DEVELOPMENT OF A DESIGN AND PERFORMANCE PREDICTION TOOL FOR THE GROUND SOURCE HEAT PUMP SYSTEM

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1 DEVELOPMEN OF A DESIGN AND PERFORMANCE PREDICION OOL FOR HE GROUND SOURCE HEA PUMP SYSEM. INRODUCION. Kaua K. Nagano S. akeda. Ibamoo S.Naia Gaduae School of Engineeing Hokkaido Univeiy Sappoo Japan el: akaok@eng.hokudai.ac.jp Y. Nakamua Nippon Seel Copoaion okyo Japan N. Homma Hokkaido Elecic Powe Co. Inc. Sappoo Japan Recenly he gound ouce hea pump (GSHP yem have been paid aenion a aacive yem wih lage poenial fo educion of CO emiion in Japan. he numbe of inallaion of he GSHP yem wa appoximaely 30 in 004. In ode o pomoe inallaion of he GSHP yem effecively he auho have developed a novel deign and pefomance pedicion ool fo he GSHP yem (Nagano e al 006. he developed ool can evaluae pefomance of he GSHP yem wih muliple gound hea exchange. Addiionally he ool include life cycle analyi in ode o demonae impac of he inallaion of he GSHP yem (Nagano e al 006. Seveal deign ool fo he GSHP yem ae commecially available (Nagano e al 006 and mo of hee ool uilize o-called G-funcion fo calculaion of he gound empeaue fo exacion of he muliple gound hea exchange. hey only cove pepaed layou of he muliple gound exchange. he ool developed by he auho i able o ea he andom layou and calculae he gound empeaue houly. I can alo coepond o he cae whee peculaion of he gound hea exchange which ae uch a ype diamee and lengh diffe and amoun of hea exacion of each gound hea exchange vay. In hi pape he calculaion algoihm of he gound empeaue fo hea exacion of muliple gound hea exchange i explained a fi. Nex he mehod ha calculae empeaue of hea caie fluid in he gound hea exchange fo he pipe aangemen i hown. he implified mehod which can be applied when i i poible o aume ha all gound hea exchange ae ame in ype diamee and lengh i alo inoduced. In addiion empeaue of he gound uounding gound hea exchange and amoun of hea exaced by each gound hea exchange fo diffeence of pipe aangemen ae examined wih he ool including hee mehod.. CALCULAION ALGORIHM Calculaion of gound empeaue fo hea exacion of muliple gound hea exchange Soil i eaed a infinie ioopic conan olid and a veical gound hea exchange (boehole o pile i egaded a a hea ouce (line o cylindical wih infinie lengh in he infinie olid. In a cae whee i much lage han he gound hea exchange adiu p (/ p 0 i i poible o apply he upepoiion pinciple by uing hemal epone fo line hea ouce in epone o hea j exacion of he uounding hea exchange. Explaining wih an acual example n (n i conan numbe of gound hea exchange i buied in andom layou a hown in Figue. he hemal epone on di di dij p Ceain gound hea exchange i Figue Muliple gound hea exchange buied in andom layou

2 he uface of a ceain gound hea exchange Δ i can be obained by umming up all hemal epone. n ( Δ i p = Δ L ( d ij + Δ C ( p (i j ( j = In hi ime i i he ceain gound hea exchange and j i one of he uounding hea exchange. he hemal epone Δ -C i calculaed by applying cylindical hea ouce heoy. In addiion when he geneaed hea on he uface of he cylinde Q vaie accoding o elaped ime he hemal epone Δ -C ( and Δ -L ( ae calculaed by he following equaion (Calaw and Jeage 959. Δ Δ C L ( q' πλ = 0 4πλ = 0 ( ( q' '( ( I E ( a 4 ( (3 Hee I( ( e a = u 0 q' E = a exp πλ 4a 4 4 β J 0( u Y ( u p Y 0( u J ( u p du u [ J ( u p + Y ( u p] ( β dβ If boh ide of he equaion ( and equaion (3 ae divided by uni hea exacion ae Q 0 and made nondimenional he following equaion ae obained. Δ Δ Hee ( ( λ Δ C C ( = = ( C q q' = 0 p 0 ( ( λ Δ L L ( = = ( L q q' = 0 p 0 q ( = q ( / q 0 he non-dimenional hemal epone Δ -C ( can be calculaed in he ho ime (Nagano e al 006. Howeve o calculae each hemal epone Δ -L ( fo non-dimenional diance dij need unallowable ime fo deigne o enginee. In hi pape he mehod which can calculae wih aified peciion and peed by uing appoximaed equaion i popoed. A hown in Figue he hemal epone -L ( i almo zeo (le han.0-3 fo < 0.05 and -L ( i inceaing linealy accoding o logaihm fo.0. hu Δ -L ( i divided ino hee pa of Δ -L ( Δ -L ( - Δ -L ( - hown following. ( = Δ ( + Δ ( + Δ ( (4 ( Figue Vaiaion of non-dimenional empeaue accoding o Fouie numbe Δ L L L L (6

3 Hee.0 =0.05 and =.0. Uing Δ -L ( Δ -L ( - and Δ -L ( - he following appoximae equaion can be expeed. n ( ( ( C Δ L Δ + q (7 Li i= = ( Hee Δ ( ( ( Li q i L i L i (8 he value q i i he aveage of q ( in he i-h pa. When he Fouie numbe i 0.05 <.0 he following equaion i given in ode o calculae he hemal epone Δ -L (. Δ L m ( Δ ( m n (9 i= Li In addiion he hemal epone can be egaded a zeo fom Figue in a cae whee he Fouie numbe i < ( 0 Δ L (0 Conequenly hi mehod can eul o calculae he gound empeaue wih allowable peciion and peed ued a a ool fo deigning of he GSHP yem. Calculaion of empeaue fo pipe aangemen of muliple gound hea exchange Deailed Mehod Fi in a cae whee m (m i conan numbe of gound hea exchange ae aanged in paallel a hown in Figue 3 inle empeaue of he hea caie fluid o he k-h gound hea exchange pink i equal o he oule empeaue fom a hea pump uni ou when hea lo in a cicui can be negleced. k = ou ( k = m ( pin hen he hea caie fluid i egaded a one ma yem and hea balance fo a vey ho peiod i conideed. Hea capaciy change of he hea caie fluid Q fk equal o aggegaion of he amoun of hea injecion o he hea pump uni - Q k and hea anfe beween he boehole uface and he hea caie fluid Q pk a well a a peviou epo (Nagano e al 006. Δ Q = Δ Q + Q ( Δ f k k p k anfomaion of Equaion ( give he following diffeenial equaion. ( pou k pin k + K A ( ( f k d ρ (3 d f k c Vf k = c ρ G f f f f f k p ou k p ou k p ou k Hee f i equal o pou and G fk i flow ae of he hea caie fluid ciculaed hough he i-h gound hea exchange. In addiion weighed aveage empeaue of he hea caie fluid fom all gound hea exchange wih epec o he flow ae give inle empeaue o he hea pump uni in. m G f k pou k k in = = (4 G f Hee G f i whole of flow ae in he pimay ide.

4 Nex when n (n i conan numbe of gound hea exchange ae aanged in eial a hown in Figue 4 conideing hea balance of he hea caie fluid in he l-h gound hea exchange lead o he following equaion along wih Equaion (3. ( pou l pin l + K A ( ( f l d ρ (5 d f l c Vf l = c ρ G f f f f f p ou l p ou l p ou l he oule empeaue fom he l-h gound hea exchange poul i equal o he inle empeaue o he l+-h gound hea exchange pinl+ and poun i equal o in. A he eul of calculaion of he each empeaue a he nex ime ep pouk n+ and poul n+ by Equaion (3 and Equaion (5 epecively in n+ i obained. Alo ( p-ou can be calculaed by he mehod hown in Chape.. hen he coefficien of pefomance (COP of a hea pump uni η elecic powe conumpion of he hea pump uni E he amoun of exaced hea of he hea caie fluid in he evapoao of he hea pump uni Q can be obained a well a peviou epo (Nagano e al 006. he oule empeaue fom he hea pump uni in he pimay ide ou n+ i calculaed by he following equaion. Q c ρ G n+ n+ n+ ou = in = in (6 f f f Q E c ρ G f f f Seconday ide Pimay ide Seconday ide Pimay ide ou in pin pou pin pou pink- pouk pinm poum pin = ou pin = pou pin3 = pou pinl = poul- pinn = poun- in = pinn f f fk fm ( p ( p ( pk ( pm f f fl fn ( p ( p ( pl ( pn k m Figue 3 Muliple gound hea exchange aanged in paallel cicui l n Figue 4 Muliple gound hea exchange aanged in eial cicui Simplified Mehod Wih egad o he deailed mehod compuaional ime i equied accoding o he numbe of gound hea exchange. Simplified mehod which can be applied when i i poible o aume ha all gound hea exchange ae ame in peculaion lengh and diamee i explained below. A hown in Figue 5 m numbe paallel cicui ae aanged and each cicui ha n numbe of gound hea exchange in eial. he flow ae i divided ino accoding numbe of he paallel cicui. If he whole flow ae i G f he Hea pump flow ae pe one cicui i G f / m. On he ohe hand n numbe Supply and eun heade of he gound hea exchange aanged in eial i egaded a a gound hea exchange whoe lengh i equal o he um of n 3 n - n numbe of he gound hea exchange and hea capaciy change of he hea caie fluid in he gound hea exchange i conideed. Fom aumpion ha all gound hea exchange ae in he ame ize he volume of he hea caie fluid in he all gound hea exchange and he uface aea of he all gound m - hea exchange ae he ame. When he volume and uface aea ae peened by V f and A p-ou epecively he following equaion m i obained a epec all cicui. Figue 5 Muliple gound hea exchange wih paallel and eial cicui

5 df G f c ( ( f ρ fvn f = c f ρ f pou pin + K p ou Ap oun ( p ou f (7 d m he gound empeaue on he uface of he gound hea exchange ( p-ou in Equaion (7 i expeed by uing aveage empeaue of he uface empeaue of all gound hea exchange calculaed by Equaion (. ( p ou m n ( p oui Δ i i= = 0 + (8 m n Hee 0 i iniial gound empeaue. 3. COMPARISON OF PERFORMANCE OF HE GSHP SYSEM FOR HE PIPE ARRANGEMN Calculaed Condiion empeaue vaiaion amoun of exaced (injeced hea and pefomance of he GSHP yem fo diffeence of he pipe aangemen wee examined wih he ool. A an example pefomance of he GSHP yem wih eel foundaion pile a gound hea exchange fo a ypical eidenial houe in okyo wa calculaed. Ouline of calculaed condiion ae hown in able. able Calculaed condiion Building Ciy Hea lo coefficien [W/m /K] oal floo aea [m ] Heaing peiod Cooling peiod oal heaing load [GJ] (Maximum load [kw] oal cooling load [GJ] (Maximum load [kw] Fom Nov. 3d o Ap. nd Fom Ap. 3d o Nov. nd 8. ( (6.3 Floo heaing 70m Heaing yem Oule empeaue in econday ide vaie accoding o heaing load Cooling yem Gound empeaue [ ] Fan-coil uni Wih efigan (Hea pump 6.5 Soil Effecive hemal conduciviy [W/m/K].0 Deniy [kg/m 3 ] 500 Specific hea [kj/kg/k].0 Exenal diamee of U-ube [m] 0.03 Gound hea Exenal diamee of eel foundaion pile [m] Indiec ype wih 0.4 exchange ingle U-ube Inenal diamee of eel foundaion pile [m] 0.3 Maeial filled ino pile Silica and (Effecive hemal conduciviy :.8 W/m/K Hea pump uni Compeo -hoe powe COP( Elecic powe conumpion of ciculaion pump [W] Hea caie fluid (Bine Pimay ide : 00W Seconday ide : 50W Oganic acid goup 40% okyo Excep gound hea exchange (eel pile he calculaed condiion ae imilaly o peviou epo (Nagano e al 005. he eel pile ae ued a indiec ype gound hea exchange. Silica and (Effecive hemal conduciviy i.8 W/m/K i filled in he pile and U-ube ae ineed ino he and. he pipe aangemen and mehod of calculaion fo each CASE ae hown in able. he empeaue a equivalen adiu i ued a aveage empeaue on he uface of he gound hea exchange in ode o evaluae hea anfe fom edge of he gound hea exchange (Ekilon 987. he equivalen adiu i obained by muliplying modificaion coefficien fo adiabaic condiion on he gound uface o he ideal gound hea exchange adiu (Nagano e al 005. In CASE

6 and CASE five pile (gound hea exchange ae conneced in eial each ohe and hee ae fou paallel cicui. In CASE3 all pile ae conneced in paallel. Flow ae of he hea caie fluid ciculaed hough he gound hea exchange i divided depending on numbe of he paallel cicui. he ool including he deailed mehod implemened imulaion of he GSHP yem opeaion fo hee CASE. A imulaion of he opeaion fo CASE4 i execued by he ool including he implified mehod. he imulaion ae caied ou by giving houly hea load hown in Figue 6. Reul and Dicuion A an example of eul of he calculaion Figue 7 how houly vaiaion of empeaue ou ou and p-ouave fo he hid yea eul in CASE. Diffeence of ou and p-ouave beween he a of he hid yea opeaion Nov. 3d and he end Nov. nd ae hadly obeved. hee empeaue vaiaion have almo achieved peiodical eady ae. hi eul ugge he poibiliy of long yea opeaion. Figue 8 illuae change of empeaue diibuion of he gound uounding pile wih paage of ime fo he hid yea eul in CASE and CASE. In CASE empeaue of he gound uounding all pile almo equally dop a elaped ime of 3000 h. Becaue he empeaue uounding pile buied inne ide i loweed by hea exacion of he uounding pile. On he ohe hand in CASE he empeaue uounding he pile ha he hea caie fluid i ciculaed hough op in he eial cicui dop much lage han one uounding ohe pile. Wih egad o empeaue diibuion a elaped ime of 7000 h he empeaue uounding he pile ha he hea caie fluid i ciculaed hough op in he eial cicui ie he lage. he incemen of he empeaue uounding he pile in CASE i lage han he one in CASE. In addiion hee i lowe empeaue diibuion in he gound uounding pile buied inne ide in boh CASE in pie of duing cooling peiod a elaped ime of 5000 h. I i fo hi eaon ha he effec of hea exacion duing heaing peiod ill emain. Figue 9 how inegaing amoun of hea exacion and injecion of each pile accoding o elaped ime in CASE and CASE epecively. Duing cooling peiod diffeence of hea exacion of he each pile in CASE ae lage han one in CASE. Wih egad o duing cooling peiod diffeence of hea injecion of he each pile in CASE ae lage han one in CASE. I i convee o he hea exacion duing heaing peiod. Alo he amoun of hea exacion of he pile buied inide (pile5 fo CASE and pile fo CASE i lage. I i due o empeaue deceaing obeved a elaped ime of 5000 h in Figue 8. I would be bee o ay ha eaonal hemal oage effec appea. oal amoun of hea exacion and hea injecion in CASE i equal o one in CASE. In hee cae alhough amoun of hea exacion of individual pile vay depending on he piping oue of he hea caie fluid he oal doen diffe. Fuhemoe aveage COP of hea pump uni and aveage COP of he yem (SCOP; including hea pump and ciculaion pump of he pimay ide duing heaing and cooling peiod ae hown in able 3. Fom Hea load [kw] Heaing peiod Cooling load Heaing load Cooling peiod -8 Nov. 3 d Feb. 3 d May. 3 d Aug. 3 d Figue 6 Houly vaiaion of hea load 50 Heaing Peiod Cooling Peio able he pipe aangemen and mehod fo calculaion fo each CASE 40 ou Pipe aangemen (Paallel Seial Mehod fo calculaion CASE 4 5 Deailed mehod CASE 4 5 Deailed mehod CASE3 0 Deailed mehod CASE4 4 5 Simplified mehod empeaue [ o C] p-ouave ou ou -0 ou Nov.3 d Feb.3 d May.3 d Aug.3 d Figue 7 Houly vaiaion of each empeaue

7 compaion beween CASE and CASE diffeence of pefomance of he GSHP yem by piping oue i hadly obeved. In CASE3 he value hown in able 3 ae lowe han one fo ohe condiion due o educion of amoun of he hea CASE 5.0 CASE 5.0 CASE CASE 5.0 CASE CASE Elaped ime of 3000 h (Ma.7 h Elaped ime of 5000 h (May. 30 h Piping oue Elaped ime of 7000 h (Aug empeaue [ o C] Figue 8 Change of empeaue diibuion of he gound uounding pile wih elaped ime.5 Heaing Peiod Cooling Peiod.5 Heaing Peiod Cooling Peiod Amoun of hea exacion [GJ] Pile Pile Pile 3 Pile 4 Pile5 fom op o boom oal amoun of hea exacion:5.65gj oal amoun of hea injecion :.87GJ Pile Pile3 Pile 4 Pile Pile5 fom op o boom Amoun of hea exacion [GJ] Nov.3 d Feb.3 d May.3 d Aug.3 d Nov. nd Nov.3 d Feb.3 d May.3 d Aug.3 d Nov. nd Pile5 Pile Pile 4 Pile 3 Pile fom op o boom Pile4 Pile5 Pile 3 Pile Pile fom op o boom oal amoun of hea exacion:5.65gj oal amoun of hea injecion :.87GJ Figue 9 Inegaing amoun of hea exacion and injecion of each pile accoding o elaped ime in CASE (lef and CASE (igh exacion occued by he lamina flow of he hea caie fluid in he gound hea exchange. Alo COP and SCOP calculaed by he implified mehod wa he ame a ha by he deailed mehod. In hi ime he compuaional ime of he CASE4 calculaed by he implified mehod i appoximaely / 0 a much a ohe CASE calculaed by he deailed mehod. hee mean ha he implified mehod povide high advance fom he viewpoin of peciion and compuaional peed. able 3 Pefomance of he GSHP yem fo each CASE Heaing Peiod Aveage COP Aveage SCOP Cooling Peiod Aveage COP Aveage SCOP CASE CASE CASE CASE

8 4. CONCLUSIONS ( Calculaion algoihm of he gound empeaue and ciculaed fluid empeaue fo pipe aangemen i developed in ode o pedic pefomance of he GSHP yem wih muliple gound hea exchange in he ho ime. ( empeaue of he gound uounding gound hea exchange and amoun of hea exaced by each gound hea exchange fo diffeence of pipe aangemen ae examined wih he ool including hee mehod. A he eul alhough amoun of hea exacion of individual pile vay depending on he piping oue of he hea caie fluid he oal doen diffe. Addiionally i i confimed ha eaonal hemal oage effec appea. (3 COP and SCOP in a cae whee all pile ae conneced in paallel ae lowe han one in ohe cae becaue of educion of amoun of he hea exacion occued by he lamina flow of he hea caie fluid in he gound hea exchange. (4 he implified mehod povide high advance fom he viewpoin of peciion and compuaional peed by compaion beween pefomance pediced by he implified mehod and he deailed mehod. ACKNOWLEDGMENS he auho would like o expe appeciaion o he laboaoy of gound hemal enegy yem of copoae donaed chai in Hokkaido Univeiy. Pa of hi udy i uppoed by he cenuy COE pogam of he Miniy of Educaion Culue Spo Science and echnology Suainable Meabolic Syem of Wae and Wae fo Aea-Baed Sociey (Pojec epeenaive: Pof. Y. Waanabe ha povided financial paicipaion in hi eeach. NOMENCLAURES A: aea [m ] a: hemal diffuiviy [m /] c: Specific hea capaciy [kj/kg/k] E: Elecic powe conumpion of hea pump [W] G: Flow ae [m 3 /] J x : xh-ode Beel funcion of fi kind K: Oveall hea anfe coefficien [W/m /K] Q: Amoun of hea exacion [W] q : Hea flux [W/m ] q : Hea injecion ae pe lengh [W/m] : adiu [m] : empeaue [ ] :Non-dimenional empeaue (=πλδ//q [-] : ime [h] : Fouie numbe (= a/ [-] u: Chaaceiic value V: Volume [m 3 ] Y x : xh-ode Beel funcion of econd kind Geek lee β: Inegaion paamee λ: hemal conduciviy [W/m/K] ρ: Deniy [kg/m 3 ] Subcip ave: Aveage value of all gound hea exchange f: Hea caie fluid in: Inle ou: Oule p: Gound hea exchange : Soil -in: inide -ou: ouide -C: hemal epone fo cylindical hea ouce -L: hemal epone fo line hea ouce : Pimay ide of hea pump uni : Seconday ide of hea pump uni REFERENCES H. S. Calaw and J. C. Jaege: Conducion of Hea in Solid Oxfod Univeiy Pe 959 Pe Ekilon: hemal Analyi of Hea Exacion Boehole Univ. Lund K. Nagano. Kaua S. akeda: Developmen of a Deign and Pefomance Pedicion ool fo he Gound Souce Hea Pump Syem Applied hemal Engineeing 006 K. Nagano. Kaua. Nogawa A. Okamoo Y. Nakamua: Developmen of a Deign and Pefomance Pedicion ool fo he GSHP yem Poceeding of 8 h IEA Hea Pump Confeence 005 La Vega 005

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