Bansal, P. K.

Xie, G.

English

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Purdue UniversityPurdue e-PubsInternational Compressor Engineering Conference School of Mechanical Engineering2000Dynamic Simulation Model of a ReciprocatingCompressor in a RefrigeratorG. XieXi'an Jiaotong UniversityP. K. BansalThe University of AucklandFollow this and additional works at: https://docs.lib.purdue.edu/icecThis document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact epubs@purdue.edu foradditional 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.htmlXie, G. and Bansal, P. K., "Dynamic Simulation Model of a Reciprocating Compressor in a Refrigerator" (2000). InternationalCompressor Engineering Conference. Paper 1376.https://docs.lib.purdue.edu/icec/1376DYNAMIC SIMULATION MODEL OF A RECIPROCATING COMPRESSOR IN A REFRIGERATOR Guozhen Xie Department of Refrigeration and Cryogenic Engineering Xi'an Jiaotong University, Xi'an, P.R. china E-mail address: xiegxjtu@263.net P. K. Bansal Department of Mechanical Engineering The University of Auckland, Auckland, New Zealand ABSTRACT In this paper, a set of mathematical model to be used for predicting the dynamics of a reciprocating compressor in a refrigerator has been developed. Based on the conservation of energy and mass, the model was established by dividing a global compressor into ten controlling volumes. The model was validated by the experimental results from literatures. It could be calculated for the transient characteristics of the compressor by using of the model. From the simulated results, it was suggested that the coefficient of performance (COP) of a compressor which is obtained normally under the steady working state should be replaced by the mean value of integrating the transient function of COP (t) within a period of time from the beginning to the steady state in order to avoid declining the real value of COP. NOMENCLATURE A cp cv g h M p p t T u u ~ (J) a e & ai =Area = Isopiestic specific heat = Isovolumetric specific heat = Gravitational acceleration = Specific enthalpy =Mass = Pressure =Power =Time = Temperature = Overall coefficient of heat transfer = Refrigerant Velocity = Volume of compressor cylinder = Angular velocity of compressor crank = Heat transfer coefficient = Compressor crank angles = Relative clearance volume of compressor SUBSCRIPTS =Air b Fifteenth International Compressor Engineering Conference at Purdue University, West Lafayette, IN, USA- July 25-28, 2000 [m2] [J I (kg·K)] [J I (kg·K)] [m/s2] [J I kg] [kg] [Pa] [W] [s] [K] [Wim2 ·K] [m/s] [m3] [rad/s] [W 1(m2 ·K)] [rad] = Compressor body 129 cab = Space between shell and body cyn = Cylinder of compressor die = Discharge chamber did = Discharge duct div = Discharge valve =Inlet met = Metal sheet 0 =Outlet rf = Refrigerant shell = compressor shell sue = Suction chamber sup =Suction pass suv = Suction valve w = Cylinder wall of compressor INTRUDUCTION In a refrigerator with a vapour compression cycle, a compressor has to be employed to actually increase the pressure of working media from the suction pressure level to the discharge pressure level by consuming energy to keep the refrigerating process on circulating successively. The challenge of non-contaminant refrigerants, hydrocarbons or mixtures, the need of optimal designs for high efficiencies, the understanding of critical points and the possibility that the numerical simulation offer to obtain the guidelines to experiment with, are strong incentives to develop general and accurate prediction methodologies. H.Erol [1] set up a dynamic model to describe the entire motion of compressor at transient and steady states by use of three positional coordinates, four Euler Parameters and the position of the crankshaft. Kirill M. [2] developed a computer model of the suction system including the suction port muffler, pipe and the suction valve of a reed type to analyse the effect of the constructive parameters on the compressor performance. An advanced numerical simulation of the thermal and fluid-dynamic behaviour of hermetic reciprocating whole compressors domain which is divided into fluid and solid control volumes was developed by J.Rigola [3]. The computational procedure offered by A.Cavallini [4] described the steady-state thermal analysis of a hermetic reciprocating compressor that is subdivided into six parts. This paper develops a global simulation model for a hermetic compressor to numerically simulate the transient thermodynamic characteristics of pressure, velocity and temperature of refrigerant, the behaviour of heat transfer between refrigerant and each part of the compressor domain, as well as the coefficient of performance (COP) of the compressor. FORMULATION OF THE COMPRESSOR The integrated model for the hermetic compressor consists of four sections, i.e. the model for inside compressor which includes seven sub-procedures, the model for the body of compressor, the model for the refrigerant filling in the space between the shell and the body of compressor, and the model of the compressor shell. The mathematical model was established on below assumptions. • Without any work acting to the refrigerant except the flowing work the refrigerant possesses. • The specific volume of refrigerant does not change when it goes through any port or pass. • Ignoring the pressure drop caused by the refrigerant passing the suction and the discharge valves. • The pulsation caused by the refrigerant vapour going through periodically the suction chamber and the discharge chamber is not taken account into the model. Each of model for the compressor is subject to the principles of conservation of energy and mass, and they are compatible each other. The control volume used for setting up these models is shown in Figure I. I . The model for suction pass: Fifteenth International Compressor Engineering Conference at Purdue University, West Lafayette, IN, USA- July 25-28, 2000 130 T = sup,o dMsupo ( ) 1 c . ·T . · · +a ·A · T -T . ·-p(sup,,) sup,/ dB sup sup w ,sup sup,t {j) dM sup,o C p(sup,o) • dB 2. The model for suction chamber: ·[c ·T + U~,c,i- U~,e.o]· dM,.,e,o +a ·A ·(T -T )·_!_ p(>71e,i) sue,i 2. g 2. g dB .we sue w,>71e sue,i {j) T =~----------------~--~~-------------------.we.o dM c . sue,o p(sue,o) dB 3. The model for suction valve: - T .. c . . dM suv,o -a . A . T . _!_ .\l#V ,I p( ~11V ,I) d (} ~liV ~11V W, V {0 T = suv,o 4. The model for the cylinder of compressor: dM dT dM,.,, dMdi aw C ·T·-+M·C ·-=C ·T ·--C ·T·---·A ·(T-T)+ • dB • dB P<·"'> "' dB p dB m w w 5. ( :) =( d~.,) -(d;;i) dp -=M·R· dB The model for the discharge valve: ( c . T _ _ ud_2;v_.o) . dMdiv,o + a . A . T . _!_ p(div,i) div,i 2 . g dB div div w,v {j) T =---------=::-:-----------div,o dM. 1 c . dtv,o _ a . A . _ p(div,o) dB div div {j) 6. The model for the discharge chamber: Fifteenth International Compressor Engineering Conference at Purdue University, West Lafayette, IN, USA- July 25-28, 2000 (1) (2) (3) (4) (5) (6) (7) 131 [ u~c,i u~c.a] dMdic,i 1 · cp(·•-·> ·T~. +-~--- · +a.,_ ·A~ ·T · uu.,l uu.,l 2. g 2. g d(} uu. uiC w,v (J) T =~-----------~~=-------------------dic.v . dM sue o } c · ·+a ·A · p(dic,o) d(} die die (J) 7. The model for the discharge duct: dMdtd,; 1 c p(did,i) · T did.i · dO + Udid · Adia · T .. a T = (J) did,o dM. 1 C (tftd o} • did,o + U did ' A did · -p • d() (J) 8. The model for the body of compressor: di;, = 1 . [ P · (1- TJ ) -a . A . (r - T ) -d(} (J) • C • M wer £,m """"' avera b rf b b -a ·A · (T - T ) a ·A · (T. - T ) -.uw suv b .suv sue svc h SllC -a sup • Asuv · (I;, T"'P) - a such • A sue, · (I;, - T SIIC,) ] 9. The model for the refrigerant filling in the space between the shell and the body of compressor: dTrf = 1 . [a~>· Ab . (r. _ T )- ashet · Ashet • (T _ T ) d(} M h rf rf she/ + d·~ m m + Udid·Aaut ·(T -T )-c ·T _dMcah +(u!b.i +h .)·dMcab,i _ (J) dtd,o rf v if d(} 2. g cah,t d(} -(u!b,o + h ) . dMcah,o] 2. g cab,o d(} I 0. The model for the shell of compressor: 5.67-[(~~r -c~n Qai,rad = Asb£1 • 1 1 ~+ -1 t; shel (met ,ai VALIDATION OF MODELS (8) (9) (10) (11) (12) A group of differential equations above could be solved simultaneously at the time condition and some boundary conditions to describe the dynamic behaviour of hermetic reciprocating compressor. To verifY the model, a group of parameters of the geometries and boundary conditions from the reference [5] and the working conditions from the study of F. Escanes [6], were put into the models. The simulated results on COP for the chosen compressor were displayed Fifteenth International Compressor Engineering Conference at Purdue University, West Lafayette, IN, USA- July 25-28, 2000 132 on the Figure 2. Comparing the experimental COP values from f. Escanes [6] with these from the simulation, a better agreement for both has been obtained within the mean discrepancy of 6.6% and the larges deviation of -15.1%. It shows that the model can be used to predict the dynamic performance for a hermetic reciprocating compressor in a refrigerator. RESULTS SIMULATED AND DISCUSSIONS Figure 3 shows the distribution of temperature simulated along each of compressor domain in a complete cycle. The temperature of refrigerant, as shown in Figure 3, rises steeply (from 343.0K to 439.7K) in the compression process and falls suddenly (from 434.3K to 373.9K) in the expansion process, while the temperature of refrigerant increases only 4.5K during the whole suction process. The energy balance of overall compressor in a complete cycle is displayed on Figure 4 which shows that the rate of heat transfer Qcyn from cylinder wall to refrigerant increases dramatically up to the value of 0.12W during the suction process and drops during the compression process, while when compression process closes to the end the refrigerant releases significantly heat into the wall and a sharp negative peak with -0.06 W was appeared. The higher rates of heat transfer for the suction pass of Qsup and the suction chamber Q.,c are respectively 0.09W and 0.06W during the suction process due to bigger area of heat transfer. Figure 5 illustrates the distribution of temperature on the compressor shell, the refrigerant filling in the space between the shell and the body of compressor, as well as the body of compressor duration of about 600 seconds. In Figure 5, the largest increasement on temperature was the compressor shell T,.1 in 21.2K, following the refrigerant 1;.1 in 15.9K while the body of compressor T;, in 1 0.39K. The results simulated indicate that the value of COP varies with time during the compressor running. According to the results, the values of COP is in 1.31 for the beginning of compressor running, in 1.22 for the compressor running 10 minutes and in 1.18 for the compressor running one hour. It means that the values of COP decreased with time during the compressor "on" cycle. If taking the value of 1.18 as the nominal COP value of the compressor liking normal calibration of COP picked up the value of steady state, the real COP may be lose 11.0% to 1.31 and 3.4% to 1.22. So, it is suitable for determining of COP for a compressor to take the average value of integrating the function of COP (t) within a period of time shown as follows, '2 JcoP(t)·dt COP"""' =...:.'•-----12 -tl Where, t1 , t 2 are the time of the beginning of compressor running and the moment of compressor running closing to the steady state respectively. CONCLUSIONS A mathematical model to be used to describe the dynamic performance for each domain inside of a hermetic reciprocating compressor has been developed in great detail. The model could predict the inter-thermal parameters and the heat transfer characteristics of a hermetic reciprocating compressor correctly. From the results simulated, it would be suggested that it is a better way to calibrate the value of COP for a compressor by using of the average value of integrating the function of COP (t) within a period of time to replace the traditional way which picked up usually COP at the steady state. Fifteenth International Compressor Engineering Conference at Purdue University, West Lafayette, IN, USA- July 25-28, 2000 133 REFERENCES [1]. H.Erol, T.Durakbasa et al, Dynamic Modeling and Measurements on a Reciprocating Hermetic Compressor, 1996 International Compressor Engineering Conference, Purdue University, USA, 1996. [2]. Kirill M. Ignative, Boris B. et al, Simulation and Parametric Analysis of the Suction Valve and Muffler of a Small Reciprocating Compressor, 1996 International Compressor Engineering Conference, Purdue University, USA, 1996. [3]. J.Rigola, C.D.Perez-Segarra and A.Oliva, Parametric Study and Experimental Comparison of Small hermetic Refrigeration Compressors Using an Advanced numerical Simulation Model, 1998 International Compressor Engineering Conference, Purdue University, USA, 1998. [ 4]. A.Cavallini, L.Doretti, et al, Thermal Analysis of a hermetic Reciprocating Compressor, 1996 International Compressor Engineering Conference, Purdue University, USA, 1996. [5]. J. Rigola, C. D. Perez-Segarra, A. Oliva et al, Parametric Study of Hermetic Reciprocating Compressors, 1996 International Compressor Engineering Conference, Purdue University, USA, 1996. [6]. F.Escanes, C.D.Perez-Segarra, J. Rigola, Numerical Simulation of Hermetic Reciprocating Compressors. Recent Improvements and Experimental Validation, Proceedings of International Compressor Engineering Conference, Purdue University, Indiana, USA, 1996. energy and mass entering the C.V. the changes of energy and mass in the control volume (C.V) energy and mass out from the C. V. Figure I Schematic of control volume for modelling Fifteenth International Compressor Engineering Conference at Purdue University, West Lafayette, IN, USA- July 25-28, 2000 134 3 2.5 2 t; 1. 5 C) 0.5 0 450 ~ 400 Q) .... ::s .... al .... Q) c:lc E Q) 350 E-< 0 5 10 15 Pressure ratio (Pd/Ps) -<>-Exp. c Sim. ··········· ···-· ·············C 20 25 Figure 2 Experimental and simulated COP with ratio of condensing pressure to evaporating pressure ,---· \ Tcyn I Ill •. T.up 30 300 +-----4-----~----~-----+-----+-----1------~--~ 0 50 100 150 200 250 300 350 400 Angles (degree) Figure 3 Distribution of refrigerant temperature along the compressor domain in a complete cycle Fifteenth International Compressor Engineering Conference at Purdue University, West Lafayette, IN, USA- July 25-28, 2000 135 0.15 ~----------------------------------------------0.1 ... c! ~ 0.05 e .... .... al u .1:1 .... 0 u .... ~ -0.05 -0.1 _L_ ______________________________________________ __j 0 50 100 150 200 250 300 350 400 Angles (degree) Figure 4 Rate of heat transfer along the compressor domain in a complete cycle 360 355 350 g345 f ,8340 as ~335 c:lo S330 Q) f-4 325 320 315 / v -~ ~ L---(....---' ----------------~ >--c.-----L..----~ I ~ -------· L---- -J-• -lb(K) ------- Trf(K) ------ Tshel (K) I 0 50 100 150 200 250 300 350 400 450 500 550 600 650 Time (s) Figure 5 Distribution of temperature with time for compressor shell, refrigerant in the cabinet space and the compressor body Fifteenth International Compressor Engineering Conference at Purdue University, West Lafayette, IN, USA- July 25-28, 2000 136 

Dynamic Simulation Model of a Reciprocating Compressor in a Refrigerator

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Dynamic Simulation Model of a Reciprocating Compressor in a Refrigerator

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