Finite-Volume Solver of the Euler Equation for Real Fluids

Abstract

The analysis of real-fluid flow have a particular importance for the description of many technological devices that operates with compressible fluids that cannot be described either as perfect gas or as incompressible fluid, such as regenerative cooling system for cryogenic rocket engine. The aim of this study is to introduce the problem of real fluid-dynamics by means of the unsteady one-dimensional Euler equation for a generic, single-phase, compressible fluid. A proper numerical solver based on a finite-volume, Godunov-type approach, which is second order accurate in space, is presented. Three different approximate Riemann solvers, which are the crucial point of the Godunov-type schemes, are extended for the case of real fluids. Finally, the accuracy and robustness of the numerical solver are proved on shock-tube experiments for methane in gas, vapor, liquid and supercritical state. Fluid properties are described by means of the high accuracy MBWR equation of state