DYNAMIC PERFORMANCE OF A FORCED CONVECTIVE DIRECT STORAGE SYSTEM USING WATER AND PHASE CHANGE MATERIALS FOR LOW TEMPERATURE APPLICATIONS

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1 DYNAMIC PERFORMANCE OF A FORCED CONVECTIVE DIRECT STORAGE SYSTEM USING WATER AND PHASE CHANGE MATERIALS FOR LOW TEMPERATURE APPLICATIONS Teamah H.M. 1, Lghtstone M.F. 1, Cotton, J.S. 1 1 McMaster Unversty, Hamlton, Ontaro, Canada teamahhm@mcmaster.ca, lghtsm@mcmaster.ca, cottonjs@mcmaster.ca ABSTRACT The paper presents the heat transfer characterstcs of a shell and tube latent thermal energy storage system. A two dmensonal computatonal flud dynamcs model based on enthalpy porosty was developed to nvestgate the chargng and dschargng of the system. Organc fatty acds were used as phase change materals n the tubes and water was used as heat transfer flud n the shell. A varety of numercal nvestgatons were carred out for both constant and varable nlet temperature profles. The gans n energy storage for the studed system were compared to a sensble water-only system. The meltng tmes were found to be reasonable (less than 12 hours) and a gan n stored energy from % can be obtaned by ncreasng phase change volume fracton from 30% to 80% for a 7 o C operatng range of temperature. NOMENCLATURE A tank Outer surface Area of the tank [m 2 ] C pl Lqud specfc heat capacty [ J/kg K] C ps Sold specfc heat capacty [ J/kg K] D h Hydraulc dameter [m] E Energy stored [J] H Dmensonless specfc enthalpy h Heat transfer coeffcent [W/m 2 K] Specfc enthalpy [J/kg] K Thermal conductvty [W/mK] L c Length of cylnder [m] M Number of axal nodes m Mass flow rate nlet to the tank [kg/s] N Number of radal nodes N c Number of cylnders n the tank Nu c Nusselt number based on cylnder outer radus T Temperature [ o C] R c,nn Inner radus of phase change materal cylnder [m] R c,out Outer radus of phase change materal cylnder [m] r s Latent heat [kj/kg] Re Reynolds number T st Intal (start) temperature of the tank [ o C] U f,mean Mean flud velocty [m/s] V Volume of control volume [m 3 ] V tank Tank volume [m 3 ] ΔF o Fourer number Δt Tme step [seconds] ΔT m Transton meltng range [ o C] Nu p Nusselt number based on Dtts Botter correlaton Abbrevatons CFD Computatonal flud dynamcs HTF Heat transfer flud LES Latent energy storage PCM Phase change materal SDHW Solar domestc hot water SES Sensble energy storage TES Thermal energy storage Latn symbols ε Convergence crtera θ Dmensonless temperature μ Dynamc vscosty ρ Densty Summaton Superscrpts t Current teraton level It-1 Prevous teraton level Subscrpts c,nn Inner surface of cylnder c,out Outer surface of cylnder conv Convectve f Flud f,m Mean for flud In Inlet k Inner surface of control volume k-1 Outer surface of control volume l Lqud m Meltng m 1 Lower meltng m 2 Upper meltng st Start t Transton Surroundng

2 INTRODUCTION Buldng energy use n the resdental sector currently accounts for 17% of Canada's secondary energy consumpton, where secondary energy s defned as the total amount of energy consumed by an end-use, and excludes the energy consumed to convert the energy nto a useable form from ts prmary resource [1]. The breakdown by end-use wthn the resdental sector shows that water heatng accounts for 17% of the secondary energy consumpton, whle space heatng accounts for 63% (.e. a total of 80% for both sectors). For those two end-uses n Canada, heatng s manly provded by ether electrcty or natural gas. Assumng 4% annual growth of energy consumpton rate, t was found that the natural gas reserves would only last untl 2070 [1]. Other relevant yet crtcal ssues are the clmate changes and the global warmng problems assocated wth fossl fuel consumpton. There s thus a need to fnd alternatve renewable resources; one of them s makng use of solar radaton to heat water drectly and on-ste. However, solar energy s characterzed by ts ntermttent nature owng to the day-nght cycle and dfferent seasons of the year. In order for the solar energy to be effectvely used to follow specfc demand patterns; energy storage systems should be carefully desgned to compensate for the msmatch between the tmes when the solar energy s avalable and the tmes when there s energy demand. Besdes solar applcatons, thermal energy storage plays a vtal role n many other applcatons as well; such as space refrgeraton and ar-condtonng, agrcultural processes. And, n addton to space, automotve and waste heat recovery applcatons. Waste heat recovery has great potental n ndustralzed countres and dependng on the temperature at whch the waste heat s dscharged t can be classfed nto three categores: (1) Low temperature waste heat (below 100 C), (2) Hgh temperature waste heat (above 400 C) and (3) Moderate temperature waste heat (between 100 C and 400 C) [1]. Our nterest throughout ths study les n the low temperature waste heat category whch fts nto the hot water and space heatng applcatons of resdental and commercal sectors. Most of the thermal energy storage applcatons have been studed and summarzed n revewed artcles by Zalba et al. [2], Sharma et al [3], and Abhat [4]. There are three types of TES systems: (1) Sensble energy, (2) Latent energy and (3) Thermo-chemcal storage (TCS) systems. Latent energy storage (LES) systems employ phase change materals (PCMs) and the energy s stored and released n the form of latent heat of fuson. LES systems have recently captured more attenton n varous applcatons owng to ther hgh energy storage densty compared to SES systems and ther ablty to store energy at constant temperature correspondng to the meltng temperature (T m ) of the PCM used. The challenge s that, most PCMs are characterzed by low thermal conductvty, low specfc heat capacty and hgh cost. Common examples of PCMs used n LES systems are: paraffn, fatty acds, organc eutectcs and hydrated salts. In order to determne an approprate PCM for an applcaton, a number of factors must be consdered. Phase change temperature of a desrable PCM must be wthn the operatng temperature range of the thermal storage system. Ideally, the specfc heat of a PCM should be hgh when t s storng heat as sensble, and the thermal conductvty of the PCM should be hgh to ensure hgh heat transfer rates from the surface to the core of the PCM module n the system. Abhat [4] classfed PCMs nto three categores: organc, norganc and eutectcs. Sharma et al. [3] extended Abhat s dvson wth subcategores classfyng the organc nto paraffn and non-paraffn compounds, the norganc nto salt hydrate and metallc and fnally eutectcs nto (organc-organc), (norganc-norganc) and (norganc-organc). Paraffn waxes are a famly of straght chan alkanes. Ther meltng temperature and latent heat ncrease wth the hydrocarbon chan length [5-6], they are generally chemcally stable, melt congruently and are non-toxc. However, paraffn wax has several dsadvantages whch are: moderate flammablty and low thermal conductvty whch lmts ts wde applcaton n ndustry (Lane [7]). Non-paraffn organc PCMs consst of fatty acds, esters, alcohols and glycols; among them, fatty acds are promsng for applcatons n solar thermal systems [8-10]. The most commonly used fatty acds are dvded nto sx groups: caprylc, caprc, laurc, myrstc, palmtc and stearc wth respectvely 8 to 18 carbon atoms per molecule. Ther meltng ponts are n the range from 16 C to 65 C wth a heat of fuson between 155 and 180 kj/kg whch s hgher than paraffn waxes [11]. Thermal and physcal propertes of laurc acd were nvestgated by Desgrosseller et al. [12]; results proved that laurc acd s a promsng canddate for LES [13-15].

3 The man problem assocated wth the PCMs operatng n low temperature s ther low thermal conductvty whch ranges from [W/m.K]. Ths can lmt the storage capacty for LES systems for a gven chargng or dschargng tme. Extensve research has been carred out to nvestgate heat transfer enhancements n latent heat thermal storage systems. The enhancement technques can be classfed nto actve and passve heat augmentaton technques [16-17], Actve technques nclude the applcaton of an external source such as electrohydrodynamcs to enhance the meltng rate as studed by Nakhla et al. [16]. Passve technques can be manly dvded nto dfferent categores [18-19]: usng extended surfaces, thermal conductvty enhancement, mcro-encapsulaton of PCM and Usng multple PCMs. Extended surface technques such as fns are based on ncreasng the heat transfer area n the thermal system to ncrease the total rate of heat transfer. Fns offer an ncreased area advantage, whle they have an adverse effect on the weght, the volume and cost of the thermal storage system for a gven storage energy requred [16-19]. Also, some research used metallc partcles to enhance the thermal conductvty and lmt the chargng and dschargng tmes to be wthn acceptable lmts but the man dsadvantage of ths technque s beng ntrusve n nature and the thermophyscal propertes of PCMs are altered [20-22]. Tryng to reduce the PCM thermal resstance by encapsulatng t n thn modules and geometrc optmzaton was a thrd aspect of enhancement technques [23-25]. Usng multple PCMs captured the attenton of researchers for concentrated solar power applcatons. Mchels and Ptz-Paal [26] expermentally tested on the cascaded latent heat storage system for parabolc trough solar power plants n whch three dfferent PCMs were used. The experments were conducted to nvestgate the effect of employng LES systems usng PCMs wth dfferent meltng temperatures arranged n seres. Hgh temperature ol was used as the heat transfer flud wth chargng temperature of 390 C and dschargng temperature at 285 C. They concluded that cascaded LES systems wth multple PCMs provde hgh storage potentals compared to the sensble system f the PCM thermal conductvty s ncreased by 4 tmes. Ths hghlghts the lmtaton of the low thermal conductvty of PCMs. Also, they showed that the energy storage n the cascaded system s hgher than usng only one of the PCMs (around 74%). Seenraj and Narasmhan [27] used fns to enhance heat transfer n a mult-pcm thermal storage system. They found that the molten fracton ncreased by 35% n comparson to a sngle PCM model. Recent research studed the hybrd energy storage to take the advantages of both sensble and latent storages, Nallusamy et al. [28] nvestgated expermentally the thermal behavor of a packed bed TES system that conssted of sphercal PCM capsules (paraffn wth T m = 60 C) surrounded by SES medum (water). Ther results showed that employng PCM n the TES system leads to better control of the HTF flow temperature owng to the constant meltng temperature of the PCM. However, the frst layer of the sphercal capsules recevng the HTF flow showed faster meltng rate than the last layer further downstream. Ths led to more energy stored n the lqud PCM n the form of sensble energy whch s at least one order of magntude less than the latent heat of fuson of the same PCM at the same temperature operaton range of the experments. The heat transfer mechansm n a cylndrcal tube heat exchanger wth PCM was studed by Shmuel et al., [29]. Numercal results showed that at the begnnng of the process, heat was transferred by conducton from the tube wall to the sold phase PCM through a relatvely thn lqud layer. As the meltng progressed, natural convecton n the lqud became the domnant heat transfer mode. Jones et al. [30] performed an expermental and numercal study explorng the thermal characterstcs of meltng n-ecosane as the PCM n a cylnder wth constant wall temperature boundary condton. They captured the melt front at dfferent stages; t was domnated by conducton n the early stages and eventually convecton domnated and they recommended one of ther conducted experments for numercal benchmarkng. Predctng the thermal behavour of phase change materals s dffcult because of the nherent non-lnear nature at movng nterfaces. Three sets of numercal methods for solvng for heat transfer n latent heat energy storage systems were summarzed by Dutl et al. [31]: namely fxed grd; adaptve mesh; and frst law and second law of thermodynamcs methods. Because of ther conceptual smplcty, fxed grd approaches have found a wde applcaton. The essental feature of fxed grd approaches s that the latent heat evoluton s accounted for n the governng

4 equatons by defnng ether an enthalpy, or an effectve specfc heat, or a heat source (or snk). Consequently, the numercal soluton can be carred out on a space grd that remans fxed throughout the calculaton process. The major problem wth fxed grds enthalpy methods s n accountng for the zero velocty condton as the lqud regon turns to sold. Morgan [32] employed the smple approach of fxng the veloctes to zero n a computatonal cell whenever the mean latent heat content, reaches some predetermned value between 0 (cell all sold) and L (cell all lqud), where L s the latent heat of the phase change. Voller et al. [33-35] have nvestgated varous ways of dealng wth the zero sold veloctes n fxed grd enthalpy solutons. Computatonal cells n whch phase change s occurrng are modelled as pseudo porous meda wth the porosty, decreasng from 1 to 0 as latent heat content of the cell decreases from latent heat of fuson value to zero. The other wdely used fxed grd method s the "heat capacty method". Wth ths method the latent heat effect s approxmated by a large effectve heat capacty over a small temperature range [36-40]. Ths approach s smple n concept and easy to mplement. It s, however, senstve to the choce of the phase change temperature nterval and the ntegraton scheme and n some cases the correct soluton or even a soluton cannot be obtaned due to non-convergence caused by the sudden change of the specfc heat at the nterface. The present work employs the enthalpy porosty method due to ts recommended smplcty and stablty over wde temperature ranges n dfferent applcatons A study of the lterature has shown that careful desgn of TES systems s very crtcal to obtan enhanced utlzaton of renewable sources as well as to the effcent recovery of waste heat. Ths wll n turn lead to sgnfcant reducton n the system s sze n addton to a reducton of greenhouse gas (GHG) emssons. Employng both SES and LES was not well explored n the avalable lterature. Ths motvated the current research work to study the performance of a hybrd storage system that uses water and organc PCMs to harvest the advantages and mnmze the dsadvantages of both meda. NUMERICAL MODELLING An enthalpy porosty model s developed to deal wth phase change process whch takes nto account the followng assumptons: 1) PCM s homogenous and sotropc 2) Thermo-physcal propertes of PCM are dfferent for dfferent phases but they are ndependent of temperature 3) The expanson of the PCM s neglected. (3) Accordng to the enthalpy porosty formulaton [41] specfc enthalpy (enthalpy per unt mass) s defned based on the cell condton (sold, lqud or transton) as follows: (T) = C p,s T T < T m1 (1) (T) = C p,s T m1 + r s(t T m1 ) T m T m1 < T < T m2 (2) (T) = C p,l (T T m2 ) + r s + C p,s T m1 T > T m2 r s s the latent heat, T m1 s the lower meltng temperature and T m2 s the upper meltng temperature. By ntroducng the followng non-dmensonal expressons for enthalpy and temperature; H = m1 r s θ = C p,s(t T m1 ) r s θ = C p,l(t T m1 ) r s (4) T < T m1 (5) T > T m1 (6) By usng expressons [4-6] together wth the fnte dfferencng n the conducton domnated meltng equaton and consderng the geometry of element shown n fgure 1; t yelds; 1 H j,k H j,k = F o [a k (θ j,k+1 θ j,k ) + b k (θ j,k 1 + C 1 (θ j+1,k θ j,k ) + C 2 (θ j 1,k θ j,k )] θ j,k ) (7) Where; k j,k t (8) F o = 2 ρc p,j,k R c,out 4 r k (9) a k = 2 (r k 1 r k+1 )(r k 1 r 2 k ) 4 r k 1 (10) b k = 2 (r k 2 r k )(r k 1 r 2 k ) C 1 = C 2 = R 2 c,out (11) L 2 r k = R k (12) R c,out

5 presents a comparson between ther performance. Comparson of cylndrcal and rectangular performance Fgure 1 studed element geometry The code was valdated on a 2D problem for meltng wth constant wall temperature condton presented by Jones et al. [30]. The schematc of ther test faclty s shown n fgure 2, an sothermal boundary condton was mantaned by mmersng the n- ecosane cylnder n a water bath. The present results were compared to both ther expermental and numercal predctons as shown n fgure 3, whch ndcated a very good agreement wth both the expermental and numercal molten fractons. The storage tank consdered n the present study s a part of domestc heatng system. The Phase change materals are enclosed n thn modules to mnmze thermal resstance mposed by the low thermal conductvty of the PCM. Prelmnary smulatons were conducted to compare the performance of rectangular module and equvalent array of cylndrcal modules shown n fgure 4 and 5. Fgure 4: (a) rectangular module and (b) equvalent cylndercal modules array Fgure 2: Schematc of the expermental faclty by Jones et al [30] Fgure 3: Comparson of present code and Jones et al. [30]. The code was also accommodated to deal wth rectangular co-ordnates. From the lterature, the most commonly used PCM encapsulatons are rectangular and cylndrcal. The followng subsecton Fgure 5: Boundary condtons for the studed modules When consderng the same volume for rectangular and cylndrcal modules;.e. the comparson between (100cm x 100cm x 2cm) rectangular slab wth a 40 cylnder array; each of 2.25 cm damter and 100 cm length ntally at the melt temperature T m = 42, the molten fracton (molten volume/total volume) s shown n fgure 6. The melt propogates faster n the cylndercal modules, especally at the early stages of meltng, then t relatvely decreases owng to the decreased heat transfer area when melt progresses but the overall performance of the cylndercal module s better. Also, Fgure 7 shows that the rato between the actual molten fracton and the deal molten fracton s hgher for the cylndrcal module compared to the rectangular one (Ideal denotes the case where the PCM conductvty s nfnte so all the convectve heat transfer s utlzed n the meltng process wthout consderng the lqud PCM superheatng; the deal meltng tme s computed as t melt,deal = mass r s h A(T T m ) )

6 the extracted hot water to meet the load s compensated wth cold water from the mans. Fgure 6: molten fracton of rectangular and cylndrcal modules versus tme consderng same volume (h = 100 W m 2 K, T = 52 ) Fgure 8: the studed doman n the code (a) the whole tank, (b) the cylndrcal jacket The developed enthalpy porosty model s expanded to take nto account the heat transfer from the water surroundng the PCM cylnders by usng the correlatons presented by Rhosenow [42] where; Fgure 7: Rato of actual molten fracton to deal molten fracton for cylndrcal and rectangular modules versus tme consderng same volume (h = 100 W m 2 K, T = 52 ) By keepng the same conducton dstance for both rectangular and cylndrcal modules (.e 2 cm dameter cylndrcal modules and 2 cm thck rectangular one), and by mantanng the same heat transfer area and the volume to area rato, the same trend s also observed. Ths result agrees wth Barba and Spga [24], who proved analytcally that the retreval rate of energy s hgher n the cylndrcal module than that of the rectangular one. The dfference between the present work and ther work s the dfferent operatng temperature ranges and propertes of the used PCMs. Based on the prevous results, cylndrcal modules seem to perform better than rectangular ones; so the tank consdered n the present work conssts of cylndrcal ppes contanng phase change materal surrounded by water flowng parallel to t as shown n fgure 8. Durng the chargng process hot water s ntroduced to the top of the tank and n dschargng For lamnar flow Nu c = ( D h Rc,out 0.205) f Re c 2200 For turbulent flow Nu c = e Nu p f Re c 2200 Where; 1.62 D h Rc,out (13) (14) Re c = ρ fu f,mean D h (15) μ f D h,c = 2 V tank (16) 2R π N c R c,out L c,out c The mean velocty can be calculated as follows (assumng unform flow dstrbuton); m U f,m = ρ f ( V tank 2 (17) Lc πn c R c,out ) Applyng energy balance on the HTF, wall and PCM control volumes yelds a system of equatons; ths set can be solved wth Gauss-Sedl teratve method. At specfc tme level the entre feld s defned by H and θ for the phase change materal and T values for the wall and the heat transfer flud. After another tme step the new values of H, θ and T are calculated. Then a convergence test s done. Dependent on the result of that test, teraton s executed at the same tme level or

7 the tme level s ncreased. Ths convergence crtera s gven by; T,t,t 1 j,k T j,k T,t,t 1 j,k + T < ε (18) j,k ε s a specfed convergence crteron based on the desred accuracy level RESULTS AND DISCUSSION A commercal 200 L tank s consdered n the present study wth length 78 cm. The number of the PCM cylnders vares accordng to the packng rato (PCM volume/ total volume). Dmensons and studed parameters are summarzed n Table 1. Thermophyscal propertes of the utlzed fatty acds are lsted n table 2. Table 1: Dmensons and studed parameters Tank volume 200 ltres (0.2 m 3 ) Tank length 78 cm Tank dameter 57 cm PCM module 2 cm, 4 cm and 8 cm dameter PCM packng rato 30%, 50% and 80% Mass flowrate m = Kg/s Table 2: Thermo-physcal propertes of organc fatty acds [4] Acd T m [ ] C p [kj kg K] r s [kj kg K s W m. k ] Caprc 31.5 NA* Laurc Myrstc (sold), 187 NA* 2.7(lqud) Palmtc 63 NA* *Not avalable n the lterature At frst smulatons were done to test the chargng process of the tank wth ts ntal temperature 40 o C. The nlet water to the tank has a mass flow rate of 0.05 kg/s and temperature of 52 o C. Laurc acd s used as the PCM (T m = 42 o C) and t s placed n 2 cm dameter cylnders. Fgure 9 shows the grd ndependence test where a grd of 300 nodes n the radal drecton and 100 nodes n the axal drecton together wth tme step wll be the most computatonally effcent one to solve the problem. It s also shown that t takes 3.2 hours to melt the PCM n the 30% packng rato condton. Fgure 9: Grd ndependence test for molten fracton result (V tank = 0.2 m 3, packng rato = 30%, T st = 40, T n = 52, m = 0.05 kg/s) The change n the stored energy wth tme n the PCM and HTF s shown n fgure 10. After fully meltng the PCM, 16.4 MJ of energy wll be stored n the tank 61.8 % of t s stored n the PCM and 38.2% s stored n water. Ths corresponds to 65% gan n energy compared to the only water system gan = E tank wth PCM E tank wthout PCM E tank wthout PCM Fgure 10: evoluton of energy wth tme n the system components (V tank = 0.2 m 3, packng rato = 30%, T st = 40, T n = 52, m = 0.05 kg/s Examnng fgure 11, whch shows the sothermals durng meltng 30% PCM (T m = 42 ) n chargng the tank (T st = 40, T n = 52, ṁ = 0.05 kg/s), t s clear that there s an axal varaton n temperature n dfferent levels of PCM module as water loses ts energy axally throughout the way, whch s also manfested n melt nterface n fgure 12. The hgher levels of PCM modules melt and superheat before the lower levels. Fgure 13 shows the evoluton of water temperatures at dfferent heghts of the tank (measured from tank top) the temperatures ncrease sensbly then t s tuned around the PCM meltng temperature (due to the effect of PCM nternal resstance) and then t superheats. Due to the axal varaton of HTF temperature t shows both temporal and spatal varatons.

8 the table, the gan can reach as hgh as 362% compared to the SES usng 80% PCM packng rato and 7 o C operatng temperature range. Fgure 11: Isothermals n PCM modules n a 200 ltre tank wth 30 % PCM (T st = 40, T n = 52, T m = 42, ṁ = 0.05 kg/s) [meltng pont s shown n dotted lne] Fgure 12: Isothermals n PCM modules n a 200 ltre tank wth 30 % PCM (T st = 40, T n = 52, T m = 42, ṁ = 0.05 kg/s) [meltng pont s shown n dotted lne] Fgure 13: Temperature evoluton n a 200 ltre tank wth 30 % PCM (T st = 40, T n = 52, T n = 42, m = 0.05 kg/s) Narrowng the operatng temperature range ncreases the gan from the system as the effect of latent heat of fuson wll be more pronounced. For example, consderng the nlet temperature to the tank to be 47 o C nstead of 52 o C, the meltng tme becomes 6.2 hours nstead of the 3.2 hours n the prevous case. A total of 13.5 MJ s stored n the whole tank after fully meltng the PCM, 72.4 % of the energy s stored n PCM and the rest n the HTF as shown n fgure 14 and ths makes the gan rse to 132% compared to the system wthout PCM. Also the PCM stores an ncreased percentage of the total energy 72.4% compared to 61.7% n the prevous case (12 o C operatng temperature range). Table 3 summarzes the results for hgher PCM packng ratos. As seen n Fgure 14: Energy evoluton wth tme n a 200 ltre tank wth 30% PCM (T st = 40 o C, T n = 47 o C, m = 0.05 kg/s ) Table 3: Summary of smulaton results 7 o C Operatng range HTF Gan energy (%) (MJ) % PCM PCM energy (MJ) Meltng tme (hrs) To assess the mpact of the non-deal propertes of the PCM, the results can be compared to the maxmum analytcal gan. The analytcal gan s computed when all the system temperature becomes equal to the nlet flud temperature whch s the ultmate case acheved after gvng the system an nfnte tme to charge. Analytcal gan Maxmum energy stored n hybrd system = Energy of tank wthout PCM Fgure 15 shows the analytcal gan for dfferent operatng temperature ranges dependng on the packng ratos. The gans that are expected from the smulaton are less than those calculated analytcally because by the end of PCM meltng the whole tank would not be at the same nlet temperature and there would be an axal temperature varaton across the HTF control volumes.

9 40 when subjected to hot water from the top ( T n = 60, m = 0.05 kg s and T m = 54 ) for 5 hours followed by dschargng by cold water from the bottom ( T n = 30, m = 0.1 kg/s) for 2 hours. It shows the tunng of temperature around the PCM temperature durng both meltng and soldfcaton. Also, the hgher levels of the tank are the frst to be affected by the ncomng hot chargng water and the last to sense the cold dschargng water. Fgure 15: Analytcal gans for dfferent PCM ratos and range of temperature The effect of varyng mass flow rate on meltng tme for the case of 30% PCM packng rato and 7 o C operatng range s shown n fgure 16. The behavour of HTF correlatons s nonlnear so doublng the mass flow rate decreases the meltng tme sgnfcantly. Doublng the mass flow rate from 0.05 kg/s to 0.1 kg/s decreases the meltng tme to 69%. Increasng the flow rate 10 tmes reduces the meltng tme to 41%. Ths s due to the nonlnear behavour of the heat transfer coeffcent correlatons. The meltng tme decreases to 38% wth the very hgh mass flow rate as t wll ensure a nearly constant temperature boundary condton on the PCM modules. Fgure 17: Temperature hstores at dfferent levels of 200 ltres tank wth 30 % PCM (T m = 53.8 ) under sequental chargng and dschargng Varable chargng profles To use the developed model for domestc applcatons, t should respond to the varable solar profles. Fgure 18 shows the effect of puttng PCM wth dfferent packng ratos on temperature profles n a 200 ltres tank when subjected to a hypothetcal sunny day profle. The temperatures are tuned durng PCM meltng and puttng more percentage of the PCM evens out the peaks of outlet temperature relatve to the case of no PCM where the tank obeys the plug flow model and the sne wave s only lagged by the tank turnover tme. Fgure 16: Effect of mass flow rate on meltng tme of 30% PCM (T st = 40, T n = 47 ) Sequental chargng and Dschargng Studyng sequental chargng and dschargng s mportant n SDHW systems to see how the demand of typcal famles affects t. Fgure 17 shows the temperature hstores n a tank whch s ntally at Fgure 18: Temperature profles n a 200 ltres tank when subjected to a hypothetcal sunny day profle (T m = 42, m = 0.05 kg/s)

10 Effect of PCM module dameter Fgure 19 shows contours of the predcted molten fracton and gans for a tank havng 50% PCM under combnatons of operatng temperature ranges and chargng perods t shows that ncreasng the PCM module dameter from 2 cm to 8 cm has a great effect on lmtng the regons of hgh expected gans and also the predcted molten fractons are low compared to the smaller dameter due to less heat transfer area. Also negatve gans can be obtaned wth the very low chargng perod that don t allow for the whole meltng of the PCM and ths can be attrbuted to the poor sensble propertes of PCM compared to water. Fgure 19: Melt fracton and gans for 50% PCM n a 200 lter tank (T st = 20, T m = T st+t n, T 2 op = T n T st ) (a) 2 cm dameter module, (b) 8 cm dameter module CONCLUSION A parametrc study s conducted on hybrd tank used for resdental applcaton. Includng PCM wth packng ratos from 30% to 80% PCM ncreases the gans of the system tmes compared to the only water system for 7 o C operatng range. The gans are very senstve to the module dameter; smaller dameters ncrease the expected gans because of the hgher heat transfer area. Hgher mass flowrates reduce the meltng tmes because of the hgher heat transfer coeffcent. Includng PCM n a tank modulates the tank outlet temperature around ts meltng pont. Care should be taken n choosng the correct PCM n dfferent applcatons as when the chargng perod of the system s less than the requred tme to fully melt the PCM the ncorporaton of PCM can yeld negatve gan compared to the only sensble system. REFERENCES [1] NRCan. "Energy Use Data Handbook to 2009." Techncal report, Offce of Energy Effcency, Natural Resources Canada, Ottawa, ON, Canada. [Onlne] /handbook11/ (2012). [2] Zalba, B., Marn, J. M., Cabeza, L. F., and Mehlng, H. (2003), Revew on thermal energy storage wth phase change: materals, heat transfer analyss and applcatons, Appled Thermal Engneerng, 23(3), [3] Sharma, A., Tyag, V.V., Chen, C.R., and Buddh, D. (2009), Revew on thermal energy storage wth phase change materals and applcatons, Renewable and Sustanable Energy Revews, 13(2), [4] Abhat, A. (1983), Low temperature latent heat thermal energy storage: Heat storage materals, Solar Energy, 30(4), [5] Zhang Z.G. and Fang X.M. (2006), Study on paraffn/expanded graphte composte phase change thermal energy storage materal, Energy Converson and Management, 47, [6] Kousksou T., Jaml A., Erhafk T. and Zeraoul Y. (2010), Paraffn wax mxtures as phase change materals, Solar Energy Materals and Solar Cells, 94, [7] Lane G. A. (1983), Solar heat storage: latent heat materals, vol. I. Boca Raton, FL: CRC Press, Inc. [8] Feldman D., Banu D., and Hawes D. (1995), Low chan esters of stearc acd as phase change materals for thermal energy storage n buldngs, Solar Energy Materals and Solar Cells, 36, [9] Feldman D., Banu D., and Hawes D. (1995), Development and applcaton of organc phase change mxtures n thermal storage gypsum wallboard, Solar Energy Materals and Solar Cells, 36,

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