Exergy Analysis of Solar Thermal System

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S U H A S K A R A N T H

2 0 0 9 B 3 A 4 5 3 7 P

Exergy Analysis of ConcentratedSolar Thermal System


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Need for the study

Exergy analysis is used to get a clear picture of thevarious losses quantitatively as well as qualitatively

Solar thermal systems are fast growing and effective

thermodynamic analysis is necessary Exergy analysis helps to pinpoint the irreversibilities

in the system


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Exergetic analysis of a solar thermalpower system

Narendra Singh, S.C. Kaushik, R.D. Misra

TRo

TRi


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Collector subsystem Qi=(Ib.Rb+Id.Rd)W0L .N

Qs= N.Ib.Rb(.)b[.Y+D0/(W0-D0)]

Exi=Qi[1-(To/Ts)]

Exc=Qs[1-(To/Tc)]


Qi- Power received by collector system(W)Qs- Power absorbed by collector system(W)Ib- Solar Intensity of beam radiation(Wm

-2 )I

d

- Solar Intensity of diffuse radiation(Wm-2 )Rb- Tilt factor of beam radiationRd- Tilt factor of diffuse radiationW0- Aperture of collector(m)L- Length of collector(m)N- No. of collectors

- glass cover transmissivity

-absorbtivity of receiver- reflectivityY- Intercept factorD0- Outer diameter of absorber tube(m)

Exi- Exergy received by collector(W)To- Ambient temperature(K)Ts- Temperature of outer layer of sun(K)Exc- Exergy absorbed by collector(W)Tc- Temperature of collector(K)


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Exi- Exc=IR1 % exergy loss=(IR1/Exi).100 II law efficiency II,1=Exc/ExiReceiver subsystem Exu= N. Mf[(Hfo-Hfi) - To(Sfo- Sfi)] IR2=Exc - Exu % exergy loss=(IR2/Exc).100 II,2=Exu/Exc

Heat engine subsystem1.Heat exchangerUseful exergy delivered by the thermic fluid(Exu) Exu= N. Mf[(Hfo-Hfi) - To(Sfo- Sfi)]

Exu Flow exergyMf Mass flow rate of fluidHfo Enthalpy of fluid outHfi Enthalpy of fluid inSfoEntropy of fluid outSfiEntropy of fluid in

Ex1uUseful exergy


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Exergy available to the working fluid of the heat engine cycle Ex1u=Qu[1-(To/TRo)] Qu=(W0-D0).L.(FR)[Qs/((W0-D0).L)-U0.(Tfi-Ta)/(CR)] IRhx=Exu-Ex

1u

% exergy loss=[IRhx/Exu].100 II,b=Ex

1u/Exu

2.Heat engine cycle Ex1u=Qu[1-(To/TRo)]= Exn Exergy output=net work done by the heat engine Wnet=Wt1+Wt2-Wp Exergy loss=irreversibility (IRhe)= Ex

1u-Wnet

Total % exergy loss=(IRhe/ Ex1u).100

II,c=Wnet/ Ex1u

Qu Useful energy delivered to the fluid in the receiverTRo- Outlet Rankine fluid temperatureFR Heat removal factorU0Overall heat transfer coefficientTfi Inlet collector fluid temperatureTaAmbient temperature

CR- Concentration ratio


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Exergy of solar radiation

Solar energy is not fully convertible because of itsentropy content and thus its exergy content is lessthan 100%

Its crucial to study exergy of solar radiation in exergyanalysis of solar thermal system

Richard Petela, P.T. Landsberg, D.C. Spanner, S.M.Jeter are few of them developed expressions for

exergy of radiation


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Exergy of undiluted thermal radiation

For a surface at the environment temperature To, thefirst fundamental formula on the exergy b (kWm-2)of black radiation emission flux was derived

For a perfectly gray surface with emissivity

Richard Petela


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Efficiency of radiation processes

Radiation to work

Richard Petela

e- Energy efficiencyW Work done by radiation (kWm-2)b Exergy of radiation (kWm-2)Maximum conversion efficiency


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Solar Radiation-to-heat conversion

where (srd) is the solid angle in which the sun is visible from the earth, and (rd) are the angle coordinates (azimuth and declension) of directions includedwithin the range of the solid angle in which from any point of the absorbing

surface the sun surface is visible


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where

bExergy due to solar radiation inangle eEmission from sunea Emission from absorber to

environment

eo Emission from environment toabsorber in angle (2-)Ta Collector temperaturebq Exergy due to q


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Richard Petela


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Richard Petela


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S.X. Chu, L.H. Liu

In their paper, Analysis of Terrestrial SolarRadiation Exergy, they derive the expression forradiation exergy

The analysis is based on validity of Candausdefinition of spectral radiative exergy intensity

The calculation of spectral radiative exergyintensity is based on the spectral radiative intensity

Terrestrial spectral intensity is derived fromterrestrial solar spectral irradiance

SMARTS (Simple Model of the Atmospheric

Radiative Transfer of Sunshine)


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Candau s spectral radiative exergy intensity

On integrating over wavelength and solid angle, the radiative exergy flux is written as

={I-I0,-T0{L(I)-L0,[I0,(T0)]}}cosdd

=cosdd

Here is the angle between radiation beam and normal direction of the surface

Spectral radiative exergy intensity(W m-2 m-1sr-1)I0,Spectral radiative intensity of the environment(W m

-2 m-1sr-1)T0 Temperature of the environment(K)L0,Spectral radiation entropy intensity of the environment(W m

-2 m-1sr-1 K-1) Radiation exergy flux (W m-2) Solid angle of sun(sr)Angle between radiation beam and normal direction of the surface (deg)


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Solar radiative exergy

Solar radiative exergy comprises of Extraterrestrialsolar radiative exergy and Terrestrial solar radiativeexergy

Terrestrial solar radiative exergy is the sum of directand diffuse radiative exergy

In the paper using the above equations, they havecalculated both, along with energy factor

They have employed SMARTS code to carry out thecalculation


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V. Siva Reddy, S.C. Kaushik, S.K. Tyagi

Exergetic analysis and performance evaluation ofparabolic trough concentrating solar thermalpower plant (PTCSTPP)

In this paper they have performed exergy analysisfor the components of the solar thermal powerplant system (parabolic trough collector/receiverand Rankine heat engine)

To calculate radiation exergy, they have used theexpression derived from Petela


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The exergy flow for steady flow process of an open system is given by

The exergetic or second law efficiency is defined as

For steady state flow the exergy balance for a thermal system is given as below

iand o- Exergy associated with mass inflow and outflows are respectivelyW- Useful work done on/by systemh0- Methalpy as summation of enthalpy(h)


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Analysis on parabolic trough concentrator

Ib- Direct normal irradiationW - Width of parabolic troughDco- Glass cover outside diameterL - Mirror lengthNc - Number of collectors

Nr - Number of rows

Nm -Number of modules - Angle of incidencesPetelasradiation exergy expressionTaAmbient temperatureTs - Apparent black body temperature of sun

The total exergetic solar power input to parabolic trough


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List of references

Guggenheim, E.A., 1957. Thermodynamics. North-Holland, Amsterdam Petela, R., 1961b. Exergy of radiation of a perfect gray body. Zesz. Nauk. Pol. Sl., Energetyka 5, 3345, in Polish.

Petela, R., 1964. Exergy of heat radiation. Trans. ASME, J. Heat Transfer No. 2, 187192.

Parrott, J.E., 1979. A letter. Solar Energy 22 (No. 6), 572573.

Planck, M., 1959. The Theory of Heat Radiation. Dover, New York.

Candau, Y., 2003. On the exergy of radiation. Solar Energy 75 (3), 241247.

Mayer, B., Kylling, A., 2005. The libRadtran software package for radiative transfer calculations description and examples ofuse. Atmospheric Chemistry and Physics Discussions 5, 18551877.

Berk, A. et al., 1999. MODTRAN4 Users Manual. Air Force Research Lab, Hanscomb, MA. Ricchiazzi, R. et al., 1998. SBDART: a research and teaching software tool for plane-parallel radiative transfer in the Earths

atmosphere. Bulletin of the American Meteorological Society 79 (10), 21012114.

Gueymard, C., 1995. SMARTS2, Simple Model of the Atmospheric Radiative Transfer of Sunshine: Algorithms and PerformanceAssessment. Report FSEC-PF-27095. Florida Solar Energy Center, Cocoa, FL.

Gueymard, C.A., 2001. Parameterized transmittance model for direct beam and circumsolar spectral irradiance. Solar Energy 71(5), 325346.

Gueymard, C.A., 2003. Direct solar transmittance and irradiance predictions with broadband models. Part I: detailed theoreticalperformance assessment. Solar Energy 74 (5), 355379.

Gueymard, C.A., 2005. Interdisciplinary applications of a versatile spectral solar irradiance model: a review. Energy 30 (9), 15511576.

Gueymard, C.A., 2006. Users Manual of SMARTS Code, version 2.9.5, Revised August.

Gueymard, C.A., 2008. Prediction and validation of cloudless shortwave solar spectra incident on horizontal, tilted, or trackingsurfaces. Solar Energy 82 (3), 260271.

Petela R. Exergy of heat radiation. ASME Journal of Heat Transfer 1964; 86:187e92.

Lippke F. Simulation of the part-load behaviour of a 30 MWe SEGS plant. Report No. SAND95-1293. Alburquerque, NM, USA:SNL; 1995.

Duffie John A, Beckman William A. Solar engineering of thermal processes. 2nd ed. New York: John Wiley and Sons, Inc.; 1991.

Exergy Analysis of Solar Thermal System

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