Thermodynamic analysis of geothermal heat pump during the cold season

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1 IOP onference eries: Mterils cience nd ngineering PAPR OPN A hermodynmic nlysis of geotherml het pump during the cold seson o cite this rticle: G Dumitrcu et l 2016 IOP onf. er.: Mter. ci. ng View the rticle online for updtes nd enhncements. Relted content - hermodynmic Anlysis on Vpor Phse pitxy of GAs by Gl 3 nd AsH 3 ystem Akinori oukitu, Fumio Hsegw nd Hisshi eki - hermodynmic Anlysis of In x G 1-x N Alloy omposition Grown by Metlorgnic Vpor Phse pitxy Akinori oukitu, Noyuki khshi, etsuy ki et l. - A hermodynmic Anlysis of the Vlidity of Wenzel nd ssie's qutions n hui-xi, Lu Xio-Ying, Li Wen et l. his content ws downloded from IP ddress on 31/12/2017 t 16:47

2 7th Interntionl onference on Advnced oncepts in Mechnicl ngineering IOP onf. eries: Mterils cience nd ngineering 147 (2016) doi: / x/147/1/ hermodynmic nlysis of geotherml het pump during the cold seson G Dumitrşcu 1, A Dumencu 1, B Horbniuc 1 nd M V Atnsiu 1 1 Automotive nd Mechnicl ngineering Deprtment, Gheorghe Aschi echnicl University of Isi, Isi, Romni -mil: dumencu@yhoo.com* Abstrct. he pper is nlysing the performnces (OP, power nd, heting het rte function of time) for ground-coupled het pump tht is used to het spce during winter, for period of 180 dys. he nlysis purpose is to evlute the time bsed chnges in vlues of OP nd, energy trnsfers of geotherml het pump, considering scenrio for the vrition of the mbient temperture in time nd n nlyticl solution for the time dependence of the soil one. he tempertures nd the energy trnsfer rtes were determined on the bsis of the eversible entropy blnce eqution. 1. Introduction he ground-coupled het pump bsed energy systems re using geotherml underground energy for spce heting nd cooling. Becuse of lrge heting efficiency nd environmentl protection, the interest in these systems is incresing tody. here is wide vriety of these systems to be used in office buildings, houses nd historicl buildings. he study[1], regrding the office building heting systems using ground coupled het pumps with different borehole dimeters, showed tht the highest svings to investment rtio, during period of thirty yers, is he pper [2]presents n open loop system tht uses for cooling wter lke het cpcity. For heting most het pump systems use closed loop. A generl review[3], presenting the most common het pumps bsed energy systems tht re used tody, is compring their performnces nd opertionl prmeters but for qusi-stedy stte opertion. he thermodynmic nlysis of ground-coupled het pump bsed energy systems emphsizes the importnt influence of underground soil temperture profile nd the geometry of the het exchngers extrcting the geotherml energy, e.g. either the superficil temperture profile of soil influenced by the nturl convection on the surfce [4], or tht fter depth of 15m, the initil underground temperture is lmost constnt. his pper perform thermodynmic nlysis of closed loop het pump bsed heting system coupling two externl het reservoirs with different vrible fetures. he het sink is the heted spce tht sks heting rte function of the environmentl temperture nd the het source is the soil with vrible temperture in time. he het pump cycle is n eversible one, nd the overll entropy blnce eqution llowed linking these two het reservoirs by choosing scenrios for the heting rte during the winter nd n nlyticl solution in time for the geotherml het rte. he het pump bsed heting system is presented in figure 1. ontent from this work my be used under the terms of the retive ommons Attribution 3.0 licence. Any further distribution of this work must mintin ttribution to the uthor(s) nd the title of the work, journl cittion nd DOI. Published under licence by Ltd 1

3 7th Interntionl onference on Advnced oncepts in Mechnicl ngineering IOP onf. eries: Mterils cience nd ngineering 147 (2016) doi: / x/147/1/ Figure 1. he heting system scheme.h heted spce; evportor; condenser; compressor; V throttling vlve; i nd o input nd output tempertures for ; i nd o input nd output tempertures for. 2. Restrictive conditions he heted spce temperture H = = const. while outside mbient temperture is vryingfrom to (from 20 to +15 ). For the mbient temperture ws dopted scenrio, respectively we considered continuous heting during the winter (180 dys) with time dependence, see figure 2 where t is the time in hours. t sin 4320 (1) Figure 2. = (t). onstnt initil soil temperture i = For the soil temperture vrition in time ws imposed n nlyticl dependence, see figure 3: 2

4 7th Interntionl onference on Advnced oncepts in Mechnicl ngineering IOP onf. eries: Mterils cience nd ngineering 147 (2016) doi: / x/147/1/ where t is the time in hours exp t (2) Figure 3. = (t). Het crriers were ssumed to hve constnt het cpcities, = 500 W/ = const. nd = 1000 W/ = const. he heting system uses the ir s het crrier flowing in loop between the condenser nd the heted spce. Het pump het exchngers (, nd soil borehole) were presumed to hve constnt effectiveness (ε = 0.75 = const., ε = 0.75 = const., nd ε = 0.95 = const.). 3. Mthemticl lgorithm 3.1. he heted spce nd the condenser he heted spce needs to be mintined t constnt temperture, H = , while outside mbient temperture is vryingfrom to hus the heting rte supplied by equlizes the lost het rte, see figure 4. Figure 4. herml energy blnce of the heted spce. he heted spce nd condenser het blnce equtions re: lost H H h A (3) lost lost N h h H H H A A H H H H N o N i N k k o on i in i. (4) 3

When the mbient temperture fluctutes between +15 nd 20 o, the ir input/output tempertures re: i = in = H = 295.15 = const. nd o = o ( ) function of the heting system design tempertures.

5 When the mbient temperture fluctutes between +15 nd 20 o, the ir input/output tempertures re: i = in = H = = const. nd o = o ( ) function of the heting system design tempertures. We imposed on = t N = he dependences nd, = ( ) nd, o = o ( ) re obtined on the bsis of the het blnce equtions1, 3 nd 4, see figure 5: in on N H H i o , [] (5) i o i, [] (6) i i o, [W]. (7) () (b) (c) Figure 5. he dependences () o = o ( ), (b) = ( ), (c) for he soil nd the evportor he het blnce equtions relted to the therml connection evportor soil re: i o i, [W] (8) o, [W]. (9) From equtions 2, 8, nd 9 we derived: i, [] (10) o, [] (11), [W]. (12) 7th Interntionl onference on Advnced oncepts in Mechnicl ngineering IOP onf. eries: Mterils cience nd ngineering 147 (2016) doi: / x/147/1/

6 7th Interntionl onference on Advnced oncepts in Mechnicl ngineering IOP onf. eries: Mterils cience nd ngineering 147 (2016) doi: / x/147/1/ Het pump eversibility he het pump eversibility (Irr) considered tht the isentropic efficiency of the compressor is 0.95, nd pressures drops in evportor nd condenser, on the suction nd dischrge nd liquid lines re of 0.1. Figure 6[5] present bsic eversible reverse cycle, consisting of processes: 1 2r eversible dibtic compression, 2r 3r eversible cooling, 3r 4r eversible dibtic process (expnsion or throttling), 4r 1 eversible heting. he internl eversibility is lso emphsized by the entropy vritions of the working fluid during the het exchnges with externl het reservoirs. Hence, the entropy vritions re: s s is the entropy vrition long the heting process 4r-1t (4-1) s s4 1 1t 4r s2r s3t s41 s s s s s41 1 s41 N (13) s 41 is the entropy vrition long the cooling process 2r-3t (2-3). 2t 1 2 s 2r s 3t 3r 4 1 s 2 3 s 4t 4r 1t s s Figure 6. cheme of n eversible reverse cycle, temperture entropy digrm. he eversible entropy internlly generted by flow with friction is stored in the entropy vrition during the cooling process, nd ccordingly we cn identify it in the first lw efficiency (OP): OP 23 W m 2r3t mq m s 2r3t mq 23 s m 23 4r1t mq s 41 2r3t mq 4r1t mq 2r3t mq 4r1t mq N N 1 Irr (14) Irr 1 where: mq is the men thermodynmic temperture during the heting nd cooling processes, nd nd re the condensing nd evporting ones in nd. 2r3t s int mq N 1 nd Irr N, Irr re the numbers of internl s 4r1t 41 mq eversibility relted to the chosen reference tempertures of processes 2r-3t nd 4r-1t. For n idel reverse cycle, both numbers of eversibility re equl to one, i.e. rnot. hus the 5

7 7th Interntionl onference on Advnced oncepts in Mechnicl ngineering IOP onf. eries: Mterils cience nd ngineering 147 (2016) doi: / x/147/1/ entropy blnce eqution becomes [6]: Irr Irr OP 1 OP nd, by using oolpck we get for R717 (mmoni): or simplified: OPR (15) 0, where 4 1 nd, 2 3 (16) OPR (17) OPR , (errors: +1.1%, 1.8%). (18) olving the entropy blnce eqution it is obtined the reference temperture (t). his issue llows to evlute i, o nd from equtions (14), (15) nd (16) Power blnce nd, first lw efficiency W (19) OP W. (20) 4. Numericl results his simultion ws developed for period of 6 months, round 180 dys. ffectiveness of het exchngers, condenser nd, evportor nd, soil het exchnger were ssumed to be ε = 0.75 = const., ε = 0.75 = const., nd ε = 0.95 = const. Initil soil temperture for this simultion is 10, i = Underground het exchnger is considered to be borehole50m depth nd rdius of 0.2m. Overll het trnsfer surfce for extrcting het by convection is A = 62.8m 2. olving the problem strts by using equtions from evportor temperture section, simulting different time steps. Results ccording to time for soil temperture ( ), mbient temperture ( ), output temperture from condenser ( o ), temperture inside condenser ( ), temperture input to evportor ( i ), temperture output from evportor ( o ) nd temperture inside evportor re presented in tble 1. he grph in figure 7 indictes the tempertures ccording to time dependences. ble 2 presents the het rte inside condenser, evportor nd the power of the het pump. Het energy rtes function of time, re presented in figure 8. heir dependences with mbient temperture/time show tht het rtes in condenser, evportor nd, the power hve their peks during the lowest mbient temperture. In figure 9 is shown the OP function of time. 6

8 7th Interntionl onference on Advnced oncepts in Mechnicl ngineering IOP onf. eries: Mterils cience nd ngineering 147 (2016) doi: / x/147/1/ ble 1. empertures in reltion to time. ime [h] [] [] o [] [] i [] o [] [] Figure 7. Opertionl tempertures(,, o,, i, o, )function of time. 7

9 7th Interntionl onference on Advnced oncepts in Mechnicl ngineering IOP onf. eries: Mterils cience nd ngineering 147 (2016) doi: / x/147/1/ ble 2. Het energy rtes functions of time. ime [h] [W] [W] W [W] OP Figure 8. Het rte in evportor, condenser nd power in time. 8

10 7th Interntionl onference on Advnced oncepts in Mechnicl ngineering IOP onf. eries: Mterils cience nd ngineering 147 (2016) doi: / x/147/1/ Figure 9. Het pump OP function of time 5. onclusions he pper dels with entropy blnce eqution in order to evlute the time dependent performnces of heting system, during the winter seson, involving geotherml het pump. he thermodynmic ssessment considered restrictive conditions describing imposed time bsed evolution of het pump externl het reservoirs. he entropy blnce eqution of the eversible het pump llowed complete linking of ll vrible in time prmeters, tempertures, energy trnsfer rtes nd OP. he mthemticl model of this ssessment might be pplied to other rel time bsed restrictive conditions. he geotherml het pump bsed heting systems seem to be very competitive to cogenertion bsed ones. hus, for this ssessment, the men vlue of the OP is round If we evlute the first lw efficiency relted to the fossil bsed het energy operting the engine delivering the power for the het pump, we obtin: FLHP, men OPmen * 5.46* 0.35 to to Here η is the first lw efficiency of the engine delivering the power to the het pump. Nomenclture temperture [] h convection het coefficient [W/(m 2 )] hetrte [W] W power consumed [W] A surfce [m 2 ] ε het exchnger efficiency [ - ] m mss flow [kg/h] het cpcity of het crrier [W/] s entropy [J/] Irr eversibility OP coefficient of performnce ubscripts: mbient evportor condenser o output i input N nominl hc het crrier soil H heted spce 6. References [1] Luo J, Rohn J, Byer M nd Priess A 2013 herml performnce nd economic evlution of double U-tube borehole het exchnger with three different borehole dimeters nergy nd Buildings 67 pp

11 7th Interntionl onference on Advnced oncepts in Mechnicl ngineering IOP onf. eries: Mterils cience nd ngineering 147 (2016) doi: / x/147/1/ [2] Lo Russo nd ivit M V 2009 Open-loop groundwter het pumps development for lrge buildings: A cse study Geothermics 38 pp [3] rbu I nd ebrchievici 2014 Generl review of ground-source het pump systems for heting nd cooling of buildings nergy nd Buildings 70 pp [4] Ouzzne M, slmi-nejd P, Aidoun Z nd Lmrche L 2014 Anlysis of the convective het exchnge effect on the undisturbed ground temperture olr nergy 108 pp [5] Dumitrscu G 2008 he wy to optimize the eversible cycles ermotehnic 2/2008 pp [6] Dumitrscu G nd Horbniuc B 2010 Optimizre exergoeconomic Politehnium 10

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