Modeling and simulations of high-density two-phase flows using projection-based Cahn-Hilliard Navier-Stokes equations

TL;DR

This paper introduces a projection-based computational framework for simulating high-density ratio two-phase flows using thermodynamically-consistent Cahn-Hilliard Navier-Stokes equations, validated through canonical problems and large density ratio simulations.

Contribution

The work develops a novel, robust numerical method for high-density ratio two-phase flows, enabling simulations with ratios up to 10^5, which were previously unreported.

Findings

Successfully simulated three physical systems with density ratios up to 10^5.

Validated the numerical method on canonical problems like capillary waves and bubble rise.

Demonstrated the method's robustness and accuracy through convergence studies.

Abstract

Accurately modeling the dynamics of high-density ratio ($\mathcal{O}(10^5)$) two-phase flows is important for many material science and manufacturing applications. This work considers numerical simulations of molten metal oscillations in microgravity to analyze the interplay between surface tension and density ratio, a critical factor for terrestrial manufacturing applications. We present a projection-based computational framework for solving a thermodynamically-consistent Cahn-Hilliard Navier-Stokes equations for two-phase flows with large density ratios. The framework employs a modified version of the pressure-decoupled solver based on the Helmholtz-Hodge decomposition presented in Khanwale et al. [{\it A projection-based, semi-implicit time-stepping approach for the Cahn-Hilliard Navier-Stokes equations on adaptive octree meshes.}, Journal of Computational Physics 475 (2023): 111874]. We validate our numerical method on several canonical problems, including the capillary wave and single bubble rise problems. We also present a comprehensive convergence study to investigate the effect of mesh resolution, time-step, and interfacial thickness on droplet-shape oscillations. We further demonstrate the robustness of our framework by successfully simulating three distinct physical systems with extremely large density ratios ($10^4$-$10^5:1$), achieving results that have not been previously reported in the literature.