Mathematical Models of Gas in Hydropneumatic Accumulators Used in Numerical Tests of Drive Systems with Energy Recovery

Abstract

In recent years, multiple studies have been carried out on drive systems with energy recovery that are composed of hydropneumatic accumulators. In preliminary studies, these drive systems are frequently tested by computer simulation. Various mathematical models of gas in the accumulator have been used in different studies. It is not clear whether the results obtained by assuming various gas models can be directly compared with each other. In this study, the gas models most frequently used in practice are presented and evaluated in terms of the accuracy in predicting the efficiency of energy recovery from a hydropneumatic accumulator; five different gas equations of state are assessed, as well as various methods for calculating the specific heat capacity at constant volume. Typical methods used in mathematical models to describe the heat transfer between the hydropneumatic accumulator and the environment are discussed. The results of this study show that all real gas models can precisely predict the efficiency of energy recovery from the accumulator in typical operating conditions. However, neither the models based on the ideal gas law nor the models neglecting the heat exchange with the environment are accurate enough for studies in that field. In the last part of this paper, the models of gases in hydropneumatic accumulators implemented in selected commercial software are described and tested against the model developed by the author in Matlab.