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, 450-0003, 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 - 318 -
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, 3956.8m length, nsde and utsde 16mm, 19.05mm dameter f tue Water temperature range f 5 C 2 C strage tank Chlled ater fl vlume 133.3 m3/h Fgure 1 Outlne f heat surce system and -n-cl placement - 319-138m2 3.5m (H) 30.1m3 4.7m3 9,3.1m3 2
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). 0.4 0.8 0.023 Pr Re Re 2100 (5) 2 r 2r 0.0668 Pr Re l Re 2100 (6) 3.65 2r 2 / 3 2r 1 0.04(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). 0.25 0.53 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). 1 1 1 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 ), - 320 -
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 - 321 -
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 2.8 6.4 9.2 Apprxmate 3.9 11.6 15.5 Develped tl 2.8 10.1 12.9 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 133.3 m 3 /h, respectvely. d) The vlume equals t the desgned maxmum vlume, and s evenly dstruted n each cl. - 322 -
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 0.07215 2 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 ) 717.51 3.28 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 0.3 0.6 0.33 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 2 2 2 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 - 323 -
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 12,142 5.23 Develped tl 1,070 9,274 4,079 13,353 9.0-324 -
Prceedngs f Buldng Smulatn 2011: REFERECES Cleman G.. 1990. Smulatn f Ice Strage Systems. M.S. thess, Unversty f Illns at Urana-Champagn, Urana. Jacsn D. I. 1986. 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. 1995. Evaluatn f RP-495 Algrthms fr Mdelng External Met, Ice-n-ppe Thermal Strage System Cmpnents, ASHRAE Transactns, Vl. 101(2), pp1342-1351. Mltz, A. 1987. 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. 2001. 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), pp893-896, Kyt, (In Japanese). Mtsh Myamae, T. Iamt, T. Sagara, T. Ara,. Takeda and M. Ichn. 1986. 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 (1986.10), pp409-412, (In Japanese). u akahara. 1984. Study n the Predctn f Characterstcs f Ice Strage Tank, Part 1 - Study n perfrmance evaluatn system, SHASE Transactns (1984.10), pp733-736, (In Japanese). SHASEJ. 1995. 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. 1988. Cmpnent Mdels fr Cmputer Smulatn f Ice Strage Systems, ASHRAE Transactns, Vl. 95(1), pp1214-1226. Zehnder J.W. 1988. 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 - 325 -