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Purdue University Purdue e-Pubs International Refrigeration and Air Conditioning Conference School of Mechanical Engineering 1990 Estimation of Thermodynamic Properties of Nonazeotropic Refrigerant Mixtures and Application to the Heat Pump System S. T. Ro Seoul National University M. S. Kim Seoul National University T. S. Kim Seoul National University K. S. Cho Seoul National University Follow this and additional works at: http://docs.lib.purdue.edu/iracc Ro, S. T.; Kim, M. S.; Kim, T. S.; and Cho, K. S., "Estimation of Thermodynamic Properties of Non-azeotropic Refrigerant Mixtures and Application to the Heat Pump System" (1990). International Refrigeration and Air Conditioning Conference. Paper 125. http://docs.lib.purdue.edu/iracc/125 This document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact epubs@purdue.edu for additional information. Complete proceedings may be acquired in print and on CD-ROM directly from the Ray W. Herrick Laboratories at https://engineering.purdue.edu/ Herrick/Events/orderlit.html NON·AZ EOTROP IC REFRIG ERANT ESTIMA TION OF THERM ODYNA MIC PROPER TIES OF SYSTEM MIXTUR ES AND APPLIC ATION TO THE HEAT PUMP Cho Sung Tack Ro, Min Soo Kim, Tong Seop Kim aod Kwao Sbik y Departm ent of Meehanical Engineering, Seoul National Universit Seoul, 151-742, KOREA ABSTRA CT non-azeotropic refrigerant mixtures using Thermod ynamic propenie s are estimated fot the selected binmy Calculations have been made for eight different the Peng-Robinson equation of state and mixing rules. l14, Rl3Bl/R l52a, Rl3Bl/R l2, R22/R1S2a mixtures including Rl3B11R ll4, R221Rll 4, Rl21Rll 4, Rl52a/R and R22/Rl4 2b. mixtures have been chosen to calculate In this Study, the binary interaction coefficients of the vapor-liquid equilibria. A con-elation is proposed thermodynamic properties, such as enthalpy, entropy and the between dipole moments of each pure refrigerant. to relate the binary interactio n coefficient with difference ntal data and they give reasonably good experime existing til= with The calc~tlated val~tes are compared prepared fot a panie~~Jar composition of are diagrams y re-entrop temperam agreements. Pressure-enthalpy and each refrigerant mixmre. to simulate the perfotma nce of a heat p11mp The simple method of property calculation makes it possible 2a, R22/Rl4 2b, and Rl3Bl/R l52a as R22/R15 4, R221Rll including mixtures nt using non-azeotropic refrigera working fluids. can be obtained by varying the mixt~tre The sim~tlated results show that the capacity modulati on ot. The variation of the coefficient of compress type ent displacem a with p11mp composition in a heat · system. mixt~tre tropic non-azeo a in performance is also stlldied NOMEN CLATUR E c~,: ~~ " coefficients conStant pteSSUre specific heat at ideal gas state f~tgacity enthalpy : kij : binary interactio n coefficient p : pressure heat transferr ed Q gas constant R entropy s temperat ure T specific volume IV: compression work mole fraction of the liq~tid phase X mole fraction of the vapor phase ." compressibility factor z Greek leners a. : coefficient related to the eq~tation of state "" : dipole moment Subscript b c ~ H j L o w brine critical value, condense r evaporat ot high temperat~tre side inlet, i compone nt j compone nt low temperat~tre side standard state, o~ttlet water 1. INTROD UCTION working fluids for simulation and effiCient It is importan t to estimate the thermody namic properties of proper working fluid muSt be chOsen for The p~tmps. beat and ors refrigerat as operation of thermal systems such s of those working fluids should be propertie ynamic -thermod the and system the best performa nce of the correctly evaluated. th= higher perfottnance of heat pumps The research and development have been progressed to achieve ropic: mixtures. The purpose of non-azem including flltids wotking of mixtures the utilizing and refrigerators by refrigerant mixtures to simulate the tropic non·azeo binary of s propertie namic thermody this study is to estimate perfonna nce of the systems. may ~. ~assified into performance The main advantages of non-azeorropic refrigerant mixt11~ by ~III_'Zillg t~ ~ean temperatll~e achieved can~ former The ]. control[2 capacity enhancem ent[l] and the charactenstlcs of ghdmg temperat ure 10 the by s1nk ot somce heat the and fluid working the difference betwo=en 404 the non-azeotropic mixtures< The latter profit of non-aze otropic refrigerants is obtained by changing the mixture rauo during the operation. In this study, the well-known Peng-Robinson equation of state is chosen to evaluate the thermodynamic properties of the non-azeotropic refrigerant mixture s and the conventional mixing rule is also applied. The calculation of enthalpy and entropy of the mixture makes it possible to analize ·rhe performance of the specifie d heat pump cycle quantitatively. The calculation covers the pure components of R13Bl. R22, Rl2, R152a and R114; and the binary mixtures of R13Bl /Rll4, R22/Rl l4, R12'Rl l4, Rl52a/ Rll4, Rl3Bl/ Rl52a, Rl3Bl/ Rl2. R22/R152a R22/Rl42b. and . . A rest rig has been assembled and experiment are in progress to measure perfonnance of a heat pump with various mixtures. In this report. we present only the result of ealcularion and analysis. 2. CALCULATION OF THERMODYNAMIC PROPE RTIES 2 1 EQuation of State In this study, Peng-Robinson equation of state is chosen for the ealculation of the thermodynamic properties of refrigerants since it predicts the properti es reasonably well and makes the calculation relativel y simple, especially for the case of mixing parametetli. The mixing rule is required to evaluate thermodynamic properties of refrigerant mixtures, and the procedure for applying mixing rules will be much complicated when a complex form of equation of state is used. Peng-Robinson equation of state is well-known in the literature[3]. The working equations are simply repeated here for the completeness of the paper. p = ...!!!._ _ a(T) v-b v(v+b ) + b(v-b ) ' (1) (2) b = R T< o.on so-- . (3) p< By using the compressibility factor Z, the cubic equatio n of the following form is obtained. z3- (l-B)z 2 + (A.- 3Jl-- 2B)Z- (AB -B 2 -B 3) ~ 0, (4) where Pv aP Z=- bP A = - - , B .. - . RT (5) Rlrl RT As usual, a(T) is expressed as follows. a(T) = l T + T< (l - -)(m + n-). (6) T. T Two parametetli, m and n can be determined from the experimental data of the saturated states. In this procedure, the fugacity equality condition is introduc ed are taken from ASHRA E's vapor pressure relation[4] to find m and n. Experimental data for vapor pressure for pure refrigerants. 2 2 Mixjnz Ruh: and Prapen y CaleuJatign The equation of state for mixtures can be completed by assigning the proper mixing parametetli for the components. The conventional mixing rules are applied in this study[SJ. a= 'X.'I.x1:riafi, i j (7) b ~ "Zl:.xtxjbij. i j a11 - (8) (1 - ku)"lla1a1 , " bl (9) + bj b.. = (1 - k l j ) - - . " 2 (10) In rhe present calculation, £ for rhe interaction parame ter bij is treated as zero. 11 405 e for enthalpy, h, entropy, s, and fugac:iry, J, are With Peng-R obinson equatio n of state, the formula as summarized v - (V'Z- 1)b da(T) 1 --[a( T)- T--] ln ,, + (V'Z + l)b dT 2V'Zb h = h0 + s- s0 + R I n - - - - - - - - I n v + (V'Z + 2V'Zb tiT RT v- b 1 da(T) + RT(Z- ,. - (V'Z - l)b 1) T (12) ' da1 Oc;"ci 1,., da 1 1 da(T) a.-). - - = -::::::::..-,..)(1- kq)(- -) •· (-a.i + 1 tiT tiT a 1a 1 2 1i tiT da 1 D m1 = - Td - n; (11) p c; + J-dT 1)b + fc 0 dT, (13) Td r' (14) lf/'Q z + (V'Z + l)B b, A. b, J, -)In In-= -(Z-1 ) -ln(Z -B)- - - · ( - - (V'Z - 1)B b a 2V'28 b x1P taken from ASHRA E(4]. are state gas ideal ln the above equatio ns, data for the spedfic heat at (15) z- Cgc:fficieot 2 :>. Vapor- Ljgujd Eguj!jbriym and Bjnazy Jnrerag jon rule on the conditio n that the fugacities for liquid Vapor-liquid equilibrium state can be found by phase in vapor given pressure and tt:mperature, composition ratios and vapor phases are the same. In this study, with one of and tempera ture data and the composition ratio in and liquid states are found. When =ither of pressure ces of fugacities differen the until DS unknOW find to ed perform liquid and vapor p~ are given, iterations are reach the order of 10- in eq. (15). are taken from various literatures: Rl3B1/ Rl14[ 6], E:<perimental data for the refrigerant milnures R12[10 ], Rl3Bl/ R152a[ ll], R22/R1S2a and Rl3B1/ 114[9], R152a/R R22/R114[7, 8], R12/R114[1], d to give the reference values of /z and s to adjuste are (12), and (11) eqs. in s R22iR142b. The values h 0 and 0 ant and at bubble point for refrigerant refriger pure for state liquid d saturate at be 200 k.llkg and 1 k.l/kgK mixtures at T .. 0°C. j;s 2 4 Calculated Results of Theanqd,marnU; Prqpert 1. With these values, vapor pressures of pure refrigerants Table in shown are n and m of values ed Estimat ble to ]. Systematic deviations appears but it is accepta dara[l4 E ASHRA with ed compar and ed are calculat are also EnthalpY and entropY of saturate d liquid and vapor ions. applicat of range the within data the utilize point or s larger as the tempera ture reaches close to critical compared with ASHRAE data. The error become region. ture tempera lower quid each refrigerant mixture from the data of vapor-li The binary interaction coefficients are found for calculated and between ce differen the ing minimiz by ned of equilibrium. In this study, ku is determi tempera ture and mole fraction. The calculated values experimentally measur ed pressure for a state of given to be a weak function seems ku 1%. about within is pressure in n deviatio k'i. are given in Table 2. The average data are ed binary interaction coefficients from ~ntal ot tempera ture and mole fraction. The calculat ents in mixtures. The following compon the of ts momen dipole in ces differen of as plotted in Fig. 1 as a function experimental data are not enough for substanees such interpolating relation may be used to estimate ku when R22iR142b and R22JR152a. (16) kq ~ c1(61.zf + czla111 + c 3 , (17) c 1 "' 0.0197931, c1 "' 0.0204207, c 3 "' 0.0016696 . ium relations for pressure, tempera ture and mole Figure 2 shows some of the vapor-liquid equilibr well with the experimental data. In spite of the agree results ted CalCIIia phases. vapor and fractions of liquid and bubble points are well predicted. Figure 3 point dew state, of n equatio obinson Peng-R of simple form the results calculated with the aids of R<ioult's shows and klj, ter. parame ion intet:lct the of indicates the effect rule. -7 are calculll:ted f~ refrig~t mixtures. Figures 4 Thermo dynami c propenies of enthalp y and entropy s at a specific rmxture rano, say, 50/50 mass frac:non diagram tropy ture-en tempera and lpy e-entha show pressur 1S2a respectively. for R22iR114, R22iR152a, R22/R142b and Rl3Bl/R 406 Table 1 Calculated values of m and n in eq. (6) for several refrigerants 0.!2 Rl52a/Rl14 D.!O Refri~~:erant R13Bl R22 R12 R152a R142b Rll4 m il 0.4380 0.4909 0.4666 0.6990 0.6789 0.5129 0.1992 0.2212 0.1887 0.1212 0.1031 0.2424 - - Eq.(16) 0.08 \ R1:21R114 0.06 Rl3Bl!Rl52a ~':;> o.o. 0.02 Table 2 Calculated values of binary interaction coefficient for several mixtures Mixture k .. l11u.l R13B1/Rl14 R22/R114 Rl2/R114 R152a/Rl 14 Rl3Bl/R1 52a R13Bl!R12 0.0104 0.0393 0.0020 0.1047 0.0802 -0.0009 0.15 0.92 !.5 O.Dl 1.77 1.62 0.14 Fig. 1 Relation between I411LI and .1: 11 (141,.. I ; difference between dipole moments {Debye), kq : binary interaction coefficient) 3.0 2.5 v 2.5 0 0 .6 2.0 0 5o 30 10 -10 -3o ·c ·c ·c ·c ·c 2.0 v eo ·c 0 40 'C 0 "' 0 ,. 6"" 2.0 -- 20 0 -20 ·c ·c ·c l.S !,;. t.S 6 "- 0.. 1.0 1.0 (a) R13Bl!Rl 14 (b) R22/Rl14 Fig. 2 Vapor-liquid equilibria for the non-azeotropic refrigerant mixtures (Marks represent experimental data.) 407 tS;-----------------------~ kij = 0.0393 klj = ts,-------------------------~ - - kij "' 0.0333 0 ----- ku = Raoult's rule --~-----~OL---~-D•• u ------~LO D.2 D.D ----...J 0.21.-----~-....... 0.0 0.2 0.0 0.8 LO (b) R22JR152a (a) R22/Rl14 LOr----------------------~ 0.1.-------------------------~ kij = 0.0247 k;i o Raoult's rule - - - t5 - - - klj = 0.0802 - - - - - ku = o.s =0 0 Raoul!'s rule ~· 0.0 ------~LO ----------0.0~------~~ 0.4 0.2 ~0 L---------o.---..0..1. ---------1LO 0.0 ~· 0.2 (d) R13Bl!R152a (c) R22/R142b Fig. 3 CoPlparison of vapor-liquid equilibria with Raoult's rule (T = 0°C) 408 10. 0.- ---- ---- ---- , 1.0 c.."' g ~ ;... ..... 0.1 0.01 .____._ 100 1~ _.__....__.. zoo zso ..___.._~__, 300 3$0 .ooo •so h (k.Tikg) s (kJikgK) (a) P·h diagram (b) T-s diagram Fig. 4 Pressure-enthalpy and temperature-entropy diagram for the refrigerant mixture R22/R114 (mass fraaion 50!50) I~Or------------~ 1.0 ....... £:: ~ ..... 0.1 •10 0.01 100 Fig. 5 200 300 .00 .... ~L---~--~~-- 600 ~~~ 1.0 1.2 1.• 1.11 1.11 ~~~ :a.o :2.2 2.• h (k.Tikg) s (k.TikgK) (a) P·h diagram (b) T·S diagrnm ~ure-enthalpy and temper ature·e ntropy diagram for tbe refrigerant mixture R22/R152a (mass fraction 50/50) 1o.o 1 - - - - - - - - - - - - , l.O ....... .r: e..... 0.1 - O.Ot'-::=--'-~-'-:~........_ 100 ~ :100 _....._._~ .00 ~L-~~~-d====~~~ 600 0.11 h (k11kg) Fig. 6 1.0 1.2 u u 1.8 :2.0 :2.2 s (kJikgK) (a) P·h diagram (b) T-s diagram Pressure-enthalpy and temperature-entropy diagram for the refrigerant mixture R22IR142a (mass fraaion 50150) 409 •oo 11.0 360 1.0 g300 ~ ! ~ f., 0.1 Fig. 7 h (kJ/kg) s (kJ/kgK) (a) P-h diagram (b) T-s diagram for the refrigerant mixture Rl3B11Rl52a Pressure-enthalpy and temperature-entropy diagram (mass fraction 50/50) 3. ANALYSIS OF HEAT PUMP CYCLE S 1 I fundam ental A<Sumptjons cycles by using the thermodynamic propenies of It is possible to perform the simulation of heat pump ns in to find the characteristi(S of heat pump operatio refrigerant mixtures. Various combinations are tried R221Rl14. s include s mixture The . capacity heating t modes of constant volumetric flow rate and constan cycles. It are the proper combinations to apply to beat pump R221Rl52a. R22/R142b and R13Bl/R1S2a. These d liquid state at saturate in is and tor evapora the of ait the at °C 5 is assumed that the fluid is superheated by the exit of the condenser. fixed stroke. The efficiency of the compressor is Compressor is thought to be reciprocating type with the outlet and the inlet. In this study, the between ratio pressure the the of assumed to be a simple function ssor are regarded as a linear function of compre the of cy efficien ssion compre the volumetric efficiency and except in the condenser and the transfer heat the and flow the in drops pressure pressure ratio[l2 ]. The counterflow type between refrigerant and be to assumed is e exchang heat The d. evaporator are neglecte ted ture-entropy diagrams of the cycle are represen secondary fluid. The pressure-enthalpy and tempera 8. schematically in Fig. t Yo!umerric Sow Rate Cycle 3 2 Mpdu!atinn qf Heatina; Capacity jn a Constan the dealt with in a heat pump cycle. We assume that In this section, modulation of heating capacity is conditions are given design and g operatin The rate. flow volume t compressor is operated in a mode of constan beat and exit of the condenser and the evaporator, overall for the temperatures of secondary fluids at inlet follows: as ant refriger of rate flow transfer coefficient and volume = 25 °C - water tempera ture at the condenser inlet (T...:~) 40 °C water tempera ture at the condenser outlet (T_,) "'" ~ 20 "C - brine tempera ture at the evaporator inlet (T,.1) 10 °C brine tempera ture at the evaporator outlet(T,..,) = = 03 kWfK overall heat transfer coefficient in the condenser (UA)0 "' 0.3 kWfK. overall heat rransfer coefficient in the evaporator q~A), . 1s volume flow rate of the refrigerant (m) "' 0.002 m ants in the heat pump by using refriger of states Iterative method is used to calculate thermodynamic g the temperature of the refrigerant at the assumin with initiated is tion Calcula s. relation energy balance and ned by heat transfer characteristics at the evaporator condenser ellit. The inlet state of evaporator is determi the lations of states at the condenser are performed with Recalcu found. is ~t ssor compre at state the then design condition of (UA )•. 9 as a function of mass fraction of lower boiler in the Variations of the heating capacity are shown in Fig. P) are drawn in Fig. 10 and defined as follows: ance(CO perform of ents mixtures. The corresponding coeffici QH (18) COP "'-. w 410 p T It s (a) Pressur e-entha lpy diagram Fig. 8 (b) Temper ature-en tropy diagram Schematic diagram of heat p11mp cyde a.o . . - - - - - - - - - - - - - , 7.0 6.0 Rl3Bl /Rl52a 7.0 R22/R l52a 5.0 8.0 i ::. 4.0 ~ 0 " u 01 5.0 3.0 2.0 4.0 Rl3Bl/ Rl52a 1.0 o.o 0.0 0.2 0.4 o.8 0.8 1.0 Mass fraction of lower boiler (R13B l, R22) Fig. 9 3.0 0.0 0.2 0.4 0.8 0.8 1.0 Mass fraction of lower boiler (R13Bl , R22) Variatio n of heating capacity with respec:t to Fig. 10 Variatio n of COP with respec:t to the mass the mass fraction of lower boiler in constan t fraction of lower boiler in constan t volume volume flow rate cyde flow rate cycle As shown in Figs. 9 and 10, heating capacity, QH, and COP vary nearly monotonic:ally as the compon ents of the mixt11res chang=s. In c:ase of mixtures with R22, heating capacity decreases while COP increases by adding higher boiler to R22. It enables the heat pump to be operate d to meet required heating load and higher perform ance is obtaine d. Similar _result is obtaine d for the Dlixture of R13Bl/ Rl52a. 1.3 Pertonn apce Enhanr.emgm in a Constant Heating Camsity Cycle Similar sim11lations are carried 0111 to find the perform ance characteristics in a heat pump operate d in a mode of a consran t heating capacity. A set of operatin g conditiOI!S are chosen to provide a heating capacity of 6 kW. They are as follows: - water temperat11re at the conden ser inlet (T~) • Z5 °C water temperar11re at the conden ser outlet (T..,) "' 45 °C 411 9.0 r---- ----- ---, 00.0~----------~ A : R22/Rl14 B : R22/Rl42b 8.0 C : R22/Rl52a D : R13B1/R152a 7.0 " '§ p.. 0 ~ 16.0 u c ~ 8.0 -6 10.0 > 5.0 4.0 .___ 0.0 A B C D R22/RU4 R22/Rl42b Rl3Bl/R152a R22/R152a 5.0 _._""""='__..__.....__........_ __, o.e 0.8 1.0 0.4 0.2 0.0 .....__ _.__ __.._ _....__ __.__ __, 0.0 0.2 0.4 0.6 0.8 1.0 Mass fraction of lower boiler (R13Bl, R22) Mass fraction of lowe:r boiler (R13Bl, R22) with respect Fig. 11 Variation of COP with respect to the mass Fig. 12 Variation of volume flow rate to the mass fraction of lower boiler in fraction of lower boiler in constant beating constant heating capacity cycle capacity cycle brine temPerature at the evaporator inlet (Tb<i) .., 20 °C brine temperature at the evaporator outlet (T,_) = S °C beating load (Q") ~ 6.0 kW The calculation procedures are same as the previous case. However, overall heat transfer coefficients, UA ,in evaporator and condenser are calculated for each mixture to meet the required heating load. of Variations of COP's for four different mixtures are shown in Fig. 11 as a function of mass fraction with pure lower boiler component. For all cases, the higher value of COP is obtained with the mixtures than temperature components only. The maldmum values of COP appear at the mass fraction where the largest a peculiar difference occurs during phase change. In case of R22/Rll4 mixture, a plot of calculated COP's has was shape. The peeuliar shape of COP resulted from the fact that the minimum temperature differenee assigned between refrigerant and heat souree or heat sink in each end of condenser and evaporator. Fig. The corresponding volume flow rates of the refrigerants at the inlet of compressor are represented in rate varies 12 for four different combinations of mixtures in terms of mass fraction of lower boiler. The flow monotonically but not linearly. • • 4. CONCLUDIN G REMARKS the Peng· Robinson equation of state is used in order to estimate the thermodynamic properties of for refrigerant mixtures. With this equation of state and mmng rules, thermodynamic properties are calculated the mixtures including R13Bl/Rll4, R22/Rll4, R121Rl14, R1S2a/Rl14, R13Bl/RlS2a, R13Bl1Rl2, R22IR152a and R22/R142b. A Necessary binary interaction parameters are found for each mixture to gencinlize the calculation. moments correlation is proposed for the binary interaction coefficients in terms of difference between the dipole on the of each pure refrigerant. Pressure-enthalpy and temperature-en tropy diagrams are presented based calculation for a certain composition ratio of each refrigerant mixture. oon· Two types of simulations are carried out to cl!antderizc the perfonnance of the heat pump by using fluids. 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