top collector surface only

One of the small segments of solar collector of length dx and width W are shown in Figure 2.Applying energy balance:

(mf

nt

)[hf |x+x − hf |x] = [α0τ0I − UL(Tf − Ta)]F ′Wx, (1)

which gives

dhf

dx= ntWF ′

mf[α0τ0I − UL(Tf − Ta)], (2)

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Figure 1. Layout and p–h diagram of indirect solar heating using CO2.

where the collector efficiency factor F ′ is given by (Kalogirou 2004):

F ′ = 1/UL

W/[πdαf ] + W/[(d + (W − d)F)UL] . (3)

It should be noted that the denominator of above equation is the heat transfer resistance fromthe fluid to the ambient air. This resistance can be represented as 1/Uo. Therefore, anotherinterpretation of F ′ is: F ′ = Uo/UL.

The fin efficiency in Equation (3) is given by (Kalogirou 2004),

F = tanh [m(W − d)/2]

[m(W − d)/2], where m = √

UL/kpδ. (4)

For constant thermophysical properties of fluid, Equation (2) can be solved by replacing dhf =cpfdTf (Kalogirou 2004). However, to take care of property variation of CO2, Equation (2) has beendiscretised and properties have evaluated based on mean fluid temperature in each computationalsegment. Hence, the discretised equation of ith segment is given by,

hi+1f − hi

f = ntWLF ′

mf

[α0τ0I − UL

(T i+1

f + T if

2− Ta

)]. (5)

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International Journal of Sustainable Energy 535

Figure 2. A computational segment of absorber plate with tube.

Considering both frictional and momentum pressure drops,

pif − pi+1

f = G2f

2ρf

[fL

d+

(ρ i

f

ρ i+1f

− ρ i+1f

ρ if

)], (6)

where friction factor is given by

f = (0.79 ln(Re) − 1.64)−2. (7)

The heat transfer coefficient of CO2 is given by (Pitla et al. 1998),

αfd

kb= Nu = Nub

(μb

μw

)0.11 (kw

kb

)0.33 (hw − hb

cpb(Tw − Tb)

)0.35

, (8)

where wall temperature can be determined by iteration using following equation:(mf

nt

)(hi+1

f − hif) = π dLαf(Tw − Tb). (9)

Nusselt number at bulk temperature is given by (Pitla et al. 1998),

Nub = (f /8)RePr

12.7√

f /8(Pr2/3 − 1) + 1.07. (10)

Heat transfer coefficient of the water has been evaluated using Dittus–Bolter correlation:

Nu = 0.023Re0.8Pr0.4. (11)

Useful heat transfer rate is given by

Quf = mf(hf,exit − hf,inlet). (12)

Now, the collector thermal efficiency is given by

ηc = Quf

AcI .(13)

The collector heat removal factor is given by

FR = Quf

Ac[α0τ0I − UL(Tf,inlet − Ta)] . (14)

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The exergy input to the collector is given by (Kalogirou 2004),

Ein = Acα0τ0I

(1 − Ta

Tas

). (15)

The exergy gain by the heat transfer fluid can be expressed as:

Egain = Quf − mfTa(sf,exit − sf,inlet). (16)

Hence, the irreversibility of the solar collector is given by,

Eloss = Ein − Egain. (17)

The second law efficiency of the solar collector is given by

ηII = Egain

Ein. (18)

The Engineering Equation Solver code has been developed to simulate the solar collector with CO2

as working fluid at various operating conditions. Property variation is very abrupt near the criticalregion and the collector encompasses this region. To consider this variation, the entire lengthof the collector has been divided equally into several discrete segments and in each segment,heat transfer coefficient for CO2 is calculated based on mean values. This way, the collector ismade equivalent to a number of collectors arranged in series and the combined heat transfer ofall the segments is the total heat transfer of the collector. Therefore, fast changing properties ofsupercritical CO2 have been modelled accurately in the solar collector.

3. Results and discussion

To investigate the characteristics of the flat-plate solar collector with water and CO2 as heattransfer fluids, the tube diameter and absorber plate thickness are assumed to be 10 mm and15 mm, respectively. The tube spacing, number of tubes and collector fluid inlet temperature havebeen taken as 20 mm, 5 and 30.9C, respectively. Transmittance–absorptance product and heat losscoefficient have been taken as 0.8 and 7.2 W/m2K, respectively. The apparent sun temperatureis taken as 4500 K. To the best of authors’ knowledge, no previous result is available in openliterature for flat-plate solar collector with CO2. Hence, the code has been quantitatively validatedwith the experimental data by Jafarkazemi and Ahmadifard (2013) for water. For comparison, allthe geometric and constant parameters of their flat-plate collector prototype have been used for thesimulation. For ambient temperature, water inlet temperature and solar radiation of 27C, 45Cand 500 W/m2, respectively, the value of (Tf,inlet − Ta)/I is 0.036 and the heat loss coefficienthas been reported as 3.5 W/m2K, and the corresponding experimental value of collector thermalefficiency has been reported as 60%. For same inputs, the present code gives the collector efficiencyvalue of 62.1%, which showed good matching with 3.5% error (overprediction). The trend is alsofairly matching with experimental results of evacuated solar collector with CO2 (Yamaguchiet al. 2010). The various performance parameters of solar collector are exhibited graphically aselucidated below.

Figure 3 shows the variation of heat transfer coefficient of CO2 (Equation (10)) with bulktemperature for various operating pressure. As shown, the heat transfer coefficient of CO2 is veryhigh near critical temperature and pressure compared to that of water. For a certain operatingpressure, the heat transfer coefficient of CO2 first increases and then decreases and yields some

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International Journal of Sustainable Energy 537

Figure 3. Variation of heat transfer coefficient for various operating pressure.

maximum value, which occurs very near to pseudo-critical temperature. With increase in operatingpressure, the peak value decreases and corresponding optimum temperature increases. On the otherhand, there will be an optimum operating pressure to yield maximum heat transfer coefficientfor a certain operating temperature and optimum pressure increases with increase in temperature.Based on regression analysis, the following correlation of optimum pressure (in bar) in terms ofmean operating temperature (in C) has been established (R2 > 99%):

popt = 40.72 + 0.52tf + 0.0175t2

f . (19)

Present discussion reveals that for the operating temperature up to about 50C, one can getthe higher heat transfer coefficient of CO2 compared with water at the corresponding optimumoperating pressure. Hence, higher value of heat transfer coefficient of CO2 in flat-plate solarcollector can be obtained for fluid outlet temperature up to 50–60C approximately, and the useof CO2 as a heat transfer fluid is expected to effective for low temperature heating applications.

In this study, performance of flat-plate collector is studied for realistic metrological conditions.Figure 4 shows the variation of month-wise average solar radiation intensity and ambient temper-ature in New Delhi in 2011. As discussed earlier that CO2 is more suitable for low temperatureapplications, and hence the forgoing results are based on data for January–March and October–December (six months), in which season, solar collector is generally used for domestic heatingpurposes. It may be noted that the optimum operating pressure exists, which yields maximumuseful heat transfer rate, and hence the collector performances have been evaluated at optimumoperating pressure.

Variation of month-wise useful heat transfer rate, collector heat removal factor and collectorthermal efficiency are shown in Figures 5–7, respectively for collector surface area of 10 m2 andfluid mass flow rate of 0.06 kg/s (this value is taken to get turbulent heat transfer for both waterand CO2). As shown, due to excellent thermophysical and heat transfer properties, CO2 yieldssignificantly better performances compared with water. For same operating conditions, the outlettemperature of CO2 is less than that of water due to higher specific heat capacity at near criticaloperation as shown in Figure 8. Heat transfer rate and collector efficiency are strongly dependent onsolar radiation and ambient temperature, whereas the variation of heat removal factor is negligibleas it mainly dependent on collector design and heat transfer fluid. Interestingly, the results showthat the improvement of all heat transfer rates, heat removal factor and efficiency is about 14%for all six months. Hence, the effects of solar radiation and ambient temperature variations on

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Figure 4. Variation of monthly average incident solar radiation and ambient temperature.

Figure 5. Monthly variation of useful heat transfer rate for water and CO2.

performance improvement are negligible and it is expected to get same improvement by usingCO2 over water for any metrological condition.

Figures 9 and 10 show the month-wise variations of non-dimensional irreversibility (ratio ofirreversibility to heat transfer rate) and second law efficiency for water and CO2. Due to highertemperature rise of water compared to CO2 for same mass flow rate (Figure 8), the available energyor exergy gain by CO2 is less and the irreversibility is more as compared with water. Hence, thesecond law efficiency of collector is lower for CO2 as compared with that for water. However, thenon-dimensional exergy loss for CO2 is less due to higher heat transfer rate, which implies thatimprovement of heat transfer rate is more predominant than increase in irreversibility by usingCO2 as heat transfer fluid in flat-plate solar collector.

The effects of collector surface area for fixed mass flow rate of 0.06 kg/s and the mass flowrate for fixed surface area of 10 m2 on collector efficiency are shown in Figures 11 and 12, respec-tively. The average incident solar radiation of 592 W/m2 and ambient temperature of 19.3Care taken as fixed parameters for evaluation. With the increase in surface area, fluid outlet tem-perature increases, and hence the heat loss increases due to increase in temperature difference,which leads to decrease in collector thermal efficiency. However, the effect on efficiency for

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International Journal of Sustainable Energy 539

Figure 6. Monthly variation of collector thermal efficiency for water and CO2.

Figure 7. Monthly variation of collector heat removal factor for water and CO2.

Figure 8. Monthly variation of collector outlet temperature for water and CO2.

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Figure 9. Monthly variation of collector irreversibility for water and CO2.

Figure 10. Monthly variation of collector second law efficiency for water and CO2.

CO2 is less predominant than that for water due to less temperature rise. Due to similar rea-son, the useful heat transfer rate increases with increase in mass flow rate as the heat lossreduces, and hence collector efficiency increases. Also, the effect of mass flow rate on col-lector efficiency is less for CO2 as compared with that for water. The collector performanceimprovement increases with increase in collector surface area or decrease in mass flow rate byusing CO2 as heat transfer fluid. For the studied operating conditions, the maximum improve-ment is evaluated as 18%. It may be noted that the useful heat transfer rate can be increasedby decreasing inlet fluid temperature (deceasing heat loss) although quality of useful heat willdegrade, and hence the collector efficiency will decrease. However, CO2 can be used for theinlet temperature up to critical temperature (≈31C) only. Solar collector performance can beaffected by collector inclination angle. As suitability of CO2 is main aim of this study, effectson radiation absorbed and loss coefficient is not considered here. Inclination angle (β) may alsoaffect the fluid heat transfer and pressure drop for inclined tube arrangement only. Consider-ing upward flow in each segment, the pressure drop will be increased by ρgL sin β for same

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International Journal of Sustainable Energy 541

Figure 11. Variation of collector thermal efficiency with collector surface area.

Figure 12. Variation of collector thermal efficiency with fluid mass flow rate.

heat transfer and increase in velocity reduces for same pressure drop, which decreases Re andhence heat transfer coefficient. However, a result at mean operating parameters for β = 30, theeffect is negligibly small. Performance graph for varying metrological conditions (Figure 13)implies the performance improvement of solar flat-plate collector by using CO2 as workingfluid.

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Figure 13. Performance characteristic of flat-plate collector for water and CO2.

4. Conclusions

Energetic as well as exergetic analyses of flat-plate solar collector using supercritical CO2 andwater have been done to study the effects of various operating, design and metrological parameterson both energetic and exergetic performances. The optimum operating pressure exists to yieldmaximum heat transfer coefficient of CO2 for a certain operating temperature and optimumpressure correlation has been established, which may be used for design. Higher value of heattransfer coefficient of CO2 in flat-plate solar collector can be obtained for fluid outlet temperatureup to 50–60C approximately.

Due to excellent thermophysical and heat transfer properties, CO2 yields significantly betterperformances compared with that of water. Effect of metrological condition on heat transfer rateand collector efficiency is significant and that on heat removal factor is negligible as it dependson design. However, the improvements are similar for all (14%). The second law efficiency ofcollector is lower for CO2 as compared with water due to lower temperature rise. However,improvement of heat transfer rate is more predominant than increase in irreversibility by usingCO2 as heat transfer fluid in flat-plate solar collector. With the increase in surface area, the collectorthermal efficiency decreases due increase in heat loss. Due to similar reason, the collector thermalefficiency increases with increase in mass flow rate. The performance improvement by using CO2

is more for higher collector surface area or lower mass flow rate. For the studied ranges, themaximum performance improvement by using CO2 as heat transfer fluid is evaluated as 18%.

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