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Energy and ExergyCalculations of Latent HeatEnergy Storage SystemsAhmet Sari, Kamil KaygusuzPublished online: 29 Oct 2010.

To cite this article: Ahmet Sari, Kamil Kaygusuz (2000) Energy and ExergyCalculations of Latent Heat Energy Storage Systems, Energy Sources, 22:2,117-126, DOI: 10.1080/00908310050014090

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E nergy Sou rces, 22:117 ] 126 , 2000

Copyr igh t Q 2000 T aylor & Fran cis

0090-8312 r 00 $12.00 q .00

Energy and Exergy Calcu lations of Laten t

Heat Energy Storage System s

AHMET SARI

Department of Chemistry

GaziosmanpasË a University

Tokat, Turkey

ÇKAMIL KAYGUSUZ

Department of Chemistry

Karadeniz Technical Unive rsity

Trabzon, Turkey

An experim ental study and a theoretical study h ave been conducted to evaluate the

perform ance for a closed latent heat energy storage system using energy and exergy

analyses. The energy storage tank is neither fu lly m ixed nor fully stratified. It m ay be

considered as sem istratified. Experim ents were performed on sunny winter days in

1996. In this study a com plete storing cycle and charging and discharging periods are

considered. Energy and exergy efficiencies, total energy and exergy variations, and

m ean energy and exergy efficiencies are also calculated by using experim ental data.

Keywords ene rgy and exergy analysis, ene rgy storage , latent he at

Thermal ene rgy storage has always been one of the most critical components in

re sidential solar space heating applications. Solar radiation is a time -dependent

energy source with an inte rmittent characte r. The heating demands of a re sidential

house are also time dependent. Howeve r, the ene rgy source and the he ating

demands of a building, in ge neral, do not match e ach othe r, especially in solar

he ating applications. The pe ak solar radiation occurs near noon, but the pe ak

he ating demand is in the late eve ning when solar radiation is not available .

Thermal ene rgy storage provides a rese rvoir of energy to adjust this mismatch and

to meet the ene rgy needs at all times. It is used as a bridge to cross the gap

between the energy source , the sun, the application, and the building. So the rmal

( )energy storage is e ssential in a solar he ating system KakacË e t al., 1989 .

( )The use of phase change mate rials PCMs for therm al ene rgy storage in solar

he ating systems has rece ived considerable attention. The motivation for using

( )phase change ene rgy storage PCES mate rials is the reduction in storage volume

( )that can be achieve d compared to sensible heat storage systems. Abhat 1983

reviewed low-temperature PCMs in the temperature range 0 ] 120 8 C and investi-

gated their me lting and fre ezing behavior. The most studied PCMs include

Received 14 September 1998, accepted 14 December 1998.This study was supported by the Karadeniz Technical University Rese arch Fund.

Address correspondence to Dr. Kamil Kaygusuz, Department of Chemistry, KaradenizTechnical University, 61080 Trabzon, Turkey. E-mail: kaygusuz@ osf01.ktu.edu.tr

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A. Sari and K. Kaygusuz118

Glauber’ s salt, calcium chloride hexahydrate , sodium thiosulfate pentahydrate ,

(sodium carbonate decahydrate, fattic acid, and paraffin waxes Telke s, 1974;

Carlsson e t al., 1979; Gultekin et al., 1991; Kaygusuz, 1995; Hasan, 1994; YanadoriÈ)& Masuda, 1986; Hahne, 1996 .

( )The energy e fficiency of a the rmal energy storage TES system, the ratio of

the ene rgy returned from storage to the heat originally delivered to storage , is

inadequate as a measure of the approach to ide al perform ance because it does not

take into account the length of time ove r which the heat is stored or the

temperatures at which the he at is supplied and delivered, or the temperature of the

surroundings. Exe rgy analysis, which is based primarily on the Second Law of

Thermodynamics, as compared to energy analysis, which is based on the First Law,

take s into account the quality of the ene rgy transfe rred. Exe rgy analysis is recog-

nized by heat transfer enginee rs to be a powerful tool for the evaluation of the

thermodynamic and economic pe rformance of thermodynamic systems in ge neral

(and of TES systems in particular Rosen et al., 1988; Bejan, 1988; Szargut e t al.,

1988; Krane , 1987; Rosen, 1992; Moran & Shapiro, 1996; Moran, 1982; Gunnewiek

)e t al., 1993 .

The present work is dire cted toward using simple methods for evaluating and

comparing the energy and exe rgy efficiencie s of a latent he at closed energy storage

tank. For this purpose, we used some use ful equations given in the literature

( )Rosen et al., 1988 , and we calculated ene rgy and exergy variations and me an

energy and exergy e fficiencies.

Exp erim en tal Setup

The water-based system investigated in this experimental study is shown in Figure

1, and the system parameters are listed in Table 1. As shown in Figure 1, this

system consists of solar colle ctors, an ene rgy storage tank filled with PCM, a

water-to-air he at exchanger, a wate r circulating pump, and othe r me asuring and

( )control equipment Sari, 1996 .

Figure 2 shows the configuration chosen for the storage tank. It consists of a

ve ssel packed in the horizontal dire ction with cylindrical tubes. The energy storage

( )material CaCl ? 6H O is inside the tubes, which are made of PV C plastic, and2 2

( )the heat transfer fluid wate r flows paralle l to them. The storage tank contains

(cylindrical PV C containe rs filled with PCM. The void fraction the ratio between

)the fluid volume and the storage tank volume is 0.3. The inside volume and inside

Figure 1. Schematic diagram of the base solar ene rgy system.

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Latent Heat Energy Storage System s 119

Table 1

W ater-based system

Parameter V alue

Colle ctor

Number of glass covers 1

Thickness of glass cover 0.004 m

Refractive index 1.45

Collector plate absorptance 0.90

Collector emittance 0.85

Collector e fficiency factor 0.852( )Black and side losses 1.20 kJ r h m K

2( )Mass flow rate 40 kg r h m2

Total colle ctor are a 30 m

Number of colle ctors 18

System circuit pipe

Length 40 m

Diameter 0.04 m

( )He at loss 20 kJ r h K3( )Fluid density water 1000 kg r m

( )Fluid specific heat 4.197 kJ r kg K

Ambient temperature 18 8 CEnergy storage tank

3V olume 3.65 m2( )Thermal loss 0.210 W r m 8 C

( )Shape L r D 2.46

Initial temperature 18 8 C

surface area of the energy storage tank are given by V and A , re spective ly. Thest st

number of cylindrical PVC containe rs inside the storage tank is N . The radius ofc

the cylinder containe rs is r , and the length of the cylindrical tube containers isc

given by L . Also, the radius and length of the ene rgy storage tank are given by R st

and L , re spective ly. The r r L is 0.01, and this ratio is small enough to minimizest c

radial he at conduction in the storage mate rial.

Energy Analysis

The following equations we re used to calculate the enthalpy variation.

Charging period

( ) ( ) ( )Q s m Cp T y T q m h q m Cp T y T 1s w m 1 sl l 2 m

( ) ( )D E s H y H y Q 21 a b 1 , l

( ) ( ) ( )D E s H y H s m tCp T y T 31 a b w s 1 2

Discharging period

( ) ( ) ( )D E s H y H s m tCp T y T 42 d c w s 2 1

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A. Sari and K. Kaygusuz120

Figure 2. Schematic configuration of the energy storage tank.

The following equation was used to calculate energy efficiency of the energy

storage system:

Energy recovered from TES during dischargingh sen ergy

Energy input to TES during charging( )5

H y H Qd c lh s s 1 yen ergy

H y H H y Ha b a b

Exergy Analysis

The following equations we re used to calculate the entropy variation.

Charging period

( ) ( ) ( )D S s S y S s m tCp ln T rT 61 a b w s 1 2

Discharging period

( ) ( ) ( )D S s S y S s m tCp ln T r T 72 d c w s 2 1

The following equations we re used to calculate the exergy variation.

Charging period

( ) ( ) ( )e y e s H y H y T S y S 8a b a b 0 a b

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Latent Heat Energy Storage System s 121

Discharging period

( ) ( ) ( )e y e s H y H y T S y S 9d c d c 0 d c

Exergy e fficiency for the energy storage system can be calculated as

Exe rgy recovered from TES during dischargingh sexe rgy

Exe rgy input to TES during charging

e y e e q Id c Q l( )h s s 1 y 10exe rgy e y e e y ea b a b

Results an d Discu ss ion

We have analyzed the exe rgy and energy performance of the latent he at TES

system for domestic he ating in Trabzon, Turkey, both expe rimentally and theore ti-

cally. The experiments we re pe rformed under cle ar-sky winter conditions so that a

quasi ] ste ady state could be re alized. For most runs the system was started we ll

ahead of solar noon, and the quasi ] steady state of the operation was usually

achieved around solar noon during the charging period. The data we re obtained for

various ambient and operational conditions, with ambient air temperature 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 rm 2 d.

From the viewpoint of the Second Law of Thermodynamics, the optimum

charge period for energy storage depends upon the total radiation on a sloped

collector surface. But the optimum discharge period for a storage tank is that

corre sponding to the maximum discharge e fficiency. We can say that the optimum

discharge period is more usefully dete rmined using exe rgy rather than energy

e fficiency. But in the TES system the ene rgy and exergy efficiencie s we re low due

to low the rm al conductivity of the PV C containe rs filled by PCM in the energy

storage tank. O n the othe r hand, exe rgy conside rs the quality and, for a he at

transfer fluid, is dependent on the temperature s of the PCM and ambient air

temperature.

( )Temperature variation of PCM CaCl ? 6H O with time of day in the storage2 2

tank is shown in Figure 3. The figure shows that there is a semithermal stratifica-

tion in the TES system. This situation shows that the time of me lting and

solidification of the PCM varie s from the bottom to the upper side of the store . In

othe r words, the PCM at the bottom me lts less than the PCM at the middle point,

and the PCM at the middle point melts less than the PCM at the upper point in

the storage tank. It is also evident that, around solar noon, the temperatures of the

PCM in the store are roughly at a maximum value .

Me an temperature variation of the he at transfer fluid at the exit of the storage

tank with time of day during charging and discharging pe riods is shown in Figure 4.

It is also evident that, around solar noon, the exit wate r temperature of the store is

roughly at a m aximum value .

Figure 5 shows the enthalpy variation with time of day during charging and

discharging periods. It shows that the amount of enthalpy is at a maximum value

( )around solar noon. It is also evident that the amount of stored enthalpy or ene rgy

during the charging period is higher than that ene rgy recovered during the

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A. Sari and K. Kaygusuz122

Figure 3. Temperature variation of calcium chloride hexahydrate with time of day in

storage tank. T1, upper temperature; T2, middle temperature ; T3, bottom temperature .

discharging pe riod. This re sult is in agreement with the result given in the

( )literature Rosen e t al., 1988 . This me ans that the ene rgy stored is gre ater than

( )the energy recovered Table 2 .

Figure 6 shows the exe rgy variation with time of day during charging and

discharging periods. It also shows that the amount of exergy is at a m aximum value

around solar noon. We can say from Figure 6 that the exergy stored is gre ate r than

( )the exe rgy recove red Table 2 .

Figure 4. Temperature variation with time of day during charging and discharging period.

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Latent Heat Energy Storage System s 123

Figure 5. Enthalpy variation with time of day during charging and discharging period.

Figure 7 shows the temperatures of the indoor and outdoor air and outlet

water of the storage and total solar insolation with time of day for the TES system.

As shown in Figure 7, total solar radiation is at a maximum value of 900 W r m2 at

local time of 1200 in the winter day time.

Con clus ion

An exergy analysis is a powe rful tool for the evaluation of the perform ance of a

thermal energy storage system, especially of a latent he at ene rgy store. An exe rgy

Table 2

Comparison of the pe rformance of a latent he at TES system

Parameter V alue

General parameters

( )Storing pe riod days 1

( ) ( )Charging fluid temperatures in rout K 315 r295

( ) ( )Discharging fluid temperature s in rout K 285 r305

Energy parameters

( )Energy input kJ 5,320,864

( )Energy recove red kJ 4,038,684

( )Energy loss kJ 1,282,182

( )Energy e fficiency % 55.20

Exergy parameters

( )Exe rgy input kJ 372,320

( )Exe rgy recovered kJ 236,228

( )Exe rgy loss kJ 136,092

( )Exe rgy e fficiency % 34.83

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A. Sari and K. Kaygusuz124

Figure 6. Exergy variation with time of day during charging and discharging period.

analysis is based on the Second Law of Thermodynamics and takes into account

the quality and use fulne ss of the energy transfe red. Meanwhile , an ene rgy analysis,

which is based on the First Law of Thermodynamics, doe s not take into account

the following factors: time required for charge and discharge processes, the

temperatures at which the heat is supplied and discharged, and the temperature of

the surroundings. The desirable characte ristics of the Second Law analysis arise s

Figure 7. Temperature and insolation variations with time of day: curve 1, insolation; 2,

outlet water temperature of storage; 3, indoor air temperature ; and 4, outdoor air tempera-

ture .

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Latent Heat Energy Storage System s 125

from the fact that the Second Law of Thermodynamics assesse s the quality of

energy, but the First Law focuses on the quantity of energy.

In this study, we used some expressions given in the lite rature for evaluating

the ene rgy and exergy e fficiencie s during charging and discharging periods, the

amounts of energy and exe rgy changing, and the changing storage -fluid tempera-

ture for the discharge process of a closed, semithe rmal stratified, latent he at

thermal energy storage system. Calculations have shown that the difference be-

( )tween the results of energy and exe rgy analysis is significant see Table 2 . The

authors fee l that, since exergy is a me asure of the quality or usefulness of energy,

exe rgy pe rformance measures are more significant than ene rgy pe rformance mea-

sure s and that the exe rgy analysis should be considered in the calculation and

comparison of the charge and discharge time for the thermal ene rgy storage system

presented here.

Nom enclature

w ( )xC specific he at kJ r kg 8 Cp

w ( )xh latent he at of phase transition J r kg Ks l

H enthalpy

( )I exergy losse s or consumption

( )m mass of PCM kg

( )m mass flow rate of wate r kg rminw

( )Q stored energy kJs

S entropy

( )t time min

( )T temperature K

( )T phase transition temperature of salt hydrate Km

( )T inle t temperature of wate r K1

( )T outle t temperature of water K2

e exergy

h efficiency

Subscripts

a inle t flow at charging period

b outle t flow at charging pe riod

c inle t flow at discharging period

d outle t flow at discharging pe riod

f final state

i initial state

l liquid

s solid

1 charging period

2 discharging period

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