Energy and Exergy Calculations of Latent Heat Energy Storage Systems

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Energy and Exergy Calculations of Latent Heat Energy Storage Systems Ahmet Sari, Kamil Kaygusuz Published online: 29 Oct 2010.

To cite this article: Ahmet Sari, Kamil Kaygusuz (2000) Energy and Exergy Calculations of Latent Heat Energy Storage Systems, Energy Sources, 22:2, 117-126, DOI: 10.1080/00908310050014090 To link to this article: http://dx.doi.org/10.1080/00908310050014090

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En ergy an d Exergy Calcu lation s of Laten t Heat En ergy Stor age System s


AHME T SARI De partme nt of Che mistry Gaziosm anpasË a Unive rsity Tokat, Turke y

Ç KAYGUSUZ KAMIL De partme nt of Che mistry Karade niz Te chnical Unive rsity Trabzon, Turke y An experim ental stu dy and a theoretical study h av e been conducted to e v alu ate the perform ance for a closed latent heat en ergy storage system using energy and exergy an alyses. The energy storage tank is neither fu lly m ixed n or fully stratified. It m ay be considered as sem istratified. Experim ents were perform ed on su nny winter d ays in 1996. In this stu dy a com plete storing cycle and ch arging and disch argin g periods are considered. Energy and exergy efficiencies, total energy and exergy v ariations, and m ean en ergy and exergy efficiencies are also calculated by using experim ental d ata. K eywor ds

ene rgy and e xe rgy analysis, e ne rgy storage , latent he at

The rm al e ne rgy storage has always bee n one of the most critic al com pone nts in re side ntial solar space he ating applic ations. Solar radiation is a time -de pe nde nt e ne rgy source with an inte rmitte nt characte r. The he ating de m ands of a re side ntial house are also time de pe nde nt. Howe ve r, the e ne rgy source and the he ating de m ands of a building, in ge ne ral, do not m atch e ach othe r, e spe cially in solar he ating applic ations. The pe ak solar radiation occurs ne ar noon, but the pe ak he ating de m and is in the late e ve ning whe n solar radiation is not available . The rm al e ne rgy storage provide s a rese rvoir of e ne rgy to adjust this m ism atch and to me e t the e ne rgy ne e ds at all time s. It is use d as a bridge to cross the gap be twe e n the e ne rgy source , the sun, the application, and the building. So the rm al e ne rgy storage is e sse ntial in a solar he ating syste m ( KakacË e t al., 1989 ) . The use of phase change m ate rials ( PCMs ) for the rm al e ne rgy storage in solar he ating syste ms has re ce ive d conside rable atte ntion. The motivation for using phase change e ne rgy storage ( PCE S ) m ate rials is the re duction in storage volume that can be achie ve d compare d to sensible he at storage syste ms. A bhat ( 1983 ) re vie we d low-te mpe rature PCMs in the te mpe rature range 0 ] 120 8 C and inve stigate d the ir me lting and fre e zing be havior. The most studie d PCM s include Received 14 Se ptember 1998, acce pte d 14 De ce mber 1998. This study was supporte d by the Karade niz Te chnical University Re se arch Fund. Addre ss correspondence to Dr. Kamil Kaygusuz, Departme nt of Che mistry, Karadeniz Te chnical University, 61080 Trabzon, Turke y. E-m ail: kaygusuz@ osf01.ktu.e du.tr

117


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A. Sari an d K. Kaygusuz

Glauber’ s salt, calcium chloride he xahydrate , sodium thiosulfate pe ntahydrate , sodium carbonate de cahydrate , fattic acid, and paraffin waxe s ( Te lke s, 1974; C arlsson e t al., 1979 ; Gulte È kin e t al., 1991 ; Kaygusuz, 1995 ; H asan, 1994 ; Y an adori & M asuda, 1986 ; H ahne , 1996 ) . The e ne rgy e fficie ncy of a the rm al e ne rgy storage ( TE S ) syste m, the ratio of the e ne rgy returne d from storage to the he at originally de live re d to storage , is inade quate as a m e asure of the approach to ide al pe rform ance be cause it doe s not take into account the le ngth of time ove r which the he at is stored or the tem pe ratures at which the he at is supplie d and de live re d, or the te mpe rature of the surroundings. E xe rgy an alysis, which is base d prim arily on the Se cond Law of The rmodyn am ics, as com pare d to e ne rgy analysis, which is base d on the First Law, take s into account the quality of the e ne rgy transfe rre d. E xe rgy an alysis is re cognize d by he at transfe r e ngine e rs to be a powe rful tool for the e valuation of the the rmodyn am ic and e conomic pe rform ance of the rmodynam ic syste ms in ge ne ral and of TE S syste ms in particular ( Rose n e t al., 1988 ; Be jan, 1988 ; Szargut e t al., 1988 ; Krane , 1987 ; Rosen, 1992; Moran & Shapiro, 1996 ; Moran, 1982 ; Gunne wiek e t al., 1993 ) . The prese nt work is dire cte d toward using simple me thods for e valuating and comparing the e ne rgy and e xe rgy e fficie ncie s of a late nt he at closed e ne rgy storage tank. For this purpose, we used some use ful e quations give n in the lite rature ( Rosen e t al., 1988 ) , and we c alculate d e ne rgy and e xe rgy variations and me an e ne rgy and e xe rgy e fficie ncie s.

Exp er im en tal Setu p The wate r-base d syste m inve stigate d in this e xpe rime ntal study is shown in Figure 1, and the syste m param e ters are liste d in Table 1. As shown in Figure 1, this syste m consists of solar colle ctors, an e ne rgy storage tank fille d with PCM , a wate r-to-air he at e xchange r, a wate r circulating pump, and othe r me asuring and control e quipme nt ( Sari, 1996 ) . Figure 2 shows the configuration chosen for the storage tank. It consists of a ve sse l packe d in the horizontal dire ction with cylindrical tubes. The e ne rgy storage m ate rial ( CaCl 2 ? 6H 2 O ) is inside the tube s, which are m ade of PV C plastic, and the he at transfe r fluid ( wate r ) flows paralle l to the m . The storage tank contains cylindrical PV C containe rs fille d with PCM. The void fraction ( the ratio be twe e n the fluid volume and the storage tank volum e ) is 0.3. The inside volume and inside

Figur e 1. Schem atic diagram of the base solar e ne rgy system.

L atent Heat En ergy Storage System s

119

Tab le 1 W ate r-base d syste m


P aram e te r

V alue

Colle ctor Numbe r of glass cove rs Thickne ss of glass cove r Re fractive inde x Colle ctor plate absorptance Colle ctor e mittance Colle ctor e fficie ncy factor Black and side losse s Mass flow rate Total colle ctor are a Numbe r of colle ctors Syste m circuit pipe Le ngth Diam e ter He at loss Fluid de nsity ( wate r ) Fluid spe cific he at Ambie nt te mpe rature E ne rgy storage tank V olume The rm al loss Shape ( L r D ) Initial te mpe rature

1 0.004 m 1.45 0.90 0.85 0.85 1.20 kJ r (h m 2 K) 40 kg r ( h m 2 ) 30 m 2 18 40 m 0.04 m 20 kJ r ( h K) 1000 kg r m 3 4.197 kJ r (kg K) 18 8 C 3.65 m 3 0.210 W r ( m 2 8 C ) 2.46 18 8 C

surface are a of the e ne rgy storage tank are give n by Vst and A st , re spe ctive ly. The numbe r of cylindrical PV C containe rs inside the storage tank is Nc . The radius of the cylinde r containe rs is rc , and the le ngth of the cylindrical tube containe rs is give n by L. Also, the radius and le ngth of the e ne rgy storage tank are give n by R st and L st , re spe ctive ly. The rc r L is 0.01, and this ratio is sm all e nough to minimize radial he at conduction in the storage m ate rial. Energy An alysis The following e quations we re use d to calculate the e nthalpy variation. Charging pe riod Q s s m Cp w ( Tm y T 1 ) q m h sl q m Cp l ( T 2 y Tm )

(1)

D E1 s ( H a y H b ) y Q 1 , l

(2)

D E 1 s ( H a y H b ) s m w tCp s ( T 1 y T 2 )

(3)

D E 2 s ( H d y H c ) s m w tCp s ( T 2 y T1 )

(4)

Discharging pe riod


120


Figu re 2. Schem atic configuration of the energy storage tank.

The following e quation was use d to calculate e ne rgy e fficie ncy of the e ne rgy storage syste m:

h

en e rgy

s

E ne rgy re cove re d from TE S during discharging E ne rgy input to TE S during charging

h

en e rgy

s

Hd y Hc H a y Hb

s 1y

Ql

(5)

Ha y Hb

Exergy An alysis The following e quations we re use d to calculate the e ntropy variation. Charging pe riod

D S1 s ( S a y S b ) s m w tCp s ln ( T1 r T 2 )

(6)

D S2 s ( S d y S c ) s m w tCp s ln ( T 2 r T1 )

(7)

Discharging pe riod

The following e quations we re use d to calculate the e xe rgy variation. Charging pe riod

e

a

y e

b

s ( H a y H b ) y T0 ( S a y Sb )

(8)


121

Discharging pe riod

e

y e

d

c

s ( H d y H c ) y T0 ( S d y S c )

(9)

E xe rgy e fficie ncy for the e ne rgy storage syste m can be c alculate d as

h

exe rgy

s

E xe rgy re cove re d from TE S during discharging E xe rgy input to TE S during charging


h

exe rgy

s

e

e

d

y e

c

a

y e

b

s 1y

e

e

Ql a

qI

y e

( 10 )

b

Res u lts an d Dis cu ss ion W e have an alyze d the e xe rgy and e ne rgy pe rform ance of the late nt he at TE S syste m for dome stic he ating in Trabzon, Turke y, both e xpe rime ntally and the ore tic ally. The e xpe rime nts we re pe rforme d unde r cle ar-sky winter conditions so that a quasi ] ste ady state could be re alize d. For m ost runs the syste m was starte d we ll ahe ad of solar noon, and the quasi ] ste ady state of the ope ration was usually achie ve d around solar noon during the charging pe riod. The data we re obtaine d for various am bie nt and ope rational conditions, with am bie nt air te mpe rature s ranging from y 1 to 12 8 C and total solar radiation in the plane of the colle ctor from 500 to 900 W r m 2 d. From the vie wpoint of the Se cond Law of The rmodyn am ics, the optim um charge pe riod for e ne rgy storage de pe nds upon the total radiation on a slope d colle ctor surface . B ut the optimum discharge pe riod for a storage tank is that corre sponding to the m aximum discharge e fficie ncy. W e can say that the optim um discharge pe riod is m ore usefully de te rmine d using e xe rgy rathe r than e ne rgy e fficie ncy. B ut in the TE S syste m the e ne rgy and e xe rgy e fficie ncie s we re low due to low the rm al conductivity of the PV C containe rs fille d by PCM in the e ne rgy storage tank. O n the othe r hand, e xe rgy conside rs the quality and, for a he at transfe r fluid, is de pe nde nt on the te mpe rature s of the PCM and am bie nt air tem pe rature. Te mpe rature variation of PCM ( CaCl 2 ? 6H 2 O ) with time of day in the storage tank is shown in Figure 3. The figure shows that the re is a se mithe rm al stratification in the TE S syste m . This situation shows that the time of me lting and solidification of the PCM varie s from the bottom to the uppe r side of the store . In othe r words, the PCM at the bottom me lts le ss than the PCM at the middle point, and the PCM at the middle point me lts le ss than the PCM at the uppe r point in the storage tank. It is also e vide nt that, around solar noon, the tempe ratures of the PCM in the store are roughly at a m aximum value . Me an tempe rature variation of the he at transfe r fluid at the e xit of the storage tank with time of day during charging and discharging pe riods is shown in Figure 4. It is also e vide nt that, around solar noon, the e xit wate r te mpe rature of the store is roughly at a m aximum value . Figure 5 shows the e nthalpy variation with time of day during charging and discharging pe riods. It shows that the am ount of e nthalpy is at a m aximum value around solar noon. It is also e vide nt that the am ount of store d e nthalpy ( or e ne rgy) during the charging pe riod is highe r than that e ne rgy re cove re d during the


122


Figu re 3. Te mpe rature variation of calcium chloride hexahydrate with time of day in storage tank. T1, uppe r te mpe rature; T2, middle temperature ; T3, bottom temperature .

discharging pe riod. This re sult is in agre e me nt with the result give n in the lite rature ( Rosen e t al., 1988 ). This me ans that the e ne rgy stored is gre ate r than the e ne rgy re cove re d ( T able 2 ) . Figure 6 shows the e xe rgy variation with time of day during charging and discharging pe riods. It also shows that the am ount of e xe rgy is at a m aximum value around solar noon. W e can say from Figure 6 that the e xe rgy stored is gre ate r than the e xe rgy recove red ( Table 2 ) .

Figu re 4. Te mpe rature variation with time of day during charging and discharging period.



123

Figu re 5. E nthalpy variation with time of day during charging and discharging period.

Figure 7 shows the tempe ratures of the indoor and outdoor air and outle t wate r of the storage and total solar insolation with time of day for the TE S syste m. As shown in Figure 7, total solar radiation is at a m aximum value of 900 W r m 2 at loc al time of 1200 in the winter day time .

Con clu s ion An e xe rgy analysis is a powe rful tool for the e valuation of the pe rform ance of a the rm al e ne rgy storage syste m, e spe cially of a late nt he at e ne rgy store. An e xe rgy

Tab le 2 Comparison of the pe rform ance of a late nt he at TE S syste m Param e ter Ge ne ral param e ters Storing pe riod ( days ) Ch arging fluid te mpe ratures ( in r out ) ( K) Discharging fluid te mpe rature s (in r out ) ( K) E ne rgy param e ters E ne rgy input (kJ ) E ne rgy recove red (kJ ) E ne rgy loss (kJ ) E ne rgy e fficie ncy ( % ) E xe rgy param e te rs E xe rgy input (kJ ) E xe rgy re cove re d (kJ ) E xe rgy loss (kJ ) E xe rgy e fficie ncy (% )

V alue

1 315 r 295 285 r 305 5,320,86 4 4,038,68 4 1,282,18 2 55.20 372,320 236,228 136,092 34.83


124


Figu re 6. Exergy variation with time of day during charging and discharging pe riod.

an alysis is base d on the Se cond Law of The rmodynam ics and take s into account the quality and use fulne ss of the e ne rgy transfe re d. Me anwhile , an e ne rgy an alysis, which is base d on the First Law of The rmodyn am ics, doe s not take into account the following factors: time re quire d for charge and discharge proce sse s, the tem pe ratures at which the he at is supplie d and discharge d, and the te mpe rature of the surroundings. The de sirable characte ristics of the Se cond Law analysis arise s

Figu re 7. Te mpe rature and insolation variations with time of day: curve 1, insolation; 2, outlet wate r temperature of storage; 3, indoor air temperature ; and 4, outdoor air temperature .



125

from the fact that the Se cond Law of The rmodyn am ics asse sse s the quality of e ne rgy, but the First Law focuses on the quantity of e ne rgy. In this study, we used some e xpre ssions give n in the lite rature for e valuating the e ne rgy and e xe rgy e fficie ncie s during charging and discharging pe riods, the am ounts of e ne rgy and e xe rgy changing, and the changing storage -fluid te mpe rature for the discharge process of a close d, sem ithe rm al stratifie d, late nt he at the rm al e ne rgy storage syste m. Calculations have shown that the diffe re nce be twe e n the results of e ne rgy and e xe rgy an alysis is signific ant (se e T able 2 ) . The authors fee l that, since e xe rgy is a me asure of the quality or usefulne ss of e ne rgy, e xe rgy pe rform ance m e asures are more significant than e ne rgy pe rform ance m e asure s and that the e xe rgy an alysis should be conside re d in the calculation and comparison of the charge and discharge time for the the rm al e ne rgy storage syste m pre se nte d he re.

Nom en clatu r e Cp h sl H I m mw Qs S t T Tm T1 T2

e h

spe cific he at wkJ r (kg 8 C ) x late nt he at of phase transition wJ r (kg K) x e nthalpy e xe rgy losse s ( or consum ption ) m ass of PCM (kg ) m ass flow rate of wate r (kg r m in ) stored e ne rgy (kJ ) e ntropy time (m in ) te mpe rature ( K) phase transition tempe rature of salt hydrate ( K) inle t te mpe rature of wate r ( K) outle t tempe rature of wate r ( K) e xe rgy e fficiency

Subscripts a b c d f i l s 1 2

inle t flow at charging pe riod outle t flow at charging pe riod inle t flow at discharging pe riod outle t flow at discharging pe riod final state initial state liquid solid charging pe riod discharging pe riod

Refer en ces Abh at, A. 1983. Low temperature latent he at the rm al e ne rgy storage: He at storage m aterials. So lar Energy 30:313 ] 331.


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Bejan, A. 1988. Ad v anced engineering therm odyn am ics. Ne w York: John Wiley and Sons. C arlsson, B., H. Stymne, and G. Wetterm ark. 1979. An incongruent he at-of-fusion system } C aCl 2 ? 6H 2 O } made congruent through modification of the chemical composition of the system. So lar En ergy 23:343 ] 350. Gultekin, N., T. Ayhan, and K. Kaygusuz. 1991. He at storage chemical m aterials which can È be use d for domestic he ating by he at pumps. En ergy Con v ersion Man agem ent 32:311 ] 317. Gunne wiek, L. H., S. Nguye n, and M. A. Rose n. 1993. Evaluation of the optimum discharge pe riod for close d the rm al energy storage s using ene rgy and e xergy analyses. So lar En ergy 51:39 ] 43. H ahne, E . 1996. The rm al conse rvation technologie s. Prese nted at the First Trabzon International E ne rgy and Environme nt Symposium, July 29 ] 31, Trabzon, Turke y. H asan, A. 1994. Ph ase-change m ate rial e ne rgy storage syste m employing palmitic acid. So lar Energy 52:143 ] 154. KakacË , S., E . P aykocË , and Y. Yener. 1989. Energy Storage System s. NATO ASI Series. Kluwer Acade mic. Kaygusuz, K. 1995. Expe rime ntal and the ore tical investigation of late nt he at storage for wate r based solar he ating systems. En ergy Con v ersion Man agem en t 36:315 ] 323. Krane , R. J. 1987. A second law analysis of the optimum design and operation of therm al ene rgy storage syste ms. In tern ation al Journ al of Heat an d Mass Transfer 30:43 ] 57. Moran, M. J. 1982. Av ailability an alysis: A gu ide to efficien t energy use. Engle wood Cliffs, N. J.: Prentice-Hall. Moran, M. J., and H. N. Sh apiro. 1996. Fu nd am entals of engineering therm odyn am ics. New York: John Wiley. Rosen, M. A. 1992. Appropriate thermodynamic pe rform ance me asures for closed syste ms for therm al e ne rgy storage . ASME Journ al of So lar Energy Engineering 114:100 ] 105. Rosen, M. A., F. C. Hooper, and L. N. B arbaris. 1988. E xe rgy analysis for the e valuation of the performance of closed thermal ene rgy storage syste ms. ASME Journ al of So lar En ergy Engineering 110:255 ] 261. Sari, A. 1996. Pe rform ance calculation of energy storage system using energy and exergy analysis. M.S. the sis, Karadeniz Te chnical University, Trabzon, Turke y. Szargut, J., D. R. Morris, and F. R. Ste ward. 1988. Exergy an alyses of th erm al, chem ical, and m etallurgical processes. New York: Hemisphe re Publishing. Te lke s, M. 1974. Solar energy storage. ASHRAE Jou rn al Septe mbe r:34 ] 44. Y anadori, M., and T. Masuda. 1986. He at transfe re ntial study on a he at storage container with phase change m ate rial. Solar Energy 36:169 ] 177.