Analysis of Terrestrial Solar Radiation Exergy

http://www.paper.edu.cn

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Based on Candaus denition of radiative exergy, the exergy of the extraterrestrial and the terrestrial solar radiation are computed and

Exergy analysis is a very eective method to analyze the

Petela (1964, 2003) investigated the exergy of thermalradiation and proposed a ratio of the relative potential ofthe maximum energy available from radiation. For undi-

P 3 T S 3 T S 0 s

ment temperature and the solar radiation temperature,

Petela (1964). Spanner (1964) applied the concept of abso-lute work instead of useful work to express the exergy ofdirect solar radiation, and expressed the maximum e-

ciency of direct solar radiation as gS 1 43 T 0T S. Based onthe analysis of heat engine, Jeter (1981) derived the resultthat the Carnot eciency is applicable to the exergy of

* Corresponding author. Tel.: +86 451 86402237.E-mail address: [email protected] (L.H. Liu).

Available online at www.sciencedirect.com

Solar Energy 83 (2009)process of heat transfer and it provides a new insight thatcannot be obtained from energy analysis. The best utiliza-tion of solar energy is evaluated by the maximum work-producing potential (exergy) or the maximum conversioneciency that is associated with thermal radiation. Themaximum conversion eciency of direct solar radiationwas studied by many researchers, such as Petela (1964,2003), Spanner (1964), Press (1976), Landsberg and Tonge(1979), Parrot (1978, 1979), Jeter (1981), Kabelac (1991),Millan et al. (1996), and so on.

respectively. For the direct sunlight, Press (1976) andLandsberg and Tonge (1979) obtained a same optimal e-ciency as Petelas formulae (1964). For any direct radiationpropagating within the solid angle 2p, Parrot (1978)derived the maximum theoretical conversion eciency of

solar energy as gPa 1 43 T 0T S 1 cos d 13 T 0T S4, where d

is the half angle of the cone subtended by the suns disc.However, by using the availability concept, Parrot (1979)obtained results which conrmed the results obtained bycompared by using the solar spectral radiation databank developed by Gueymard. The results show that within the spectrum region from0.28 to 4.0 lm, the total energy quality factor (i.e., the exergy-to-energy ratio) of extraterrestrial solar radiation is about 0.9292, and thatof the global terrestrial solar radiation is about 0.9171 under US standard atmosphere condition and zero solar zenith angle. The ter-restrial solar spectral radiation exergy ux is large in the near ultraviolet and the visible light region. The reference radiation exergy spec-tra are obtained under atmospheric conditions consistent with ASTM standard G173-03. The eect of tilt angle on the terrestrial solarradiative exergy for inclined surface, and the eect of air mass on total energy quality factor of the terrestrial solar radiation for hori-zontal surface are analyzed. With the increase of tilt angle, the terrestrial solar spectral radiation exergy ux initially increases and thendecreases, the total energy quality factor of the diuse part decreases monotonically, while that of the direct part is invariant. The totalenergy quality factor of the direct, the diuse and the global terrestrial solar radiation all decrease with the increase of air mass. 2009 Elsevier Ltd. All rights reserved.

Keywords: Solar radiation; Exergy; Energy quality factor

1. Introduction luted solar radiation this limiting eciency was written as

g 1 4 T 0 1 T 0 4, in which T and T are the environ-Analysis of terrestrial

S.X. Chu,

School of Energy Science and Engineering, Harbin Institute of Techno

Received 5 July 2008; received in revisedAvailable onl

Communicated by: A

Abstract0038-092X/$ - see front matter 2009 Elsevier Ltd. All rights reserved.doi:10.1016/j.solener.2009.03.011olar radiation exergy

.H. Liu *

y, 92 West Dazhi Street, Harbin 150001, Peoples Republic of China

3 March 2009; accepted 4 March 20095 April 2009

iate Editor R. Petela

www.elsevier.com/locate/solener

13901404??


Nomenclature

c0 speed of light in vacuum, 2.99792458 108 (ms1)

Eb;k direct terrestrial solar spectral irradiance for hor-izontal surface (W m2 lm1)

Ebt;k direct terrestrial solar spectral irradiance for in-clined surface (W m2 lm1)

Eb direct terrestrial solar radiation energy ux forhorizontal surface (W m2)

Ebt direct terrestrial solar radiation energy ux forinclined surface (W m2)

Ed;k diuse terrestrial solar spectral irradiance forhorizontal surface (W m2 lm1)

Edt;k diuse terrestrial solar spectral irradiance for in-clined surface (W m2 lm1)

Ed diuse terrestrial solar radiation energy ux forhorizontal surface (W m2)

Edt diuse terrestrial solar radiation energy ux forinclined surface (W m2)

Eg;k global terrestrial solar spectral irradiance forhorizontal surface (W m2 lm1)

Ert;k diuse terrestrial solar spectral irradiance re-ected by the foreground for inclined surface(W m2 lm1)

Es;dt;k sky diuse terrestrial solar spectral irradiance forinclined surface (W m2 lm1)

EETSk extraterrestrial solar spectral irradiance (W m2

lm1)h Plancks constant, 6.626176 1034 (J s)Ik spectral radiative intensity (W m

2 lm1 sr1)I0;k spectral radiative intensity of the environment

(W m2 lm1 sr1)Ib;k direct terrestrial solar spectral radiative intensity

for horizontal surface (W m2 lm1 sr1)Ibt;k direct terrestrial solar spectral radiative intensity

for inclined surface (W m2 lm1 sr1)Id;k diuse terrestrial solar spectral radiative inten-

sity for horizontal surface (W m2 lm1 sr1)Idt;k diuse terrestrial solar spectral radiative inten-

sity for inclined surface (W m2 lm1 sr1)IETSk extraterrestrial solar spectral radiative intensity

(W m2 lm1 sr1)kb Boltzmanns constant, 1.380662 1023 (J

K1)Lk spectral radiation entropy intensity (W m

2

lm1 sr1 K1)L0;k spectral radiation entropy intensity of the envi-

ronment (W m2 lm1 sr1 K1)m air massPD percent dierence between the extraterrestrial

and the global terrestrial solar spectral radiationexergy ux,%

r EarthSun distance, 1.4959787 1011 (m)rs solar radius, 6.95508 108 (m)

Rb geometry factorRd factor of sky diuse terrestrial solar radiationRr factor of diuse terrestrial solar radiation re-

ected by the foregroundT temperature (K)T 0 temperature of the environment (K)T s solar radiative temperature (K)T k spectral radiation temperature (K)

Greek Symbolsd the half angle of the cone subtended by the suns

disc (deg)us solar azimuth angle (deg)ut surface azimuth angle (deg)gP the limiting eciency of undiluted solar radia-

tion proposed by PetelagPa the maximum theoretical conversion eciency of

solar energy derived by ParrotgS the maximum eciency of direct solar radiation

proposed by SpannergETSk spectral energy quality factor of the extraterres-

trial solar radiationgTSb;k spectral energy quality factor of the direct terres-

trial solar radiation for horizontal surfacegTSb total energy quality factor of the direct terrestrial

solar radiation for horizontal surfacegTSbt total energy quality factor of the direct terrestrial

solar radiation for inclined surfacegTSd;k spectral energy quality factor of the diuse ter-

restrial solar radiation for horizontal surfacegTSd total energy quality factor of the diuse terres-

trial solar radiation for horizontal surfacegTSdt total energy quality factor of the diuse terres-

trial solar radiation for inclined surfacegTSg;k spectral energy quality factor of the global ter-

restrial solar radiation for horizontal surfacegTSg total energy quality factor of the global terres-

trial solar radiation for horizontal surfacegTSgt total energy quality factor of the global terres-

trial solar radiation for inclined surfacegETS total energy quality factor of the extraterrestrial

solar radiationk wavelength (lm)h angle between radiation beam and normal direc-

tion of the surface (deg)hd the angle of incidence on the inclined surface

(deg)hs solar zenith angle (deg)ht tilt angle for the inclined surface (deg)qk spectral reectancewk spectral radiative exergy intensity (W m

2 lm1

sr1)DX solid angle of the suns disc (sr)

S.X. Chu, L.H. Liu / Solar Energy 83 (2009) 13901404 1391


Enethermal radiation. With the same conclusion as Jeter(1981), Kabelac (1991) and Millan et al. (1996) adoptedthe Carnot eciency as the upper limit exergy eciencyof solar radiation. Petela (2003) discussed in detail thesethree formulae proposed by Petela (1964), Spanner (1964)and Jeter (1981), respectively, and conrmed Petelas(1964) formula for undiluted direct solar radiation.

As we know, the direct radiation is attenuated on itspath through atmosphere and a part of the scattered energyreaches the surface as diuse radiation. To the authorsknowledge, the eciency of diuse radiation has not beenstudied extensively. Press (1976) pointed out that the dif-fuse sunlight allowed about 25% less conversion of energybecause of the greater entropy in the diuse radiation.Landsberg and Tonge (1979) indicated that the eciencyof diuse solar radiation is 70% and that of direct solarradiation is 93% for a black absorber.

X solid angle (sr)W radiation exergy ux (W m2)WETSk extraterrestrial solar spectral radiation exergy

ux (W m2 lm1)WTSb;k direct terrestrial solar spectral radiation exergy

ux for horizontal surface. (W m2 lm1)WTSb direct terrestrial solar radiation exergy ux for

horizontal surface (W m2)WTSbt;k direct terrestrial solar spectral radiation exergy

ux for inclined surface (W m2 lm1)WTSbt direct terrestrial solar radiation exergy ux for

inclined surface (W m2)WTSd;k diuse terrestrial solar spectral radiation exergy

ux for horizontal surface. (W m2 lm1)WTSd total diuse terrestrial solar radiation exergy ux

for horizontal surface (W m2)

1392 S.X. Chu, L.H. Liu / SolarHowever, the former works on maximum work e-ciency of the direct or the diuse solar radiation mentionedabove did not consider the spectral distribution. The inci-dent terrestrial solar radiation irradiance varies abruptlywith wavelength and the terrestrial solar radiation cannotbe regarded as blackbody radiation in engineering. The uti-lization of multispectral solar energy is important for manyscientic disciplines as well as engineering and biologicalapplications. Therefore, the maximum useful work, i.e.,the spectral radiation exergy ux of terrestrial solar radia-tion is necessary to be studied.

Before the calculation of total radiation exergy, a deni-tion of monochromatic radiation exergy intensity shouldbe given. However, the denition of monochromatic radia-tion exergy intensity has not been well formulated. Animportant problem is that whether the GouyStodola the-orem is suitable for non-equilibrium thermal radiation. TheGouyStodola theorem proves that, for any given system,there is a linear correlation between the correspondingexergy losses and entropy generated by the system, andthe ratio between them is the environment temperatureT 0 used in the exergy analysis. Based on Plancks (1959)formula of spectral radiative entropy intensity, Candau(2003) presented a derivation of the spectral radiative exer-gy intensity. Following the work of Candau (2003), Liuand Chu (2007) deduced a radiative exergy transfer equa-tion in the semitransparent medium, and showed that therelation between exergy losses and entropy generation areconsistent with the GuoyStodola theorem in classicalthermodynamics, which on the other hand demonstratedthe validity of Candaus denition of spectral radiativeexergy intensity.

The calculation of spectral radiative exergy intensity isbased on the spectral radiative intensity. The terrestrialsolar spectral radiative intensity is derived from the terres-trial solar spectral irradiance, which can be obtained bysome advanced radiative transfer codes, such as LibRad-

WTSdt;k diuse terrestrial solar spectral radiation exergyux for inclined surface. (W m2 lm1)

WTSdt diuse terrestrial solar radiation exergy ux forinclined surface (W m2)

WTSg;k global terrestrial solar spectral radiation exergyux for horizontal surface (W m2 lm1)

WTSgt;k global terrestrial solar spectral radiation exergyux for inclined surface (W m2 lm1)

WETS total extraterrestrial solar radiation exergy ux(W m2)

AbbreviationsETS extraterrestrial solarTS terrestrial solar

rgy 83 (2009) 13901404tran (Mayer and Kylling, 2005), MODTRAN (Berket al., 1999), SBDART (Ricchiazzi et al., 1998) and soon. However, the shortages of these three radiative transfermodels mentioned above, such as, complexity and lack ofsupport for the prediction of spectral irradiance on tiltedsurfaces etc, make their utilization inappropriate for energyapplication. In recent years, a spectral model and FOR-TRAN code, namely, SMARTS (Simple Model of theAtmospheric Radiative Transfer of Sunshine) were pro-posed by Gueymard (1995, 2001, 2003) and the latest ver-sion was SMARTS 2.9.5 revised by Gueymard (2006).This code can be used to predict the direct beam, diuseand global irradiance incident on surfaces of any geometryat the Earths surface. SMARTS is a spectral radiativecode, which covers the whole shortwave solar spectrum(2804000 nm) with unequal wavelength intervals, i.e.,0.5 nm between 280 and 400 nm, 1 nm between 400 and1702 nm, and 5 nm between 1705 and 4000 nm. Gueymard(2005) reviewed the spectral solar irradiance models, andpointed out that the applications of SMARTS model have


SMARTS model on predicting clear-sky shortwave irradi-ance spectra on horizontal, tilted, or tracking surfaces.

EneThe spectral selection is important in biological, chemi-cal and physical processes and so on. The solar photovol-taic conversion one of the spectral selective processesfor instance, in which photons with energy less than thebandgap energy or photons with wavelengths longer thanthe cuto wavelength are not used by photovoltaic devices(De Vos, 1992; Coutts, 1999) is also one of the mainapproaches to utilize solar energy. As monitoring the spec-trally selective processes experimentally is quite dicult,the prediction of such system at the initial design stagewould be necessary. In spectrally selective system or devicesto be tested or rated, reference spectra are very necessary toevaluate the relative performance of PV materials anddevices. A typical application of SMARTS is to obtain ref-erence spectra for better photovoltaic design, PV cell per-formance analysis, and rating (Gueymard et al., 2002).Traditionally, the analysis of utilization of solar energy isfrom the viewpoint of energy analysis (e.g., Baruch et al.,1995; Badescu and Landsberg, 1995; Labuhn and Kabelac,2001; Markvart and Landsberg, 2002), however, the view-point of exergy analysis has not been extended in the solarenergy application. It is similar to the energy analysis ofsolar energy application; the exergy analysis also needs toconsider the spectral characteristics of solar radiation.For better utilization of solar energy, the terrestrial solarspectral radiation exergy needs to be studied.

The objective of this paper is to study the exergy ofterrestrial solar radiation. The SMARTS model isadopted to predict the direct beam, the diuse and theglobal irradiance incident on surfaces of any geometryat the Earths surface. The exergy of the extraterrestrialand the terrestrial solar radiation are compared. Thespectral energy quality factor (i.e. the ratio of the spec-tral radiation exergy ux to the spectral radiationenergy ux) of the extraterrestrial and the terrestrialsolar radiation are analyzed. The reference radiationexergy spectra are obtained under atmospheric conditionconsistent with ASTM (American Society for Testingand Materials) standard G173-03 (ASTM, 2003). Theterrestrial solar spectral radiation exergy uxes at dier-ent tilt angles are compared. Finally, the eects of tiltangle and air mass on total energy quality factor of ter-restrial solar radiation are analyzed.

2. Radiative exergy

In the following analysis, only the incoherent radiationis considered and the wave interference and diractionbeen accepted in both the atmospheric and engineeringelds because of its versatility, ease of use, execution speed,and various renements. Recently, Gueymard (2008) con-rmed the excellent accuracy and high performance of

S.X. Chu, L.H. Liu / Solarare neglected. The direct terrestrial solar radiation is atten-uated on its path through atmosphere and a part of thescattered energy reaches the surface as diuse terrestrialsolar radiation. The polarization only aects the diuse ter-restrial solar radiation. Kabelac and Drake (1992) analyzedthe eect of the degree of polarization on diuse terrestrialsolar radiation entropy. The results show that in the clearsky condition, the value of entropy ux for the isotropicdiuse radiation calculated under polarized radiation isonly


3. Solar radiative exergy and energy quality factor

3.1. Extraterrestrial solar radiative exergy and energy

quality factor

The solar radius is rs = 6.95508 108 m (Braun, 2002)and the average SunEarth distance is r = 1.4959787 1011 m (NIST, 2001). The solid angle of the suns disc forpresent study is DX pr2s=r2 6:7905244 105 sr, andwhich was also recommended by Darula et al. (2005) tocalculate the luminance and illuminance. However, if cal-culations for a specic day or time are intended, the actualSunEarth distance should be used. The extraterrestrialsolar spectral irradiance EETSk is read from extraterrestrial

gETS WETSR

k EETSk dk

10

3.2. Terrestrial solar radiative exergy and energy quality

factor for the horizontal surface

The direct and the diuse terrestrial solar spectral irradi-ance incident on a horizontal surface are denoted by Eb;kand Ed;k, respectively, the detailed calculation of themcan be done with SMARTS code. The global terrestrialsolar spectral irradiance incident on the horizontal surfacecan be written as:

Eg;k Eb;k Ed;k 11

frouey

gle, 180 surface azimuth Inclined surface, 180surface azimuth

Horizontal surface

re

1394 S.X. Chu, L.H. Liu / Solar Energy 83 (2009) 13901404spectrum. The extraterrestrial solar spectral radiative inten-sity focused in DX is

IETSk EETSk

DX cos hs6

where hs is solar zenith angle.The extraterrestrial solar spectral radiation exergy ux

incident on a surface WETSk is calculated as

WETSk DXcoshsfIETSk I0;k T 0fLkIETSk L0;kI0;kT 0gg 7

and the total extraterrestrial solar radiation exergy uxincident on a surface WETS is derived by integrating Eq.(7) over wavelength as follows

WETS DXcoshsZkfIETSk I0;k T 0fLkIETSk

L0;kI0;kT 0ggdk 8The spectral energy quality factor of extraterrestrial

solar radiation is dened as

gETSk WETSkEETSk

9

Correspondingly, the total energy quality factor ofextraterrestrial solar radiation is dened as

Table 1Conditions considered in four dierent cases.

Conditions Case 1 Case 2

Solar zenithangle (deg)

0 48.236

Air mass 1.0 1.5Extraterrestrial

spectrumGueymard (2004) Synthetic spectrum revised

SMARTS 2.8 spectrum, GSolar constant

(W/m2)1366.1 1367.0

Surface Horizontal surface Inclined surface, 37 tilt an

Ground albedo Albedo.dat, Lambertianreectance

Light soil, non-LambertianVersion ofSMARTS

SMARTS 2.9.5 SMARTS 2.9.2ectance Light soil, non-Lambertianreectance

Light soil, non-LambertianreectanceThe direct terrestrial solar spectral radiative intensity,which is relative to the SunEarth geometry, is focused inDX. So the direct terrestrial solar spectral radiative inten-sity incident on the horizontal surface is

Ib;k Eb;kDXcoshs 12

In this paper, the diuse terrestrial solar spectral radia-tive intensity is derived by assuming the isotropic hemi-spheric distribution,

Id;k Ed;kp 13

The direct and the diuse terrestrial solar spectral radi-ation exergy ux incident on the horizontal surface aregiven respectively as

WTSb;k DX cos hsfIb;k I0;k T 0fLkIb;k L0;kI0;kT 0gg 14

WTSd;k pfId;k I0;k T 0fLkId;k L0;kI0;kT 0gg 15The global terrestrial solar spectral radiation exergy uxWTSg;k incident on the horizontal surface is the sum of the di-rect and the diuse terrestrial solar spectral radiation exer-gy uxes. The spectral energy quality factors of the direct,

Case 3 Case 4

48.236

1.5m the previousmard

Gueymard (2004) Gueymard (2004)

1366.1 1366.1SMARTS 2.9.5 SMARTS 2.9.5


the diuse and the global terrestrial solar radiation for hor-izontal surface are dened respectively, as

gTSb;k WTSb;kEb;k

; gTSd;k WTSd;kEd;k

; gTSg;k WTSb;k WTSd;kEb;k Ed;k

WTSg;k

Eg;k16

Because the wavelength range in SMARTS code is from0.28 to 4.0 lm, the direct and the diuse terrestrial solarradiation exergy uxes incident on the horizontal surfaceare derived by integrating Eqs. (14) and (15) over wave-length range from 0.28 to 4.0 lm, respectively, as

WTSb DX cos hsZ 40:28

fIb;k I0;k T 0fLkIb;k

L0;kI0;kT 0ggdk 17

WTSd pZ 40:28

fId;k I0;k T 0fLkId;k L0;kI0;kT 0ggdk18

The direct terrestrial solar radiative energy ux Eb andthe diuse terrestrial solar radiative energy ux Ed can bederived by integrating Eb;k and Ed;k over wavelength rangefrom 0.28 to 4.0 lm as

Eb Z 4

Eb;kdk; Ed Z 4

Ed;kdk 19

Then, the total energy quality factor of the direct, thediuse and the global terrestrial solar radiation can be writ-ten respectively as

gTSb WTSbEb

; gTSd WTSdEd

; gTSg WTSb WTSdEb Ed 20

The percent dierence between the extraterrestrial andthe global terrestrial solar spectral radiation exergy ux isdened as

PD WETSk WTSg;k

WETSk 100% 21

3.3. Terrestrial solar radiative exergy and energy quality

factor for inclined surface

The direct spectral terrestrial solar irradiance incidenton the inclined surface Ebt;k; the sky diuse terrestrial solarspectral irradiance Es;dt;k and the diuse spectral irradianceErt;k reected by the foreground are given, respectively, as(Gueymard, 1987)

Ebt;k RbEb;k 22aEs;dt;k RdEd;k 22b

(m) 0.50

S.X. Chu, L.H. Liu / Solar Energy 83 (2009) 13901404 13950:28 0:28

Spec

tral E

xerg

y Fl

ux (W

m-2

m-1 )

0.30 0.35 0.40 0.45

0

400

800

1200

1600

20000s = o

Spec

tral E

xerg

y Fl

ux (W

m-2

m-1 )

1.0 1.5 2.00

200

400

600

800

1000

1200Fig. 1. Spectral radiation exergy ux of the extraterrestrial and the global terreregion from 0.76 to 4.0 lm. (m) 2.5 3.0 3.5 4.0

(b)

0s = o

,

TSg

ETSErt;k qkRrEg;k 22c

0.55 0.60 0.65 0.70 0.75

(a)

,

TSg

ETSstrial solar radiation, (a) ultraviolet and visible region and (b) near infrared


0.5

Ene0.30 0.35 0.40 0.450

400

800

1200

1600

20000s = o

Spec

tral I

rradi

ance

(W m

-2

m-1 )

1.0 1.5 2.00

200

400

600

800

1000

1200

Spec

tral I

rradi

ance

(W m

-2

m-1 )

1396 S.X. Chu, L.H. Liu / Solarwhere

Rb Maxfcos hd= cos hs; 0g 23acos hd cos hs cos ht sin hs sin ht cosus ut 23bRr 1 cos ht=2 23cin which hd is the angle of incidence on the inclined surface,ht is the tilt angle of the inclined surface, us and ut are solarazimuth and surface azimuth (both counted clockwise fromnorth) respectively, and Eg;k is the global terrestrial solarspectral irradiance incident on the horizontal surface. Thefactor of sky diuse terrestrial solar radiation Rd is givenin Gueymard (1987) in detail, and the selection of spectralreectance qk is detailed in the Users manual of SMARTScode (Gueymard, 2006).

The total diuse terrestrial solar spectral irradiance Edt;kincident on an inclined receiver is the sum of the sky diuseterrestrial solar spectral irradiance Es;dt;k and the diuse ter-restrial solar spectral irradiance reected by the foregroundErt;k, as provided in the SMARTS outputs. The direct ter-restrial solar spectral radiative intensity incident on theinclined surface and the diuse terrestrial solar spectralradiative intensity can be expressed respectively, as

Ibt;k Ebt;kDX cos hd 24

Idt;k Es;dt;k Ert;kp Edtp

25

Fig. 2. Spectral irradiance of the extraterrestrial and the global terrestrial solafrom 0.76 to 4.0 lm.2.5 3.0 3.5 4.0

0s = o

ETSE

(m) ,gE 0 0.55 0.60 0.65 0.70 0.75

,gE

ETSE

(m)

(b)(a)

rgy 83 (2009) 13901404By using Eqs. (4), (24), and (25), the direct and the dif-fuse terrestrial solar spectral radiation exergy uxes inci-dent on the inclined surface can be expressed respectivelyas

WTSbt;k DX cos hdfIbt;k I0;k T 0fLkIbt;k L0;kI0;kT 0gg 26

WTSdt;k pfIdt;k I0;k T 0fLkIdt;k L0;kI0;kT 0gg 27

The global terrestrial solar spectral radiation exergy uxWTSgt;k incident on the inclined surface is the sum of the spec-tral radiation exergy ux WTSbt;k and W

TSdt;k .

The direct and the diuse terrestrial solar radiation exer-gy uxes incident on the inclined surface can be obtainedby integrating Eqs. (26) and (27) over wavelength rangefrom 0.28 to 4.0 lm, respectively, as

WTSbt DX cos hdZ 40:28

fIbt;k I0;k T 0fLkIbt;k

L0;kI0;kT 0ggdk 28

WTSdt pZ 40:28

fIdt;k I0;k T 0fLkIdt;k

L0;kI0;kT 0ggdk 29

r radiation, (a) ultraviolet and visible region and (b) near infrared region


(0.50

etwel an

twel and

(

EneP D (%

)

1.0 1.5 2.00

20

40

60

80

100

120 % Difference be of the extraterrestriaP D(%

)

0.30 0.35 0.40 0.450

20

40

60

80

100

% Difference b of the extraterrestria

S.X. Chu, L.H. Liu / SolarThe direct terrestrial solar radiative energy ux Ebt andthe diuse terrestrial solar radiative energy ux Edt can bederived by integrating Ebt;k and Edt;k over wavelength rangefrom 0.28 to 4.0 lm as

Ebt Z 40:28

Ebt;kdk; Edt Z 40:28

Edt;kdk 30

The total energy quality factor of the direct, the diuseand the global terrestrial solar radiation for inclined sur-face are dened respectively as

gTSbt WTSbtEbt

; gTSdt WTSdtEdt

; gTSgt WTSbt WTSdtEbt Edt 31

4. Cases and assumptions

Four cases are discussed in present paper, Case 1 is forcomparisons between the radiation exergy ux and energyquality factor of the terrestrial and the extraterrestrial solarradiation; Case 2 is used to derive terrestrial solar radiationexergy reference spectra under atmospheric conditions con-sistent with ASTM G173-03; Case 3 is used to analyze theeect of tilt angle on total energy quality factor for inclinedsurface; and Case 4 is used to discuss the eect of air mass(m) on total energy quality factor. These four cases con-sider a US Standard atmosphere with following conditions:(1) standard pressure is 1013.25 mbar; (2) columnar

Fig. 3. Percent dierence between spectral radiation exergy ux of the extraterregion and (b) near infrared region from 0.76 to 4.0 lm.m) 0.55 0.60 0.65 0.70 0.75

en spectral radiation exergy flux d the global terrestrial solar radiation

(a)

2.5 3.0 3.5 4.0

(b)en spectral radiation exergy flux the global terrestrial solar radiation

m)

rgy 83 (2009) 13901404 1397amounts of ozone is 0.3438 atm-cm; (3) precipitable wateris 1.416 cm; (4) columnar volumetric concentration of car-bon dioxide is 370 ppmv; (5) all gas abundances isdefaulted by average vertical proles except carbon diox-ide, ozone and water vapor; (6) the relatively low turbidity,i.e., an aerosol optical depth (AOD) of 0.084 at 500 nm fora rural aerosol model (Shettle and Fenn, 1979) is consid-ered; (7) the eld of view of the simulated radiometer is5.8; (8) the illuminance, luminous ecacy and photosyn-thetically active radiation (PAR) and special UV calcula-tions are bypassed; (9) the solar azimuth is defaulted tous 180 (south facing).

Other conditions considered in four dierent cases areshown as Table 1. The choice of a zero solar zenith angleis adopted in Case1. This is not a good choice as this casenever occurs at most locations on Earth. However, theincident solar radiation is perpendicular to the horizontalsurface under zero solar zenith angle, as a result the radi-ation beam pathway is minimum and the solar radiationenergy attenuated by atmosphere is the least. Thereforethe choice of zero solar zenith angle is taken into accountin order to compare radiation exergy ux of extraterres-trial with that of the global terrestrial solar radiationtheoretically.

The reference spectra ASTM standard G173-03 is onlyproduced with the whole set of variables in Case 2. Thesynthetic extraterrestrial spectrum adopted in Case 2 is also

restrial and the global terrestrial solar radiation, (a) ultraviolet and visible


Spec

tral e

nerg

y qu

ality

fact

or

0.8 1.0 1.2 1.4 1.6

0.00.10.20.30.40.50.60.70.80.9

Spec

tral e

nerg

y qu

ality

fact

or

2.8 2.9 3.0 3.1 3.2 3.3

0.00.1

0.2

0.3

0.4

0.50.60.7

0.80.9

Spec

tral e

nerg

y qu

ality

fact

or

0.30 0.35 0.40 0.45 0.500.70

0.75

0.80

0.85

0.90

0.95

Fig. 4. Spectral energy quality factor of the extraterrestrial and the global terre

(m)

Spec

tral e

nerg

y qu

ality

fact

or

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00.00.10.20.30.40.50.60.70.80.91.0

,

TSb

,

TSd

Fig. 5. Spectral energy quality factor of the direct and the diuseterrestrial solar radiation.

1398 S.X. Chu, L.H. Liu / Solar Ene(m) 0.55 0.60 0.65 0.70 0.75

(a)

,

TSg

ETS

rgy 83 (2009) 13901404one option of the extraterrestrial spectrum in SMARTS2.9.5, however, the extraterrestrial spectrum proposed byGueymard (2004) is recommended for normal use inSMARTS 2.9.5. Therefore, two slightly dierent extrater-restrial spectrums are chosen in these four dierent cases.

One important assumption is the isotropic hemisphericdistribution of the diuse terrestrial solar radiation. Theterrestrial solar spectral radiative intensity cannot bederived from SMARTS code directly. The calculation ofradiative exergy intensity is based on the radiative inten-sity. So as to obtain the diuse terrestrial solar radiativeintensity, the angular distribution of diuse terrestrial solarradiation should be assumed. Though the angular distribu-tion of diuse terrestrial solar radiation may be anisotropicdistribution in fact, however, here the isotropic assumptionapproximation is adopted for simplicity.

(m) 1.8 2.0 2.2 2.4 2.6

(b)

,

TSg

ETS

(m) 3.4 3.5 3.6 3.7 3.8 3.9 4.0

(c)

,

TSg

ETS

strial solar radiation, (a) 0.280.759 lm; (b) 0.762.56 lm; (c) 2.814.0 lm.


5. Results and discussion

5.1. Comparisons between ETS and TS radiative exergy for

horizontal surface

In the following analysis, the spectral radiation exergyof extraterrestrial and terrestrial solar radiation are forcedto use the same extraterrestrial spectrum to minimize thesources of disagreement. The extraterrestrial spectrum with2002 wavelengths between 0.28 and 4.0 lm proposed byGueymard (2004) is adopted to calculate the extraterres-trial solar radiation exergy and energy quality factor.

Within the spectrum region from 0.28 to 4.0 lm, the totalenergy quality factor of extraterrestrial solar radiation is0.9292 and that of the global terrestrial solar radiation is0.9171. The total energy quality factor of the diuse terres-trial solar radiation is 0.7937 and that of the direct terres-trial solar radiation is 0.9307 for the atmosphere conditionunder consideration. The entropy accompanying the diuseterrestrial solar radiation is larger than that accompanyingthe direct terrestrial solar radiation (Kabelac and Drake,1992), explaining why the total energy quality factor ofthe diuse terrestrial solar radiation is less than that ofthe direct terrestrial solar radiation. And it implies that

(m)

Spec

tral E

xerg

y Fl

ux (W

m-2

m-1 )

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.90

200

400

600

800

1000

1200

1400

1600

Reference radiation exergy spectra of TS under atmospheric conditions consistent with ASTM standard G173-03

,

TSgt

,

TSbt

Fig. 6. Comparison of the direct and the global reference radiation exergy spectra under atmospheric conditions consistent with ASTM standard G173-03.

t =

t =

S.X. Chu, L.H. Liu / Solar Energy 83 (2009) 13901404 1399Perc

ent D

iffer

ence

(%)

-40

-30

-20

-10

0

10

20

30

Perc

ent D

iffer

ence

(%)

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1

-40

-30

-20

-10

0

10

20

307t =

6t =

(

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1

(

Fig. 7. Comparison of terrestrial solar radiation exergy uxes at dierent tilt anexergy spectra, (a) global and (b) direct.(a)

7o 37t = o

87t = o67o

48.236t = o.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9

(b)

o 37t = o

87t = o7o48.236t = o

m)

.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9

m)

gle under atmospheric conditions dened in Case 3 and reference radiation


for systems utilizing solar radiation, such as, the PV sys-tems, can be more ecient with the direct than the diuseterrestrial solar radiation.

The spectral radiation exergy uxes of the extraterres-trial and the global terrestrial solar radiation are proledin Fig. 1. The spectral irradiances of the extraterrestrialand the global terrestrial solar radiation are given inFig. 2. It can be clearly seen that the trend of spectral radi-ation exergy ux distribution is similar with that of thespectral irradiance distribution for extraterrestrial and theglobal terrestrial solar radiation, respectively. However,the spectral radiation exergy ux is less than the spectralirradiance for extraterrestrial and the global terrestrialsolar radiation, respectively.

restrial solar radiation (gETSk ).The spectral energy quality factor (gTSg;k) is larger than 0.9

in the near ultraviolet, the visible light region and infraredregion (1.1511.343 lm, 1.4891.78 lm and 2.0252.375lm). The dierence between the spectral energy quality fac-tor (gTSg;k) and (g

ETSk ) varies with wavelength. The maximum

value of this dierence for the whole spectrum region underconsideration is 0.9075 at wavelength 2.56 lm. Because theattenuation by atmosphere layers is the largest in the farultraviolet region and in the near infrared region of1.3521.401 lm and 1.821.93 lm, the spectral energyquality factor (gTSg;k) is relatively far less than the spectralenergy quality factor (gETSk ) at these same wavelength range.

For the systems constituted by the diuse terrestrialsolar radiation and the environment, the diuse terrestrialsolar radiation in the near infrared region from 1.362 to

1400 S.X. Chu, L.H. Liu / Solar EneAs could be expected, the spectral radiation exergy uxof the global terrestrial solar radiation (WTSg;k) is less thanthat of the extraterrestrial solar radiation (WETSk ). The trendof the spectral radiation exergy ux (WTSg;k) distribution issimilar with that of the spectral radiation exergy ux(WETSk ) in the near ultraviolet and visible light region. Thedistribution of spectral radiation exergy ux (WETSk ) is quitesmooth in the near infrared region; however, the uctua-tion of the spectral radiation exergy ux (WTSg;k) is large inthe near infrared region because of the presence of strongabsorption bands. The spectral radiation exergy ux(WTSg;k) is quite small in the far ultraviolet region. The spec-tral radiation exergy ux (WETSk ) and (W

TSg;k) in visible light

are larger than those in infrared region. The maximumvalue of the spectral radiation exergy ux (WETSk ) and(WTSg;k) are 2082.73 W m

2 lm1 and 1828.40 Wm2

lm1, respectively, and the wavelength corresponding tothese maximum values are all 0.451 lm.

The dierence between the spectral radiation exergyuxes of the extraterrestrial and the global terrestrial solarradiation is shown in Fig. 3. The reason for this dierenceis that the solar radiation is attenuated by atmosphere onits path. It can be clearly seen from Fig. 3 that the dier-ences in the ultraviolet region below about 0.32 lm andin the near infrared region (particularly in the 1.3531.401 lm, 1.8301.915 lm, and 2.5252.860 lm bands),are nearly 100%. In the near ultraviolet (above 0.33 lm)

Rad

iatio

n En

ergy

Flu

x(W m

-2 )

t (deg) 10 20 30 40 50 60 70 80 90

0

200

400

600

800

1000

btE

dtEFig. 8. Distribution of terrestrial solar radiation energy ux for inclinedsurface.and visible light region the dierences are relatively smalland vary smoothly, in contrast with what occurs in the nearinfrared region, where these dierences are large and highlyuctuating. This structure is directly related to the intricatefeatures of the various extinction processes involved in theterrestrial atmosphere.

The spectral energy quality factors of the extraterrestrialand the global terrestrial solar radiation are proled inFig. 4. Owing to the attenuation of atmosphere layers,the global terrestrial solar spectral irradiance (Eg;k) is lessthan the extraterrestrial solar spectral irradiance (EETSk ).The spectral irradiance (Eg;k) is the sum of the direct anddiuse terrestrial solar spectral irradiance. So both thedirect and the diuse terrestrial solar spectral radiationtemperature are all less than the extraterrestrial solar spec-tral radiation temperature. As a whole, the energy qualityfactor of radiation increases with the increase of the tem-perature of high-temperature heat source for a system con-stituted by a solar radiation (high-temperature heat source)and environment (low-temperature heat source). There-fore, the spectral energy quality factor of the global terres-trial solar radiation (gTSg;k) within the spectrum region of0.282.56 lm and 2.814.0 lm is less than that of extrater-

10 20 30 40 50 60 70 80 900.72

0.76

0.80

0.84

0.88

0.92

0.96

TSgt

TSdt

TSbt

Tota

l Ene

rgy

Quali

ty Fa

ctor

t (deg)

Fig. 9. Distribution of total energy quality factor of terrestrial solarradiation for inclined surface.

rgy 83 (2009) 139014044.0 lm cannot all be regarded as the high-temperaturesource at some wavelength range, such as 2.5254.0 lm


and so on. Within these wavelength range, the diuse ter-restrial solar spectral radiative intensity is far less thanthe spectral radiative intensity emitted by environment atT 0, thus is negligible. In this case, it is better to dene theeciency relative to the energy lost by the environment.The focus of present paper is mainly on the exergy of ter-restrial solar radiation. Therefore, when the diuse terres-trial solar spectral radiative intensity is less than thespectral radiative intensity emitted by environment at T 0,the diuse terrestrial solar spectral radiation exergy ux(WTSd;k) is considered to be zero. Similar to the diuse terres-trial solar spectral radiative intensity, the direct terrestrialsolar spectral radiative intensity within the spectrum regionfrom 2.565 to 2.805 lm is also far less than the spectral

S.X. Chu, L.H. Liu / Solar Eneradiative intensity emitted by environment at T 0, thus isnegligible. As a whole, the spectral radiation exergy ux(WTSg;k) is zero in the near infrared region from 2.565 to2.805 lm, which can also be observed from Fig. 1. There-fore, the spectral energy quality factor (gTSg;k) within thespectrum region from 2.565 to 2.805 lm is not shown inFig. 4.

The spectral energy quality factor of the direct and thediuse terrestrial solar radiation are proled in Fig. 5. Itcan be seen clearly that the spectral energy quality factorof direct terrestrial solar radiation (gTSb;k) is larger than 0.9in the near ultraviolet, the visible light region and infraredregion (0.761.116 lm, 1.1481.343 lm, 1.4881.79 lm and2.0252.38 lm). However, the diuse terrestrial solar spec-tral energy quality factor (gTSd;k) within the whole spectrumregion is less than 0.9, and the maximum value of whichis only 0.8656 at 0.326 lm. Because the spectral irradiance(Ed;k) and its fraction in the spectral irradiance (Eg;k) arerelatively large at short wavelength, the spectral energyquality factor (gTSd;k) is relatively large in the near ultraviolet.

From the analysis above, for practical application, theglobal terrestrial solar radiation in the near ultraviolet,the visible light region and the infrared region (1.1511.343 lm, 1.4891.78 lm and 2.0252.375 lm) should betaken into account. The direct part in the near ultraviolet,the visible light region and the infrared region (0.761.116lm, 1.1481.343 lm, 1.4881.79 lm and 2.0252.38 lm)

Tota

l Ene

rgy

Quali

ty Fa

ctor

m1 2 3 4 5 6

0.76

0.80

0.84

0.88

0.92

0.96

TSg

TSd

TSbFig. 10. Eect of air mass on total energy quality factor of terrestrial solarradiation for horizontal surface.can be best utilized, while the diuse part can only be bestutilized in the near ultraviolet.

5.2. Terrestrial solar reference radiation exergy spectra and

comparisons

The reference spectra (ASTM standard G173-03) arereproduced here under the exact same atmospheric condi-tions it species by adopting version 2.9.2 of the SMARTScode. This is what was labeled Case 2 above. The refer-ence radiation exergy spectra are obtained from the refer-ence spectra mentioned above. Fig. 6 proles thereference radiation exergy spectra within the wavelengthrange from 0.3 to 1.9 lm. For the sun-facing surface tiltedat 37 and atmospheric conditions under consideration, thereference radiation exergy spectra of the direct TS is nowsubstantially closer to that of the global TS. However,the wavelength corresponding to the maximum value ofthe direct terrestrial solar spectral radiation exergy ux(WTSbt;k) is 0.531 lm, and that corresponding to the maxi-mum value of the global terrestrial solar spectral radiationexergy (WTSgt;k) is 0.495 lm. That is to say the direct radiationexergy spectrum is slightly red-shifted compared to the glo-bal radiation exergy spectrum. The reason for this phenom-enon is that the scattering eect induced by molecules andaerosols is the maximum at shorter wavelengths, which isinvolved in the global terrestrial solar radiation. Therefore,similar to the reference spectra ASTM standard G173-03,these two reference radiation exergy spectra are not inter-changeable, particularly in the case of highly spectrallyselective devices.

The terrestrial solar spectral radiation exergy ux at dif-ferent tilt angle is calculated under atmospheric conditionsdened in Case 3. Similar to the percent dierence denedin Eq. (21), the percent dierence between terrestrial solarspectral radiation exergy uxes at dierent tilt angle andreference radiation exergy spectra obtained above is pro-led in Fig. 7. With the increase of tilt angle, this percentdierence rst decreases and then increases. And it couldbe clearly seen that the eect of tilt angle on spectral radi-ation exergy ux (WTSbt;k) is larger than that of tilt angle onspectral radiation exergy ux (WTSgt;k) at the smaller tilt angleand the larger tilt angle.

For the inclined surface with tilt angle of 37, the spec-tral radiation exergy ux (WTSbt;k) and (W

TSgt;k) under atmo-

spheric conditions dened in Case 3 are dierent fromthose obtained under atmospheric conditions consistentwith ASTM standard G173-03. The reasons for this dier-ence are the discrepancy of the extraterrestrial solar spec-trum and the version of the SMARTS code. The spectralradiation exergy ux (WTSbt;k) and (W

TSgt;k) under atmospheric

conditions dened in Case 3 at tilt angle 48.236 and 67are close to those obtained under atmospheric conditionsconsistent with ASTM standard G173-03, respectively.However, the utilization of solar energy cannot be well

rgy 83 (2009) 13901404 1401evaluated only from comparison between terrestrial solarspectral radiation exergy uxes and reference radiation


Eneexergy spectra. The evaluation of utilization of solar energyalso needs the analysis of terrestrial solar radiation exergyux and energy quality factor.

5.3. The eect of tilt angle on terrestrial solar radiation

exergy

The eect of tilt angle on terrestrial solar radiation irra-diance and total energy quality factor for inclined surfaceunder atmospheric conditions dened in Case 3 is shownin Figs. 8 and 9 respectively. The angle of incidence hdon the inclined surface is the angle between the normal ofinclined surface and the solar radiation beam. With theincrease of tilt angle, the incidence angle hd rst decreasesand then increases. The incident solar radiation beam isperpendicular to the inclined surface in the case that the tiltangle ht is equal to the solar zenith angle hs, and the path-way here is the minimum. The solar radiation energy atten-uated by atmosphere layer is the least. Hence, as seen fromFig. 8, the tilt angle corresponding to the maximum valueof the direct terrestrial solar radiation energy ux (895.95W/m2) is 48.236, which is equal to the solar zenith angle.The diuse terrestrial solar spectral irradiance (Edt;k)includes two parts, one is the sky diuse terrestrial solarspectral irradiance (Es;dt;k) and the other is the diuse terres-trial solar spectral irradiance reected by the foreground(Ert;k). According to Eq. (22b) and the factor of sky diuseterrestrial solar radiation Rd given by Gueymard (1987),the sky diuse terrestrial solar spectral irradiance (Es;dt;k)rst increases and then decreases with the increase of tiltangle ht. This spectral irradiance (Es;dt;k) is also correlatedwith such spectral irradiance (Ed;k) for horizontal surface,which is part of the global terrestrial solar spectral irradi-ance (Eg;k). As per Eqs. (22c) and (23c), the diuse terres-trial solar spectral irradiance reected by the foreground(Ert;k) increases with the increase of tilt angle ht, and thisspectral irradiance (Ert;k) is correlated with spectral irradi-ance (Eg;k). Therefore the decrement of the spectral irradi-ance (Es;dt;k) is less than the increment of the spectralirradiance (Ert;k). Hence the diuse terrestrial solar radia-tion energy ux (Edt) increases with the increase of tilt angleht.Because the entropy accompanying with the diuse radi-ation is relatively large (Kabelac and Drake, 1992) and thediuse terrestrial solar radiation energy ux (Edt) increaseswith tilt angle, the total energy quality factor of the diuseterrestrial solar radiation (gTSdt ) is relatively small anddecreases with the increase of tilt angle. The direct solarradiation energy is a high-grade energy, and the entropyaccompanying with the direct radiation is relatively small(Kabelac and Drake, 1992). Therefore the total energyquality factor of direct terrestrial solar radiation (gTSbt ) is rel-atively large. The total energy quality factor (gTSbt ) is theo-retically independent on the incidence angle hd , which canbe concluded from Eqs. (24), (28), and (31). If solar zenithangle hs, solar azimuth angle us and surface azimuth angle

1402 S.X. Chu, L.H. Liu / Solarut are given, the incidence angle hd is the function of tiltangle ht only. Hence the total energy quality factor (gTSbt )is independent on the tilt angle ht of the inclined surface.Therefore the variation of total energy quality factor (gTSbt )with titled angle ht is negligible.

The eect of the tilt angle ht on the total energy qualityfactor for the global terrestrial solar radiation (gTSgt ) is notlarge, which is due to the direct terrestrial solar radiationdominating in the global terrestrial solar radiation for theproblem under consideration. The percentage of the directpart in the global terrestrial solar radiation energy ux rstincreases slightly and then decreases with the increases ofthe tilt angle. According to Eq. (31), the total energy qual-ity factor (gTSgt ) is correlated with the percentage of thedirect part in the global terrestrial solar radiation energyux for the conditions under consideration. Therefore thetotal energy quality factor (gTSgt ) rst increases slightly andthen decrease with the increase of the tilt angle. The totalenergy quality factor of the global terrestrial solar radia-tion is less than that of the direct terrestrial solar radiationbecause of the inuence of diuse terrestrial solarradiation.

5.4. The eect of air mass on total energy quality factor

The eect of air mass (m) on total energy quality factorof terrestrial solar radiation for Case 4 under considerationis shown in Fig. 10. It could be clearly seen that the totalenergy quality factor of the direct, the diuse and the glo-bal terrestrial solar radiation all decrease with the increaseof air mass (m). Air mass (m) is the function of the solarzenith angle only. Air mass (m) corresponding to the solarzenith angle by hs 0 is 1.0 (Gueymard, 2003). As theincident solar radiation is perpendicular to the horizontalsurface under zero solar zenith angle, the radiation beampathway is minimum and the solar radiation energy atten-uated by atmosphere is the least. Hence the terrestrial solarradiation energy and the total energy quality factor aremaximum in the Case of air mass m = 1. With the increaseof solar zenith angle, air mass (m) increases and then theterrestrial solar radiation attenuated by atmosphereincreases. Therefore, the terrestrial solar radiation energyux of the direct, the diuse and the global incident on hor-izontal surface all decrease with the increase of air mass(m). As per Eq. (2), the spectral radiation temperaturedecreases with the decrease of spectral radiative intensity.For the system utilizing solar radiation (high-temperatureheat source) and environment (low-temperature heatsource), the spectral radiation energy quality factorincreases with the increase of terrestrial solar spectral radi-ation temperature. Therefore the total energy quality factorof the direct and the diuse terrestrial solar radiation alldecrease with the increase of air mass (m). As stated in Sec-tion 5.3, the direct solar radiation energy is high-gradeenergy, and the entropy accompanying with the direct radi-ation is relatively small (Kabelac and Drake, 1992). So thetotal energy quality factor of direct terrestrial solar radia-

rgy 83 (2009) 13901404tion (gTSb ) is larger than that of the diuse terrestrial solarradiation (gTSd ). The total energy quality factor of the global


Ene6. Conclusions

The SMARTS code is adopted to predict the direct, thediuse and the global terrestrial solar radiation irradiance.By using Candaus denition of radiative exergy, the proce-dure of calculating radiation exergy ux has been detailed.The spectral radiation exergy ux of the extraterrestrialand the terrestrial solar radiation are presented and com-pared under US standard atmosphere condition and zerosolar zenith angle for horizontal surface. The referenceradiation exergy spectra under atmospheric conditions con-sistent with ASTM standard G173-03 are obtained. Theeect of tilted angle on terrestrial solar spectral radiationexergy ux and total energy quality factor for inclined sur-face is analyzed. The eect of air mass on total energy qual-ity factor of terrestrial solar radiation for horizontalsurface is also analyzed. The main conclusions drawn frompresent analysis are summarized as follows:

1) Practical application, for example, photovoltaicdevices can operate more eciently with direct terres-trial solar radiation than that with diuse terrestrialsolar radiation. The direct terrestrial solar radiationcan be best utilized in the near ultraviolet, the visiblelight region and the infrared region (0.761.116 lm,1.1481.343 lm, 1.4881.79 lm and 2.0252.38 lm),while the diuse part can only be best utilized in thenear ultraviolet.

2) The global terrestrial solar radiation in the near ultra-violet, the visible light region and the infrared region(1.1511.343 lm, 1.4891.78 lm and 2.0252.375 lm)should be taken into account for practicalapplication.

3) Both of the global and the direct radiation referenceexergy spectra are not interchangeable.

4) With the increase of tilt angle, the direct and the glo-bal terrestrial solar spectral radiation exergy uxesrst increase and then decrease, the total energy qual-ity factor of diuse terrestrial solar radiationdecreases and that of direct terrestrial solar radiationis nearly invariant.

5) With the increase of air mass, the total energy qualityfactor of the direct, the diuse and the global terres-trial solar radiation all decrease.

6) Because of the inuence of diuse terrestrial solarradiation, the total energy quality factor of the globalterrestrial solar radiation is less than that of the directterrestrial solar radiation.

Acknowledgement

The support of this work by the National Natural Sci-terrestrial solar radiation (gTSg ) decreases from 0.9164 to0.8651 when air mass (m) increases from 1.0 to 5.59.

S.X. Chu, L.H. Liu / Solarence Foundation of China (No. 50836002) is gratefullyacknowledged.References

ASTM, 2003. Standard Tables for Reference Solar Spectral Irradiances:Direct Normal and Hemispherical on 37 Tilted Surface. StandardG17303, American Society for Testing and Materials, West Cons-hohocken, PA, Available from: .

Badescu, V., Landsberg, P.T., 1995. Statistical thermodynamic foundationfor photovoltaic and photothermal conversion. II. Application tophotovoltaic conversion. Journal of Applied Physics 78 (4), 27932802.

Baruch, P., De Vos, A., Landsberg, P.T., Parrott, J.E., 1995. On somethermodynamic aspects of photovoltaic solar energy conversion. SolarEnergy Materials and Solar Cells 36 (2), 201222.

Berk, A. et al., 1999. MODTRAN4 Users Manual. Air Force ResearchLab, Hanscomb, MA.

Braun, J.M., 2002. Astrophysical Data; Available from: .

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

Coutts, T.J., 1999. A review of progress in thermophotovoltaic generationof electricity. Renewable and Sustainable Energy Reviews 3 (23), 77184.

Darula, S., Kittler, R., Gueymard, C.A., 2005. Reference luminous solarconstant and solar luminance for illuminance calculations. SolarEnergy 79 (5), 559565.

De Vos, A., 1992. Endoreversible Thermodynamics of Solar EnergyConversion. Oxford University Press.

Gueymard, C., 1987. An anisotropic solar irradiance model for tiltedsurfaces and its comparison with selected engineering algorithms. SolarEnergy 38 (5), 367386.

Gueymard, C., 1995. SMARTS2, Simple Model of the AtmosphericRadiative Transfer of Sunshine: Algorithms and Performance Assess-ment. Report FSEC-PF-27095. Florida Solar Energy Center, Cocoa,FL.

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

Gueymard, C.A., Myers, D., Emery, K., 2002. Proposed referenceirradiance spectra for solar energy systems testing. Solar energy 73(6), 443467.

Gueymard, C.A., 2003. Direct solar transmittance and irradiance predic-tions with broadband models. Part I: detailed theoretical performanceassessment. Solar Energy 74 (5), 355379.

Gueymard, C.A., 2004. The suns total and spectral irradiance for solarenergy applications and solar radiation models. Solar energy 76 (4),423453.

Gueymard, C.A., 2005. Interdisciplinary applications of a versatilespectral 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 shortwavesolar spectra incident on horizontal, tilted, or tracking surfaces. SolarEnergy 82 (3), 260271.

Jeter, S.M., 1981. Maximum conversion eciency for the utilization ofdirect solar radiation. Solar Energy 26 (3), 231236.

Kabelac, S., 1991. A new look at the maximum conversion eciency ofblackbody radiation. Solar Energy 46 (4), 231236.

Kabelac, S., Drake, F.D., 1992. The entropy of terrestrial solar radiation.Solar Energy 48 (2), 239248.

Labuhn, D., Kabelac, S., 2001. The spectral directional emissivity ofphotovoltaic surfaces. International Journal of Thermophysics 22 (5),15771592.

Landsberg, P.T., Tonge, G., 1979. Thermodynamics of the conversion ofdiluted radiation. Journal of Physics A: Mathematical and General 12(4), 551562.

Liu, L.H., Chu, S.X., 2007. Radiative exergy transfer equation. Journal of

rgy 83 (2009) 13901404 1403Thermophysics and Heat Transfer 21 (4), 819822.


Markvart, T., Landsberg, P.T., 2002. Thermodynamics and reciprocity ofsolar energy conversion. Physica E 14 (12), 7177.

Mayer, B., Kylling, A., 2005. The libRadtran software package forradiative transfer calculations description and examples of use.Atmospheric Chemistry and Physics Discussions 5, 18551877.

Millan, M.I., Hernandez, F., Martin, E., 1996. Available solar exergy inan absorption cooling process. Solar Energy 56 (6), 505511.

National Institute of Standard and Technology, 2001. The InternationalSystem of Units, NIST Special Publication SP330; Available from:.

Parrot, J.E., 1978. Theoretical upper limit to the conversion eciency ofsolar energy. Solar energy 21 (3), 227229.

Parrot, J.E., 1979. A letter. Solar Energy 22 (6), 572573.Petela, R., 1964. Exergy of heat radiation. Transaction of ASME. Journal

of Heat Transfer 86 (2), 187192.

Petela, R., 2003. Exergy of undiluted thermal radiation. Solar Energy 74(6), 469488.

Planck, M., 1959. The Theory of Heat Radiation. Dover, New York.Press, W.H., 1976. Theoretical maximum for energy from direct and

diuse sunlight. Nature 264, 734735.Ricchiazzi, R. et al., 1998. SBDART: a research and teaching

software tool for plane-parallel radiative transfer in the Earthsatmosphere. Bulletin of the American Meteorological Society 79(10), 21012114.

Shettle, E.P., Fenn, R.W., 1979. Models for the aerosols of the loweratmosphere and the eects of humidity variations on their opticalproperties. Report AFGL-TR-790214. Air Force Geophysics Labo-ratory, Hanscom, MA.

Spanner, D.C., 1964. Introduction to Thermodynamics. Academic Press,London and New York.

1404 S.X. Chu, L.H. Liu / Solar Energy 83 (2009) 13901404

Analysis of terrestrial solar radiation exergyIntroductionRadiative exergySolar radiative exergy and energy quality factorExtraterrestrial solar radiative exergy and energy quality factorTerrestrial solar radiative exergy and energy quality factor for the horizontal surfaceTerrestrial solar radiative exergy and energy quality factor for inclined surface

Cases and assumptionsResults and discussionComparisons between ETS and TS radiative exergy for horizontal surfaceTerrestrial solar reference radiation exergy spectra and comparisonsThe effect of tilt angle on terrestrial solar radiation exergyThe effect of air mass on total energy quality factor

ConclusionsAcknowledgementReferences

Documents

Analysis of Terrestrial Solar Radiation Exergy