NUMERICAL SIMULAION OF HE HERMAL BEHAVIOUR OF AN ENERGY SORAGE UNI WIH PHASE CHANGE MAERIALS FOR AIR CONDIIONING APPLICAIONS BEWEEN 7ºC AND 40ºC. INRODUCION AND OBJEC P. Dolado A. Lázaro B. Zalba J.M. Marí heral Egieerig Divisio Deartet of Mechaical Egieerig Uiversit of Zaragoza Ed. Agustí de Betacourt c/maría de Lua s/ 5008 Zaragoza SPAIN el: (34) 976 76 000 Et. 558 Fa: (34) 976 76 66 ablodolado@gail.co heral eerg storage ca shift eak load of electricit eliiate art of the heatig or coditioig loads ad ehace the erforace of alteratives to fossil fuel cobustio heatig. he alicatio of hase chage aterials () i coditioig sstes ca sooth dail fluctuatios i roo teerature b lowerig the eak teeratures resultig fro eteral dail teerature chages. also reduce hoe heatig or coolig loads roducig eerg savigs for the cosuer. Aother wa to reduce the ower cosutio is the use of the cobied sste free-coolig ad. o diiish the use of the coditioed equiet the free-coolig sste takes advatage of the low ethal whe the outer coditios are favourable. he use of to store cooless have bee develoed for coditioig alicatios (Zalba 004) where cold is collected ad stored fro abiet durig ight ad it is released to the idoor abiet durig the hottest hours of the da. Usig techolog is suitable because of the sall teerature ga betwee da idoors ad ight outdoors. Eerg is stored i a sall teerature iterval that ca agree with the loadig ad uloadig teeratures of the. I this aer a eerg storage uit with is uericall odelled i order to itegrate it i coditioig sstes for secific roos ad whose fial urose is to aitai the teerature of that roo i the aroriate theral levels. ur uerical odels are develoed ad coared. o do so 4 are selected to be used i differet teerature rages accordig to the secific roo ecessities. he are aalzed i the lab ad their theral behaviours are tested with the eerietal istallatios ad are siulated with the theoretical odels so the roer uerical odel ca be chose after validatio.. SELECION CRIERIA First of all it is essetial to select the aroriate geoetr of the ecasulatio. At this oit it is ecessar to cosider which are the features to rovide to the storage sste. Power ecessit ad required oeratio tie are two of these factors. he acroecasulatio i late shae has bee selected because it is a deel studied geoetr (Lodo ad Seba 943) that suoses: Facilit for cotrollig the thickess of the which is a crucial desig factor to be able to regulate the tie of loadig ad uloadig rocesses. Uiforit of the thickess of the ad therefore of the hase chage rocess. Facilit for aufacturig as uch as o sall scale as o a large scale ad versatilit of hadlig. Coercial accessibilit to a wide variet of late-shae ecasulatios of differet aterials (HDPE aluiiu...). Evetuall the aluiiu ecasulatio is chose i order to avoid lastic coatibilit troubles (Lázaro 006). Aother outstadig factor i order to establish the itself is obviousl the teerature rage of the alicatio. Deedig o the destiatio roo differet teeratures are required. his is show i able.
able : eerature rages (*fro ASHRAE Stadard 55-99) eerature (ºC) Roo te eerature (ºC) Roo te Suer Witer Patries/groceries 5 to 8 Idoor theral cofort* 3 to 6 0 to 4 Meet ad fish roo 4 to 6 Offices 3 to 7 7 to 4 Fruit ad vegetable roo 6 to 0 Couter roos to 40 Closed ushroo orchard 50 to 60 Biotech Laboratories 7 to Freezig roo -8 to -4 Calibratio Laboratories 8 to 7 Rubbish roo 3 to 6 Accordig to the first three etries of able where free-coolig is ost cool used the teerature rage goes fro 9ºC u to 40ºC. Soe eales of coercial with hase chage at these teeratures are show i Figure. Figure : cadidates I order to fit with several free-coolig alicatios i roos four of the are selected as the were aalzed i the lab: E (fro EPS Ltd) SH4 (fro Pluss Polers Pvt. Ltd) R7 (fro Rubither GbH) ad C3 (fro Cliator AB). 3. HEOREICAL MODELS ur theoretical odels are develoed i order to siulate the theral behaviour of the late ecasulated eosed to a flow. Each of these four odels takes ito accout differet assutios: Sei-aaltical odel; this ver sile odel cosiders the teerature alost uifor. Fiite differeces odel oe diesio ilicit; i this odel heat trasfer iside the ol occurs i the directio oral to the flow ad it cosiders ol coductio iside the slab. Fiite differeces odel two diesios ilicit; i this case both directios iside ( ad ) are aalzed. Fluid daic odel; this odel uses a CFD tool so covectio iside the or eve gravit effect ca be take ito accout. NOMENCLAURE w () width λ (W/ K) theral coductivit (t): thickess of hase-chagig z (): Cartesia coordiates L () legth ρ (kg/ 3 ) desit ls (K ºC) sol/liq hase chage teerature (K ºC) teerature e () thickess & (kg/s) ass flow h ls (J/kg) h sol/liq hase chage ethal c (J/kg K) effective secific heat h chael () chael high h h (W/ K) covectio q & (W/ ) heat flow er area uit Q E(J kj) caacit A( ) heat echage area coefficiet t(s) tie U (W/ K) heat trasfer global coefficiet HF: Heat heral Fluid : Phase Chage Material
Sei-aaltical odel his odel is based o the followig hotheses:. It is cosidered that the border solid-liquid of the hase chage is at the hase chage teerature at a tie of the rocess.. he heat trasfer i the b covectio is egligible coared to the heat trasfer due b coductio. 3. he flows arallel to the late surface ad its teerature reais costat. 4. I the flow the heat trasferece is cosidered like i a heat echager. eerature gradiets oral to the flow are egligible agaist teerature gradiets roduced i the flow directio. 5. Iside the late the aalsis is ol D oral to the flow. 6. Gravit effect is ot take ito accout. 7. he storage uit is adiabatic: there are ot heat losses through its walls. First a aalsis of a differetial eleet of the late is doe d (see figure ); i that iece of late it is cosidered that the teerature of the is costat. Figure : Differetial eleet of the late he three - heat trasfer echaiss cosidered are: rced covectio i the. Coductio through the wall of the ecasulatio. Coductio i the thickess of that has hase-chaged b the heat trasfer. Accordig to these echaiss the eressio of the heat flow is: q" U ( ) ( ) h ewall ( t) λ λ wall () he heat trasferred to the will be equal to the latet heat ut i la i the hase chage of that thickess of the. hat is the eerg balace to the : q" h / ρ sol liq d dt Whe equallig eressios () ad () the equatio (3) is obtaied. I it all the ters ca be cosidered costats ecet for the thickess of the laer that has hase-chaged. h ( ewall ( t) λ λ wall ) h sol / liq ρ d dt Itegratig a eressio of the elted thickess is obtaied: e wall ( ) t h λ wall λ hsol / liq ρ () (3) (4)
he revious odel is ol valid for sall teerature variatios i the ; evertheless i a colete storage sste the teerature varies areciabl as the asses through the sste. he chage of teerature of the that is circulatig et to the late will coe deteried b: q A & c ( ) (5) " i out therefore the results of the late odel caot be etraolated to the full storage cell odel. his variatio will ifluece i the heat flows ad i the evolutio of the thickess of the laer that elts. I order to cofrot this roble the odel is due to discretize (see figure 3). I the uerical discretizatios the roble alwas arises whe lookig for the suitable size of the esh. Greater the aout of oits that is used better the aroach to the eact reresetatio of the curve but o the other had the tie of calculatio will be icreased. Figure 3: Sei-aaltical odel discretizatio It is cosidered that i each eleet i the teerature is costat ad equal to the oe eterig that eleet. With this teerature ad the value of the thickess of the elted the heat flow to each eleet ca be calculated at a give oet. r ever tie ste fro 0 to M (where tm t) with icreets of tie t ad for each ositio i fro i0 to N (where LN ) with icreets of sace the heat trasferred fro the flow to the is: i q i { w e wall i Area (6) h λ λ wall Oce the value of the heat flow is obtaied i the give coditios alig the eerg balace to the ad to the the icrease of the teerature after its assage through the eleet i is acquired. he the ilet teerature of the followig eleet i i is calculated as well as the variatio of the thickess of the laer that has hase-chaged. Fro the eerg balace to the the followig eressio is obtaied: i i q & C (7) i [ ] ad the: qi i i & C Fro the eerg balace: i i qi hsol / liq ρ w (9) t i i h q sol/ liq i ρ t w Fiite differeces odel D ilicit ad Fiite differeces odel D ilicit he sei-aaltical odel does ot cosider the distributio of teeratures withi the late. o kow the it is ecessar to cosider other odels ore rigorous. wo late odels i fiite differeces (ilicit forulatio) have bee develoed (D ad D). Both odels aalze the teerature of the flow i a bidiesioal wa ad icororate the effective heat caacit obtaied i the lab. he storage caacit of the is usuall give b its latet heat value. he used are coercial oes ot ure substaces. herefore the elt ad solidif i a teerature rage istead of i a set teerature; the also have sub-coolig ad eve hsteresis. I these (8) (0)
cases latet heat ad c values are ot eough to kow the storage caacit at each teerature. Nevertheless the ethal versus teerature curves of the give this iforatio. I this aer the are obtaied b the - Histor ethod (Yiig 999 Marí 00) ad the are icororated i the D D ad CFD odels. Figures 4 ad 5 show two eales of the curves obtaied i that istallatio. Figures 4 ad 5: Ethal-eerature curves for SH4 (left) ad R7 (right) Nevertheless while the D odel suoses ol heat trasferece iside late i the directio oral to the flow the D odel cosiders also the trasferece i directio of the flow. Figures 6 ad 7 show the odal distributio of the D ad D slab-chael sstes. Figures 6 ad 7: Node distributio i both D ad D late sstes he fiite differece equatios for both odels are suarized i the table. able : Node eerature equatios Nodes D sste D sste Surface ( ) ( ) Bi Bi / ( ) ( ) Bi Bi Ier ( ) ( ) ( ) / ( ) Cetral ( ) ( ) N N N / ( )
Corer Frotal ( Bi ) Bi Bi ( Bi ) ( ) Bi ( Bi ) h c & h Air Flow ( ) ( ) & c Fluid daic odel Aother late odel has also bee develoed usig the tool of Coutatioal Fluid Daics Fluet. his rogra icludes a hase chage calculatio odule. It uses a techique deoiated Ethal-Porosit to odel the rocesses of solidificatio ad eltig (Voller ad Swaiatha 99). Oe of the advatages to siulate i Fluet is the data ost-rocessig ad the ossibilit of visualizatio of roerties rofiles throughout all the odelled geoetr. Fro the oit of view of the iroveet of the calculatio Fluet icororates the oveet of the liquid bags that are geerated i the. Although it is kow that the heat trasferece b covectio is goig to be egligible as the theral coductivit is ver low it is ot evidet that both echaiss of heat trasferece are ot coetitive (authors like Sarrow Bathelt Gobi ad Farid 986 iclude the covectio i their odels of heat trasferece for eltig rocesses) reaso wh it is useful to use a odel i Fluet. Oe of the ai disadvatages is the eorous coutatioal cost eeded to solve each articular case. Whe usig Fluet to ru the siulatios a other factors tha those cosidered i the other odels ca be take ito accout; aog others: covectio i the liquid effect of the gravit effect of viscosit (oet equatio) teerature gradiets i all the cosidered directios (deedig o the uber of diesios D D ad 3D) 4. DISCUSSION OF RESULS: COMPARISON BEWEEN MODELS A setu based o eerg balace of latet heat storage eleets is used to test the heat trasfer betwee the latet heat storage eleet ad the as a trasfer fluid (Zalba 00). I Figure 8 the results obtaied fro the first three odels develoed for the eltig rocess of a late are coared with the eerietal results. Figure 8: Coariso betwee odels for C3 late eltig Figure 8 illustrates how fit the eerietal results ad the curves obtaied fro the siulatios of the four differet odels. Models D ad D agree erfectl with the eerietal dischargig rate curve beig this a fudaetal araeter whe desigig the storage sste. r the sei-aaltical odel the differece with the
eerietal results is cosiderable due to the silicit of the hotheses; the CFD odel is still beig develoed so results are ot reseted as it ust be iroved. Cosiderig the revious observatios the D odel is selected as the basis odel to desig the storage sste sice: It fits erfectl with the eerietal results. It is ot liited to calculate how the solid-liquid border of the advaces but it also studies the whole late (it is ore rigorous i the calculatios tha the sei-aaltical odel). he D heat trasfer aalsis of the late avoids the coleit of the D aalsis that ot eve rovides additioal iforatio. It allows u-scalig fro a sigle slab to a greater uber of lates (that is the storage uit) i a fast ad accurate wa avoidig the eorous effort of desigig eshig ad the coutatioal cost associated to ru cole sstes i Fluet. Figures 9 ad 0: Suar of eerietal results of heatig of the -histor istallatio for E SH4 R7 ad C3 (left) ad stored eerg i secific teerature rages for each o each alicatio (right) Attedig eclusivel to the stored eerg desit the figures 9 ad 0 are useful to select the roer for each alicatio. he four selected were eected to fit with the four eales of alicatios. It is areciable that the teerature rage i which the hase chage of each takes lace is ver siilar. herefore the are ot suitable to use i alicatios with lower teerature rages such as geeral roos or biotech labs. he results obtaied with the Eerg Balace istallatio are show i the figures ad. Figures ad : Heatig stage i the Eerg Balace istallatio for SH4 (left) ad R7 (right) he eerietal results obtaied fro the Eerg Balace istallatio are coared with the siulatios ru with the D odel.
5. CONCLUSION Figure 3: Coariso betwee late discharge rates eerietal ad theoretical he D ilicit fiite differeces odel sees to be a aroriate odel i order to siulate both sigle slabs ad full storage sstes. I fact it offers equilibriu aog recisio ad rigor agaist tie required ad coutatioal cost eeded to ru the siulatios. Moreover the odel ca be ileeted i a full coditioig sste. he odel allows chagig the heat theral flow ad laig with variables like heat geeratio thickess of the late flows... r active storage sstes the ressure dros are also calculated reaso wh the equiet ca be desiged to balace the vetilators cosutio ad the heat echage. It is iortat to ehasize that o odel is discarded at all each oe resets its advatages ad disadvatages. hus the sei-aaltical odel gives a fast first aroach allowig to odif a desig variable; the odel D is recoeded whe thicker lates are studied ad the CFD odel oce refied allows to ake a rigorous cole aalsis ad uch ore i detail. ACKNOWLEDGMENS his work was artiall sosored b the Saish roect DPI00 0408-C0 0 (Pla Nacioal de Ivestigació Cietífica Desarrollo e Iovació ecológica 000 003). he authors also eress their gratitude to the coaies Rubither GbH (Gera) Cliator AB (Swede) EPS Ltd (UK) ad Pluss Polers Pvt Ltd (Idia). REFERENCES Farid M.M. Solar Eerg Storage with hase chage J. Sol. Eerg Res. 4 (986). Lázaro A. Zalba B. Bobi M. Castelló C. Cabeza L.F Eerietal stud o hase chage aterials ad lastics coatibilit AIChE Joural Volue 5 Issue Februar 006 804-808 USA. Lodo A.L. Seba R.A. Rate of Ice ratio rasactios of ASME 65 October 943. 77-778. Marí J.M. Zalba B. Cabeza L.F. Mehlig H. Deteriatio of ethal teerature curves of hase chage aterials with the -Histor ethod - Iroveet to teerature deedet roerties Measureet sciece ad techolog (00). Voller V.R. Swaiatha C.R.. Geeralized source-based ethod for solidificatio hase chage. Nuer. Heat rasfer B 9():. 75-89 99. Yiig Z. YI J. YI J. A sile ethod the -histor ethod of deteriig the heat of fusio secific heat ad theral coductivit of hase-chage aterials Measureet Sciece ad echolog0 (999) 0-05. Zalba B. Marí J.M. Cabeza L. Mehlig H. Free-coolig of buildigs with hase chage aterials Iteratioal Joural of Refrigeratio 7 (004). 839-849.
Zalba B. heral eerg storage with hase chage. Eerietal rocedure Ph D. hesis Uiversit of Zaragoza 00.