Purdue University Purdue e-pubs International Compressor Engineering Conference School of Mechanical Engineering 1998 Compression Model for Open Reciprocating Compressor Application to Cylinder Wall Cooling Study C. Arzano-Daurelle Electricite de France D. Clodic Ecole des Mines de Paris B. Hivet Electricite de France Follow this and additional works at: https://docs.lib.purdue.edu/icec Arzano-Daurelle, C.; Clodic, D.; and Hivet, B., "Compression Model for Open Reciprocating Compressor Application to Cylinder Wall Cooling Study" (1998). International Compressor Engineering Conference. Paper 1350. https://docs.lib.purdue.edu/icec/1350 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
COMPRESSION MODEL FOR OPEN RECIPROCATING COMPRESSOR. APPLICATION TO CYLINDER WALL COOLING STUDY. C. ARZANO-DAURELLE, D. CLODIC*, B. HIVET. Electricite de France, Direction des Etudes et Recherches Applications de l'electricite dans l'industrie Site des Renardieres 77818 MORET SUR LOING Cedex FRANCE tel : +33 1 60 73 65 41 :fux : +33 I 60 73 64 40 bertrand.hivet@der.edfgdf.fr * Centre d'energetique Ecole des Mines de Paris 60, Boulevard St Michel 75272 PARIS Cedex 06 FRANCE tel :+33140519249 fux :+33146342491 clodic@cenerg.ensmp.fr ABSTRACT A compression model for open reciprocating compressor is elaborated. Relevant literature has been analyzed, assumptions and equations related to gas flow through valves, characteristic of valves, choice of gas-wall heat transfer correlation are given. A numerical resolution is performed and results are compared to experimental measurement. Intrusive instrumentation has been set in the compressor and a pressure sensor has been introduced in one cylinder. The model running deals with wall cooling during compression. NOMENCLATURE Cv [J.kg"'.K- 1 ] specific heat of fluid at constant volume s [m2] area Cam [N.m- 1.s] damping coefficient T [K] temperature Cg pressure force coefficient t [s] time D [m] cylinder bore V [m 3 ) volume h [J.kg"1! specific enthalpy Vel [m 3 ] clearance volume hconv [W.m.K' 1 ] heat transfer coefficient V [m 3.mor'] molar volume k [N.m-1] spring stiffuess v [m 3.kg' 1 ] specific volume L [m] connecting rod length X [m] valve lift m [kg] mass Xo [m] uncharged valve lift p [Pa] pressure ro [rad.s- 1 ] angular speed Q [J] heat y isentropic exponent Rc [m] crank radius Re REYNOLDS number r [J. kg-'.k''] gas constant Nu NUSSELT number Indices : w wall up upstream sue suction dam damping dw downstream val valve INTRODUCTION Open reciprocating compressors are widely used in refrigeration and especially in food industry where most ci systems are run with ammonia. Heat pump applications are possible since a range of compressors which accept a design working pressure of 4 MPa has been developed. This compressor has been studied and tested ([4], [8]). Numerical models with various degrees of complexity elaborated ([7],[9],[12],[13]). This paper presents a simple model which describes the compression chamber and valve motion. This model permits studying the heat transfer 865
impact on energy performance during compression. It can be extended to the study of cylinder wall cooling. Because of this extension, some values hardly available by experimentation can be calculated and compared with other data ([2], 3], IO], [II]). The system The study deals with the compression chamber of an open reciprocating compressor. For a complete cycle, four stages of simulation are considered: compression and expansion work with closed valves and, suction and discharge as soon as the respective valves start to open. A complete cycle is from expansion to discharge (from 0 to 360 for crank angle). The assumptions Assumptions are as follows: the rotational speed of the compressor is constant, the flow is one-dimension, the potential and kinetic energies are neglected, the conduction heat flux in flow direction is neglected,. system is uniform and gas is perfect, lubricating oil effects are neglected. Concerning the mass flow through valves, the upstream conditions are the stagnation conditions, and the gas flow is assumed to be adiabatic so the fluid dynamic equations can be used. SYSTEM EQUATIONS >- Mass flow equation : dm = Lj dmi >- Mass flow rate through valves Generally the gas flow through a valve is assumed to be a flow through an orifice for a compressible gas. dm 2y -- i 2 '(+I For a perfect gas: dt= Pup Su1 (y -l) r. Tup 't Y -'t Y where 't is the ratio between downstream and upstream pressures. (1) (2) This equation is adapted for a subsonic flow [1]. >-Energy conservation equation: mcvdt=-mt(ap) dv+ oq+ L hjdmj- hdm (3) For example at suction port (4) >- Convective heat transfer equation at v j A bibliographic study has been performed [4] for correlation choice, we use ANNAND's correlation. = conv wall- fluid Q. h S (T T. ) where Nu=0,7 Re 0 7 The flow speed is chosen equal to the mean piston absolute speed for the REYNOLDS number calculation. >- Valve motion equation (5) (6) 866
> Cylinder volume equation Cylinder volume variation ~~;nds on{ crank angle :t [: V(t)=Vc~+- 4 --Rc l+coso:t+rc 1- (7) EXPERIMENTAL PROCESS The compressor has eight cylinders and the swept volume is 0.054 m 3 /s. The loop sensors allow to perform tests with respect to Iso917 standard (refrigerating compressor testing standard). The mass flow rate is obtained by applying the standard methods. A piezoelectric sensor has been introduced in one cylinder and measurements are compared to results obtained with the model. A crankshaft position sensor is also added. RESULTS Coefficients used in equation (6) are in accordance with the real refrigerating compressor which performance has been tested [4]. Experimental data allow fitting of coefficients for spring stiffness and damping coefficient. mls m O,(X}I.t. m/s m 0.0012 10 0,0010 0,0008 0,0006 0,0004 0,0002-2 lo 60 0,0000 90 l20 llo 11!0 210 Crank angle(").o+--..l--... ----------1---Lo,oooo 270 ( Discharge ) 100 ]]0 Crank angle(') Figure 1 : Motion and Speed of Suction and Discharge Valves. 360 Figure 1 presents the opening and the speed of the suction and discharge valves. The valve oscillations and collisions between the plate and the valve stop or seat can be seen. The model mass flow rate is 1.4% higher than experimental mass flow rate. Experimental input power is 6.5 % higher than the power calculated by the model. Discharge temperatures differ from 2 K. 867
0,85 0,75 0,65 0,55 0,45 0,35 0,25 0,15 O,OE+OO S,OE-05 l,oe-04 1,5E-04 Volume(m 3 ) 2,0E-04 -- Experimental -Model 2,5E-04 3,0E-04 Figure 2 : Comparison Between Model and Experiment Watt Diagrams. When comparing experimental measurement to model results (figure 2), the model shows better stability for the discharge valve. Since gas behavior has not been simulated in the discharge chamber, this could explain the lack of pressure pulsations in the model results. On the other hand, the slope of the model compression curve is higher: experiment shows higher pressure at the end of the suction phase, and heat exchanges occurring during real operation (gas-wall heat transfer) are probably more significant. Gas leakage's (neglected in the model) can happened at the closed valves or at piston-cylinder clearance; also the pressure is lower. The comparison between diagram areas obtained from the model and from experiment shows a difference of 12%. This results is in agreement with the variation of the input power given previously. Study of the heat transfer correlation Input power Heat transfer Discharge Mass flow hconv (%) (kw) temp_erature ( C) rate_(o/o) I 2 hconv + 0.1-2.2 128.2-1.0 I hconv - 0.1-0.6 128.2 + 0.7 Table 1 :Convective Heat Transfer Coefficient Variation. Results are given in relation to calculation with hconv Table 1 presents some results obtained from the model. These results can be related to Figure 3 showing the gaswall heat transfer during a complete cycle. w 1000 80 120 160 ; 200-1000 -2000-3000 -hconv 1 2-4000 expansion --hconv. 2 ~ -hconv -5000_... Heat transfer during suction phase (this stage is equal to half a cycle) is greater than during other stages and particularly when compared to discharge. This preponderance of heat transfers during suction has a direct effect on heat transfer during a complete cycle Crank angle(") Figure 3: Instantaneous Heat Transfer Between Gas and Wall During a Complete Cycle. Results obtained by the correlation fitting 2.hconv are more in the same range as experimental measurements than results obtained with the reference working test hconv, especially the mass flow rate. Moreover this remark would come to an agreement with other works in the literature [10] perfonned on heat transfers during compression. 868
As literature review on convective heat transfers between gas and wall supposed, the correlations chosen for "simple" models underestimate these transfers. The correlation has been fitted and model results are in the same range as experimental tests. COMPRESSION COOLING STUDY In most of the models, the wall temperature is usually chosen equal to the mean fluid temperature at the inlet and the outlet of the compression chamber. Table 2 presents various parameters as a function of the wall temperature evolution. Input power Heat transfer Discharge Mass flow (%) (kw) tentperature_( C) rate(%) Tmov ~20K ~ 0.6 ~4.5 123.9 + 1.4 Tmov~lOK ~ 0.3 ~2.2 128.3 + 0.7 Tmov+lOK + 0.1 +2.3 137.3-0.3 Table 2: Cylinder Wall Temperature Variation. Results in relation to simulation with Tmoy 3000...---r--- 2000 1000-1000 -2000-3000 -4000 80 120 160 200 320 360 -Twall - ~oy - 20 K -Twall - ~oy- 10 K -5000 -Twall -~oy -Twall - ~ oy + 10 K -6000 "-----'-----------11--------L------' Figure 4 indicates that the lower the wall temperature, the smaller the heat transfer during suction (the superheating of the gas is low during suction in this case) and the greater it is during discharge. For the temperature called mean temperature (Tmoy), the global heat transfers over a complete cycle is 0 k W. The combining of an endothermic and then an exothermic transfer during compression results in a nil global heat transfer for one cycle. Figure 4: Instantaneous Heat Transfer Power for Various Wall Temperatures, During a Complete Cycle. The cylinder wall cooling allows improvement of compressor energy performance: mass flow rate is increasing and input power and discharge temperature are decreasing. Cooling is more efficient when temperature discharge decreases than when obtained by cylinder~heads cooling during experiment. On the other hand, the wall temperature variation shows that the choice of the wall temperature for simulations is important. However the heat transfer is low compared to the input power. CONCLUSIONS A compression model has been developed and its results have been compared to experimental measurements. This model has been applied to the evaluation of heat transfer during the four phases of the compression cycle. Comparison between experimental and simulation results shows that usual calculations underestimate heat transfers. The model indicates that cooling of the cylinder wall implies improvement of the compressor energy efficiency. This improvement is due to the increase of the mass flow rate and to the decrease ofthe input power. 869
REFERENCES [1] "Introduction to computer simulation of positive displacement type compressors". Short Courses. Int. Comp. Eng. Conf. ofpurdue 1972. [2] 'ADAIR R.P., QVALE E.B. & PEARSON J.T. "Instantaneous heat transfer to the cylinder wall in reciprocating compressors". Int. Comp. Eng. Conf. of Purdue 1972. Proceedings, pp 521 526. [3] ANNAND W.J.D. "Heat transfer in the cylinders of reciprocating internal combustion engines". Proceedings of Instn. Mech. Engrs, 1963. pp 973-996. [4] ARZANO c. II Etude et modelisation d'une pompe a chaleur haute pression a!'ammoniac''. These de l'universite Pierre et Marie Curie (Paris 6). decembre 1997. [5] BOSWIRTH L. "Valve flow experiments with enlarged models. Part 1" Int. Comp. Eng. Conf. of Purdue 1986. Proceedings, vol 1 pp 28-44. [6] FERREIRA R.T.S. & DRIESSEN J.L. "Analysis of the influence of valve geometric parameters on the effective flow and force areas." Int. Comp. Eng. Conf. of Purdue 1986. [7] HAFNER J. & GASPERSIC B. "Dynamic modeling of reciprocating compressor". Int. Comp; Eng. Conf. cf Purdue 1990. Proceedings, vol 1, pp 216-221. [8] HIVET B., ARZANO C., DUCRUET C. & BRIENDGAARD B. "Test of a reciprocating compressor for ammonia heat pump". Applications for natural refrigerants conference. Aarhus, Denmark septembre 1996. pp 233 240. [9] PEREZ-SEGERRA C.D., ESCANES F. & OLIVA A. "Numerical study of the thermal and fluid-dynamic behaviour of reciprocating compressors". Int. Comp. Eng. Conf. Purdue 1994. Proceedings vo1 I, pp 145-150. [lo]recktenwald G.W., RAMSEY J.W & PATANKAR S.V. "Predictions of heat transfer in compressor cylinders". Int. Comp. Eng. Conf. ofpurdue 1986. Proceedings, voll, pp 159-174. [11] TODESCAT M.L., FAGOTTI F., FERREIRA R. T.S. & PRATA A.T. "Thermal energy analysis in reciprocating hermetic compressors". Int. Comp. Eng. ofconf. Purdue 1992. Proceedings vol4, pp 1419-1427. [12] TOUBER S. "A contribution to the improvement of compressor valve design. " These de doctorat de l'universite de technologie de Delft, Pays-Bas. Mai 1976. [13] ZHOU z. & HAMILTON J.F. "Multicylinder reciprocating refrigerating compressor modeling". Int. Comp. Eng. Conf. ofpurdue 1986. Proceedings, vol2, pp 669-683. 870