Modeling high density ratio two-phase and three-phase flows using Cahn-Hilliard Navier-Stokes equations
Date
2024-05
Authors
Rabeh, Ali Abd
Major Professor
Advisor
Ganapathysubramanian, Baskar
Lee, Jonghyun
Rossmanith, James
Krishnamurthy, Adarsh
Shrotriya, Pranav
Committee Member
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Abstract
Developing numerical methods to simulate multiphase flows is crucial to advancing several chemical, biomedical, and industrial applications. With the recent advancement in computational technologies, developing accurate two-phase and three-phase flows that can model large density ratios will help improve the analysis and design of many scientific applications. This is mainly due to the difficulty in conducting multiphase flow experiments involving more than two phases. In this work, we first develop a fully-coupled thermodynamically consistent Cahn-Hilliard Navier-Stokes (CHNS) model using the residual-based variational multiscale stabilization (VMS) to remove the pressure saddle point problem. Using a conforming continuous Galerkin (cG) finite element method, tuning the VMS parameters enables the simulation of two-phase flows up to a 117K density ratio. However, this tuning approach fails to solve the CHNS equations when used with adaptive mesh refinement (AMR). We then use the pressure projection CHNS model by decoupling pressure from the momentum equation solved using the block-iterative scheme. This approach requires less computational effort than the pressure-stabilized fully-coupled model, enabling 3D simulations of large density ratio two-phase flows using AMR. The third part of this work is developing a thermodynamically consistent volume-averaged three-phase flow model using pressure projection CHNS equations. By solving two Cahn-Hilliard equations in a block-iterative approach, we can track all three interfaces as a result of the volume fraction conservation property. Using a carefully constructed mobility matrix which is symmetric positive semi-definite, the three-phase model is symmetric with respect to the phase fields and demonstrates reduction-consistency with two-phase flows. In this work, we illustrate numerically the reduction consistency of our three-phase model, meaning that in the absence of any fluid, the model reduces to a two-phase flow and does not artificially generate a third phase.
We provide comprehensive validation to showcase the accuracy of our model by comparing it with results from the literature. We deploy the pressure-stabilized, fully-coupled two-phase model to simulate the Oscillating Droplet Method (ODM) of very high density ratios of up to 117K in 2D and compare results with Rayleigh theory. We also simulate the ODM in 2D and 3D using the pressure-projection approach with adaptive mesh refinement and validate results with theory and simulations. To validate our three-phase model, we test it on the swirling flow of drops in a periodic shearing flow and compare results with other numerical results from the literature. We also validate the accuracy of our three-phase solver by simulating the spreading of the floating oil lens on the air-water interface.
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dissertation