Hysteretic Smoothed Equation-of-Sate Type Vapor-Liquid Phase Transformation Model

Abstract

Vapor-liquid phase transformation is an important phenomenon in many technological applications, since boiling and condensation are associated with high heat transfer efficiency. Establishing accurate, numerically easy to handle models of this complex process has recently been the focus of many scientific and engineering research projects. Mathematical models for vapor-liquid phase transformations can be divided into two classes: diffuse interface models and sharp interface models. With the diffuse interface method, all governing equations can be solved over the entire computational domain without any priori knowledge of the location of the interfaces, therefore using the diffuse interface is a popular tool for simulations of two-phase flows in engineering applications. Generally the diffuse interface model consists of three conservation equations of mass, momentum and energy, and of an evolution equation of the order parameter that represents the transition between the phases, i.e. the so-called four-equation model. In this work, we focused on the governing equation of the phase transition. The goal was to increase the equation-of-state type equilibrium models by enabling occurrence of metastable states. The introduced model is similar to the equation-of-state type models since it is a function of an intensive state variable (temperature), but in this case this function is hysteretic. The proposed hysteresis function can be easier parameterized than the kinetic type phase transition models. The model can be very useful in several engineering applications, in which an expert could estimate the assumable degree of supersaturation/superheating. The hysteresis model of the thermally induced phase transformation has been derived from the statistics of the model fluid consists of bistable, constant-mass clusters of molecules. We have used a PDE based hysteresis operator to describe the phase change. To ensure that unstable conditions could be always avoided, we have proposed a saturation temperature dependent upper limit of the allowable supersaturation.