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.