An efficient preconditioning scheme for real-fluid mixtures using primitive pressure–temperature variables

An improved preconditioning scheme incorporating a unified treatment of general fluid thermodynamics is developed for treating fluid flows over the entire regime of fluid thermodynamic states at all speeds. All of the thermodynamic and numerical properties (such as eigenvalues and Jacobian matrices) are derived directly from fundamental thermodynamics theories, rendering a self-consistent and robust algorithm. Further efficiency is obtained by employing temperature instead of enthalpy as the primary dependent variable in the preconditioned energy equation. No iterative solution of a real-fluid equation of state is required. This approach, combined with the use of explicit treatments of temporal and spatial derivatives, results in a scheme for which load balance is much easier to achieve in a distributed computing environment. A numerical stability analysis is performed to assess the effectiveness of the scheme at various fluid thermodynamic states. Sample calculations are also carried out. These include injection and mixing of cryogenic fluids and flame dynamics of coaxial jets of liquid oxygen and methane under supercritical conditions. The robustness and efficiency of the present work are demonstrated over a wide range of thermodynamic and flow conditions.

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