Using a Gas Dynamic Model to Predict the Supercharging Phenomenon in a Variable Speed Compressor

A non-linear gas dynamic model is used in this paper to study the pressure pulsations in the intake of a variable speed compressor, since the perturbation pressure in this study is so large that the linear acoustic theory is no longer valid. Friction and heat transfer are considered in the model. Three numerical schemes are applied to solve the governing equations which are non-linear hyperbolic partial differential equations. The computed results from different numerical algorithms are compared with each other, and are also verified by experiment data. The supercharging phenomenon resulting from wave action in the suction line of the compressor is studied. Volumetric efficiency gain and energy loss due to supercharging are explained. Introduction Simulation of the unsteady flow processes which occur in the intake and discharge systems is a very important part of a complete mathematical simulation of a compressor. Unsteady flow and gas pulsations are inherent to compressors. This causes the pressures in piping systems and cavities to be functions of both time and space. Without including a mathematical model describing gas pulsations, the compressor simulation may suffer significantly in both accuracy and reliability. The importance of gas pulsations has been recognized in the last three decades. Pressure fluctuations in the suction and discharge plenums affect the valve response and mass flow rates through the suction and discharge passages, which, in tum, influence the compressor thermodynamic performance because of the interaction of the suction and discharge flows with the cylinder processes. Gas pulsations can also result in valve fluttering, piping vibration, and noise radiation. In addition to its effects on vibration and noise, gas pulsations in the suction line can considerably affect the volumetric efficiency of a compressor. If the wave action in the suction pipe is tuned properly, the pressure in the suction port can be higher than the pressure in the inlet to the suction pipe. When this occurs, the volumetric efficiency, referenced to the inlet condition of the suction pipe, is more than 100%. This is called a supercharging effect. The effect of supercharging on the volumetric efficiency, and therefore the capacity of the compressor, has been investigated by several authors. It was reported by Jaspers [1) that "change of between 30% and ~50% in the compressor output can be produced simply by a change in the design of the suction line." Czaplinski [2) studied the effect of the length of the suction line and the compressor speed on volumetric efficiency, and reponed a maximum improvement of 15%. Various methods have been utilized to study gas pulsations. If the acoustic pressure is relatively small compared with the mean pressure (less than 20% of the mean pressure), the gas pulsations can be approximated by the acoustic (linear) theory [3). Among these methods based on linear theory, an iterative method first used by Elson and Soedel [4) has been proven to be very efficient. By taking the volume velocity, which can be obtained by dividing the mass flow rate into or out of the compressor cylinder by the mean density of the flow, as the excitation of the acoustic