A sharp interface method for coupling multiphase flow, heat transfer and multicomponent mass transfer with interphase diffusion

Abstract

Mixing of partially miscible fluids plays an important role in many physical and chemical processes. The modeling complexities lie in the tight coupling of the multiphase flow, heat transfer and multicomponent mass transfer, as well as diffusions across the phase interface. We present a sharp interface method for modeling such process. The non-ideal equation of state is used to compute the fluid properties such as density, fugacity and enthalpy, and to predict phase equilibrium composition. The phase interface location is tracked using the phase propagation velocity. A third-order one-sided finite difference scheme using a variable grid size according to the interface location is utilized to discretize the partial derivatives immediately next to the interface, while a second-order central scheme is used for the bulk of fluids. An optimization method, the Nelder–Mead method, is applied to search for (1) the phase compositions on both sides of the interface, and (2) the phase propagation velocity based on the coupling of the multicomponent phase equilibrium and the species' balance across the interface. The temperature at the interface is determined by the energy balance. Numerical results are used to demonstrate the convergence of our method and show its capability to simulate the mixing of multicomponent partially miscible fluids.