Soave-Redlich-Kwong Adiabatic Equation for Gas-loaded Accumulator

Abstract

In this paper, a Soave-Redlich-Kwong adiabatic equation of real gas charged in accumulators is proposed. The Soave-Redlich-Kwong equation is the most accurate real gas model for representing accumulator behavior, but it is relatively complex mathematical equation. For simulating accumulator dynamic behavior, it has been used by combining with a thermal time constant model. The mathematical procedure for the Soave-Redlich-Kwong equation for the adiabatic equation is described in this paper. The Soave-Redlich-Kwong adiabatic equation is discussed by comparing the van der Waals adiabatic equation. By comparing representative gas models, the Soave-Redlich-Kwong adiabatic equation is found to be valid. 研究論文 1．Introduction Selection of accumulator size and prefill pressure have been discussed by many researchers. A typical practice is to assume that the process involved is isothermal, adiabatic, or polytropic 1）. Isothermal operation maintains a constant temperature, which requires the rate of expansion and compression of the gas at such a rate that the gas temperature inside the accumulator remains relatively constant throughout the entire cycle. For the adiabatic operation, the gas temperature inside the accumulator increases or decreases at a high rate due to the rapid compression or expansion of the gas. However, in practical processes, the temperature is increasing during charge process and decreasing during discharge process. A concept of polytropic change is used to describe the phenomena, where the polytropic exponent n is used to compensate the inaccuracy for calculating accumulator. For the polytropic exponent of the currently employed gas, nitrogen, the value has been predicted by experiment according to charging and discharging time and average working pressure 2）. Simultaneously, for taking intermolecular forces and molecular volume into account, real gas models have been presented and developed by researchers. Modeling of thermodynamic behavior of fluid over the whole range of temperatures, densities and pressures is not an easy task. At low pressure, the isotherms are fairly easily modeled with something like the ideal gas model. However, at higher density the behavior becomes more difficult to model with a simple equation 3）. As the first correction to the ideal gas equation, the van der Waals equation was developed for engineering purposes 4）. The two most commonly used cubic equations of state are the Redlich-Kwong 5） and Soave's modification of the Redlich-Kwong equation of state （Soave-Redlich-Kwong equation 6） ）. These models were developed by modifying the van der Waals equation, and it has been applied in a commercial software. It is necessary to consider the energy balance in accumulator. The nitrogen gas in accumulator has internal energy which receives heat energy from the environment and performs work to the working fluid. Predicting thermodynamic loss is necessary. Otis has presented a thermal time constant model which has been combined with the Beattie-Bridgman equation of state to describe the heat transfer from the accumulator wall 7）-8）. It is relatively easy to use the van der Waals equation of state. Its isothermal model and the adiabatic model are also easy to obtain mathematically. However, the Soave-Redlich-Kwong equation has relatively complex mathematical expression. The adiabatic equation has not been found. Therefore, for calculating accumulator, only one possibility was to combine the Soave-Redlich-Kwong equation with the thermal time constant model to carry out numerical integration. The purpose of this paper is to propose an adiabatic expression of ＊ Manuscript