Purdue University Purdue e-pubs International Compressor ngineering Conference School of Mechanical ngineering 1998 Theoretical Study of Design and Operating Parameters on the Reciprocating Compressor Performance S. Manepatil Indian Institute of Technology G. S. Yadava Indian Institute of Technology B. C. Nakra Indian Institute of Technology Follow this and additional works at: https://docs.lib.purdue.edu/icec Manepatil, S.; Yadava, G. S.; and Nakra, B. C., "Theoretical Study of Design and Operating Parameters on the Reciprocating Compressor Performance" (1998). International Compressor ngineering Conference. Paper 1343. https://docs.lib.purdue.edu/icec/1343 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/vents/orderlit.html
THORTICAL STUDY OF DSIGN AND OPRATING PARAMTRS ON TH RCIPROCATING COMPRSSOR PRFORMANC Smita Manepatil, G.S. Yadava, B.C. Nakra Industrial Tribology, Machin~ Dynamics and Maintenance ngineering Centre (ITMMC), Indian Institute of Technology, New Delhi-110016, India ABSTRACT Mathematical simulation for the reciprocating compressor cycle incorporating the effects of common faults has been developed. The governing equations for different processes are derived by using first law of thermodynamics, continuity equation, equation of mass flow through valves, kinematic equation for piston movement and the cylinder heat transfer correlations. This paper gives the results of theoretical study of effects of design and operating parameters on compressor performance. p B y A Ak Cd cdf De Fd Finit h Re m p k density of air inside NOMNCLATUR the cylinder Pr square root of the R ratio of orifice and flow area at inlet n ratio of specific heats at constant pressure and constant volume t angular velocity of T crank shaft viscous damping factor V for valve springs ana ~ spring stiffness of y valve valve discharge suffix coefficient c drag coefficient of d valve plate e specific heat of air at f constant volume s equivalent diameter o valve plate area on p which the pressure acts w initial force on valve plate instantaneous heat transfer coefficient Reynolds number mass of air inside cylinder cylinder air pressure thermal conductivity of cylinder air Prandtl number specific gas constant ratio of connecting rod length to crank radius time temperature of air inside cylinder volume of cylinder air clearance volume valve lift cylinder discharge equivalent flow suction orifice piston wall 821
INTRODUCTION Most of the simulation studies on the reciprocating compressors carried out to date do not incorporate the effect of common faults like leaking valves, weak valve springs, leaking piston rings, slipping belt drives and clogged air filters [l,2]. A mathematical model has been developed [3] to simulate the reciprocating compressor cycle incorporating the effects of common faults for a single stage reciprocating compressor with disc type of valves. The compressor performance is dependent on the values of the design parameters like initial force on the valve disc, stiffness of the valve springs and some other constants like drag coefficient of valve disc and valve discharge coefficient. In addition, the performance is also dependent on operating parameter like suction air temperature. These parameters are used in the input data for simulating the compressor performance and the computed results depend on the correctness of the chosen values of these parameters. This paper gives the results of the theoretical study of their effect on the compressor performance. MODLLING OF COMPRSSOR THRMODYNAMIC CYCL Physical model of a single stage reciprocating compressor and its thermodynamic cycle are given in Figures 1 and 2. The equations governing the different processes of expansion, suction, compression and discharge are derived by applying the continuity equation, equation of mass flow through valves [4], first law of thermodynamics, the cylinder heat transfer correlation, valve dynamics equation and kinematic equation of piston movement to the control volume shown in Figure 1. The (1) governing equations used are as followsdmo =Cd. A ~ 2p4P ctt a 1-P4 (2) (3) h(t) De(t) '-0.053 (Re(t) ]O.B[pr (t) ]0,6 k (t) (4) 822
(5) (6) All these equations are solved using Runge-Kutta method. This simulation model can give cylinder air pressure, temperature, mass and valve displacement for the complete compressor cycle and also the harmonic components of pressure. It can predict the compressor performance giving the values of volumetric efficiency, volume flow rate and the performance ratio. STUDY OF PARAMTRS AFFCTING COMPRSSOR PRfORMANC The compressor performance is dependent on the values of the design parameters like initial force on valve disc (F 1 nh), stiffness of valve spring (Ak) and some other constants like drag coefficient of the valve disc ( cdf) and valve discharge coefficient (Cd). In addition, the performance is also dependent on operating parameters like suction air temperature (Ts) Some ot these design and operating parameters like F 1 n 1 t, Ak and Ts may vary in practice in due course of time. The study of the effect of the variation of each of the above parameters has been carried out by assigning different values to each of these parameters individually in the known range while keepinq the others as constant for a fixed discharge pressure. The initial force [ F,inJ:t.J depends upon the stiffness and the initial compression of the spring. To study the effect of F J.nit on suction valve plate, the values in the range of 7 to 47 N were assigned and the compressor performance was computed.the cylinder air pressure, temperature and mass time diagrams are shown in Figures 3,4 and 5 respectively. With the increase in FJ.l\it the suction and discharge processes are delayed. The compression process begins at a little lower pressure and the maximum cylinder air pressure increases. The mass of air inside the cylinder decreases with increase in F 1 nit The cylinder air temperature is not much affected. The instantaneous valve displacement for different values of F init are given in Figure 6. It has been observed that the suction and discharge valves open for shorter duration as F init increases. The performance parameters are given in Table 1. The mean cylinder pressure, volume flow rate, volumetric efficiency and performance ratio decrease with the increasing values of F 1 nn The cylinder air pressure harmonics for different values of F 1 n 1 t are given in Table 2, which indicate a prominent increase in 4th and 12th harmonic. Similar study on F 1 n 1 t, range 25-100 N, for discharge valve plate indicates that its increase leads to the shifting of 823
compression and discharge curves of the pressure-time diagram towards the right hand side. The performance parameters are not affected significantly. The 1st, 2nd, Jrd, 4th and loth pressure harmonics show an increasing trend and 6th harmonic shows a decreasing trend with the increase in F 1.,u.. ' The study on spring stiffness [AkJ of suction valve, range 0.45-18 kn/m, indicates no significant variation in the cylinder air pressure and temperature-time diagrams. The duration of suction valve opening is minimum for an optimum value of Ak and increases for the other values. The performance parameters have optimum values corresponding to a particular value of Ak causing suction valve closure at BDC. For other values the performance parameters show a decreasing trend. The Jrd, 5th, 9th pressure harmonics show an increasing trend and 7th, 8th harmonics show a decreasing trend for increasing values of Ak. In case of discharge valve, (range 10-45 kn/m), weak spring shows lower pressure during the discharge process and complete closure. of discharge valve at the end of the cycle. The variations in the magnitude of valve lift are also reduced. With the increase in Ak a slight decrease in the performance ratio has been observed. The 1st, 2nd, 3rd, 4th, 5th, 9th and loth pressure harmonics show an increasing trend whereas 6th, 11th and 12th harmonics show a decreasing trend with the increasing Ak. The study on suction air temperature [Ts] in the range 20-450C shows that cylinder air temperature decreases and mass of cylinder air increases with decrease in its value. The performance parameters decrease with the increase in Ts The study on drag coefficient of valve disc [Cd~], in the range 0.25-0.40, shows that increase in its value shifts the compression curve of the cylinder air pressure-time diagram towards left hand side. The maximum cylinder pressure and the fluctuations of pressure during the discharge process are reduced with the increased value of em. The durations of opening of suction and discharge valves also increase with the increasing Cdf" The performance parameters increase with the increasing values of Cdf" The 1st, 2nd, 7th, loth, 11th and 12th pressure harmonics show an increasing trend while, 3rd, 4th, 5th, 6th, 8th and 9th harmonics show a decreasing trend with the increasing values of C 11 ~ The study on the discharge coefficient [Cd] in the range 0. 5-0. 9 shows that increase in its value indicates increased fluctuations in the cylinder air pressure during the discharge process. The duration of suction valve opening is minimum for a particular value of the cd and increases for all other values of cd. Other performance parameters have maximum values for the particular value of cd and decrease for all other values. The 5th pressure harmonic increases whereas the 2nd and 3rd harmonics decrease with the increase in the value of cd. 824
CONCLUSIONS The computed results in the simulation program depend on the design parameters like Finit and Ak. Some other constants like cd and Cdf affect the compressor performance significantly and hence it is important to choose these parameters carefully in pr'actice for getting meaningful results. The performance is also dependent on operating parameter like Ts. RFRNCS 1. Benson, R. S and Ucer, A. s., "A Theoretical and xperimental Investigation of a Gas Dynamic Model for a Single Stage Reciprocating Compressor with Intake and Deli very Pipe systems", J. Mech. ngg. sc., v. 14, No. 4, 1972, 264-279. 2. Prakash, R. and Singh, R., " Mathematical Modelling and simulation of Refrigerating compressors", Proceedings of Compressor Technology Conference, Purdue University, 1974 274-283. 3. Manepatil Smita, "Simulation and Condition Monitoring studies on Reciprocating Compressor", Ph.D. thesis, Indian Institute of Technology, Delhi, 1996. 4. Schwerzler, D. D. and Hamil ton, J. F., "An Analytical Method for Determining ffective Flow and Force Areas for Refrigeration compressor Valving Systems", Proc. camp. Tech. cont., Purdue University, 1972, 30-36. Table 1. Performance parameters for different values of Initial force on suction valve plate. Performance parameters Initial force on suction valve plate, (N) 7 17 27 47 Mean.cylinder pressure(pa) 1.89 X 10 5 1.85 X 10 5 1. 77 X 10 5 1.63 X 10 5 Volume flow rate (scfm) 25 24 22 18 Volumetric efficiency (%) 81.7 78.9 72.5 60.1 Performance ratio (kg/j) 4.66 X 10-6 4.60 X 10-6 4.39 X W 6 3.96 X W 6 Table 2. Amplitude of cylinder air pressure harmonics for different values of initial force on suction valve plate(pa). Harmonics Initial force on suction valve plate, (N) 7 17 27 47 1 167615 16880-3 167285 163830 2 110346 110343 110856 112550 3 60054 61327 63818 67057 4 24751 25687 28185 34911 5 9102 10001 10394 10901 6 13961 14962 13396 10409 7 19808 17025 16'508 19418 8 17140 18587 18989 16775 9 9557 10898 12085 9942 10 3316 3659 3794 4277 11 4715 4439 2837 1474 12 6091 5714 4400 1953 825
Sud'u~m chamber Dlschorg~ charnbel" 4 P<! _'D_is_c~-:_r~~ pressure p j Ps ~- Fig.1 Physical model of the single stage reciprocating air compressor. 700--.------,--------------r-----.., IDO a_ - 2:!500 ;;;l ~400" 0. i 300 :;; ~200 is 100 Sucli 011 valve opi!.ns -j Yc r------v.swepl:'-----""" v- [H2] :xpan ion [2 3] Suction [3-4] Compression [4-1] -Discharge Fig 2. Thermodynamic cycle of the reciprocating air compressor ooo,-----.---------------.------, 500 :.::400 :'! ;;;l 'j!130o c. ~200 100-7.0 f>l 17.0 N -27.0 N -47.0 N 0.01 0.02 0.03 0.04 0.0!1 0.011 0.07 O.OB Time, sec. Fig.3 Cylinder air pressure time diagram for different values of Finit on suction valve. 0 o.oo o.o1 0.02 o.03 o.04 o.os o.os o.01 o.oa Time. sec. Fig.4 Cylinder air temperature diagram for different values of Finit on suction valve 1.4-,-----------.,-------------... -7N 17N -271'1-47N "i., OJ u '5. '6 ]!_ 0.500 ~ 1.0 IIi ~o.g ~o.e 'Cl ~04?;' M! 0.01 0.02 0.03 0.04 o.os 0.08 0.07 0.01 Time, sec. Fig.5 Valve displacement-time diagram for different values of Finit on suction valve. 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 Time, sec. Fig.6 Cylinder air mass-time diagram for different values of Finit on suction valve. 826