Transcritical CO 2 Heat Pump Simulation Model and Validation for Simultaneous Cooling and Heating

Transcription

1 World Academy of Scence, Engneerng and Technology Transcrtcal CO Heat Pump Smulaton Model and Valdaton for Smultaneous Coolng and Heatng Jahar Sarkar Abstract In the present study, a steady-state smulaton model has been developed to evaluate the system performance of a transcrtcal caon doxde heat pump system for smultaneous ater coolng and heatng. Both the evaporator (ncludng both to-phase and superheated zone) and gas cooler models consder the hghly varable heat transfer characterstcs of CO and pressure drop. The numercal smulaton model of transcrtcal CO heat pump has been valdated by test data obtaned from experments on the heat pump prototype. Comparson beteen the test results and the model predcton for system COP varaton th compressor dscharge pressure shos a modest agreement th a maxmum devaton of 5% and the trends are farly smlar. Comparson for other operatng parameters also shos farly smlar devaton beteen the test results and the model predcton. Fnally, the smulaton results are presented to study the effects of operatng parameters such as, temperature of heat exchanger flud at the nlet, dscharge pressure, compressor speed on system performance of CO heat pump, sutable n a dary plant here smultaneous coolng at 4 o C and heatng at 73 o C are requred. Results sho that good heat transfer propertes of CO for both to-phase and supercrtcal regon and effcent compresson process contute a lot for hgh system COPs. Keyords CO heat pump, dary system, experment, smulaton model, valdaton. I. INTRODUCTION O has reganed nterest lately due to ts eco-frendlness, C lo prce, non-flammablty, non-toxcty, compatblty th varous common materals, compactness, excellent transport propertes, etc. and several theoretcal and expermental studes have been done on transcrtcal CO systems thn last ffteen years partcularly n heat pump applcatons []. CO heat pumps offer extensve possbltes n smultaneous coolng and heatng applcatons due to the large temperature glde present n the gas cooler. Due to ts transcrtcal nature, the performance of caon doxde system ll not be exactly the same as the conventonal subcrtcal vapour compresson refrgeraton and heat pump systems. Hence, smulaton models developed for the conventonal systems cannot be employed for ths ne system. But, there s a need for theoretcal system smulaton studes as expermental performance evaluaton s dffcult, expensve and tme consumng. So, accurate computer smulaton of the system to predct ts steady state performance and effects of varous desgn and operatng parameters on the steady state performance ll be very useful, although emprcal nature of heat transfer and pressure drop correlatons needs valdaton. Recently, smulaton studes on ar-to-ater CO heat pumps ere done for comparson th tradtonal soluton [] and study the nfluence of ambent temperature [3]. Whte et al. [4] have developed smulaton model of CO heat pump for hgh temperature heatng ncorporatng the component performance parameter correlatons based on the test conducted on CO heat pump prototype. Km et al. [5] conducted performance test and smulaton studes on CO heat pump th nternal heat exchanger for ater heatng. Although, such studes on smultaneous ater coolng and heatng are scarce. Author th hs coorkers [6] prevously presented smulaton study on CO heat pump for smultaneous ater coolng and heatng and subsequently, Agraal and Bhattacharyya [7] have done smlar study usng capllary tube as an expanson devce. In the present study, the prevous smulaton model has been modfed by ncorporatng the superheated zone n the evaporator model and more recent heat transfer correlatons. Valdaton of the present smulaton model th author s on expermental data on transcrtcal CO heat pump prototype for smultaneous ater coolng and heatng s presented as ell. Fnally, effects of operatng parameters such as, ater nlet temperatures and compressor speed at optmum dscharge pressure on system performance are presented for dary applcatons; n such systems smultaneous coolng and heatng at 4 o C and 73 o C, respectvely, are requred. J. Sarkar s th the Department of Mechancal Engneerng, Insttute of Technology, B.H.U, Varanas-005, Inda (phone: ; fax: ; e-mal: jahar_s@hotmal.com). 49

2 World Academy of Scence, Engneerng and Technology II. SIMULATION MODEL The smulated caon doxde based heatng and coolng system conssts of compressor, expanson valve, evaporator and gas cooler. Water s taken as secondary flud for both gas cooler and evaporator to gve the useful coolng and heatng outputs. Both these heat exchangers are of double-ppe counter flo type, here the refrgerant flos through the nner tube and ater flos through the outer annular space. The correspondng temperature-entropy dagram th ater flo lnes s shon n Fg.. The entre system has been modeled based on energy balance of ndvdual components yeldng conservaton equatons presented belo. To consder the lengthse property varaton, all the heat exchangers have been dscretzed and momentum and energy conservaton equatons have been appled to each segment. The follong assumptons have been made n the analyss:. Heat transfer th the ambent s neglgble.. Only Sngle-phase heat transfer occurs for ater (external flud). 3. Compresson process s adabatc but not sentropc. 4. Pressure drop on atersde and n connectng ppes are neglgble. 5. Changes n knetc and potental energes are neglgble. 6. Refrgerant s free from ol. Fg. Temperature-entropy dagram of a transcrtcal caon doxde system m ref m gc T + T gc, P + + gcr gcr T, P Fg. A computatonal segment of gas cooler A. Compressor Model The refrgerant mass flo rate through the compressor s gven by, N mr = ρη vv () s 60 here, volumetrc effcency η v for the sem-hermetc compressor s estmated from [8]: P ds P ds ηv = () Psuc Psuc The sentropc effcency of the compressor s estmated by employng the follong correlaton for the sem-hermetc compressor [8]: P ds P ds ηs,c = P suc P suc (3) 3 4 P ds P ds P P suc B. Gas Cooler Model T, P ΔL Water flo (Annular sde) Q gc α k α r T gc T, P gcr As mentoned earler, the gas cooler s segmented lengthse to accommodate the property varaton. One of the computatonal segments of gas cooler of length Δ L s shon n Fg.. Employng LMTD expresson, heat transfer n th segment of the gas cooler s gven by, + + ( Tgcr Tgc ) ( Tgcr Tgc ) Qgc = ( UA) (4) gc Tgcr T gc ln + + Tgcr T gc Addtonally, energy balance n gas cooler for both the fluds yeld: Q = m ( h h ) = m c ( T T ) (5) suc + + gc ref gcr gcr gc p gc gc gcr d Refrgerant flo (Inner sde) d o D 50

3 World Academy of Scence, Engneerng and Technology The overall heat transfer coeffcent for the segment of gas cooler has been calculated usng the fundamental equaton for overall heat transfer coeffcent yeldng: ln ( do / d) = + + (6) UAgc αrar πδlk αa To estmate heat transfer rates, Gnelnsk [9] equaton s not sutable for normal tube (may be useful for mcro-channel) due to large varaton of flud propertes n the radal drecton. To allevate ths defcency, Ptla et al. [0] proposed a modfcaton for supercrtcal n-tube caon doxde coolng, ncorporatng both bulk and all propertes. Ths correlaton, used for gas cooler model, s gven by; Nu + Nu k Nur Nur = α r = k (7) k d Here, Nu and Nu are the Nusselt numbers at bulk and all temperature respectvely, predcted by Gnelnsk [9] 6 equaton thn the range 300 < Re < 0 and 0.6 < Pr < 5 0. ( f / 8)(Re 000) Pr Nu = (8) / / ( f / 8) (Pr ) here f s the frcton factor gven by: f = (0.79 ln(re).64) α s the atersde heat transfer coeffcent and has been evaluated by the conventonal Dttus-Boelter equaton for annular flo. All ater propertes are assumed to be temperature dependent only, and polynomal expressons based on text book values have been used. Neglectng nerta effect, the refrgerant-sde pressure drop n each hat exchanger segment s gven by [], + Ggcr ΔLgc Pgcr Pgcr = f. ρ + d (9) here modfed frcton factor f s gven by Petrov and Popov equaton [], f s (.8 ln(re ).64) ρ μ = ρ μ Qgcr here, the exponent s s gven by, s = G C. Evaporator Model gcr 0.4 (0) Employng the LMTD-concept, heat transfer n each segment of the evaporator s gven by, Q + + Tev Tevr Tev Tevr ev = ( UA) ev + + Tev T evr ln Tev T evr ( ) ( ) () Energy balance n the evaporator for the refrgerant ( CO ) and ater, respectvely, yelds: + + Qev = m ref ( hevr hevr ) = m evcp( Tev Tev ) () The overall heat transfer coeffcent for each segment of the evaporator has been calculated n the same ay as for the gas cooler. In ths analyss, the recently developed Yoon et al. [] correlaton has been employed to estmate the bolng heat transfer coeffcent. For superheated zone, Gnelnsk [9] equaton has been used to estmate convectve heat transfer coeffcent of caon doxde. The atersde heat transfer coeffcent has been evaluated by the conventonal Dttus- Boelter equaton for annular flo for both to-phase and superheated sectons. The refrgerant sde pressure drop, Δ P ev, r, s gven by (usng Lockhart and Martnell equaton): + ΔLev fr Gevr Pevr Pevr = 4 ( x) φl (3) d ρl 0.5 here, frcton factor f r = 0.079Re l and the to-phase frctonal pressure drop multpler s evaluated from: / 7.4 φl = X tt here X s the Lockhart-Martnell factor. tt It can be noted that the evaporator conssts of to zones: to-phase zone and superheated zone. Smlar to the gas cooler, both zones n the evaporator are dvded nto a fnte number of equal-length segments along the refrgerant flo drecton. Each segment s treated as one counter-flo heat exchanger and the outlet condtons of each segment should become nlet condtons for the next segment. For each segment LMTD method s used and propertes are evaluated based on mean temperature and pressure. D. Expanson Devce The expanson process s consdered to be senthalpc under the assumpton that the heat exchange th ts surroundngs s neglgble, yeldng: h = h (4) 4 3 E. Numercal Procedure A computer code, ncorporatng the subroutne COPROP [6] for thermophyscal and transport propertes, has been developed to smulate the transcrtcal caon doxde system for smultaneous ater coolng and heatng at varous operatng condtons. Water nlet temperatures and ater mass flo rates or outlet temperatures for both heat exchangers, compressor data, evaporator and gas cooler dmensons, compressor dscharge pressure and degree of superheat are the nput data for the smulaton. As mentoned earler, the property varatons are encompassed by both evaporator and gas cooler models. Usng dscretzaton, the heat exchanger s 5

4 World Academy of Scence, Engneerng and Technology made equvalent to a number of counter flo heat exchangers arranged n seres and the combned heat transfer of all the segments s the total heat transfer of the heat exchanger. Therefore, fast changng propertes of CO have been modeled accurately n both evaporator and gas cooler. The code solves the system equatons by sutable teratve method and tolerance has been mantaned n the range of 0 3. Pressure drop and heat loss n connectng lnes are not consdered; therefore, the outlet state of one component becomes the nlet state of the next component. By assumng sucton pressure, refrgerant mass flo rate, compressor outlet condtons, refrgerant condtons as ell as enthalpes (h 4 and h 3 ) at evaporator nlet and at gas cooler outlet are calculated based on mathematcal model presented above. The sucton pressure s adjusted by the teraton n order for the enthalpy of nlet and outlet expanson valves to converge thn a presced tolerance and performances such as coolng and heatng output, compressor ork and COP are calculated. By varyng the dscharge pressure, maxmum COP and correspondng optmum dscharge pressure can be calculated. III. MODEL VALIDATION The present numercal smulaton model of transcrtcal CO heat pump for smultaneous ater coolng and heatng applcatons has been valdated by test data obtaned from experments on the prototype. The expermental CO heat pump prototype conssts of Dorn compressor (dsplacement s. m rpm), evaporator, gas cooler, manually controlled needle valve, recever, accessores and nstrumentaton. Both the heat exchanger are tube-n-tube, coaxal, countarflo types, made of standard stanless steel, here refrgerant flos n nner tube and ater n annulus. For evaporator, outer dameters of nner and outer tubes are 9.5 mm and 6 mm, respectvely (thckness of mm for both tubes) and total length s 7. m. For gas cooler, outer dameters of nner and outer tubes are 6.35 mm (thckness s 0.8 mm) and mm (thckness s mm), respectvely and total length s 4 m. Separate ater crcuts are used for both evaporator and gas to mantan constant nlet temperatures. Prototype descrpton th nstrumentatons, testng, data reducton and error analyss, hch shos the uncertanty range of ± 6%, have already reported earler [3]. The expermental results clearly shoed that superheatng takes place n the evaporator rangng from 5- o C. Fg. 3 shos the comparson of model predcted and test data for system COP (combned heatng and coolng outputs per compressor ork), varaton th the compressor dscharge pressure, for ater mass flo rates of.5 kg/mn and kg/mn, and ater nlet temperatures of 30 and 30.5 o C n evaporator and gas cooler, respectvely and evaporator pressure of 40 bar. Comparson beteen the test results and the model predcton shos a modest agreement th a maxmum devaton of 5% and the trends are farly smlar. Comparson for other operatng parameters also shos farly smlar devaton beteen the test results and the model predcton. Hence, the present smulaton model can be used to predct the performance. System COP Dscharge pressure (bar) Expermental numercal Fg. 3 Valdaton of numercal results aganst expermental data IV. EFFECTS OF OPERATING PARAMETERS Effects of operatng parameters on the system performance beng studed for smultaneous ater heatng and coolng applcatons are evaluated on the bass of maxmum system COPs at optmum dscharge pressure. Gas cooler and evaporator dmensons, and compressor specfcatons, nput to the smulaton model, are same as for expermental prototype. It can be noted that as the ater outlet temperatures of evaporator and gas cooler are fxed at 4 o C and 73 o C, respectvely, ater mass flo rates are assumed to be adjustable parameters n smulaton, unlke to the expermental study. The degree of superheat s taken n the smulaton as 0 o C. The parameters vared are: compressor speed from 500 to 3500 rpm, ater nlet temperature from 0 o C to 40 o C for both evaporator and gas cooler. Unless othese specfed, the mean values of these parameters are: compressor speed of 900 rpm, ater nlet temperature of 30 o C. Fg. 4 Varaton of performance th compressor speed 5

5 World Academy of Scence, Engneerng and Technology The effect of compressor speed on system performance at ater nlet temperature of 30 o C for both evaporator and gas cooler s presented n Fg. 4. It s observed that the system COP at optmum dscharge pressure decreases as both compressor ork and coolng output ncrease th compressor speed due to an ncrease n mass flo rate of refrgerant th compressor speed. Hoever, the optmum dscharge pressure as found to reman almost constant varyng beteen 07 and 09 bar as the speed as modulated beteen 500 and 3500 rpm. The effect of ater nlet temperature (same ater nlet temperature for both evaporator and gas cooler) at a compressor speed of 900 rpm s shon n Fgs. 5 and 6. As the ater nlet temperature ncreases, the coolng COP decreases due to the combned effect shftng of cooler ext refrgerant temperature to hgher value that cause the degradaton of heat transfer propertes n gas cooler and decrease n to-phase regon range. Water nlet temperature has a neglgble effect on refrgerant mass flo rate as shon n Fg. 6. Hoever, the optmum dscharge pressure ncreases rapdly th ncrease n ater nlet temperature due to rapd change of refrgerant outlet temperature as rapd changes n heat transfer propertes n the gas cooler. (kw) Compressor ork Coolng output System COP Water nlet temperature ( o C) Fg. 5 Varaton of performance th ater nlet temperature System COP P ds,opt (bar) optmum pressure mass flo rate Water nlet temperature ( o C) Fg. 6 Varaton of optmum pressure and mass flo rate th ater nlet temperature V. CONCLUSION The steady state performance of a caon doxde based transcrtcal heat pump for smultaneous ater heatng and coolng s presented here. The smulaton model has been valdated th the expermental data. Results are obtaned by varyng mportant operatng parameters such as compressor speed and ater nlet temperature over a gven range. Comparson beteen the test results and the model predcton shos a modest agreement th a maxmum devaton of 5% and the trends are farly smlar. Comparson for other operatng parameters also shos farly smlar devaton beteen the test results and the model predcton. Effect of ater nlet temperature on the optmum dscharge pressure s very sgnfcant hereas effect of compressor speed s neglgble. Results sho that good heat transfer propertes of caon doxde for both to-phase and supercrtcal regon and effcent compresson process contute a lot for hgh system COPs. NOMENCLATURE A heat transfer area (m ) c p specfc heat capacty (J/kgK) d nner tube dameter (m) D outer tube dameter (m) G mass velocty (kg/m s) h specfc enthalpy (kj/kg) k thermal conductvty (W/mK) k all thermal conductvty (W/mK) m mass flo rate (kg/s) N compressor speed (rpm) Nu Nusselt number (-) P pressure (bar) Pr Prandtl number (-) Q heat transfer rate (W) Re Reynolds number (-) T, t temperatures (K, o C) U overall heat transfer coeffcent (W/m K) Refrgerant mass flo rate (kg/s) 53

6 World Academy of Scence, Engneerng and Technology V s sept volume of compressor (m 3 ) x qualty of saturated caon doxde lqud vapor mxture α heat transfer coeffcent (W/m K) L segment length (m) f frcton factor (-) µ vscosty (kg/ms) ρ densty (kg/m 3 ) Subscrpts -4 stateponts b bulk ds compressor dscharge ev evaporator evr refrgerant n evaporator ev evaporator ater gc gas cooler gcr gas cooler refrgerant nner o outer l lqud opt optmum r refrgerant suc sucton all, ater ater nlet supercrtcal CO, Int. Journal of Refrgeraton, vol. 5, pp , 00. [] X. Fang, C. W. Bullard and P. S. Hrnjak, Heat transfer and pressure drop of gas coolers, ASHRAE Transactons, vol. 07, pp , 00. [] S. H. Yoon, E. S. Cho, Y. W. Hang, M. S. Km, K Mn and Y. Km, Characterstcs of evaporatve heat transfer and pressure drop of caon doxde and correlaton development, Int. Journal of Refrgeraton, vol. 7, pp. -9, 004. [3] J. Sarkar, S. Bhattacharyya and M. Ramgopal, Transcrtcal CO heat pump prototype development for smultaneous ater coolng and heatng, Internatonal Congress of Refrgeraton, Bejng, 007. Jahar Sarkar receved hs M. Tech. and Ph.D. degrees n Mechancal Engneerng from Indan Insttute of Technology Kharagpur, Inda n 00 and 006, respectvely. After, he joned the faculty of Insttute of Technology, Banaras Hndu Unversty, Inda and orkng as a Lecturer n Mechancal Engneerng Department tll date. Author has publshed 4 research papers n nternatonal journal and n natonal and nternatonal conferences n several areas of Heat Transfer and Refrgeraton. Superscrpt segmental step REFERENCES [] P. Neksa, CO heat pump systems, Int. Journal of Refrgeraton, vol. 5, pp. 4-47, 00. [] L. Cecchnato, M. Corrad, E. Fornaser and L. Zambon, Caon doxde as refrgerant for tap ater heat pumps: A comparson th the tradtonal soluton, Int. Journal of Refrgeraton, vol. 8, pp , 005. [3] R. Yokoyama, T. Shmzu, K. Ito and K. Takemura, Influence of ambent temperatures on performance of a CO heat pump ater heatng system, Energy, vol. 3, pp , 007. [4] S. D Whte, M. G. Yarrall, D. J. Cleland and R. A. Hedley, Modellng the performance of a transcrtcal CO heat pump for hgh temperature heatng, Int. Journal of Refrgeraton, vol. 5, pp , 00. [5] S. G. Km, Y. J. Km, G. Lee and M. S. Km, The performance of a transcrtcal CO cycle th an nternal heat exchanger for hot ater heatng, Int. Journal of Refrgeraton, vol. 8, pp , 005. [6] J. Sarkar, S. Bhattacharyya and M. Ramgopal, Smulaton of a transcrtcal CO heat pump cycle for smultaneous coolng and heatng applcatons, Int. Journal of Refrgeraton, vol. 9, pp , 006. [7] N. Agraal and S. Bhattacharyya, Optmzed transcrtcal CO heat pumps: Performance comparson of capllary tubes aganst expanson valves, Int. Journal of Refrgeraton, vol. 3, pp , 008. [8] T. M. Ortz, D. L and E. A. Groll, Evaluaton of the performance potental of CO as a refrgerant n ar-to-ar ar condtoners and heat pumps: system modellng and analyss, ARTI fnal report, no. CR/ , 003. [9] V. Gnelnsk, Ne equatons for heat and mass transfer n tuulent ppe and channel flo, Internatonal Chemcal Engneerng, vol. 6, pp , 976. [0] S. S. Ptla, E. A. Groll and S. Ramadhyan, Ne correlaton to predct the heat transfer coeffcent durng n-tube coolng of tuulent 54