Accurate and computationally efficient equations of state for the numerical simulation of dense gas flows

In this paper, an analytical equation of state for dense gases has been developed, cast into a mathematical form that is particularly suited for implementation within CFD codes. The aim is to obtain a mathematical model that relates directly the thermodynamic quantities of interest to the conservative variables. This avoids the use of an iterative procedure to solve a highly non-linear equation for the temperature. An optimization strategy based on Genetic Algorithms and Gradient Method has been considered to find the coefficients of this new equations. This strategy has been applied to two different class of substances: heavy fluorocarbons and siloxanes. These new models have been tested within a CFD code through detailed cross-comparisons with the original Martin-Hou and Span-Wagner models in terms of efficiency and computational cost. The new models allows reproducing with a great accuracy the results obtained with the standard equations, with a dramatic decrease of the global cost per iteration and per grid point.