Thermodynamic modeling for numerical simulations based on the generalized cubic equation of state

TL;DR

This paper develops a generalized thermodynamic model for cubic equations of state, enabling flexible CFD simulations and comparisons among different models like Peng-Robinson and Redlich-Kwong, validated against reference data.

Contribution

It introduces a unified formulation for cubic equations of state, facilitating generic implementation and comparison in CFD applications.

Findings

The generalized model accurately describes thermodynamic properties for various fluids.

The Redlich-Kwong-Peng-Robinson equation overcomes limitations of simpler models.

The provided Python library and OpenFOAM implementation enable practical use and validation.

Abstract

We further elaborate on the generalized formulation for cubic equation of state proposed by Cismondi and Mollerup [Fluid Phase Equilib. 232 (2005)]. With this formulation all well-known cubic equations of state can be described with a certain pair of values, which allows for a generic implementation of different equations of state. Based on this generalized formulation, we derive a complete thermodynamic model for computational fluid dynamics (CFD) simulations by providing the resulting correlations for all required thermodynamic properties. For the transport properties, we employ the Chung correlations. Our generic implementation includes the often used equations of state Soave-Redlich-Kwong and Peng-Robinson and the Redlich-Kwong-Peng-Robinson (RKPR) equation of state. The first two assume a universal compressibility factor and are therefore only suitable for fluids with a matching critical compressibility. The Redlich-Kwong-Peng-Robinson overcomes this limitation by considering the equation of state parameter as function of the critical compressibility. We compare the resulting thermodynamic modeling for the three equations of state for selected fluids with each other and CoolProp reference data. As supplementary material to this paper, we provide a Python tool called real gas thermodynamic python library (realtpl). This tool can be used to evaluate and compare the results for a wide range of different fluids. Additionally, we also provide the implementation of the generalized form in OpenFOAM.