A unified treatment of general fluid thermodynamics and its application to a preconditioning scheme

A unified treatment of general fluid thermodynamics is developed to handle fluid flows over their entire thermodynamic states. The analysis is based on the concepts of partial-mass and partial-density properties, and accommodates thermodynamic non-idealities and transport anomalies in the transcritical regime. The resultant routine is incorporated into a preconditioning scheme. All the thermophysical properties and numerical Jacobian matrices are derived directly from fundamental thermodynamic theories, rendering a robust algorithm valid for fluid flows at all speeds and at all thermodynamic states. As a specific example, a modified Soave-Redlich-Kwong equation of state is employed to obtain the fluid p-V-T properties. Several test cases concerning supercritical droplet vaporization in both quiescent and convective environments are presented to demonstrate the effectiveness of the present algorithm.