Theoretical Study of Thermal Performance of Rock Bed Storage

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1 Theoreticl Study o Therml Perormnce o oc Bed Storge Sud H. Dno, Ehsn F. Abbs, Mous M. Weis Abstrct--- In this theoreticl study, het trnser nd pressure drop in two cses o roc bed therml storge hs been studied, in the irst cse the equivlent dimeter is chnged when the mss low rte per unit re is constnt, nd in the second cse is inversely. The unstedy numericl simultion is employed to nlyze the perormnce o the het low nd temperture ield in the storge. While the best therml storge is obtin t equivlent dimeter is (0.01) m. nd show tht the reltion o pressure drop is decrese with increse in equivlent dimeter except in rnge o (0.05 to 0.038) m is constnt. Key words--- oc bed, therml storge, Pressure drop. T I. Introduction: HE limited mount o ossil energies hs orced scientists ll over the world to serch or lterntive renewble energy source. The use o renewble energies hs, thereore, seriously been considered in the lst three decdes by reserchers. The sun hs been the mjor source o renewble energy rom long time go. This energy hs hd determinte contribution to the lie o humn being rom the inormtion o lie on the erth up to now. Solr energy collectors re employed to gin energy incident solr rdition. Solr ir heter is type o solr collectors extensively used in mny pplictions such s in industril nd griculturl ield. The vrious conigurtions o solr heter hve been developed to increse the het trnser rte or to diminish het loss lie pced bed therml storge. There re some wors on both theoreticlly nd experimentlly studies o roc bed therml storge. Snderson [1] studied theoreticlly simple model o pced bed hs which explins how vrying (D ) (the equivlent sphere dimeter o the pcing) will inluence the degree o xil dispersion. This model ws urther veriied with experimentl results in pper chieved by Snderson et l. []. On verticl low pced bed consisted o hollow high density polyethylene spheres Sud H. Dno, is teching st member in erigertion & Air Conditioning Technicl Eng. Dept., Kiru Technicl College, Irq.(em. tlebshebb@yhoo.com, Mobile No ). Ehsn F. Abbs, is teching st member in erigertion & Air Conditioning Technicl Eng. Dept., Kiru Technicl College, Irq.(em. ehsndhil@gmil.com, Mobile No ). Mous M. Weis is teching st member in Fuels & Energy Technicl Eng. Dept., Kiru Technicl College, Irq.(em musmec@yhoo.com, Mobile No ). illed pproximtely 95% with wter, nd wter ws lso used s the woring luid. The experimentl result shows the eect o ltering (D ) on the degree o xil dispersion in thermlly short pcing s. The signiicnce o thermlly short system is discussed nd the verge temperture wve during het exchnger opertion is lso demonstrted. They hve shown tht the one dimensionl temperture proiles in the pcing cn be obtined using rectngulr storge tn in conjunction with low distributors. Choudhury C. et l.[3] studied the optimiztion o design nd opertionl prmeters o roc bed therml energy storge device coupled to two pss single cover solr ir heter, i.e., chrging time, roc bed size, nd cross- sectionl re or squre cross section, roc size,ir mss velocity per unit bed cross-sectionl re nd void rction. The optimiztion hs been ccomplished by investigtion the eects o the bove prmeters on the totl energy stored nd the cost per unit energy stored in the roc bed or winter climtic condition o Delhi. Anthony G. Dixon[4] developed n improved eqution o overll het trnser coeicient in pced bd s new ormul 1 1 t Bi U h 3 B + 4 w r i nd bsed on single rdil collection point whose position depends on the wll Biot number, which gives n error less thn 3.8% in the exct symptotic vlues o (U) over the entire rnge o (Bi).A ormul is lso gives (UU ), the overll het trnser coeicient bsed on the dierence between tube wll nd bed center tempertures where (Bi,h w, t nd r ) re tube Biot number, wll het trnser coeicient, tube rdius, nd eective rdil therml conductivity respectively. Hessri et l.[5] studied the behvior o pced bed by set o dierentil equtions. A numericl solution is developed or pced bed storge tn ccounting to the secondry phenomen o the therml losses nd conduction eect. The eect o het loss to surrounding, conduction eect nd ir cpcities re exmined in the numericl solution. The solution indictes the proiles o ir nd roc bed tempertures with respect to time nd length o the bed. The current study is including the eect o equivlent dimeter o the roc (D ) nd mss o ir low rte (G) on the therml perormnce o the cylindricl therml storge s well s on the pressure drop ( pp) by two cses s shown in the Tble (). In the irst cse they will be used roc o our dierent in (D ) s (0.01, 0.05, 0.038, nd 0.05) m. with (G) is constnt t g/s.m, nd in the second cse they will be used roc o (D 0.01m) with our dierent quntity o (G) s (0.51, 0.764, 1.018, nd 1.53)g/s.m. ISBN:

2 II. The model The roc bed bced therml storge unit under investigtion shown schemticlly in Fig (1) with model prmeters illustrted in the Tble (1) or prticulr ppliction o group o processes involving ir low through porous medi. In this model the therml perormnce nd pressure drop re studies in two cses. The ir is supplied in dierent tempertures vrible with time to the therml storge bed s shown in Figs ( nd 1). Strting rom the initil time (t0), the luid is orced to low in the porous bed through inlet section nd the solid prticles re t the sme temperture. the bed contin the sme mss nd size o roc nd hd the sme, uniorm, cross sectionl re. The ssumptions o Schumnn [6] hve been employed to model roc beds. Schumnn ssumed tht : 1. The luid lowing through the bed ws incompressible.. The temperture in the bed nd in luid ws unctions only o coordinte in the low direction. 3. The Biot number o the rocs ws suiciently smll so tht the temperture distribution in the rocs ws uniorm. 4. The het low between the luid nd roc ws proportionl to the temperture dierence between them. 5. The properties o the luid nd roc were constnt. Tble (1) System description Are o the pced bed (A) m Speciic het o the roc (c ) 837J/g. Speciic het o the ir (c ) 1J/g. Density o the roc ( ρ ) 400g/m 3 Therml conductivity o the roc ( ) 0.45W/m. Dimeter o the bed (D) 1m Height o the bed (H) 1.5m The void rction () 0.45 Number o the nodes 9 Distnce increment ( x ) m Time increment ( t ) 160 sec Dynmic viscosity o the ir µ g/m.s Tble () Simultion prmeters o two cses Insultion Direction o low T in Upper surce Insultion Cse1 Cse G1.018 g/s.m D 0.01m D (m) G(g/s.m ) H 0 x dx n Consider cylindricl storge roc bed long (x) xis. An elementl volume locted between the bsciss x nd x+dx is considered or het trnser evlution. The governing dierentil eqution or the energy supplied by ir to the roc bed through convection (qq vv ) into the elementl volume during dt is [5] : ( T ) dx dt qv hv A T. (1) Lower surce T out Fig (1) schemtic o roc bed therml storge h vv : Volumetric convective het trnser coeicient, W/m 3.. AA: Cross section re o bed, m TT : Air temperture,. ISBN:

3 TT : oc bed temperture, xx: Distnce long the bed, m tt: Time, sec The quntity o het crried wy by the ir (qq ) is: q T cga dx dt () x. GG: The mss low rte o ir per unit cross sectionl re, g/s.m cc : The het cpcity o the ir, J/g. The het loss to the surrounding (q s ) is: ( T T ) dx dt qs UDπ. (3) UU : Overll het trnser coeicient, W/m. TT : Surrounding temperture,. The energy blnce or the ir is obtined by summing up (1, nd 3): T qv + q + qs ρ c A dx. dt (4) dt ρρ : The ir density, (g/m 3) : The void rction The irst energy blnce dierentil eqution is derived or ir (gseous phse): T 0) T ( x) nd T ( x 0) T ( x) When:, t t0 (7) T ( x) T nd T ( x 0) T And the boundry conditions re:, (8) TT (xx, 0) TT TT (xx, 0) TT tt 0 (9) T T ( When xh nd t>0 () in Equtions (5 nd 6) cn be written in terms o inite dierence or nodes (n-1>x>1) s: W T W T + T 1 ( x 1, + H T + ( x + 1, T L T E T ( x 1, + F T ( x + 1, T For lower surce o the bed (x0) A T E T + B T ( x + 1, ( x +, T For upper surce o the bed (xn) A T E T + B T ( x 1, ( x, T (11) (1) (13) (14) T + t ρ πud ρ c G T x ( T T ) hv ρ c ( T T ) (5) W 1 () x Het blnce or the roc bed (solid stte) is similrity obtined rom: T t + ρ c h v ( ) ( T T ) ρ c 1 (6) ( ) 1 x ρρ : The roc density, (g/m 3 ) cc : Speciic het o the roc, J/g. : Therml conductivity o the roc, W/m. The equtions (5 nd 6) re solved by inite dierence method, the initil conditions re: H (16) 1 L 3 (17) 1 A + 1 (18) x B (19) x E 1 (0) ISBN:

4 1 F + 1+ (1) x 1 U Dh ν h () ν (3) G c 3 ρ c (4) ρ c ( 1 ) Loo nd Hwley gve the volumetric het trnser coeicient s [6] : 0.7 G 650 h (5) ν D TEMPEATUE ( C ) Fig () Temperture distribution in the roc bed during 48 hrs, or D 0.01m hr,18 C 4 hr,5 C 6 hr,3 C 8 hr,4 C hr,39 C 1 hr,6c 14 hr,16 C 16 hr,13 C 18hr, 1C 0hr,1C hr,1 C 4 hr, 1 C 6 hr, 1 C 8 hr, 1 C hr, 1 C 3 hr, 1 C 34 hr, 1 C 36 hr, 1 C 38 hr, 1 C 40 hr, 1 C 4 hr, 1 C 44 hr, 1 C 46 hr, 1 C 48 hr. 1 C BED HEIGHT (m) hr, 18 C 4 hr, 5 C 6 hr,3c 8 hr 4C hr,39c 1 hr,6c 14 hr,16c 16 hr,13 C 18 hr,1 C 0 hr,1 C hr,1 C 4 hr,1 C 6 hr,1 C 8 hr,1 C hr,1 C 3 h,1 C 34 hr,1 C 36 hr,1 C 38 hr,1 C 40 hr,1 C 4 hr,1 C 44 hr,1 C 46 hr,1 C 48 hr,1 C Where DD the equivlent sphericl roc dimeter (m) is: D 6M πnρ 3 (6) TEMPEATUE ( C ) BED HEIGHT ( m ) MM: Mss o rocs (g) nn: Number o rocs xx: Distnce increment, m t: Time increment, sec To estimte pressure drop cross inlet nd outlet low chnnels o the pced bed therml storge my be used (Ergun eqution) [7] s ollows: H P F D G 1 3 ρ ( ) (7) 0 1 F (8) ep Fig (3) Temperture distribution in the roc bed during 48 hrs, or D 0.05m. TEMPEATUE ( C ) 5 0 hr,tin13c 4 hr, Tin5 C 6 hr, Tin3 c 8 hr,tin4 C hr, Tin39 C 1 hr,tin6 C 14 hr, Tin16 C 16 hr, Tin13 C 18 hr,tin1 C 0 hr, Tin1 C hr, Tin1 C 4 hr, Tin1 C 6 hr,tin1 C 8 hr,tin1 C hr,tin1 C 3 hr,tin1 C 34 hr,tin1 C 36 hr,tin1 C 38 hr,tin1 C 40 hr,tin1 C 4hr, Tin1 C 44 hr,tin1 C 46 hr,tin1 C 48 hr,tin1 C BED HEIGHT ( m ) Fig (4) Temperture distribution in the roc bed during 48 hrs, or D 0.038m. GD ep (9) µ Where µ is viscosity o the ir. 5 hr,18 c 4 hr, 5 C 6 hr, 3 C 8 hr, 4 C hr, 39 C 1 hr, 6 C 14 hr, 16 C 16 hr,13 C 18 hr, 1 C 0 hr, 1 C hr, 1 C 4 hr,1 C 6 hr,1 C 8 hr,1 C hr, 1 C 3 hr,1 C 34 hr, 1 C 36 hr,1 C 38 hr,1 C 40 hr,1 C 4 hr, 1 C 44 hr,1 C 46 hr,1 C 48 hr, 1 C III. esultnt nd discussion This study considered two cses, the prmeters o them illustrted in Tble ().In both cses the inlet ir tempertures(tt iiii ) re sme t ech time during 48 hr s input dt. The results obtined re plotted to compres the perormnce o the roc bed storge. Figures (, 3, 4, nd 5) represent temperture distribution long the height o the roc bed t every two hours or equivlent dimeters (0.01, 0.05, 0.038, nd 0.05) m. respectively. TEMPEATUE ( C ) BED HEIGH (m) Fig (5) Temperture distribution in the roc bed during 48 hrs, or D 0.05m. ISBN:

5 The sets o curves re divided in two prts with reltive time; irst prt o them is similr shpe curves o temperture distribution rom the strting time up to (16) hrs., this men tht no eect o dimension o equivlent dimeter on the temperture distribution in the roc bed t this limited time but lter on the eect o dimension o equivlent dimeter is very obvious, where the vlue o temperture t ech node is greter thn other dimensions o (D ). Figures (6, 7, 8, nd 9) represent the chnge o temperture t ech node in the bed roc with respect o time or equivlent dimeter (D ) (0.01, 0.05, 0.038, nd 0.05) m. respectively. The results obtined re putted in the Tble (3). Which re represents the dierence between the upper nd the lower temperture. The results re indicte tht the higher temperture dierences re hppen in the roc bed when (D 0.01m.). TOP OF BED XH/9 H/9 3H/9 4H/9 5H/9 6H/9 7H/9 8H/9 LOWE OF BED TEMPEATUE ( C ) 5 0 TOP OF BED XH/9 H/9 3H/9 4H/9 5H/9 6H/9 7H/9 8H/9 LOWE OF BED TIME ( hr ) Fig (9) Node temperture chnge with respect o time or D 0.05m. Tble (3) Dierent between upper nd bottom tempertures in ech equivlent dimeter t the sme time 5 Time (hr) TEMPEATUE ( C ) 0 D (m) TIME (hr) Fig (6) Node temperture chnge with respect o time or D 0.01m. TOP OF BED XH/9 H/9 3H/9 4H/9 5H/9 6H/9 7H/9 8H/9 LOWE OF BED TEMPEATUE (C ) TIME (hr) Fig (7) Node temperture chnge with respect o time or D 0.05m. TEMPEATUE ( C ) 5 0 TOP OF BED XH/9 H/9 3H/9 4H/9 5H/9 6H/9 7H/9 8H/9 LOWE OF BED TIME ( hr) Fig (8) Node temperture chnge with respect o time or D 0.038m. Figure () shows the dierence between inlet nd outlet ir tempertures through the roc bed system. It is indicted tht the best outside temperture is ound t (D 0.01m).The second cse the roc bed exmined with vrible mss low rte per cross section re s shown in Tble (). The result obtined shown in Figure(11) which indicte very low outside ir temperture o the bed in condition o (G0.51 g/s.m ), nd by incresing the mss low rte during the sme intervl o time (48 hrs).the outlet ir tempertures re shown in Fble (4). Figure (1) is representing the reltion between pressure drop ( p) nd equivlent dimeter (D ) o the rocs in the cse 1. From this reltion the higher quntity o ( p) is hppen t (D 0.01m), nd it is reduce very quicly with increse in ISBN:

6 (D ) up to (D 0.05m), nd in rnge o (D 0.05m) up to (D 0.05m) the chnge o ( p) is smll. Figure (13) is shown the reltion between ( p) nd mss low rte per cross re (G) in the cse. It indicted tht the quntity o ( p) is increse s the quntity o (G) is increse. For reson o solution o the equtions (5 nd 6) by inite dierence method more suitble or lrge o intervl o time, but this condition in nlytic solution unsuitble becuse the results re un rel, in ddition to this reson the sensitivity o the model is not obtin correctly by nlytic solution. TEMPEATUE ( C ) Fig () Chnge in tempertures between inlet nd outlet ir in cse1 TEMPEATUE ( C ) TIME (hr) Tin Tout,Dr0.01m Tout, Dr0.05m Tout, Dr0.038m Tout, Dr0.05m Tin Tout,G0.51 g/s.m^ Tout, m0.764 g/s.m^ Tout, m g/s.m^ Tout,G1.73g/s.m^ Tout,G 1.53g/s.m^ PESSUE DOP (P) Fig (13) Pressure drop with respect o mss low rte per cross section re in cse. Tble (4) Shown the outlet temperture rom the roc bed t ech mss low rte per unit cross section re G (g/s.m ) G (g/s.m^) Strt time temperture End time temperture Mx. temperture Averge temperture IV. Conclusion TIME ( hr ) Fig (11) Chnge in tempertures between inlet nd outlet ir in cse PESSUE DOP (P) EQUIVLENT OCK DIAMETE ( m ) Fig (1) Pressure drop with respect o equivlent dimeter in cse1. An nlyticl solution cn be written or equtions (5 nd 6) with more boundry conditions o TT(0, t TT(1, t in the inlet ir temperture. In this cse, the solution is limited to reltively smll vlues o the time. In order to extend solution to rel cse where n initil non-uniorm sptil temperture distribution within the bed is considered t lrge time, initil boundry conditions re to be in corporte in the respected in the solution. The solution shows the response o the roc bed during the chnging period (Energy recovery mode) nd the proiles o ir nd roc bed tempertures with respect to time nd length o the bed in the inl equtions (11,1,13,nd 14), thereore, be expressed in inite dierence orm nd solved by numericl method. Since the ir is used s the het trnser medium t low temperture, the eect o losses (het loss, conduction through solid nd het cpcity o luid respectively) re ound to be negligible in the solution o the cse o ir s moving luid. The best o het recovery cn be obtined t smll equivlent dimeter which controlled by the optimum hed loss nd this give suitble mss low rte o ir which cn used in ppliction o pssive heting. ISBN:

7 eerences:- 1. Snderson T.M. nd Cunninghm G.T. Pced Bed Therml Storge Systems Applied Energy Vol. 51, pp , nd Snderson T.M. nd Cunninghm G.T. Perormnce nd Eiciency Design o Pced Bed Therml Storge System. Prt 1 Applied Energy Vol. 50, pp , Choudhury C.,Chuhn P.M. nd Grg H.P. Economic Design o oc Bed Storge Device or Storing Solr Therml Energy Solr Energy Vol.55, No.1, pp.9-37, Anthony G. Dixon An Improved Eqution or the Het Trnser Coeicient in Pced Bed Chemicl Engineering nd processing Vol.35, pp , Hessri F.A., Prs S., nd Khshechi A.K. Behvior o Bced Bed Therml Storge IJE Trnsctions A: Bsic, Vol. 16, No., pp , Crndell D.M. nd Thcher E.F. Segmentl therml Storge Solr Energy, Vol. 77, pp , El-Sebii A.A., Aboul-Enein S., mdn M..I, nd El-Bily E. Yer ound Perormnce o Double Pss Solr Air Heter with Pced Bed Energy Conversion o Mngement Vol. 48, pp , 007. Sud H. Dno holds PhD in Mechnicl Engineering rom Seville University, 1993 (Spin) in the ield o enewble Energy. His min reserch interests include enewble Energy, nd Fluid mechnics. He hs published more thn ppers in peer-reviewed journls. He is lso reviewer locl journl. Currently Sud is n Assistnt Proessor in the erigertion & Air Conditioning Technicl Engineering Deprtment in Kiru Technicl College, Irq. Emil ddress: tlebshebb@yhoo.com, Mobile No Ehsn Fdhil Abbs holds MSc in Mechnicl Engineering Deprtment rom University o Technology (Irq) in 1999, in the ield o therml power plnts. His min reserch interests include Het Trnser, enewble Energy, nd luid mechnics. He hs published more thn 18 ppers in peer-reviewed journls. He is lso reviewer locl journl. Currently Ehsn is n Assistnt Proessor in the erigertion & Air Conditioning Technicl Engineering Deprtment in Kiru Technicl College, Irq. Emil ddress: ehsndhil@gmil.com, Mobile No Mous M. Weis holds PhD in Mechnicl Engineering rom Bghdd University,014 (Irq) in the ield o Fluid Mechnics nd Het Trnser. His min reserch interests include Het Trnser, nd Fluid mechnics. He hs published bout 3 ppers in peer-reviewed journls. Mus is lecturer in Fuels & Energy Technicl Eng. Dept., Kiru Technicl College, Irq.(em musmec@yhoo.com, Mobile No ). ISBN:

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