ScienceDirect. Influence of outdoor air conditions on the air source heat pumps performance. Pamela Vocale a, *, Gian Luca Morini b, Marco Spiga a

Transcription

1 Avalable onlne at ScenceDrect Energy Proceda 45 ( 214 ) th Conference of the Italan Thermal Machnes Engneerng Assocaton, ATI213 Influence of outdoor ar condtons on the ar source heat pumps performance Pamela Vocale a, *, Gan Luca Morn b, Marco Spga a a Department of Industral Engneerng, Unversty of Parma, Parco Area delle Scenze 181/A, Parma, Italy b DIN, Alma Mater Studorum Unverstà d Bologna, Vale Rsorgmento 2, 4136 Bologna, Italy Abstract The purpose of the present work s the nvestgaton of the effect of the outdoor ar temperature and relatve humdty on the performance of an ar heat pump, when the reverse-cycle defrostng s consdered. The frost formaton process has been analyzed by developng a smplfed model whch relates the number of defrost cycles to the outdoor ar condtons. Moreover the energy consumpton due to the defrostng has been taken nto account n the evaluaton of the heat pump performance. The results, carred out for many Italan stes, pont out that the outdoor ar condtons play an mportant role n determnng the amount of defrost cycles; however the frost formaton s manly affected by the relatve humdty. The analyss hghlghts also that the defrostng contrbuton on the heat pump performance s not neglgble when the heat pump that operates n wet weather, although cold; n these condtons the hourly COP may be reduced by up to 2%. However, ths effect becomes less relevant, but not neglgble, when the seasonal heat pump performance s evaluated; the maxmum decrease of SCOP, observed for the all analyzed cases, s less than 13%. 213 The Authors. Publshed by Elsever Ltd. 213 The Authors. Publshed by Elsever Ltd. Open access under CC BY-NC-ND lcense. Selecton and peer-revew under responsblty of ATI NAZIONALE. Selecton and peer-revew under responsblty of ATI NAZIONALE Keywords: Ar source heat pumps; defrostng effect; defrostng cycles; SCOP. 1. Introducton The reducton of buldngs energy consumpton and the use of the renewable energes are necessary measures for decreasng the European greenhouse gas emssons, as ndcated n the last EPBD (.e. Drectve 21/31/EU). In * Correspondng author. Tel.: ; fax: E-mal address: pamela.vocale@unpr.t The Authors. Publshed by Elsever Ltd. Open access under CC BY-NC-ND lcense. Selecton and peer-revew under responsblty of ATI NAZIONALE do: 1.116/j.egypro

2 654 Pamela Vocale et al. / Energy Proceda 45 ( 214 ) order to mprove the effcency of the buldng heatng and coolng systems, dfferent solutons can be adopted. The use of the heat pumps represent certanly an mportant measure to acheve energy savng. Heat pump performance s sgnfcantly affected by the operatng condtons, such as the features of the heat sources, the heatng demand and the heat pump control system. Snce the outdoor ar temperature s extremely varable over the heatng perod the Coeffcent Of Performance (COP) of the ar heat pumps cannot be evaluated by consderng the steady state monthly values of the outdoor ar temperature but by usng the so-called bn method, based on an evaluaton of the cumulatve frequency of the outdoor ar temperature n a fxed localty. However the energy performance of ar heat pumps s affected not only by the outdoor ar temperature, but by the ar humdty as well. When the ar mosture content s hgh and temperature s lower than 6 C, frost formaton on the surface of the arsde heat exchanger may occur and consequently the heat pump performance can be reduced or even the system may stop. The frost formaton s a complex process. In lterature several works whch nvestgate the mechansm of frost formaton n heat exchangers characterzed by smple geometry (.e. cylnders, flat plates and parallel plates), have been presented [1 1]. Moreover the frost formaton process n heat exchangers characterzed by more complex geometres, has been nvestgated by many authors [11-21]. However they analyze specfc geometres, therefore t becomes dffcult to use these results for general purpose nvestgaton. The frost needs to be removed perodcally to mprove the effcency of operaton. Ths can be carred out n dfferent ways: by resortng to the electrc resstance or by nvertng the cycle or by stoppng the compressor or by usng hot gas. When the heat pump can operate n reversble mode the defrost s generally obtaned by nvertng the cycle. The energy consumpton due to the defrost cycles has to be consdered n calculatng the heat pump performance but the calculaton methods proposed by the European standards gnore ths effect. The present paper ntends to numercally nvestgate the effect of the outdoor ar temperature and relatve humdty on the frost producton and the mpact of defrostng on the performance of an ar heat pump (COP and Seasonal COP), n the case of reverse-cycle defrostng. For the purpose of ths study the amount of defrost cycles per season has been evaluated by usng a smplfed model whch enables to estmate the needed defrost cycles dependng on the outdoor ar condtons. The numercal smulatons have been carred out by consderng many Italans towns. Nomenclature c p Specfc heat at constant pressure (kj kg -1 K -1 ) COP Coeffcent of Performance E Energy (kj) h Specfc enthalpy (kj kg -1 a ) m Dry ar mass flow rate (kg s -1 ) p Pressure (Pa) P Buldng heatng demand (kw) Q Heat flow rate, thermal power (kw) RH Relatve humdty SCOP Seasonal Coeffcent of Performance t Temperature ( C) x Mosture content (kg v kg -1 a ) W Electrc power (kw) z Number of bn hours Greek symbols Performance reducton coeffcent Heat of fuson (kj kg -1 ) Tme nterval (s) Subscrpt a Ar adj Adjusted

3 Pamela Vocale et al. / Energy Proceda 45 ( 214 ) c elbu ev dp fr n out sat sb th w Coolng Electrc backup heater Evaporaton Dew pont Frost Inlet Outlet Saturaton Stand-by Thermal Wall 2. Problem statement 2.1. Frost producton In order to explan the frost formaton process, let us start from the analyss of the heat transfer n the external col. If one consders a specfc -th bn ar temperature, the rate of heat captured from the cold heat source (outdoor ar) by means of the external evaporator can be estmated by applyng the energy conservaton prncple to the heat pump: Q 1 1 Q ev, th, COP (1) where Qth, s thermal output and COP denotes the Coeffcent of Performance of the heat pump. For any bn ar temperature, the value of the rate of energy transferred to the buldng and of COP s known by usng the manufacturer data. The specfc enthalpy of the ar at the outlet secton of the evaporator can be estmated by the balance equaton: h Q ev, out, hn, (2) ma beng ma the dry ar mass flow rate through the external sde of the evaporator (ths value can be evaluated by the manufacturer data) and h n, the specfc enthalpy of the ar at the nlet of the external col whch can be calculated as a functon of the ar temperature (t) and of the mosture content (x) by solvng the classcal equatons descrbng the physcal propertes of most ar (ASHRAE [22]): h1, 6tx t RH psat (t) x.622 ptot RH psat (t) (3) where p tot s the total pressure of the most ar whch depends on the alttude, p sat s saturaton pressure and RH denotes the ar relatve humdty. For each -th bn the value of the outdoor ar enthalpy (h n. ) s known f the values of the outdoor temperature and of the relatve humdty are known. In ths way, by usng equaton (3) and equaton (2) the value of the ar enthalpy at the ext of the evaporator can be calculated as a functon of the -th bn temperature and of the outdoor ar relatve humdty. The value of the ar

4 656 Pamela Vocale et al. / Energy Proceda 45 ( 214 ) enthalpy obtaned by equaton (2) has to be compared wth the dew pont value (h dp, ) whch can be obtaned by equaton (3) usng the value of the mosture content of the outdoor ar (x n, ) and the value RH=1: hout, hdp, xout, xn, ( no frost producton) hout, hdp, xout, xn, ( frost producton) (4) If h out, <h dp, the value of the mosture content of the outdoor ar at the ext of the evaporator (x out, ) s estmated by solvng the system of equaton (3), wth RH=1 and h=h out,. Once the decrease of the water vapor content n the ar through the evaporator s known, the frost accumulaton rate on the cold surface of the external col can be calculated by: fr, a n, out, m m x x (5) However the choce of the RH value of the outsde ar for any bn s not a smple task because there s not a unvocal lnk between the RH values and the ar temperature Defrostng cycles Expermental results showed that f the outdoor col temperature s above -3 C there s practcally no frost accumulaton on the outdoor col when the ambent temperature s n the range of to 6 C, whch s the range at whch frost s most lkely to accumulate [18]. When the ambent temperature s outsde the range of -6 C the defrostng cycles are generally not necessary because above 6 C the col temperature wll be warm enough to prevent frost formaton on the evaporator, and below C the mosture content of the ar wll be too low for a heavy frost accumulaton on the col. When the frost s bult up on the external surface of the evaporator the refrgerant pressure durng the evaporaton process tends to decrease and ths accelerates the frost formaton because the surface temperature of the heat exchanger decreases. In order to avod ths effect, when the surface temperature of the external col (or the refrgerant pressure) becomes lower than a setup value, the heat pump actvates a defrost cycle. If the heat pump s reversble the most used defrostng method s the nverson of the thermodynamc cycle; ths acton temporarly warms up the outdoor col and melts the frost from the col. In ths defrost cycle, the outdoor fan s prevented from turnng on when the heat pump swtches over, and the temperature rse of the outdoor col s accelerated and ncreased. A heat pump unt wll defrost regularly when frost condtons occur. The defrost cycle should be long enough to melt the frost, and short enough to be energy-effcent. The energy requred to melt the frost produced durng one hour s: fr, fr, fr p, fr w, E m c t (6) beng fr and c p,fr the heat of fuson and the specfc heat at constant pressure of the frost respectvely. ndcates the seconds n one bn (1 hour) and t w, denotes the wall temperature whch depends on the outdoor ar temperature, external col features, refrgerant temperature and heat transfer coeffcents. Once the energy requred to remove the frost s known, the mnmum defrostng tme can be evaluated by consderng the rato of the energy requred to melt the frost to the coolng capacty of the heat pump: E fr, fr,mn, (7) Qc, In general, fr,mn s lower than 1 hour and, dependng on the ambent temperature and humdty condtons, t can vary from 1 s up to 2-5 mnutes. Actually the defrostng cycle duraton s longer than fr,mn. Typcal

5 Pamela Vocale et al. / Energy Proceda 45 ( 214 ) defrostng cycles are represented n Fgure 1; before actvatng the nverson, the heat pump s swtched off for a perod equal to sb (.e. 1 mnute). Fg. 1. Typcal defrostng cycles and stand-by perods for an ar heat pump (N=2). Durng the stand-by perod the defrost relays turn on the compressor, swtch the reversng valve of the heat pump, turn on the nteror electrc heatng element, and stop the fan at the outdoor col from spnnng and fnally the heat pump operates followng the coolng cycle. The unt remans n the defrost cycle (or coolng cycle) untl the thermostat on the bottom of the outdoor col senses that the outdoor col temperature has reached the desred value (typcally about 1-12 C). At ths temperature, the outdoor col should be free of frost. A typcal defrost cycle mght run from 3 seconds to a few mnutes ( fr ) and t s generally fxed by the heat pump manufacturer. After that perod, the frost thermostat opens the crcut then the defrost cycle stops, the nternal heater turns off, the valve reverses, and the unt returns to the heatng cycle after a stand-by perod equal to ' sb. (.e. 3 seconds). The defrost cycles are repeated regularly at tmed ntervals durng an hour. Therefore the duraton of the whole defrostng perod for each hour can be evaluated by: fr, tot N sb fr ' sb (8) where the needed number of defrostng cycles per hour N can be estmated as follows: N max fr,mn, fr (9) Generally N=1 can be suffcent f the tmer of the sngle defrostng cycle fr s set as equal to the maxmum value of fr,mn durng the wnter season; n ths case, the defrostng cycle wll be actvated each 6 mnutes Heat pump performance When the frost s removed by nvertng the cycle, the defrost cycles effect on heat pump performance s twofold: the energy suppled to the buldng decreases and the buldng heatng demand ncreases due to the energy carred off by the heat pump n the coolng mode. At the same tme, the electrcal consumpton ncreases due to the energy spent to melt the frost and to feed the electrc-resstance heater equpped wth the heat pump whch allows to match the requred heatng demand. The hourly overall electrcal consumpton can be computed wth: Wadj, W fr, tot Wc, fr Welbu fr 1 W ( sb ' sb) (1)

6 658 Pamela Vocale et al. / Energy Proceda 45 ( 214 ) where W and W denote the electrc power suppled to the heat pump when t operates n heatng and n coolng c mode, respectvely and W s the requred capacty of the nternal electrc backup heater whch operates durng the elbu nverson of the cycle. The last term on the rght sde of equaton (1) takes nto account, by means of the coeffcent, the heat pump performance reducton due to the ntermttent operaton. By consderng the thermal energy transferred to the heat dstrbuton flud and the overall electrcal consumpton for each -th bn temperature of the heatng season (n s the number of bns havng a number of hours larger than ) the seasonal performance of the heat pump can be calculated: SCOP n 1 n 1 zq th, zw adj, (11) 3. Results The model defned above was appled to 6 northern Italan towns and 4 central and southern Italan stes, characterzed by dfferent weather condtons. To calculate the bn dstrbuton for each localty durng the whole heatng season, the procedure descrbed by the UNI TS 113/4 Italan standard was followed. The frost accumulaton rate was estmated by assumng a monthly average value of the outdoor ar relatve humdty (RH) derved from the UNI 1349 Italan standard. The heat pump model chosen for the study (Gallett MCA 1H) s an ar-to-water electrcally-drven heat pump whch can reach the thermal output of kw and the water output temperature can range from 3 C to 5 C. The unt s equpped wth two fans of axal type whch move ar at a volumetrc flow rate of 558 m 3 /h. The compressor s of varable speed operaton: the thermal output of the heat pump can range from 25% to 1% of the maxmum heat power, to match the buldng heatng demand. The heat pump performance for each bn temperature was evaluated accordng to the UNI TS 113/4 Italan standard; the trend of thermal output s shown n Fgure 2. The results here presented were carred out consderng a buldng whose the overall heat transfer coeffcent (transmsson + ventlaton) s equal to W/K. For the consdered buldng the heatng demand (P) becomes zero when the outdoor ar temperature s equal to 16 C, accountng for the effects due to the nternal and solar heat gans, as shown n Fgure 2. The bvalent temperature (.e. the outdoor temperature pont at whch the heat pump s declared to have a heatng capacty able to meet 1% of the buldng heatng demand) was 2 C, as shown n Fgure 2 and the cut-off temperature of the ASHP was fxed at -5 C. P [kw] HP Thermal output Heatng demand Bvalent temperature Q th,max [kw] t e [ C] Fg. 2. Thermal output of the heat pump and buldng heatng demand as a functon of the external ar temperature.

7 Pamela Vocale et al. / Energy Proceda 45 ( 214 ) For the consdered heat pump the stand-by perod ( sb + sb ) s set to 2 mnutes and the performance reducton due to the ntermttent operaton () s equal to 2%. For sake of brevty, only the most nterestng cases are presented. In Fgure 3 the monthly average values of COP for two Italan Northern stes, namely Bologna and Bolzano, s presented. The maxmum and mnmum reducton observed for Bologna was equal to 16.47% and 5.36%, respectvely; the monthly COP reducton ranges between 3.41% and.19% f the heat pump operates n Bolzano (Fgure 3b). The dfference among the values obtaned for Bologna and Bolzano hghlghts that the heat pump performance s more affected by the ar relatve humdty than the ar temperature; the RH value ranges from 67% to 9% and from 54% to 74% for Bologna and Bolzano, respectvely. On the contrary, Bologna s generally less cold than Bolzano (.e. the mnmum value of the outdoor ar temperature s equal to -4 C and -14 C, respectvely). a Wthout defrost Wth defrost b Wthout defrost Wth defrost 2 2 COP ave,month COP ave,month Nov Dec Jan Feb Mar Nov Dec Jan Feb Mar Month Month Fg. 3. Monthly average value of the COP: a) Bologna; b) Bolzano. The needed number of defrostng cycles for the whole heatng season are depcted n Fgure 4, for the most nterestng localtes. The analyss ponts out that the number of defrostng cycles vares strongly by movng from Northern to Southern towns, rangng from to 14 cycles per season. Ths effect s due to the amount of hours durng the wnter season n whch the outdoor temperature ranges between C and 5 C (z -5 ) and to the RH value. Table 1 shows the values of z -5 and the mnmum and maxmum RH value for the localtes consdered n Fgures 4 and 5. Table 1. Weather data of the selected stes. Town z -5 (h) RH (%) Bologna Bolzano Mlan Turn Vence Verona Florence Rome Bar Naples

8 66 Pamela Vocale et al. / Energy Proceda 45 ( 214 ) Defrost cycles Bologna Bolzano Mlan Turn Vence Verona Florence Rome Bar Naples Localty Fg. 4. Number of defrostng cycles per heatng season. The data shown n Fgure 4 confrm that towns characterzed by larger values of the relatve humdty need more defrostng cycles. Fgure 5 shows the comparson between the SCOP evaluated by takng nto account the defrostng effect and the theoretcal value of the SCOP obtaned by gnorng the defrost of the external col. The Seasonal COP reducton ranges between 1.51% (Bolzano) and 12.67% (Bologna). By observng Fgure 5 t can be notced that n many cases n Italy, f the defrostng effect s gnored, as suggested by the calculaton methods proposed by the European standard (EN 14825), the real energy consumpton of the ASHP can be underestmated and hence the value of the SCOP overestmated. As dscussed above, ths effect becomes less relevant when the heat pumps operate n stes characterzed by low values of the ar relatve humdty (RH<8%) and by outdoor ar temperature that s out of the range -5 C for many hours. For the other localtes, t can be recommended to account for the defrostng effect n order to properly evaluate the energy consumpton of the ar heat pump Wthout defrost Wth defrost 2 SCOP Bologna Bolzano Mlan Turn Vence Verona Florence Rome Bar Naples Localty Fg. 5. Defrostng nfluence on the seasonal heat pump performance (SCOP).

9 Pamela Vocale et al. / Energy Proceda 45 ( 214 ) Snce the RH value plays a leadng role n determnng the frost formaton, further numercal smulatons, by usng the hourly weather data provded by Meteonorm database [23], were performed. More specfcally three dfferent cases were analyzed: n the case 1, a monthly average value of the outdoor ar RH was assumed for each ar bn temperature of the month; n the case 2, a bn average value of the outdoor ar RH was used for each bn of the month and n the case 3 the hourly data of RH were consdered (.e. hourly smulaton). The results of ths further analyss pont out that the effect of defrost can be overestmated f a monthly average value of RH s assumed; on the contrary by consderng a bn average value of the RH the reducton of the heat pump performance may be underestmated. Obvously the hourly smulaton (case 3) consttute the reference case, snce hourly data for both temperature and RH of the outdoor ar, were consdered. a b Fg. 6. Influence of RH value on the monthly average value of the COP: a) Bologna; b) Bolzano. Fgure 6 shows the comparson between the monthly average values of COP calculated by consderng the above mentoned cases. The results depcted n Fgure 6 were obtaned by consderng the weather data of Bologna and Bolzano, respectvely. The same trend can be observed for other towns. The maxmum COP ave,month reducton s about 17% (case 1), 4% (case 2) and 6% (case 3), for Bologna; f the heat pump operates n Bolzano, ts performance can be reduced by about 9%, 1% and 4%. However by consderng the whole heatng season the seasonal performance of the heat pump (SCOP) can be reduced by about 11% (case 1), 2% (case 2) and 5% (case 3), for Bologna; the SCOP reducton can be less than 6%, 1% and 2%, respectvely, f the heat pump operates n Bolzano. These results confrm that the choce of the RH value s very crucal n order to properly evaluate the frost accumulaton rate on the cold surface of the external col and consequently the effect of the defrost on the heat pump performance. 4. Conclusons The nfluence of the outdoor ar temperature and relatve humdty on the energy performance of the ar source heat pumps has been numercally nvestgated. Many Italan stes characterzed by dfferent weather data have been analyzed; temperature and relatve humdty values wthn the range -5 C - 5 C and 5% - 9%, respectvely, have been consdered. For the purpose of the here presented study the frost formaton process has been analyzed by developng a smplfed model whch enables to correlate the frost producton and the external ar condtons.

10 662 Pamela Vocale et al. / Energy Proceda 45 ( 214 ) The numercal analyss ponts out that both temperature and relatve humdty of the outdoor ar affects the frost formaton process; however the relatve humdty plays a leadng role n determnng the amount of frost that can be accumulated. The effect of defrostng process has been also nvestgated, when the defrost s obtaned by nvertng the cycle of the refrgerant. The numercal results hghlght that the monthly average of the COP can be reduced by up to 17% when the heat pump operates n stes n whch the values of ar relatve humdty are very hgh (RH>8%) and the outdoor ar temperature s wthn the range -6 C durng the wnter for many hours. Therefore n these localtes the role of the defrostng cannot be gnored for an accurate evaluaton of the real energy consumpton of an ar source heat pump. By consderng the whole heatng season the SCOP reducton may range between 1.51% and 12.67%, for the consdered localtes. Fnally, further nvestgatons on the role of the ar relatve humdty n the frost formaton process have been performed, by usng hourly data derved from the Meteonorm database. Ths latter analyss hghlghts that dependng on the chosen value of the RH for each ar bn temperature, the heat pump performance can be overestmated or underestmated. Moreover the hourly smulaton ponts out that the COP can be reduced by about 2% n wet stes. References [1] Jones B W, Parker J D. Frost Formaton wth Varyng Envronmental Parameters. J. Heat Transfer 1975;97: [2] Schneder H W. Equaton of the growth rate of frost formng on cooled surfaces. Int. J. Heat and Mass Transfer 1978; 21: [3] Tao Y X, Besant R W, Rezkallah K S. A mathematcal model for predctng the densfcaton and growth of frost on a flat plate. Int. J. Heat and Mass Transfer 1993; 36: [4] Lee K S, Km W-S, Lee T-H. A one-dmensonal model for frost formaton on a cold flat surface. Int. J. Heat and Mass Transfer 1997; 4: [5] Lee Y B, Ro S T. An expermental study of frost formaton on a horzontal cylnder under cross flow. Int. J. Refrgeraton 21; 24: [6] Yun R, Km Y, Mn M-K. Modelng of frost growth and frost propertes wth arflow over a flat plate. Int. J. Refrgeraton 22; 25: [7] Seker D, Karatas H, Egrcan N. Frost formaton on fn- and- tube heat exchangers. Part II Expermental nvestgaton of frost formaton on fn- and- tube heat exchangers. Int. J. Refrgeraton 24; 27: [8] Kandula M. Frost growth and densfcaton n lamnar flow over flat surfaces. Int. J. Heat and Mass Transfer 211; 54: [9] Hermes C J L. An analytcal soluton to the problem of frost growth and densfcaton on flat surfaces. Int. J. Heat and Mass Transfer 212; 55: [1] Wang W, Guo Q C, Lu W P, Feng Y C, Na W. A generalzed smple model for predctng frost growth on cold flat plate. Int. J. Refrgeraton 212; 35: [11] Kondepud S N, O Neal D L. Frostng performance of tube fn heat exchangers wth wavy and corrugated fns. Expermental Thermal and Flud Scence 1991; 4: [12] Kondepud S N, O Neal D L. Performance of fnned-tube heat exchangers under frostng condtons: I. Smulaton model. Int. J. Refrgeraton 1993; 16: [13] Yan W-M, L H-Y, Wu Y-J, L J-Y, Chang W-R. Performance of fnned tube heat exchangers operatng under frostng condtons. Int. J. Heat and Mass Transfer 23; 46: [14] Xa Y, Zhong Y, Hrnjak P S, Jacob A M. Frost, defrost, and refrost and ts mpact on the ar-sde thermal-hydraulc performance of louvered-fn, flat-tube heat exchangers. Int. J. Refrgeraton 26; 29: [15] Da Slva D L, Hermes C J L, Melo C. Expermental study of frost accumulaton on fan-suppled tube-fn evaporators. Appled Thermal Engneerng 211; 31: [16] Yao Y, Jang Y, Deng S, Ma Z. A study on the performance of the arsde heat exchanger under frostng n an ar source heat pump water heater/chller unt. Int. J. Heat and Mass Transfer 24; 47: [17] Hewtt N, Huang M J. Defrost cycle performance for a crcular shape evaporator ar source heat pump. Int. J. Refrgeraton 28; 31: [18] Guo X-M, Chen Y-G, Wang W-H, Chen C-Z. Expermental study on frost growth and dynamc performance of ar source heat pump system. Appled Thermal Engneerng 28; 28: [19] Jenkns D, Tucker R, Ahadz M, Rawlngs R. The performance of ar-source heat pumps n current and future offces. Energy and Buldngs 29; 4: [2] Chen Y-g, Guo X-m. Dynamc defrostng characterstcs of ar source heat pump and effects of outdoor ar parameters on defrost cycle performance. Appled Thermal Engneerng 29; 29: [21] Gong G, Tang J, Lv D, Wang H. Research on frost formaton n ar source heat pump at cold-most condtons n central-south Chna. Appled Energy 213; 12: [22] Amercan Socety of Heatng, Refrgeratng and Ar-Condtonng Engneers 21 ASHRAE Handbook of Fundamentals Atlanta. [23] METEONORM-Global Meteorologcal Database for Solar Energy and Appled Clmatology, Verson 5, (