Performance Prediction of Reciprocating Compressor

The technique of the modeling and analysis procedures of reciprocating compressor is described which predict the basic performance of the compressor, compute the pressure pulsations in cylinder and suction line and simulate valve motions. The polytropic process assumption was used for modeling cylinder thermodynamic process and four-pole transfer matrix for gas pulsations and spring-mass model for valve dynamics. The commercial software ANSYS and SYSNOISE were also used for numerical analysis of valve properties and impedance of suction line which can be used for a boundary condition. And comparing the simulated data such as energy efficiency ratio, cylinder pressure, suction pressure, etc to the experimental data, we confirmed the feasibility of developed technique. NOMENCLATURE k : Specific heat ratio R : Gas constant ρ : density c : Speed of sound INTRODUCTION The developments of the reciprocating compressors for high efficiency and low noise had been performed constantly, since this machine was invented. Nowadays some particular methods were required to upgrade the performance. Among them, one of the most potential means is a simulation tool which can interpret the states of compressor in more details with high accuracy. There have been numerous researchers in these areas. W. Soedel et al simulated the compressor with cylinder process and gas pulsations separately and Wambsgans developed the basis of detailed simulation model without gas pulsations. Brablik was the first who coupled the cylinder process and gas pulsations in the compressor line. And Elson et el. employed Fourier transformation technique to connect the cylinder process and pressure pulsations in compressor line. This approach was used in many situations and modified numerously. In modeling gas pulsations, W. Soedel et al adapted the linearized acoustic theory because typical components in gas manifold are small compared to the smallest wave length of general interest. In this study, we simulated the compressor with coupling the cylinder process and pressure pulsation using the Fourier transformation tool and the commercial FEM code for calculating the pressure pulsation because the linear acoustic model does not valid any more in manifold with complex geometry and the frequency we are interested in is raised, so the small geometry and components was considered to the simulations for higher accuracy. STRUCTURE OF ANALYSIS Modeling Compression Parts A Refrigerant flow passage from suction pipe to discharge pipe through the compressor is composed of many elementary component such as shell cavity, suction muffler, suction port/valve, cylinder, discharge port/valve, discharge plenum, discharge silencer and loop pipe in sequence. Following these passages, temperature and pressure of refrigerant was raised to a discharge state from a suction state. These states of refrigerant are predetermined by ASHRAE conditions. Kinematics The compression part is composed of crank arm, connecting rod, piston and cylinder. And the volume of the cylinder is expressed by the rotation angle of crank. ( ) ( ) ( )      − + − + + = β θ π Cos R Cos R e R R e D dead V c V 2 1 2 2 2 1 4 2 , ( ) ( ) ( )         + − + = − 2 1 2 2 1 1 e Sin R R e Sin R Tan θ θ β (1) where Vc is volume of cylinder, R1 is eccentricity and R2 is con-rod pitch. The piston is offset by the amount of e from the center line of the crank. Thermodynamics Assuming ideal gas, one dimensional flow and polytropic process, the pressure in cylinder is given as follows; ( ) ( ) n s s c t V t m P P       = ρ (2) where Pc is the pressure of cylinder, m is refrigerant mass in cylinder and Ps is pressure of suction port. Refrigerant mass in cylinder is conserved during compression and expansion process. Valve Flows and Valve Dynamics The flow through valve port can be modeled by a simple orifice flow assuming one-dimensional isentropic process, steady flow and stagnation upstream condition. The mass flow rate through the suction port is expressed as follows. ( )                     −       − = ⋅ s s s s s s sv s r f r T T r f RT k k P A m 1 ) ( 1 2 2 / 1 2 / 1 ( ) ( ) ( ) 1 1 , 0 , 0 , 2 / 1 1 / 2 2 / 1 1 / 2