A wavelet based numerical simulation technique for the two-phase flow using the phase field method

TL;DR

This paper introduces a wavelet collocation method for simulating two-phase flows using the phase field approach, accurately capturing interface dynamics and surface tension effects in multiphase CFD simulations.

Contribution

It presents a novel wavelet-based numerical scheme for phase field multiphase flow simulation, demonstrating high accuracy and efficiency in modeling interface phenomena.

Findings

Accurate simulation of bubble rise velocity matching experiments

Excellent agreement in surface tension force calculations with experiments

Effective modeling of Rayleigh-Taylor instability disturbances

Abstract

In multiphase flow phenomena, bubbles and droplets are advected, deformed, break up into smaller ones, and coalesce with each other. A primary challenge of classical computational fluid dynamics (CFD) methods for such flows is to effectively describe a transition zone between phases across which physical properties vary steeply but continuously. Based on the van der Waals theory, Allen-Cahn phase field method describes the face-to-face existence of two fluids with a free-energy functional of mass density or molar concentration, without imposing topological constraints on interface as phase boundary. In this article, a CFD simulation methodology is described by solving the Allen-Cahn-Navier-Stokes equations using a wavelet collocation method. The second order temporal accuracy is verified by simulating a moving sharp interface. The average terminal velocity of a rising gas bubble in a liquid that is computed by the present method has agreed with that computed by a laboratory experiment. The calculation of the surface tension force by the present method also shows an excellent agreement with what was obtained by an experiment. The up-welling and down-welling disturbances in a Rayleigh-Taylor instability are computed and compared with that from a reference numerical simulation. These results show that the wavelet based phase-field method is an efficient CFD simulation technique for gas-liquid or liquid-liquid flows.