Simulated Performance of Packed Bed Solar Energy Storage System having Storage Material Elements of Large Size - Part I

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1 The Open Fuels & Energy Science Journl, 2008, 1, Open Access Simulted Performnce of Pcked Bed Solr Energy Storge System hving Storge Mteril Elements of Lrge Size - Prt I Rnjit Singh *,1, R.P. Sini 2 nd J.S. Sini 3 1 Deprtment of Mechnicl Engineering, Bent College of Engineering nd Technology, Gurdspur, Punjb, , Indi 2 Alternte Hydro Energy Centre, 3 Deprtment of Mechnicl nd Industril Engineering, Indin Institute of Technology Roorkee, Roorkee, Uttrkhnd, , Indi Abstrct: Pcked bed or rock bed is very commonly known therml energy storge component for solr ir heters. The mjor concern for design of pcked bed energy storge system is to mximize the het trnsfer with minimum pressure drop or pumping power. Under the given operting conditions, system prmeters could ffect het trnsfer nd pressure drop in the bed considerbly. An ttempt hs been mde to report the simulted performnce of pcked bed solr energy storge system. Lrge size storge mteril elements of five different shpes hve been used to crry out the present simultion study. usselt number nd friction fctor correltions reported by the uthors under previous experimentl study hve been utilized to nlyze the pcked bed energy storge system for rnge of system nd operting prmeters. Performnce of the system hs been evluted bsed on temperture distribution, therml energy stored nd vilble energy stored in the bed, energy consumption by fn to propel ir through the bed nd therml efficiency of the collector s function of system nd operting prmeters. In present prt of the pper, vrious component models of pcked bed solr energy storge system nd development of computer progrm hve been reported. Results of simulted system performnce hve been reported nd discussed in Prt-II nd III of this pper. Keywords: Pcked bed, solr ir heter, therml energy storge. 1. ITRODUCTIO Solr energy is most importnt mong renewble energy sources due to its quntittive bundnce. In order to fce the problem of energy crisis nd environmentl thret s result of continuous use of fossil fuels, scientists nd reserchers re putting efforts to develop technologies for n effective use of solr energy. People my use energy for mny purposes, but few generl tsks like heting, cooling, electricity genertion, trnsport nd industry consume most of the energy. Solr energy cn be pplied to ll these tsks with different levels of success. However, intermittent nture of solr energy demnds n integrtion of energy storge system with the solr collectors in order to mke solr energy source more relible. Pcked bed or rock bed system is well known for vrious engineering pplictions. It cn lso be used with solr ir heting system for storing therml energy of hot ir. Therml energy stored in the pcked bed my be useful to hve uninterrupted supply of energy in the bsence of solr rdition nd lso to fulfill the pek lod energy demnds even in the presence of solr rdition. Pcked bed consists of energy storge mteril elements pcked in continer. Hot ir from solr collector/s flows from top to bottom of the bed in order to trnsfer het energy to the storge mteril elements during chrging phse. *Address correspondence to this uthor t the Deprtment of Mechnicl Engineering, Bent College of Engineering nd Technology, Gurdspur, Punjb, , Indi; Tel: , E-mil: rsolr70@yhoo.co.in X/08 Energy stored in the bed cn be extrcted by mking flow of ir through the bed from bottom to top during dischrging phse. Het trnsfer to nd from flowing fluid in pcked bed hs been the subject of mny theoreticl nd experimentl investigtions for vrious engineering pplictions. Schmidt nd Willmott [1] mentioned tht the distinct disdvntge of pcked bed is the lrge pressure drop, which cuses lrge mount of energy consumption by fn to propel hot ir through the bed. The literture revels tht system design must be bsed on the methods to reduce pressure drop in the bed in order to enhnce the effective use of solr energy storge system. Sgr nd khr [2] reported tht lrge size mteril elements cn be used for reducing pressure drop in the bed. Singh et l. [3] crried out n extensive experimentl study to nlyze the effect of shpe of lrge sized mteril elements nd void frction of the bed under set of operting conditions. In order to predict the performnce of the pcked bed system usselt number nd friction fctor correltions s function of Reynolds number, sphericity nd void frction of the bed hve been developed by the uthors. Authors reported tht the system prmeters ply predominnt role to influence het trnsfer nd fluid flow chrcteristics of pcked bed energy storge system. Therefore, it is necessry to investigte the effect of these prmeters on therml nd hydrodynmic performnce of pcked bed energy storge system. The present prt of the pper dels with development of computer progrm by using the component models in order to predict performnce of the system bsed on temperture distribution in the bed, therml energy stored in the bed, energy consumption by fn to propel the ir through 2008 Benthm Open

2 92 The Open Fuels & Energy Science Journl, 2008, Volume 1 Singh et l. the bed nd therml efficiency of the collector s function of system nd operting prmeters. usselt number nd friction fctor correltions reported by Singh et l. [3] hve been used in the present simultion study. Results of simulted system performnce hve been reported nd discussed in Prt-II nd III of this pper. 2. MODELIG AD AALYSIS OF PACKED BED SOLAR EERGY STORAGE SYSTEM The schemtic of conventionl pcked bed solr energy storge system operting in closed cycle is shown in Fig. (1). For crrying out the present simultion study, it is ssumed tht during chrging phse, temperture of ir t the outlet of collector will become n inlet temperture to the bed nd temperture of ir t outlet of the bed will become n inlet temperture to the collector. It hs lso been ssumed tht system hs no het loss to the surroundings. The rnge of system nd operting prmeters nd vlues of other prmeters used in the present simultion study re given in Tble 1. The chrging time ( t ch ) for the bed hs been tken s eight hours by considering verge sunshine hours during sunny dy. Development of computer progrm for crrying out the present simultion study involves sizing of the pcked bed nd mthemticl models of solr ir heter nd pcked bed. Solr rdition Fn Solr ir heter Pcked bed Fig. (1). Schemtic of pcked bed solr energy storge system Sizing of Pcked Bed It is generlly required to size the bed corresponding to the mount of energy to be stored t the required temperture. The size of the bed should be fixed in such wy tht the bed bsorbs mximum mount of energy delivered by the flowing ir during chrging phse nd men temperture of the bed t the end of the chrging should Tble 1. Vlue/Rnge of System nd Operting Prmeters S. o. Prmeter Vlue/Rnge 1. Volume of pcked bed (V b) 15 m 3 2. Length of pcked bed (L) 6 m 3. umber of bed elements () Initil bed temperture (T bi) 25 C 5. Equivlent dimeter of mteril element (D e) Corresponding to the mteril element under considertion 6. Sphericity of mteril element () Corresponding to the mteril element under considertion ( ) 7. Void frction () Corresponding to the vlue under considertion ( ) 8. Density of storge mteril ( s) 1920 kgm Density of ir ( ) 1.1 kgm Specific het of storge mteril (C s) 835 Jkg -1 K Specific het of ir (C p) 1008 Jkg -1 K Dynmic viscosity of ir (μ ) 18.5x10-6 kgs -1 m Ambient temperture (T mb) 25 C 14. Inlet ir temperture to bed (T i or T ib) 40 C 15. Insoltion (I) 500 Wm Collector re (A c) 20 m F R ( ) e (for collector) F R U l (for collector) Initil inlet ir temperture to the collector (T i) 25 C 20. Time intervl (t) 15 minute

3 Simulted Performnce of Pcked Bed Solr Energy Storge System The Open Fuels & Energy Science Journl, 2008, Volume 1 93 become nerly equl to inlet ir temperture. Therefore, to evlute the bed size, following energy blnce eqution hs been used. mc p ( ) t ch ( C) s ( 1 )V b ( T bm T bi ) (1) ( ) T i T bi In the present simultion study, storge mteril elements of different shpes hve been ssumed to be mde from n esily nd economiclly vilble msonry brick mteril. Thermo-physicl properties of msonry brick mteril re listed in Tble 2. Inlet ir temperture to the bed ( T i ) nd initil temperture of the bed ( T bi ) re ssumed to be 40 C nd 25 C respectively. While sizing the bed, it is ssumed tht the temperture of the ir leving the bed during chrging phse is equl to initil temperture of the bed ( T bi ) nd inlet ir temperture to the bed ( T i ) is equl to temperture of ir t outlet of the collector (T o ). Tble 2. Thermo-Physicl Properties of Msonry Brick Mteril S. o. Property Vlue 1. Specific het 835 Jkg -1 K Therml conductivity 0.70 Wm -1 K Density 1920 kgm Pcked Bed Model In closed cycle of pcked bed solr energy storge system, hot ir leving the collector enters into the bed. Therefore temperture of ir t collector outlet nd bed inlet will be sme. During chrging phse, temperture of lower portion of the bed strts to rise, which my chnge the temperture of ir t the outlet of the collector. Abbud et l. [5] recommended tht for preserving the strtifiction in the bed, the hot ir from collector to the bed should be supplied t constnt temperture by vrying flow rte of ir. Therefore, in the present simultion study, flow rte of ir during chrging of the bed hs been llowed to vry, in order to mintin constnt inlet ir temperture to the bed. For predicting therml performnce of pcked bed, mny mthemticl models hve been reported in the literture. However, most of the investigtors hve used Mumm nd Mrvin model reported by Howell et l. [6]. This model hs been dopted to crry out the present simultion study. In the present study, bed is ssumed to be consisting of number of elements of equl xil thickness x s shown in Figs. (2) nd (2b). The following governing equtions of Mumm nd Mrvin model re used to evlute the temperture distribution for ir nd solid in the bed; Hot ir inlet 2.2. Solr Air Heter Model The mount of energy to be delivered by the collector depends upon the collector re, insoltion, flow rte of ir nd mbient conditions. A model of conventionl solr ir heter hs been dopted to crry out the present study. The chnge in collector outlet temperture cn be expected with chnge of collector inlet temperture under the condition of constnt insoltion nd constnt mbient temperture. However, temperture t the outlet of the collector cn be kept constnt by chnging the flow rte of ir. The flow rte of ir ws clculted from the following Hottel-Willir-Bliss eqution reported by Duffie nd Beckmn [4] for useful energy gin in the collector: Q u A c IF R ( ) F R U l ( T i T mb ) (2) L D b x Useful energy gin Q u is lso given by; Q u ( mc p ) T ( o T i ) (3) Therefore m A c F R ( ) e I F R U l ( T i T mb ) ( ) C p T o T i where T i is inlet ir temperture to the collector, which is ssumed to be equl to the initil temperture of the bed i.e. T bi. T o is ir temperture t outlet of the collector, required to be kept equl to 40 C i.e. the temperture of ir t inlet to bed T i. (4) Fig. (2). Pcked bed (voids re not shown). T,m+1 T b,m + ( T,m T b,m )exp 1 where 1 Air outlet h v AL TU ( mc p ) ( ) (5) nd L / x (6)

4 94 The Open Fuels & Energy Science Journl, 2008, Volume 1 Singh et l. ( ) ( ) T b,m ( t+ t ) T b,m () t + T 2,m T,m+1 3 T b,m T mb where 2 3 ( U A) m ( mc p ) nd s AL( 1 )C s t (7) ( mc p ) 2 (8) T, m x T b, m The bove eqution for vilble energy stored in the bed cn be trnsformed to finite difference form s; Q or Q ( C) s ( 1 )A L ( C) s 1 T mm T bi n1 T bi ln T 1 m T 2 m T 3 m... T m T bi ( T T bm bi ) T bi ln ( )V b T 1 m T 2 m T 3 m... T m T bi (15) (16) The following friction fctor correltion reported by the Singh et l. [3] is used to clculte pressure drop ( P) in the bed. f 4.466( Re) 0.2 ( ) ( ) exp 11.85( log ) 2 { } (17) Fig. (2b). Element m of pcked bed. The following usselt number correltion reported by Singh et l. [3] is used to evlute the volumetric het trnsfer coefficient. { } u 0.437( Re) 0.75 ( ) 3.35 ( ) 1.62 exp 29.03( log ) 2 where u h D 2 v e K (9) nd R e GD e μ (10) Therml energy stored in the bed is clculted by using the following generl eqution; L Q ( C) s o ( 1 )AT ( mm T im )dx (11) Initilly bed is ssumed t uniform temperture of T bi nd hs been divided into number of elements of equl thickness. The bove governing eqution for therml energy stored Q cn be written in finite difference form s; Q ( C) s ( 1 )A L T nm n1 T bi (12) or Q ( C) s ( 1 )V b ( T bm T bi ) (13) Avilble energy stored in the bed (Q ) is clculted by using the following eqution given by Torb nd Besley [7]; L ( ) s Q C o T, m+1 Element m ( 1 )A ( T mm T mi ) T mi ln T mm dx (14) T mi where f P D e G 2, s e nd V b V s V b (18) Energy consumption by the fn (W) to propel ir through the bed is clculted by using the following eqution; W m Pt ch (19) Therml efficiency of the collector is evluted by using the following eqution; th Q u 100 (20) A c I In the present simultion study, following vlues of sphericity nd void frction prmeters, similr to n experimentl study reported by Singh et l. [3] hve been used long with vlues of system nd operting prmeters listed in Tble 1; Sphericity (): 0.55, 0.63, 0.72, 0.80 nd 1.00 Void frction (): 0.31, 0.40, 0.45, 0.54 nd 0.63 It my be noted tht lthough non-sphericl elements cn yield different vlues of void frctions, rndomly pcked spheres cn hve void frction of 0.40 only. The bed elements get chrged in the given time intervl of 15 minutes corresponding to the clculted flow rte of ir. Hence 32 result sets hve been obtined with chrging of the bed for eight hours in ech cse. 3. DEVELOPMET OF COMPUTER PROGRAM The performnce of pcked bed solr energy storge system hs been predicted with the help of computer progrm developed in C++ lnguge by using the bove discussed component models. The objective of developing the computer progrm ws to obtin vlues of vrious prmeters like mss flow rte of ir, temperture of ir t the outlet of ech element of the bed, men temperture of

5 Simulted Performnce of Pcked Bed Solr Energy Storge System The Open Fuels & Energy Science Journl, 2008, Volume 1 95 ech element of the bed, men temperture of the bed, therml energy stored in the bed, vilble energy stored in the bed, energy consumption by fn nd therml efficiency of the collector. The required dt were generted for time intervls of 15 minutes. The temperture vrition in the bed t the end of ech time intervl ws considered n initil condition for next time intervl of 15 minutes. This process ws repeted for eight hours. For chrging of the bed in next time intervl of 15 minutes, the inlet temperture to the collector ws kept equl to the ir temperture t the outlet of the bottom most bed element, which ws noted from the dt of previous temperture distribution. 4. COCLUSIOS In the present prt of this pper n ttempt hs been mde to describe the component models of pcked bed solr energy storge system, in order to develop computer progrm for predicting simulted performnce. The results of simulted performnce w.r.t. temperture distribution in the bed, therml nd vilble energy stored in the bed, energy consumption by fn to propel ir through the bed nd therml efficiency of the collector hve been reported nd discussed in Prt-II nd III of this pper. OMECLATURE A Cross sectionl re of pcked bed (m 2 ) A c Collector re (m 2 ) A Surfce re of pcked bed for thickness or height of x (m 2 ) s Surfce re of sphere hving volume equl to volume of mteril element (m 2 ) e Surfce re of mteril element (m 2 ) C p Specific het of ir t constnt pressure (Jkg -1 K -1 ) C s Specific het of storge mteril (Jkg -1 K -1 ) D e Equivlent dimeter of mteril element (m) D b Dimeter of pcked bed (m) F R Het removl fctor (dimensionless) f Friction fctor (dimensionless) G Mss velocity of ir (kg s -1 m -2 ) h v Volumetric het trnsfer coefficient (Wm -3 K -1 ) I Insoltion (Wm -2 ) K Therml conductivity of ir (Wm -1 K -1 ) L Length or height of the bed (m) m Mss flow rte of ir (kgs -1 ) umber of bed elements (dimensionless) u usselt number (dimensionless) TU umber of trnsfer units (dimensionless) P Pressure drop in bed ( m -2 ) Useful energy gin in collector (W) Q u Re Reynolds number (dimensionless) T i, T ib Temperture of ir t inlet to bed ( C, K) T bi Initil temperture of the bed ( C, K) T,m, T im Air temperture t inlet to bed element m ( C, K) T,m+1 Air temperture t outlet of bed element m ( C, K) T bm Men temperture of bed ( C, K) T i Air temperture t inlet of collector ( C, K) T o Air temperture t outlet of collector ( C, K) T mi Initil temperture of bed element m (K) T mm Men temperture of bed element m ( C, K) T nm Men temperture of n th element of the bed ( C, K) T b,m () t Men temperture of bed element m t time t ( C, K) T b,m ( t+ t ) Men temperture of bed element m fter time intervl t ( C, K) T mb Ambient temperture ( C, K) t ch Chrging time (s) t Time intervl (s) U,U l Overll het loss coefficient (Wm -2 C -1, Wm -2 K -1 ) V b Volume of pcked bed (m 3 ) V s Volume of storge mteril pcked in the bed (m 3 ) x Thickness or height of bed element (m) Density of ir (kgm -3 ) s Density of storge mteril (kgm -3 ) Sphericity (dimensionless) Void frction of bed (dimensionless) μ Dynmic viscosity of ir (kgs -1 m -1 ) th Therml efficiency of collector (%) ( ) e Effective trnsmittnce-bsorptnce product (dimensionless)

6 96 The Open Fuels & Energy Science Journl, 2008, Volume 1 Singh et l. REFERECES [1] Schmidt, F.W.; Willmot A.J. Therml Energy Storge nd Regenertion, McGrw-Hill Book Co., [2] Sgr, K.; khr,. Therml performnce nd pressure drop of pcked beds with lrge storge mterils. Solr Energy, 1991, 47, [3] Singh, R.; Sini, R.P.; Sini, J.S. usselt number nd friction fctor correltions for pcked bed solr energy storge system hving lrge sized elements of different shpes. Solr Energy, 2006, 80, [4] Duffie, J.A.; Beckmn W. A. Solr Engineering of Therml Processes, 2 nd Ed.; John Wiley & Sons Inc., [5] Abbud, I.A.; Löf, G.O.G.; Hittle, D.C. Simultion of solr ir heting t constnt temperture. Solr Energy, 1995, 54, [6] Howell, J. R.; Bnnerot, R. B.; Vliet G. C. Solr Therml Energy Systems-Anlysis nd Design, McGrw-Hill Book Co., [7] Torb, H.; Besley, D.E. Optimiztion of pcked bed therml energy storge unit. Sol. Energy Eng., 1987, 109, Received: August 19, 2008 Revised: August 25, 2008 Accepted: ovember 12, 2008 Singh et l.; Licensee Benthm Open. This is n open ccess rticle licensed under the terms of the Cretive Commons Attribution on-commercil License ( which permits unrestricted, non-commercil use, distribution nd reproduction in ny medium, provided the work is properly cited.