Available online at ScienceDirect. Energy Procedia 69 (2015 )

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1 Available nline at ScienceDiect Enegy Pceia 69 (2015 ) Intenatinal Cneence n Cncentating Sla Pwe an Chemical Enegy Sytem, SlaPACES 2014 Numeical invetigatin PCM-bae themal enegy tage ytem Selvan Bellan a, Je Gnzalez-Aguila a *, Manuel Rme a, Muhamma M. Rahman b,c, D. Ygi Gwami b,, Elia K.Steanak b,e a IMDEA Enegy Intitute, Ramn e la Saga 3,Mótle 28935, Spain b Clean Enegy Reeach Cente, Univeity Suth Flia, 4202 E. Fwle Ave., Tampa, FL 33620, USA c Depatment Mechanical Engineeing, Univeity Suth Flia, 4202 E. Fwle Ave., Tampa, FL 33620, USA Depatment Chemical & Bimeical Engineeing, USF, 4202 E. Fwle Ave., Tampa, FL 33620, USA e Depatment Electical Engineeing, Univeity Suth Flia, 4202 E. Fwle Ave., Tampa, FL 33620, USA Abtact A latent themal enegy tage ytem, which cnit ium nitate ille pheical capule in a cylinical tank, i analyze cncentating la pwe plant applicatin. The high tempeatue ynthetic il, Theminl 66, i ue a heat tane lui. A numeical mel i evelpe t invetigate the behavi the ytem. The evelpe mel i valiate uing the epte expeimental an numeical ata. The inluence capule ize an the lw ate heat tane lui (HTF) n the tempeatue itibutin, lui lw, melting an liiicatin the ytem i tuie. The natual cnvectin eect peent in the liqui egin uing melting i elve by the eective themal cnuctivity, which i calculate by enthalpy mulatin meth. The eult inicate that the heat tane ate i inceae an eventually the chaging/ichaging time i eceae when the capule ize i eceae, the HTF lw ate i inceae The Auth. Publihe by Elevie Lt. Thi i an pen acce aticle une the CC BY-NC-ND licene 2015 The Auth. Publihe by Elevie Lt. ( Pee Pee eview eview by by the the cientiic cientiic cneence cneence cmmittee cmmittee SlaPACES SlaPACES 2014 une 2014 epnibility une epnibility PSE AG PSE AG. Keyw: Latent themal enegy tage, Themcline ytem, Encapulate phae change mateial, Mlten alt, Cncentating la pwe * Cepning auth. Tel.: ae: je.gnzalez@imea.g;elvan.bellan@imea.g The Auth. Publihe by Elevie Lt. Thi i an pen acce aticle une the CC BY-NC-ND licene ( Pee eview by the cientiic cneence cmmittee SlaPACES 2014 une epnibility PSE AG i: /j.egyp

2 Selvan Bellan et al. / Enegy Pceia 69 ( 2015 ) Nmenclatue C p h L Nu P P c i m R Ra t T u z iamete the capule (m) heat tane ceicient (W/m 2 K) latent heat uin (J/kg) Nuelt numbe peue (Pa) Pantl numbe aial cinate (m) ute aiu inne laye cating (m) inne aiu the capule (m) li-liqui inteace (m) ute aiu the capule (m) tage tank aiu (m) Rayleigh numbe time () tempeatue (K) velcity vect (m/) axial cinate (m) Geek ymbl melt actin at each element enity (kg/m 3 ) Subcipt e eective lui i inne init initial liq liqui phae m melting nik nickel ute pl plyme li l li phae Abbeviatin CHTZ cntant high tempeatue zne CLTZ cntant lw tempeatue zne CMTZ cntant melt tempeatue zne CSP cncentate la pwe HEZ heat exchange zne HTF heat tane lui PCM phae change mateial R&D eeach an evelpment TES themal enegy tage

3 760 Selvan Bellan et al. / Enegy Pceia 69 ( 2015 ) Intuctin Themal enegy tage play an imptant le in cncentating la pwe (CSP) plant. Thu, igniicant R&D activitie ae being evelpe in the iel themal enegy tage (TES) in ecent yea. Numeu tage meth vaiu tempeatue ange have been invetigate an eviewe [1-2]. At peent, latent heat tage in phae change mateial (PCM) i cniee a ne the mt attactive meth. Seveal PCM have been ientiie lw [3] an high tempeatue [4] applicatin an expeimental an numeical tuie have been cnucte t chaacteize them. Gag et al. [5] ummaize ealy liteatue n packe be themal tage ytem. The eult vaiu numeical mel bth enible an latent heat tage meth wee cmpae by Imail an Stuginky [6]. Review n PCM bae themcline tage ytem wee peente [7-8]. Vaiu numeical mel have been evelpe in the pat ew ecae t peict the themal an hyynamic behavi an pemance the packe be latent heat themal enegy tage ytem. Thee mel ae geneally claiie int thee maj gup: Single phae mel, tw phae cntinuu li phae mel an the cncentic ipein mel. Since the etail meling each element inie the ytem i cmplicate ue t it cmplex cniguatin an pce ynamic, many hypthee an celatin have been ue in thee mel. T impve the accuacy the mel, an eective mel ha been evelpe an epte ecently [9], which i ieent m the peviu mel. In thi mel, the lui lw thugh the vi amng the PCM phee an the themal gaient inie the capule can be invetigate. Expeimental celatin empiical expein ae nt invlve in thi mel except the teatment the eective themal cnuctivity, which i ue t inclue the natual cnvectin eect in the liqui PCM uing melting. Althugh eveal tuie have been epte in the liteatue n themal enegy tage ytem, phae change pce, heat tane chaacteitic inie the packe be an themal gaient inie the capule at high tempeatue have nt been tuie cmpletely. Accingly, in thi tuy, the eective packe be mel i ue t invetigate the themal behavi an pemance the TES ytem. Tempeatue itibutin, lui lw, melting an liiicatin the ytem ae peicte an the inluence ytem cniguatin an peating paamete n the pemance the ytem i tuie. 2. Numeical melling 2.1. Melling appach an gvening equatin Fig.1. Schematic the cmputatinal main Fig. 1 hw the chematic a lab-cale themal tage tank packe by pheical capule. The capule ae ille with ium nitate, an the hell the capule i mae up nickel. Since the tenency the ium nitate-hell inteace i highly cive, a plyme cating i mae at the inne uace the hell t avi cntact between the ium nitate an hell. The high tempeatue ynthetic il, Theminl 66, i ue a heat tane lui. In e t imulate the lui lw an heat tane inie the tank, a numeical mel i evelpe bae n the llwing aumptin: Due t the axial ymmety cniguatin an bunay cnitin, the 2D mel i apte. The lw inie the tank i aume a lamina an incmpeible an the aiatin heat tane between the capule i negligible. The hmbic packing i aume, a a eult, the cntact between the capule i pint-tpint, an eventually the heat tane between the capule i negligible. Theee, the vi pace between the capule i aume, becaue the 2D mel e nt lea t lw thugh the be i the capule cntact t each

4 Selvan Bellan et al. / Enegy Pceia 69 ( 2015 ) the [9]. Bae n the eging aumptin, the gvening equatin t peict the heat tane an lui lw in the vi egin the ytem ae given by t u 0. u ( u. ) u P t C C. T. T p T t p T 2 u u u 3 u (3) whee u, μ, P, C p, T an ae velcity vect, enity, ynamic vicity, peue, peciic heat, tempeatue an themal cnuctivity epectively. The enegy equatin in the PCM egin i given by h t. T (4) Whee, the peciic enthalpy (h) i eine a the um the enible enthalpy h en an enthalpy change ue t phae change, whee L an ae the latent heat the mateial an the melt actin epectively. The ubcipt an epeent the HTF main an PCM main epectively. Table 1. Bunay cnitin Bunay T Vi Inlet T (t) Ma lw ate (kg/) Outlet Wall hw ( Ta T ) 0 The tempeatue epenent them-phyical ppetie the PCM, HTF an hell the capule ae btaine m the Re. [2]. The themal eitance caue by the hell the capule i inclue in the mel. The bunay cnitin ae given in Table 1. Gi epenent tet wee caie ut in the peliminay calculatin vaiu gi ize; 0.001, an m. The gi ize m wa un t be aequate. All the gvening equatin ae lve uing the cmmecial CFD ce FLUENT Deteminatin eective themal cnuctivity Fm the liteatue n melting an liiicatin pcee the PCM, it i ntice that the themal cnuctin i the maj heat tane mechanim uing liiicatin pce, wheea natual cnvectin play a vital le uing melting pce [10-11]. Mt the melting pce mel nly cniee the themal cnuctin ue t cmplexity in ecibing the natual cnvectin uing melting pce. In thi tuy, the cnvective eect peent in the liqui egin i elve by the eective themal cnuctivity. T peict thi, ne imeninal cnuctin mel phae change pce inie a capule i evelpe by enthalpy mulatin meth, bae n the liteatue mel [12-13]. The gvening equatin an bunay cnitin ae given belw 2 T T 2 T C p (5) t 2 T / z 0 / z 0 Duing chage me, the tempeatue the capule i initially aume at lwe than melting pint the PCM. When the t > 0, the pheical capule i ubjecte t the cnvective heating at the ute uace ue t the tempeatue the lui, which i highe than the melting tempeatue. Bunay cnitin at the extenal uace an the cente the phee ae given a llw V i (1) (2)

5 762 Selvan Bellan et al. / Enegy Pceia 69 ( 2015 ) at T an at h T T t T i c i pl i c c c nik i i (6) Whee i, an c ae inne aiu, ute aiu an ute aiu the plyme laye the capule epectively. The ht heat tane lui heat up the capule. When the tempeatue the PCM cle t the inne uace the capule eache the melting tempeatue, the PCM melt an the liqui laye gaually gw up twa the cente pint the capule. The cnvectin eect peent in the mlten PCM epen n the Rayleigh numbe, which i calculate by the thickne the liqui laye (L = i m ). The eective themal cnuctivity i calculate uing Raithby celatin [14], 4 1/ 5 7 / 5 7 / / ) ( P P 0.74 m m L m liq e Ra (7) Fig. 2. Expeimentally meaue [13] an numeically peicte li-liqui inteace pitin a a unctin time vaiu Stean numbe Fig. 3(a) Sli-liqui inteace pitin a a unctin time ieent capule ize, (b) R int pitin 25 mm aiu capule peicte by Xia celatin vaiu m ceicient.

6 Selvan Bellan et al. / Enegy Pceia 69 ( 2015 ) The heat tane ceicient (h ) between the HTF an the pheical capule i btaine m the empiical celatin [15]. In e t valiate thi mel, peent mel eult ae cmpae with the epte expeimental an numeical eult [13]. In the epte invetigatin, the paain wax wa ille in a pheical capule, 49 mm aiu, an place inie a wate ille veel which wa heate by an electical heate; the melting pce inie the capule wa tuie an the tempal vaiatin li-liqui inteace pitin wa peicte. In thi tuy, imulatin ae peme the ame etup an cnitin uing the evelpe mel. Fig. 2 hw the expeimental an peicte value (peent an peviu mel) li-liqui inteace pitin a unctin time vaiu Stean numbe. The imeninle inteace pitin, R int, i eine a the ati the inteace aial itance ( m ) m the cente the capule t the inne aiu the capule ( i ). A can be een in the igue, the peicte an expeimental inteace pitin ae in cle ageement in the initial tage wheea a igniicant eviatin i un in the late tage. The main ean thi eviatin cul be the peence 10% ai gap in the capule, but thi mel aume a cmpletely ille capule. All in all, the peent mel eult ae cmpaable with peviu mel peictin an expeimental meauement. Uing the valiate mel, calculatin ae mae the peent tuy; the li-liqui inteace pitin the ium nitate ille capule at P1 (a hwn in Fig.1) i peicte. The cnvective heat lux bunay cnitin at the ute uace the capule i calculate accing t the them-lui lw at P1. Fig. 3 (a) hw the li-liqui inteace pitin a a unctin time ieent capule ize. A expecte, the cmplete melting time i eceae when the capule ize i eceae. Hee the eective themal cnuctivity i calculate accing t the li-liqui inteace pitin. Thi appach i apppiate the melting pblem ingle capule wheea which i cmplicate the whle tage tank, becaue it i cmplex t peict li-liqui inteace pitin each capule inie the tank. Thu, the Xia` celatin i apte t calculate the eective themal cnuctivity a given belw [9, 16-17]. e liq C Ra m L In e t btain the C an m ceicient, vaiu value ae aume an thei li-liqui inteace pitin ae peicte a a unctin time. Then, the apppiate ceicient ae btaine by cmpaing the R int pitin an cmplete melting time btaine by Raithby celatin (Eq. 7). Initially, the ceicient C i ixe at 0.18 [9], an calculatin ae mae 25 mm aiu capule. Fig. 3(b) hw the li-liqui inteace pitin peicte by Xia celatin (Eq. 8) vaiu m ceicient. R int pitin peicte by the Raithby celatin (Eq. 7) i pltte cmpain. A can be een in the igue, a g appximatin i un when the ceicient m i 0.186, which i ue t calculate the eective themal cnuctivity, an the ame appach i extene t peict the apppiate ceicient the cae. (8) Fig. 4. Expeimentally meaue [18] an numeically peicte tempeatue itibutin the PCM capule at 16th w uing chaging an ichaging pcee.

7 764 Selvan Bellan et al. / Enegy Pceia 69 ( 2015 ) Valiatin the mel F valiatin pupe, the ieence between the numeically peicte eult an the expeimentally meaue eult [18] i peente. The expeimental eult Aka et al., [18] ae ue an the cniguatin the ytem i given in Fig. 4. The tempeatue the PCM capule at the 16th w the axi uing chaging an ichaging pcee ae hwn in Fig. 4 tw ieent lw ate. A g ageement i un between the peent numeical eult an the expeimental meauement. 3. Reult an icuin T tuy the eect capule ize n the pemance the themal tage ytem, the ga lw ate an the HTF tempeatue ae ixe an imulatin ae peme the packe be ille with vaiu capule ize, by auming the tank wall i inulate. The phae change i aume between an K (muhy zne). Chage me: 529 tempeatue, T m = K. When t > 0, the HTF tempeatue an the lw ate at the inlet ae ixe at K an 1 m 3 /h epectively. Dichage me: Initially, the tage tank i aume a ully chage tate, at K. When t > 0, the tempeatue the HTF an the lw ate at the inlet ae given a K an 1 m 3 /h epectively. F thee cnitin, imulatin ae peme the packe be cmpe ieent capule aii: 10, 15 an 20 mm. Fig. 5. Tempeatue, melt actin an velcity vect the tage tank at 1800 uing chage me The tempeatue, melt actin an velcity itibutin the tage tank at 1800 uing chage me ae hwn in Fig. 5, which i cmpe 20 mm aiu capule. In Fig. 5 (a), the bttm ie epeent the tempeatue itibutin the PCM an lui main, an the tp ie epeent the melt actin the PCM main an the velcity vect the HTF main. In e t hw the themal gaient inie the capule an the cepning melt actin, HTF lw aun the capule an the cepning velcity vect, a mall ptin Fig. 5 (a) i expane an hwn in Fig. 5 (b). It i beve that, thi mel nt nly pvie the accuate eult than cntinuu li phae mel, but it enable t btain me etail the lui lw an heat tane chaacteitic the ytem. The tempeatue itibutin an melt actin the packe be uing chage

8 Selvan Bellan et al. / Enegy Pceia 69 (2015) Fig. 6. Tempeatue an melt actin the packe be uing chage pce vaiu capule ize at 900, 1800, 3600 an

9 766 Selvan Bellan et al. / Enegy Pceia 69 ( 2015 ) pce ae hwn in Fig. 6 vaiu capule ize at 900, 1800, 3600 an The 1t, 2n an 3 w epeent the packe be ille with 10, 15 an 20 mm aii capule epectively. In each plt, the let ie epeent the tempeatue an the ight ie epeent the melt actin. It i beve that the heat tane between the PCM capule an the lui i api except the phae change egin (muhy zne) ue t the latent heat tane an themal eitance caue by the mlten laye. It i al beve that the heat tane ate at nea wall egin i high ince the velcity the HTF i high in nea wall egin than the et the egin, a a eult, the melting initially tate cle t the inlet-wall egin an gaually pea thughut the tank. Thi eect i beve in all cae. It can be een that the heat tane ate the be i high the mall ize capule than the lage ize capule. Fig.7. Melt actin the be uing chaging an ichaging pcee a a unctin time ieent capule ize Melt actin the be uing chaging an ichaging pcee i hwn in Fig. 7 a a unctin time ieent capule ize. It i ntice that the time cmplete melting an liiicatin i inceae when the capule ize i inceae. Thi i ue t the heat tane aea between the capule an the HTF, which i eceae when the capule ize i inceae ince the uace t vlume ati i eceae. It i al beve that the cmplete liiicatin time i lnge than the melting time ue t the cnvectin eect in the liqui egin uing melting pce. In e t tuy ively ixe at 10 mm an 50 K, imulatin ae peme vaiu lw ate: 1, 2, 3, 4 m 3 /h. The intantaneu tempeatue itibutin the HTF an the PCM at vaiu axial lcatin inie the ytem uing chaging an ichaging pcee ae hwn in Fig. 8. The heat tane pce at each element the ytem geneally unege any ne the llwing tage; (1) Cntant high tempeatue tage (CHTS) the ht tage, when the tempeatue the element i at the initial tempeatue, A-B tage, which i make in the PCM tempeatue plt at 1m 3 /h-p2. (2) Cntant lw tempeatue tage (CLTS) the cl tage, when the tempeatue the element i equal t the HTF tempeatue, E-F tage. (3) Heat tane tage (HTS), which cnit cntant melt tempeatue tage (CMTS), when the tempeatue the element i between the muhy zne, C-D tage, an Heat exchange tage (HES), when T init <T <T l an T liq <T <T, tw intemeiate tage B-C an D-E. Thee thee tage at P1, P2 an P3 ae appaently een in the igue vaiu cae. In the cntant high an lw tempeatue tage, the HTF an the PCM ae in themal equilibium; in the CMTS, latent enegy tane between the PCM an the HTF take place; an in the HES, enible heat tane between the HTF an the PCM ccu. A etimate, the CMTS an HES ae inceae when the lui lw ate i eceae ue t the heat tane ate. Melt actin the be uing chaging an ichaging pcee i hwn in Fig. 9 a a unctin time vaiu lui lw ate. A etimate, the cmplete melting/liiicatin time i eceae when the lui lw ate inceae ue t the heat tane ate, which i high high lw ate.

10 Selvan Bellan et al. / Enegy Pceia 69 ( 2015 ) Fig. 8. Intantaneu tempeatue itibutin the PCM an HTF at P1 (cle t the inlet), P2 (cente) an P3 (cle t the exit) uing chage (let) an ichage (ight) pcee Fig. 9. Tempal vaiatin melt actin the tage tank uing chage an ichage pcee vaiu HTF lw ate 4. Summay an Cncluin The eective packe be mel i evelpe an ue t tuy the themal behavi an pemance the TES ytem. The inluence capule ize an HTF lw ate n the tempeatue itibutin, lui lw, melting an

11 768 Selvan Bellan et al. / Enegy Pceia 69 ( 2015 ) liiicatin the ytem i peicte. The llwing imptant eult ae ntice; the heat tane ate i igniicantly inceae when the capule ize i eceae ue t the uace t vlume ati, the cmplete melting time i hte than the liiicatin time ue t the cnvectin eect uing melting pce. Thi mel nt nly pvie the accuate eult than cntinuu phae mel, but it enable t btain me etail the lui lw an heat tane chaacteitic the ytem. Thu, thi mel can be ue t ptimize the eign the packe be ytem an t invetigate the inluence peating paamete n the pemance the ytem. Acknwlegment Thi eeach wa une by E.ON AG a pat the E.ON Intenatinal Reeach Initiative. Repnibility the cntent thi publicatin lie with the auth. In aitin, the Eupean cmmiin i acknwlege a well the eeach gant thugh FP7 STAGE-STE Pject Scientiic an Technlgical Alliance Guaanteeing the Eupean Excellence in Cncentating Sla Themal Enegy (FP7, Pject N ) Reeence [1] Kuavi S, Taham J, Gwami DY, Rahman MM, Steanak EK. Themal enegy tage technlgie an ytem cncentating la pwe plant. Pge in Enegy an Cmbutin Science 2013; 39: [2] Bellan S, Gnzalez-Aguila J, Rme M, Rahman MM, Gwami DY, Steanak EK, Culing D. Numeical analyi chaging an ichaging pemance a themal enegy tage ytem with encapulate phae change mateial. Applie themal engineeing; DOI: /j.applthemaleng [3] Zalba B, Main JM, Cabeza LF, Mehling H. Review n themal enegy tage with phae change: mateial, heat tane analyi an applicatin. Appl Them Eng 2003;23: [4] Keniain MM. High-tempeatue phae change mateial themal enegy tage. Renew Sutain Enegy Rev 2010; 14: [5] Gag HP, Mullick SC, Bhagava AK. Sla themal enegy tage. Kluwe Acaemic Publihe; [6] Imail KAR, Stuginky R. A paametic tuy n pible ixe be mel PCM an enible heat tage. Appl Them Eng 1999;19: [7] Felix RA, Slanki SC, Saini JS. Heat tane chaacteitic themal enegy tage ytem uing PCM capule: a eview. Renew Sut Enegy Rev 2008; 12: [8] Singh H, Saini RP, Saini JS. A eview n packe be la enegy tage ytem. Renew Sut Enegy Rev 2011;14: [9] Xia L, Zhang P, Wang RZ. Numeical heat tane analyi the packe be latent heat tage ytem bae n an eective packe be mel, Enegy 2010; 35: [10] Alawahi EM. Numeical analyi a cl-themal tage ytem with a themal cnuctivity enhance peating une a eezing cnitin. Enegy 2008; 33: [11] Tan FL, Heinizae SF, Khaai JM, Fan LW. Expeimental an cmputatinal tuy cntaine melting phae change mateial (PCM) inie a pheical capule. Intenatinal Junal Heat an Ma Tane 2009; 52: [12] Bellan S, Gnzalez-Aguila J, Rme M, Rahman MM, Gwami DY, Steanak EK, Culing D. Numeical analyi packe be themal enegy tage ytem cncentating la pwe plant, 2013 ISES Sla Wl Cn. Pc. (2013) SWC2013-ID475 [13] Felix RA, Slanki SC, Saini JS. Expeimental an numeical analyi melting PCM inie a pheical capule, 9th AIAA/ASME Jint Themphyic an Heat Tane Cn. Pc.(2006) AIAA [14] Raithby GD, Hllan KGT. A geneal meth btaining appximate lutin t lamina an tubulent ee cnvectin pblem, Avance in Heat Tane 1975; 11: [15] Gnielinki V, Equatin calculating the heat an ma tane in peue ball at et hiite line meium an lage Peclet numbe (in Geman: Gleichungen zu Beechnung e Wäme- un Stautauche in uchtömten uhenen Kugelchüttungen bei mittleen un gßen Pecletzahlen), Veahentechnik 1978; 12: [16] Chiu CP, Chen WR. Tanient natual cnvectin heat tane between cncentic an vetically eccentic phee. Intenatinal Junal Heat an Ma Tane 1996;39: [17] Aine HA, Qania HE. Numeical analyi the themal behaviu a hell an tube heat tage unit uing phae change mateial. Applie Mathematical Melling 2009;33: [18] Aka C, Meve S. Inluence accuacy themal ppety ata phae change mateial n the eult numeical mel packe be latent heat tage with phee, Themchemica Acta 2005; 438: