STUDY ON EFFECTIVE USE OF AN ICE THERMAL STORAGE SYSTEM WITH SIMULATION. Mingjie Zheng 1. Nagoya, Aichi, , Japan

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1 Prceedngs f Buldng Smulatn 2011: STUDY O EFFECTIVE USE OF A ICE THERMAL STORAGE SYSTEM WITH SIMULATIO Mngje Zheng 1 1 Technlgy Dvsn, SAKO Ar Cndtnng CO., LTD. agya, Ach, , Japan ABSTRACT It s mprtant t evaluate hether an thermal strage system can perate effectvely as the ay planned at the desgn stage. Whle desgnng an thermal strage system, generally, the thermal strage tme s calculated y usng rated capacty f refrgeratr r the heat exchange capacty f -n-cl, and the heatng capacty tme s calculated y usng the average meltng alty f the thermal strage tank. In ths paper, the authr develps a smulatn prgram fr mult-cnnected cmplete-lendng thermal strage tank and dscusses the effectve usalty f a practcal assemled strage system y usng the prgram. ITRODUCTIO The smulatn mdel f the external meltng Ice-n-cl type f thermal strage system can e dvded nt drect and ndrect smulatn. In drect smulatn, the -n-cl s mdeled as a cmpnent f evapratr. In ndrect smulatn, the thermal strage tank can e mdeled as a cmpnent f a heat exchanger. A drect thermal strage smulatn mdel that cntans a detaled mdel fr heat transfer frm the thermal strage tank t the refrgerant as develped (Jacsn, 1986) y usng a quas-steady thermal resstance netrk heat transfer mdel. Cleman (1990) extended the rk f Jacsn y develpng a mre cmplete mdel usng the thermal resstance netrk technque appled t the entre cl. Slver et al. (1988) develped anther mdel usng the thermal resstance netrk technque. Hever, Slver et al. dvded the cls n a fnte numer f segments. Generally, the refrgeratn capacty and heat exchange amunt f evapratr change dependng n the thckness and the evapratng temperature. In the Jacsn R's mdel, the evapratr capacty s set equal t the rated cmpressr capacty, s t can nt exactly reprduce the dynamc perfrmance f the -n-cl thermal strage system. The prlem th the mdel s n the asence f nfrmatn such as the tue length, s users must estmate the tank specfcatns, hch destrys the accuracy f the detaled mdel. In addtn, the executn tme f the detaled mdel s unfavraly lng fr an annual smulatn, hch means pr applcalty t a real -n-cl thermal strage system. A dynamc -n-cl evapratr mdel as develped as a stand-alne smulatn prgram cnsderng the heat transfer and pressure drp crrelatns avalalty (Mltz, 1987). In ths mdel, ased n the heat alance f the layer n the length f the tue n the steady state, t calculate amunt f the makng and meltng. Calculatn f the evapratn amunt ncludes the effects f the refrgerant superheat, changes f the evapratng pressure and thckness. Jnes and Shddapur (1995) appled and mprved Mltz s drect -n-cl evapratr mdel t an ndrect -n-ppe cmpnents mdel and develped an ndrect thermal strage system smulatn prgram y usng a fnte dfference apprach. The results ndcated that the mdel lacks sme accuracy, manly durng the egnnng f the chargng perd as ell as durng the meltng perd. A smulatn mdel f a temperature stratfcatn thermal strage tank as develped (u, 1984) ased n the expermental results f an ndrect thermal strage tank th a fnte dfference apprach. In ths smulatn mdel, the capacty f the chller as mdfed y the rne temperature that changes due t the change f the ater temperature and the heat alance eteen the amunt f the heat transfer thrugh the cl and chller utput. Mngje et. al (2001) mdfed akahara's mdel, and ncrprated t nt HVACSIM + (J). Mtsh et. al. (1986) develped anther smulatn mdel f ndrect thermal strage tank. In ths mdel, althugh the changes f the external heat transfer ceffcent f the cl alng the tue length drectn as taken nt accunt, the capacty f the chller as nt mdfed. Hever, these smulatn mdel shn ave, except fr u s mdel hen gven certan parameters as nputs, can nt smulate an actually assemled mult-cnnected cmplete-lendng thermal strage tank. Therefre, In ths paper, takng nt accunt the effect f the thckness n the makng and meltng alty, and the chller COP varatn due t the changes f the nlet and utlet rne temperature, the authr develps a smulatn

2 Prceedngs f Buldng Smulatn 2011: prgram fr mult-cnnected cmplete-lendng thermal strage tank and dscusses the effectve usalty f a practcal strage system y usng the prgram. OUTLIES OF BUILDIGS AD ICE THERMAL STORAGE SYSTEM The utlnes f target uldngs and thermal strage system are sh n Tale 1. And the utlne f target heat surce system and the Ice-n-cl placement s sh n Fgure 1. The target thermal strage system cnssts f t rne heat pumps and eleven -n-cls. In addtn, ecause each -n-cl cnssts f 17 parallel clumns f hrzntal tue and each clumn f tue s cnnected t the heat pump chllers va the vertcal headers (See Fgure 2), almst n temperature dfference exsts fr vertcal drectn n each tank durng the makng, s the target thermal strage tanks can e assumed f eng a mult-cnnected cmpletelendng thermal strage tank. Fgure 2 The structure f target -n-cl Tale 1 The utlnes f the target uldngs and thermal strage system Structure Buldn gs Heat surce system Renfrced cncrete made Usage Research faclty Ttal flr area 9,734m2 Brne heat pump 100 Hp 2 chller Strage capacty 440kW Brne temperature -7 C -3 C range Chlled capacty 560kW Chlled ater temperature range 7 C 12 C Dmensn f a tank Maxmum vlume umer f -n-cl Ice thermal strage tanks Avalale ater vlume 208.9m3 Materal and cncentratn Ethylene glycl f rne 60% Materal f rne, ttal Cpper, m length, nsde and utsde 16mm, 19.05mm dameter f tue Water temperature range f 5 C 2 C strage tank Chlled ater fl vlume m3/h Fgure 1 Outlne f heat surce system and -n-cl placement m2 3.5m (H) 30.1m3 4.7m3 9,3.1m3 2

3 Prceedngs f Buldng Smulatn 2011: CALCULATIO OF CAPACITY AD TIME OF THERMAL STORAGE When desgnng an thermal strage system, generally, the thermal strage tme s calculated y the use f rated capacty f refrgeratng machne r the heat exchange capacty f -n-cl, respectvely. Smple Calculatn Methd f Thermal Strage Tme Assumng the alty f heat strage equals t the rated capacty f the chller durng the thermal strage peratn, the sensle and latent heat strage tme can e calculated as fllng. The calculated results are shn n Tale 2. hk M C Tm / HP (1) h M C HP (2) s, max / Where, t as assumed that the rne temperature f utlet and nlet f chller are ther desgn values, and the heat exchanger temperature dfference s the average temperature dfference eteen the rne and ater temperature. Frm Tale 2, t can e understd that the ttal thermal strage tme s 9.2 hurs, less than the 10 hrs f nghttme duty eteen 22:00 and 8:00 f the cheaper electrcty rate schedule set fr the peak shft peratn frm the daytme. Apprxmatn Methd f Thermal Strage Tme On the ther hand, hen the -n-cl strage system s n actual peratn, the thermal strage capacty perates apart frm the rated capacty f the chller, ut s lmted t heat exchange capacty f cl. Mrever, the heat exchange capacty f -n-cl s decreasng th ncrease f thckness. In an apprxmatn methd, th an assumptn that the rate f sensle heat exchange n -n-cl prprtns t the average temperature dfference eteen the rne and ater, and frmatn s n prprtn t the latent heat exchange rate as ell, h s and h k are calculated y usng Equatn (3) and (4) respectvely. The calculatn results are als shn n Tale 2. hk M C Tm / KLT m Tm (3) h M C / KLT 0 (4) s, max m In Equatn (4), t s assumed that the heat exchange rate f -n-cl equals t the ne hen the vlume s a half f the desgned maxmum vlume. Frm Tale 2, t s shn that the ttal thermal strage tme s 15.5 hurs that s 1.7 tmes f the result th a smple calculatn methd, hch shs a g dfference eteen the t methds. Thermal Strage Tme Smulatn th the Present Tl T methds descred ave d nt accurately calculate changes f the ver-all heat transfer amunt f -n-cl due t the change f thckness. Therefre, t calculate the thermal strage tme mre accurately, a smulatn prgram that takes nt accunt the changes f the thckness and the rne chller COP changes due t the changes f the rne temperature that nfluence the makng capacty f the thermal strage system. Assumptns n the thermal strage smulatn (a) The ater temperature n the tank s n a fully mxed state and s 5 degree C n the egnnng f thermal strage. () The ater temperature n the tank s 0 degree C hen the egns t prduce. (c) The ler lmt f the rne temperature n the chller utlet s -10 degree C. (d) The chlled ater temperature n the tank nlet s cnstant. Heat transfer n the nsde and utsde surface f the tue As the nsde surface f the tue s n the frced cnvectn state, the heat transfer ceffcent can e taned y Equatn (5) r Equatn (6) (SHASEJ, 1995) Pr Re Re 2100 (5) 2 r 2r Pr Re l Re 2100 (6) r 2 / 3 2r (Pr ) Re l As the utsde surface f the tue s n the natural cnvectn, heat transfer ceffcent can e taned y Equatn (7) (SHASEJ, 1995) Gr 10 4 Gr Pr 10 8 (7) 2 r Smulatn f thermal strage capacty a) The ver-all heat transfer rate f the cl (Q c ) Q c 2Lc KT g (8) Where, T g s the lgarthmc mean temperature dfference and can e calculated y Equatn (9). T, c T, c Tg (9) ln[( T T, c ) /( T T, c )] K s the ver-all heat transfer ceffcent f tue, and can e calculated y Equatn (10) r 1 ln (10) K r cl r r ) The rne temperature at the cl utlet (T,c ) T, c T, c c Q / C F (11) c) The capacty f the chller s mdfed usng a theretcal COP frmula (akahara, 1984). ' ' ' T 273 T Tcd T T HP HP ' ' (12) T 273 T Tcd T T d) When the capacty f the chller (HP ) s larger than the ver-all heat transfer amunt f the cl (Q c ),

4 Prceedngs f Buldng Smulatn 2011: revse the rne temperature n the chller nlet (T ) t dnard untl the T equals t ts ler lmt value. And hen HP s smaller than Q c, adjust T t upard. e) The ater temperature n the tank s represented th dfferental Equatn (13). 1 dt Lc K Tg dt (13) M C f) When the ater temperature n the tank reaches 0 degree C, frmatn egns. The vlume s represented th dfferental Equatn (14). 2 K T g L c dm dt (14) C Hever, at the mment f the phase change frm ater t at the uter surface f the -n-cl, the heat transfer ceffcent ecmes almst nfnte, s that the calculatn f the thermal transmttance n the -n-cl (K ) ll ecme as Equatn (15). 1 K 1 1 r cl r 1 ln r r D ln r (15) The calculatn f thermal strage tme a) The sensle heat changes f ater n the tank (Q) can e calculated y Equatn (16) Q C M dt (16) ) The sensle heat strage tme As the ver-all sensle heat transfer amunt f the cl equals t the varatn f sensle heat f ater n the tank, lnkng Equatn (8) and (16), and then ntegratng Equatn (17) frm ntal ater temperature n the tank t 0 degree C, the sensle heat strage tme (h k ) can e taned as Equatn (17). 0 C M (17) h k T 2 L c KT g dt c) The Latent heat strage tme When the tank ater temperature ecmng 0 degree C, the latent heat strage amunt equals t the latent heat rate fr makng, and t can e taned y ntegratng Equatn (14) up t desgned maxmze vlume, as shn n equatn (18). Smulatn results f the sensle and latent heat strage tme are als shn n Tale 2. h s M, max 0 C 2 L dm (18) c K T g Smulatn fl Because the capacty f the chller (HP ) depends n the rne temperature n the chller nlet, t s needed (a) t mdfy the capacty f the chller th Start Intalzatn f T, T cd, T Calculate HP Calculate, 0,K h s =h s + t Calculate T,Q c Upard T HP = Q c? Y HP Q c? Y T -10 C? h k = h k + t Y Calculate T, M Dnard T T = 0 C? Y M = M,max? Y Output h k, h s End Fgure 3 A fl chart f the smulatn

5 Prceedngs f Buldng Smulatn 2011: the rne temperature n the chller nlet at frst tme; () t calculate, 0, K, T and M th the average temperature f the rne and t calculate Q c and T y usng them; (c) t mdfy T y cmparng HP th Q c and t repeat calculatns untl HP ecmes equal t Q c ; (d) The smulatn shall e carred ut untl that the desgned maxmum vlume s attaned, and then h k and h s s taned. Fgure 3 shs the fl f smulatn. Cmparng Results f Three Calculatn Methds Fgure 4 and 5 sh the amunt f sensle and latent heat strage n target thermal strage system and the rne temperature f the nlet and utlet n the chller, respectvely. Frm Fgure 4, 5 and Tale 2, the fllng fndngs are taned. a) Fllng the ncrease f the thckness, the amunt f the thermal strage decreases. ) The makng tme smulated s lnger than that calculated y the smple methd, and s less than that calculated y the apprxmatn methd. The dfferences amng three methds can e explaned as flls. (a) Increase f the thermal resstance accrdng the thckness t e cnsdered n smulatn. () The average rne temperature as used n an apprxmatn methd. (c) The rne temperature n the chller utlet as adjusted dnard as the capacty f the chller t maxmze value n smulatn. c) After egnnng t make, the rne temperature n the chller utlet arrved at the lest lmt value, -10 degree C, and ths ndcates that ttal uter surface f cl n ject thermal strage system s t small. d) Accrdng t the smulatn result, the thermal strage tme f ject thermal strage system s 12.9 hurs. If just 10 hurs f nghttme peratn s desred fr strage peratn, nsuffcent cl surface area s the cause f t. Hever, ths ll e allale cnsderng that ths nsuffcency nly ccurs at a fe days f peak clng seasn n summer. Tale 2 Cmparng calculatn results f thermal strage tme (h) f three methds Methd Sensle heat strage tme Latent heat strage tme Ttal tme Smplfy Apprxmate Develped tl Fgure 4 The amunt f sensle and latent nlet f the chller CALCULATIO OF CAPACITY AD TIME REQUIRED FOR HEAT DISSIPATIO Apprxmatn Methd f Clng Capacty Tme The clng capacty s reduced accrdng t reductn f surface area. The apprxmatn methd used y the desgner assumed that there s a lnear relatnshp eteen the clng capacty and the resdual vlume, and calculated the clng capacty tme usng a half f the desgned maxmum vlume. The calculatn methds and results are shn n Tale 3. The meltng tme s 5.23 hurs, and there s suffcent meltng alty n the ject thermal strage system. Hever, ths methd can nt reprduce the effects f nn-lnear changes f the vlume durng the meltng. Fgure 5 The rne temperature f utlet and heat strage Smulatn fr Alty and Tme f the Ice Meltng Assumptns f the meltng smulatn a) The target thermal strage tank cnssts f eleven cl unts and fur tanks, and all -n-cl s nt placed n seres alng the ater fl drectn. Therefre, fur tanks ere changed t nne tanks n the smulatn, as ndcated y thn dashed lnes n Fgure 1. ) The ater temperature n each tank s n a fully mxed state and s 0 degree C hen egnnng t melt. c) The temperature and fl rate f the returnng chlled ater frm the secndary sde equal t the desgn values, 5 degree C and m 3 /h, respectvely. d) The vlume equals t the desgned maxmum vlume, and s evenly dstruted n each cl

6 Prceedngs f Buldng Smulatn 2011: Tale 3 The calculatn frmula and results f apprxmatn methd Sgn Unt Interpretatn Calculatn methds Results M m 3 /m Ice vlume f unt cl length hen the vlume 3.8E-3 M 1/ 2M, max / L s 1/2 f the desgned maxmum vlume d,m m Dameter f uter surface f the hen the d M d 1/ vlume s 1/2 f the desgned maxmum vlume 2, m 4 / A xm m 2 Outer surface area f hen the vlume s 1/2 f the desgned maxmum vlume T gm C Lgarthmc mean temperature dfference A T d xm, m gm L T T Ln( T ) Ln( T ) Q MJ Mean alty f the meltng Q T A ( 180) 1,773 Q s MJ Latent heatng capacty Qs M C 9,274 Q k MJ Sensle heatng capacty Qk M C Tgm 2,868 h h Ice meltng tme h M C / Q 5.23 ater temperature f the last tank, frm hch the The meltng smulatn mdel chlled ater s suppled t the clng crcut, If a large numer f tues are arranged n parallel t gradually rses. Therefre, t s cnsdered that the each cls, the cnvectve heat transfer ceffcent smulated sensle heatng capacty s larger than the f the uter surface f the s calculated y ne th an apprxmatn methd. Equatn (19) (SHASEJ, 1995). Fgure 7 shs the varatn f resdual vlume n hn Pr Re each tank durng the meltng prcess. After fur 0 (19) hurs f clng peratn, n s fund n the tank d 1 and 2; ut the tank 8 and 9 mantan the untl the last mment as shn. The varatn f the sensle, latent and ttal clng capacty durng the meltng are shn n Fgure 8-Fgure 10, respectvely. Frm these fgures, the fllng fndngs are taned: a) The clng capacty f each tank s dfferent ecause the length f the tue f -n-cl n each tank s als dfferent. ) Because the ntal ater temperature n the tank s 0 degree C, there s the sensle clng capacty durng all the meltng perd. c) The meltng tme s 9 hurs, lnger than that calculated y the apprxmatn methd. Heat alance f ttal clng capacty f each thermal strage tank durng the meltng s represented y the dfferental Equatn (20) dt ( 1 IPF) VC FC T n T Ax T 0(20) dt Dfferencng and srt ut Equatn (20), Equatn (21) s taned and temperature f each tank can e calculated. 1 1 T {(1 IPF ) VT FTnt}/ B IPF 0 (21) 1 T { VmT FTnt}/ A IPF 0 Where, 1 A x B (1 IPF ) V ( F ) t, A V F t (22) c IPF s a percentage f the vlume n the tank, and s calculated y Equatn (23). IPF r D r (23) r The amunt f meltng n each tank s represented y the dfferental Equatn (24). dm A x T 0 (24) dt C The meltng tme can e taned y ntegratng Equatn (24) frm the desgned maxmum vlume t 0 as shn n Equatn (25). h 0 M,max C dm A ( T 0) x (25) The meltng smulatn results and dscussn Smulatn n the step respnse f 5 degrees C ater temperature nput as executed and Fgure 6 shs the temperature prfles f the ject thermal strage tanks durng the meltng prcess. The gm xm Fgure 6 Temperature prfle n tanks Fgure 7 Changes f vlume n each tank

7 Prceedngs f Buldng Smulatn 2011: Fgure 8 Changes f latent heatng capacty n each tank Fgure 9 Changes f Sensle heatng capacty n each tank Fgure 10 Changes f ttal heatng capacty Cmparsn eteen the Results f T Calculatn Methds Cmparsn eteen the results f t calculatn methds s shn n Tale 4. The result f ther latent heatng capacty s same; hever, the meltng tme taned y each calculatn methd s dfferent. Ths s ecause the average rates f the meltng eteen the t calculate methds are dfferent. The result f the sensle clng capacty th smulatn s greater than that y the apprxmatn methd. The dfference appeared n the ater temperature n the tank utlet, n hch t rased up t 5 degree C fr the smulatn methd, ut t keeps 2 degree C, the desgned value, fr the apprxmatn methd. When a real thermal strage system perates n a cndtn f the meltng, the altes f the meltng vary alng th changes f the resdual vlume and the ater temperature n tank utlet. Fr ths reasn, t s cnsdered that the smulatn results are mre accurate than the ne y usng an apprxmatn methd. DISCUSSIO In ths paper, takng nt accunt the effect f the thckness n the makng and meltng alty, and the chller COP varatn due t the changes f the nlet and utlet rne temperature, the authr develped a smulatn prgram fr an assemled mult-cnnected cmplete-lendng thermal strage tank and dscussed the effectve usalty f a practcal strage system y usng the prgram. The fllng results ere taned. 1) Because the calculated capacty strage alty f the target thermal strage tank s smaller than the rated capacty f the chller, the smulatn value f the thermal strage tme s lnger than that y a smplfy calculatn, and shrter than that usng the average verall heat transfer ceffcent f the -n-cl. Ths shs that the smulatn prgram reprduces the ncrease f the verall thermal resstance f the cl, due t freezng n the uter surface f the cl, and the actual chller capacty changes and rks n the cndtns dfferent frm the rated. 2) In the smulatn f the clng capacty durng the daytme, the smulatn reprduces the changes f the meltng alty due t changes f the ater temperature and resdual n each thermal strage tank. The smulatn value f the meltng tme s lnger than that calculated y an apprxmatn methd th the average meltng alty f the -n-cl, the frmer f hch taned a value that s clse t the actual ne. Mrever, hen a real thermal strage system perates n a cndtn f the meltng, returned chlled ater temperature frm the secndary sde vares dependng n changes f the clng lad. Hever, accrdng t the smulatn descred n ths paper, 5 degree, the desgned value f the chlled ater, as appled. Therefre, t s cnsdered there s a small dfference eteen the smulatn value f the meltng tme and actual value. Tale 4 Cmparsn f the Results eteen T Calculatn Methds Methds Average altes Latent heatng Sensle Ttal heatng The f the capacty heatng capacty meltng tme meltng [MJ] [MJ] capacty [MJ] [MJ] [h] Apprxmatn 1,773 9,274 2,868 12, Develped tl 1,070 9,274 4,079 13,

8 Prceedngs f Buldng Smulatn 2011: REFERECES Cleman G Smulatn f Ice Strage Systems. M.S. thess, Unversty f Illns at Urana-Champagn, Urana. Jacsn D. I Smulatn and Optmzatn f the Operatn f an Ice Strage System. M.S. thess, Unversty f Illns at Urana- Champagn, Urana. Jnes J.W. and Shddapur G. S Evaluatn f RP-495 Algrthms fr Mdelng External Met, Ice-n-ppe Thermal Strage System Cmpnents, ASHRAE Transactns, Vl. 101(2), pp Mltz, A A umercal Mdel f an Ice Strage Tank Evapratr, M.S. Thess, Department f Mechancal Engneerng, Unversty f Texas at Austn. Mngje Zheng, Techuj Yasutm and u akahara Dynamc Smulatn f HVAC th the Heat Strage System y Usng HVACSIM +, Part 1 A smulatn mdel f the strage tank f the temperature-stratfed type, SHASE Transactns (2001.9), pp , Kyt, (In Japanese). Mtsh Myamae, T. Iamt, T. Sagara, T. Ara,. Takeda and M. Ichn Study n Ar Cndtnng System ased n Ice Energy Strage fr Large Buldngs, Part 10 Mdel valdatn n the meltng and estmatn f varus parameters, SHASE Transactns ( ), pp , (In Japanese). u akahara Study n the Predctn f Characterstcs f Ice Strage Tank, Part 1 - Study n perfrmance evaluatn system, SHASE Transactns ( ), pp , (In Japanese). SHASEJ Ar Cndtnng and Santary Engneerng Handk, The 12 th Edtn, Maruzen, Tky, (In Japanese). Slver S.C., Mltz A., Jnes J.W., Petersn J.L. and Hunn B.D Cmpnent Mdels fr Cmputer Smulatn f Ice Strage Systems, ASHRAE Transactns, Vl. 95(1), pp Zehnder J.W Cmputerzed Mdel f an Ice Thermal Strage System. M.E. thess, Department f Mechancal Engneerng, Unversty f Lusvlle, Lusvlle, KY. menclature A x Outer surface area f [m 2 ] C Specfc heat f rne [kj/kg] C Heat f fusn f [kj/kg] d Dameter [m] D Ice Thckness [m] F Fl rate [m 3 /h] G r Grashf numer h Strage tme [h] h The meltng tme [h] IPF Ice packng factr [%] K Over-all heat transfer ceffcent f tue at nn-freezng [kw/(mk)] K Over-all heat transfer ceffcent f tue at freezng [kw/(mk)] l Tue length f each layer n an cl [m] L Ttal tue length n all tanks [m] L c Ttal tue length f each cl [m] M Vlume [m 3 ] M,max Desgn maxmum amunt f [m 3 ] n Crrectn factr ased n Re and the rat eteen the tue dameter and ptch f adjacency tues HP Refrgeratr capacty [kw] P r Prandtl numer Q Amunt f latent heat strage [kj] Q c Amunt f ver-all heat transfer f tue [kj] r Radus f tue [m] R e Reynlds numer t Tme [h] T Temperature [ C] T m Average rne temperature f strage [ C] T g Lgarthmc mean temperature dfference at heat strage [ C] T n Return chlled ater temperature frm the secndary sde [ C] T m The average temperature dfference f heat exchange at sensle heat strage [ C] T Intal ater temperature n tank [ C] V ater vlume n each tank [m 3 ] V m Ice vlume melted n each tank [m 3 ] Heat transfer ceffcent [W/(m 2 K)] Cl percentage fllng n tank [%] Thermal cnductvty [W/(m/K)] Crrectn factr ased n the tues numer f clumns alng the drectn f ater fl Densty [kg/m 3 ] T Temperature dfference eteen rne utlet temperature and evapratng temperature [ C] T cd Temperature dfference eteen the clng ater utlet temperature and cndensatn temperature [ C] T T +T cd [ C] t Tme step f dfference calculatn [h] Suscrpts : Value fr rne : Value f chller nlet,c: Value f cl nlet : Value f chller utlet,c: Value f cl utlet cd: Value aut clng ater cl: Value fr cl : Value f the cl nter surface : Value fr k: Value fr sensle heat : Value f the cl uter surface s: Value fr Latent heat : Value fr ater : Value f any cndtns