A NEW INVISCID FLUX-SPLITTING ALGORITHM FOR MULTI-SPECIES REAL GASES

The purpose of this paper is to develop a high-fidelity numerical algorithm to model multi-species real gases in local thermodynamic equilibrium. The Euler equations for the mixture is considered which is coupled with the mass... [ view full abstract ]

The purpose of this paper is to develop a high-fidelity numerical algorithm to model multi-species real gases in local thermodynamic equilibrium. The Euler equations for the mixture is considered which is coupled with the mass conservation equation for each species. This coupled approach consists of seeing the Euler and species system of equations as a whole; however, they can be updated using different schemes. In this work, the Euler equations are solved using a finite-volume method based on Roe’s flux difference splitting scheme including real gas effects whereas species are updated using a classical upwind approximation. As the solution evolves, the developed method preserves the positivity as well as the monotonicity of the mass fractions of all species. However, the main interest of the method is avoiding unnecessary assumptions and approximations or using auxiliary quantities to consider real gas effects in the flow solver. In Roe’s scheme these assumptions are specifically used to calculate the partial derivatives of pressure with respect to density and internal energy in the average state. In this work, we present a novel algorithm to calculate the Jacobian matrix which satisfies perfectly the flux difference splitting in the average state. This algorithm rises the robustness and accuracy of the method specially around the contact discontinuities where the gas properties jump appreciably. In this work, the change in the gas (mixture) properties are taken into account by a dynamic coupling of the solver to a thermodynamic database.
To verify our method, the shock tube problem involving different gas mixtures separated by an interface are solved. Various mixtures using SF6, CF4 and C2F4 gases with severe initial conditions have been performed to evaluate the robustness of the method. The results are compared with the analytical solution which considers real gas effects as well. It is shown that in several cases the results are perfectly match with the analytical solution.