Simulation of two-phase flows at large density ratios and high Reynolds numbers using a discrete unified gas kinetic scheme

TL;DR

This paper develops a 3D discrete unified gas kinetic scheme for simulating two-phase flows with large density ratios and high Reynolds numbers, demonstrating its effectiveness through multiple benchmark problems.

Contribution

The paper introduces two key improvements to the DUGKS method, enabling accurate simulation of complex two-phase flows at large density ratios and high Reynolds numbers.

Findings

Successfully simulates flows with density ratios and Reynolds numbers up to O(1000)

Results agree well with previous numerical and experimental data

Demonstrates capability on both 2D and 3D benchmark problems

Abstract

In order to treat immiscible two-phase flows at large density ratios and high Reynolds numbers, a three-dimensional code based on the discrete unified gas kinetic scheme (DUGKS) is developed, incorporating two major improvements. First, the particle distribution functions at cell interfaces are reconstructed using a weighted essentially non-oscillatory scheme. Second, the conservative lower-order Allen-Cahn equation is chosen, instead of the higher-order Cahn-Hilliard equation, to evolve the free-energy based phase field governing the dynamics of two-phase interfaces. Five benchmark problems are simulated to demonstrate the capability of the approach in treating two phase flows at large density ratios and high Reynolds numbers, including three two dimensional problems (a stationary droplet, Rayleigh-Taylor instability, and a droplet splashing on a thin liquid film) and two three-dimensional problems (binary droplets collision and Rayleigh-Taylor instability). All results agree well with the previous numerical and the experimental results. In these simulations, the density ratio and Reynolds number can reach a large value of O(1000). Our improved approach sets the stage for the DUGKS scheme to handle realistic two-phase flow problems.