TECHNICAL NOTE SIZING OF A PACKED BED STORAGE FOR SOLAR AIR HEATING SYSTEMS

TECHNICAL NOTE SIZING OF A PACKED BED STORAGE FOR SOLAR AIR HEATING SYSTEMS K. Aspour-sni Solr Energy Reserch Group, Deprtment o Energy, Mterils nd Energy Reserch Center P. O. Box 14155-4777, Tehrn, Irn, k-spour@merc.c.ir (Received: Novemer 10, 2002 Accepted: Ferury 6, 2003) Astrct Pcked ed units generlly, represent the most suitle storge units or ir heting solr systems. In these systems the storge unit receives the het rom the collector during the collection period nd dischrges the het to the uilding t the retrievl process. A method or sizing o pckeded storge in n ir heting system is represented. The design is sed on the K-S curves, which hve een generted or the storge used in the CSU solr House II through simultion. The complete simple solr heting system is simulted numericlly during oth the heting nd retrievl processes. The simultion, which utilizes the hourly meteorologicl dt, tkes into ccount considertion o the principle prmeters such s pressure drop cross the ed, prticle dimeter, nd men voidge. The results re compred with the reported dt rom rel size o storge nd lso with the criteri o - chrt recommendtion. Key Words Pcked Bed Storge, Air Heting Solr System, Simultion يكي از اجزاي مهم سيستم هاي خورشيدي هوايي مخزن ذخيره انرژي از نوع بستر فشرده مي باشد. چكيده اين مخزن در طي فرا يند جذب انرژي حرارت را از جمع كننده خورشيدي دريافت و هنگام بازيافت ا نرا به محيط مورد نظر مي رساند. در اين مقاله روشي براي تعيين ابعاد اين مخزن مورد استفاده در سيستم خورشيدي اراي ه مي شود. اين روش بر اساس منحني هاي كاركرد مخزن بوده كه در موقع شبيه سازي سيستم خورشيدي ايجاد مي گردد. سيستم كامل يك خانه خورشيدي در طي فرا يند جمع ا وري و بازيافت انرژي به روش عددي شبيه سازي شده كه ورودي ا ن اطلاعات جو ي و تابش خورشيدي در هر ساعت براي محل نصب خانه خورشيدي مي باشد. اين شبيه سازي برخي پارامترهاي اصلي از قبيل افت فشار در طول بستر قطر متوسط سنگدانه ها و تخلخل متوسط را در نظر ميگيرد. در اين مقاله ضمن بحث پيرامون الگوي مورد استفاده در اين شبيه سازي نتايج بدست ا مده از روش -chrt و اطلاعات بدست ا مده از عملكرد يك سيستم واقعي مقايسه شده اند. 1. INTRODUCTION Pcked ed units generlly, represent the most suitle storge units or solr ir heting systems where, the storge unit receives the het rom the collector during the collection period nd dischrges the het to the uilding t the retrievl process. Two importnt considertions re involved in the design nd opertion o pcked - ed storge. Firstly, the rtes o het trnser tht will tke plce etween the irlow nd solid prticles is chrcterized y the volumetric het trnser coeicient. Secondly, sizing o the ed involving determining, the our most criticl prmeters: the irlow rte per unit o collector surce re, the equivlent prticle dimeter, the ed length, nd inlly, the ed rontl re. While the het trnser within pcked ed ssocited with solr heting system hs een ound in the literture [1,2,3] here, we del with the second considertion. The design nd sizing o storge unit or solr heting system is very complicted process since it requires tht ll the system components; collector, storge unit, heting lod, nd uxiliry unit should e tken on the considertion. The dily vrition in the solr rdition incident on the IJE Trnsctions B: Applictions Vol. 16, No. 2, July 2003-155

Figure 1. Schemtic digrm o simple solr system. collector surce, nd the dily spce-heting lod must e dequtely represented. Since these vritions re irregulr, sttisticl pproch to relect ll the possile considertions is desired. One o the methodologies used in the design o solr heting system is the -chrt method descried y Beckmn et l. [4]. In this method the results o mny numericl experiments re correlted in terms o two dimensionless vriles; one represents the monthly verge het loss rom collector nd other descries the monthly verge sored solr energy s unction o monthly verge totl heting lod. For given solr heting system, the method provides mens to estimte the rction o totl heting lod tht will e supplied y solr energy in respect to these vriles. A numer o dierent ctors were tken into ccount in developing the design recommendtion with the - chrt method nd mny simpliying ssumptions were necessry. Severl reports on the design o storge or solr heting systems hve een prepred [5,6]. It is recommended tht one o the ville clcultion methods; the -chrt is used to TABLE 1. Selected Design Prmeter or Collector. Prmeter Recommended vlue [6] Overll het loss coeicient, U L 7.7 W/m 2. o K Eectiveness, F 0.85 Trnsmittnce-sornce 0.75 Product, τα Air low rte per unit re o the 0.01 kg/m 2.s collector, ϑ & Tilt Angle, β Ltitude+15 156 - Vol. 16, No. 2, July 2003 IJE Trnsctions B: Applictions

TABLE 2. Averge Dily Totl Rdition on Horizontl Surce t Alquerque (Ltitude 35.5 o ) in MJ/m 2. Jn. Fe. Mr. Apr. My June Aug. July Sept. Oct. Nov. Dec. 1 9.9 14.9 19.0 25.0 28.5 29.0 27.5 25.3 21.1 17.2 12.9 9.5 2 11.5 15.2 20.0 25.3 28.8 30.4 28.2 26.0 22.4 17.6 12.3 10.5 1- Simultion results using recorded dt nd Er et l. [8] correltion. 2- Dt rom SOLMET progrm[7]. determine the size o the collector. The volume o the storge device is ssumed to e directly proportionl to the collector re. The sizing o the storge, its surce re, nd length re sed directly on pressure drop considertions. The purpose o this pper is to present simple method, yet ccurte, or the design o the pcked eds used or therml storge in simple heting system. 2. THERMAL MODEL OF THE SYSTEM The design procedure developed in this study is sed on the results otined rom the computer simultion o the solr heting system, shown in Figure 1. The system consists o collector, n, ypss controller or the retrievl process, nd pcked ed storge unit. Collector The solid line in Figure 1 shows the pth tken y the ir during the collection nd storing period. The pth is closed loop nd the collector outlet temperture is dependent on the incident solr rdition nd the storge outlet temperture. In the stedy stte the ctul useul energy gin in collector descried y ollowing eqution: q u R c [( τα) I U ( T T )] = F A (1) L Where, F R is the collector removl ctor nd is given y [7]. i CSU solr House II [7]. They re listed in Tle 1. Insoltion To estimte the insoltion on the collector surce re during time step, the simultion o the solr system requires hourly dt. This is done using the meteorologicl dt o the loction o interest y the correltion o Er et l. [8]. The results or clculting the monthly verge dily totl rdition on horizontl surce re shown in Tle 2. Pcked Bed Storge The ir lows through the pcked ed during the retrievl process in counter-low mnner. The perormnce o the pcked ed is descried y Schumnn model [1]. For common conditions encountered in solr pplictions, where the therml conductivity o the ed in the low direction compred to tht in the perpendiculr direction is very smll, thus the Schumnn model or this cse is reduced to: ( mc & ) A ( T T ) T ( ρc ) ( 1 ε) = h ( T T ) p p T = h x t v v + ( UA) s ( T T ) V (3) The volumetric het trnser coeicient, h v, which is unction o the low rte through the ed is clculting using the correltion o Ergun [9]: F R G oc = U L p U LF 1 exp G oc p (2) h v G o 650 dp = 0.7 (4) Here, or simultion purposes the system prmeters re ssocited with the collectors instlled in the Where G o is mss velocity per unit o rontl re o the ed nd dp is the prticle dimeter. IJE Trnsctions B: Applictions Vol. 16, No. 2, July 2003-157

voidge, ε, gretly inluences the pressure drop while it hs less drmtic eect on the storge chrcteristics o the ed or given length. A vlue o 0.35 ws used in otining the dt to e presented. Bypss Control A ypss rrngement is necessry during the retrievl process, in order to mintin the temperture o the ir delivered to the lod nd lso the temperture o the ir returning rom the lod ws considered to e time independent nd to hve constnt prescried vlue. It is ssumed tht the ir circultion through the storge is terminted when the storge is no longer le to mintin the desired dischrge temperture. 3. SIMULATION ) Wrm months To simulte the solr heting system shown in Figure 1, Eqution 1 nd Eqution 3 were solved numericlly. The procedure ollowed in generting the results to e presented is s ollows: 1. The meteorologicl dt nd design prmeters ssocited with the collector nd storge re selected. 2. The hourly insoltion incident on the collector surce is clculted. 3. The monthly verge insoltion is computed. 4. A mximum pressure drop through the ed is selected. 5. For the initil mss velocity o the ir, the length o the ed is clculted. 6. The monthly verge energy supply during the retrievl process per unit re o the collector surce re is determined. This represents one point on the perormnce chrcteristics to e noted s K-S curves [10]. 7. A new vlue o mss velocity is selected nd steps 4-6 repeted until complete K-S curves re otined. This procedure is repeted or ech month o the yer. ) Cold months Figure 2. K-S curves or the solr heting system. The physicl properties o the storge medium, grvel, were considered to e constnt. The men 4. RESULTS AND DISCUSSION The perormnce o the solr system shown in Figure 1 ws determined using the descried procedure in Section 3. The pressure drop cross the pcked ed storge ed ws 0.76 Cm o wter, the men 158 - Vol. 16, No. 2, July 2003 IJE Trnsctions B: Applictions

Figure 3. The eect o men voidge on vrition o ed length. Figure 5. The eect o mximum pressure drop on dily energy retrievl or solr heting system. Figure 2- nd 2- in solid lines. These perormnce curves re reerred to s K-S curves. The pressure drop cross the pcked ed is determined using the correltion o Ergun [9], which is deined y: P G 1 g = L ρ dpε ( ε) ( 1 ε) 3 µ 1.75G + 150 dp 0.7 (5) Figure 4. The eect o rock ed dimeter on dily energy retrievl or solr heting system. rock dimeter ws 2 Cm, nd men voidge o the ed ws 0.35. For given rnge o rontl mss velocity, clcultion hs een mde or ed length nd dily recovery energy. The results re shown in The plot o this reltion is shown s dshed line in Figure 2- nd Figure 2-. Once the ed length is selected, this plot cn determine the mss velocity, G. The solid lines then determine the verge dily energy retrievl or ech month. The heting lod nd the retrievl rtes re compred nd the surce re o the collector is selected so est meets the heting lod. The rontl re o the ed is: A va & cρ = (6) G o The results re shown in Tle 2. The size o the collector is selected so tht the system cn meet the demnd in Mrch, nd is ound to e 79.6 IJE Trnsctions B: Applictions Vol. 16, No. 2, July 2003-159

TABLE 3. Lod nd Solr Energy Retrievl or Pcked Bed Storge. Month Jn. Fe. Mr. Apr. My June July Aug. Sept. Oct. Nov. Dec. Spce heting lod MJ/dy 681.8 609.8 485.9 280.6 125.8 42.6 7.7 16.3 80.3 240.1 496.6 657.2 Rte o Energy retrievl MJ/dy.m 2 2.0 3.9 5.4 7.3 5.0 2.8 0.3 3.1 4.9 5.1 4.6 2.4 - Dily Retrievl o Energy exceeds the heting lod requirements. Energy supplied MJ/dy 159.2 310.4 437.8 366.2 191.0 Solr Frction 0.26 0.61 0.90 0.74 0.29 TABLE 4. Comprison o Design Dt with the F-chrt Recommendtion nd Reported Dt. Design dt Reported Predicted results dt[5] F-chrt[6] Collector low rte per unit o surce re, m 3 /m 2.s 0.01 0.01 0.005-0.02 Storge cpcity per unit o rontl re, m 3 /m 2 0.152 0.158 0.15-0.30 Pressure drop, Cm wter - 0.70 0.55-0.76 Mss velocity, kg/m 2.s 0.187 0.139 Min 0.0216 Bed length, m 2.2 2.2 1.25-2.50 m 2. By exmining the energy supplied s indicted in Tle 2, it revels tht in some months uxiliry heting will e required. The rontl re o the storge unit using Eqution 6 is ound to e 5.72 m 2. The totl volume o the storge ed is 12.6 m 3 or 0.158 m 3 /m 2 o collector surce re. In Tle 4 some design dt re compred with the reported dt rom rel size o storge unit nd criteri o the -chrt recommendtion. Two vriles, which were considered to e primry importnce in the design o the storge unit re the prticle dimeter nd the totl pressure drop through the ed. The eect o vritions in these prmeters on the perormnce chrcteristics ws investigted. It is pprent rom Eqution 3 tht the pressure drop is strongly inluenced y the men voidge o the ed. The eect o men voidge on mss velocity is shown in Figure 3. Another signiicnt vrile in the design o storge unit is the prticle dimeter. From Figure 4 it cn 160 - Vol. 16, No. 2, July 2003 IJE Trnsctions B: Applictions

e seen tht, or ed with given length, the mss velocity is increses with incresing o the prticle dimeter ut it cuses decrese in het trnser rte. The eect o the mximum pressure drop cross the ed on the sizing o the storge is shown in Figure 5. This indictes tht i the llowle pressure drop is decresed, the ed must e shortened nd the rontl re incresed in order to otin the sme therml chrcteristics or the system. 5. CONCLUSIONS A simple method hs een developed to design o pcked ed storge or solr heting systems. The design is sed on the K-S curves tht hve een generted or the storge used in the CSU solr House II through simultion. This simultion, which utilizes the hourly meteorologicl dt, tkes into ccount considertion the principle prmeters such s pressure drop cross the ed, prticle dimeter, nd men voidge. The criteri sed on the generl design method (-chrt) revels stisctory greement etween simultion results nd reported dt rom rel size storge. The proposed method should, however, e veriied on ull-scle system either y the design nd considertion o unit or spce heting or y modiiction o n existing unit to conirm the system previously descried. It is ovious tht the het retrievl in the ctul unit will e slightly less thn the predicted vlue y the simultion, ecuse the simultion ignored the ir lekge nd het loss rom the ducts connecting collector nd storge. These losses cn e gretly reduced y insulting the ducts. 6. NOMENCLATURE A Surce re, m 2 Cp Speciic het cpcity, J/m 2.K dp Prticle dimeter, m F Collector Eiciency ctor F R Collector het removl ctor g Grvittionl ccelertion, m/s 2 h Het trnser coeicient, J/m 2.K Go Mss low rte per rontl re, kg/m 2.s L Bed length, m P Pressure, P T Temperture, o C U Overll het trnser coeicient, J/m 2.K τα Asornce-Trnsmittnce product β Collector slope ρ Density, kg/m 3 µ Asolute viscosity, N.s/m 2 Suscripts A L s v Amient Bed column Fluid Loss Surce Volumetric 7. REFERENCES 1. Schumnn, T. E. W., A Liquid Flowing Through Porous Prism, In Solr Engineering o Therml Processing, Duie, J. A. nd Beckmn W. A., John Wiley, New York, (1991), 393-396. 2. Shewn, E. C., Sullivn, H. F., Hollnds K. G. T. nd Blkrishnr A. R., A Het Storge Su-System or Solr Energy, Tech. Rep. STOR-6, Wterloo Reserch Institute, University o Wterloo, Cnd, (1978). 3. Shitzer, A. nd Levy M., Trnsient Behvior o Rock- Bed Therml Storge System Sujected to Vrile Inlet Air Temperture: Anlysis nd Experimenttion, Trns. o ASME Journl o Solr Energy, Vol. 105, (1983), 200-206. 4. Beckmn, W. A., Klein, S. A., nd Duie, J. A., Solr Heting Design, Wiley Inter-science, New York, (1977). 5. Cole, R. L., Nield, K. J., Rohde, R. R. nd Wolosewics, R. M., Design nd Instlltion Mnul or Therml Energy Storge, Tech. Rep. ANL-79-15, Argonne Ntionl Lortory, US, (1985). 6. Duie, J. A. nd Beckmn, W. A., Solr Engineering o Therml Processing, John Wiley, New York, (1991). 7. Krki, S. nd Hwken, P., Perormnce Evlution o Solr Assisted Het Pump System in CSU Solr House IJE Trnsctions B: Applictions Vol. 16, No. 2, July 2003-161

II, Tech. Rep. COO-30122-27, Solr Energy Appliction Lortory, Fort Collins, CO: CSU, (1982). 8. Er, D. G., Klein, S. A. nd Duie, J. A., Estimtion o the Diuse Rdition Frction or Hourly, Dily, nd Monthly-Averge Glol Rdition, Solr Energy, Vol. 28, (1982), 293-299. 9. Ergun, S., Fluid Flow through Pcked-Bed Columns, Chem. Eng. Progr., (1952), 48. 10. Kulkowski, B. T. nd Schmidt, F. W., Discrete Control Algorithm or Het Storge System, ASME Dynmic System, Mesurements, nd Control, Vol. 102, (1980), 226-232. 162 - Vol. 16, No. 2, July 2003 IJE Trnsctions B: Applictions