Mathematical modeling of multicylinder compressor discharge system interactions

Abstract Gas oscillations are complicated in a multicylinder compressor discharge system because of the cylinder interactions. These are identified and modeled here as kinematic and geometric types of coupling. The kinematic coupling effect is incorporated with the input volume velocities, at the values, which are derived from the discharge mass flow rates. To account for the geometric interactions arising because of the interconnected cavities and passages, impedance matrices are formulated. The discharge system components are described by steady state acoustic impedances, in distributed parameters format. The overall discharge system mathematical model (in the frequency domain) is then coupled with the time domain compressor cylinder thermodynamic, and valve fluid and structural dynamic models. An iterative is used to account for the back pressure effect. The theory is applied to a two cylinder high speed refrigeration compressor. Unsteady flow pressures are predicted in the valve chamber (for capacity and energy consumption considerations), and at the manifold end (for muffling effectiveness consideration). Excellent agreements between theory and experiment are obtained. The technique as outlined in this paper should be applicable to any multicylinder/interstaged positive displacement type of fluid machine.