A phase field model for compressible immiscible fluids with a new equation of state. (April 2022) - Dai, Hao; Xu, Shixin; Xu, Zhiliang; Zhao, Ning; Zhu, Cheng-Xiang; Zhu, Chunling
Abstract: In this paper, we propose a new compressible phase field model of two different immiscible fluid components, in which the density of each phase is variable. In order to establish the compressible phase field model, a new P-V-T equation of state is introduced to solve the pressure. The new model is derived by the physics law of conservation, and conforms to the second law of thermodynamics. The model adopts an innovative expression of Helmholtz free energy, taking into account the new state equation of pressure and the varying material properties of each phase. A high-order accurate numerical scheme is introduced to solve the model equations. The convection terms of the governing equations are discretized by the fifth-order WENO scheme, and the residual terms are discretized by the Lax–Friedrichs method. Finally, the reliability and validity of the compressible two-phase model are verified by numerical simulations. Highlights: The compressibility of fluid cannot be ignored when the velocity is high. Deriving compressible phase field equation based on entropy increasing principle. The viscosity and thermal conductivity of mixture are different. An equation of state for mixture is established.