A regularized isothermal phase-field model of two-phase solid–fluid mixture and its spatial dissipative discretization equations

2021 ◽  
Vol 36 (4) ◽  
pp. 197-217
Author(s):  
Vladislav Balashov
Keyword(s):  
Phase Field ◽  
Solid Phase ◽  
Numerical Study ◽  
Strain Tensor ◽  
Phase Field Model ◽  
Evolutionary Equation ◽  
Two Phase ◽  
Fluid Mixture ◽  
Component Mixture ◽  
Eulerian Description

Abstract The present paper is devoted to a model describing a two-phase isothermal mixture, in which one of the phases obeys solid-like (namely, elastic) rheology. A fully Eulerian description is considered. To describe the stress–strain behaviour of the solid phase the elastic energy term is added to the Helmholtz free energy. The term depends on Almansi strain tensor. In its turn, the strain tensor is defined as the solution of the corresponding evolutionary equation. Considered model belongs to the phase field family. Formally it describes two-component mixture and uses mass densities of the components as order parameters. A distinctive feature of the considered model is its preliminary regularization according to the quasi-hydrodynamic framework. The dissipativity in total energy is proved when periodic boundary conditions are imposed. A spatial dissipative semi-discrete (continuous in time and discrete in space) scheme based on staggered grids is suggested. The theoretical results remain valid in the absence of the regularization. The results of a numerical study in a 2D setting are presented.

scholarly journals A Numerical Study on Stratified Shear Layers With Relevance to Oil-Boom Failure

2014 ◽  
Author(s):  
David Kristiansen ◽  
Odd M. Faltinsen
Keyword(s):  
Numerical Model ◽  
Phase Field ◽  
Field Model ◽  
Numerical Study ◽  
Phase Field Model ◽  
Processing Unit ◽  
Stable Model ◽  
Interface Instability ◽  
Two Phase ◽  
Oil Boom

Interface dynamics of two-phase flow, with relevance for leakage of oil retained by mechanical oil barriers, is studied by means of a 2D lattice-Boltzmann method combined with a phase-field model for interface capturing. A Multi-Relaxation-Time (MRT) model of the collision process is used to obtain a numerically stable model at high Reynolds-number flow. In the phase-field model, the interface is given a finite but small thickness where the fluid properties vary continuosly across a thin interface layer. Surface tension is modelled as a volume force in the transition layer. The numerical model is implemented for simulations with the graphic processing unit (GPU) of a desktop PC. Verification tests of the model are presented. The model is then applied to simulate gravity currents (GC) obtained from a lock-exchange configuration, using fluid parameters relevant for those of oil and water. Interface instability phenomena are observed, and obtained numerical results are in good agreement with theory. This work demonstrates that the numerical model presented can be used as a numerical tool for studies of stratified shear flows with relevance to oil-boom failure.

Mass and Volume Conservation in Phase Field Models for Binary Fluids

2013 ◽  
Vol 13 (4) ◽  
pp. 1045-1065 ◽  
Author(s):  
Jie Shen ◽  
Xiaofeng Yang ◽  
Qi Wang
Keyword(s):  
Phase Field ◽  
Numerical Study ◽  
Mixing Layer ◽  
Phase Field Model ◽  
Fluid Phase ◽  
Binary Fluids ◽  
Fluid Mixture ◽  
Volume Fractions ◽  
Phase Field Models ◽  
Constraints Model

AbstractThe commonly used incompressible phase field models for non-reactive, binary fluids, in which the Cahn-Hilliard equation is used for the transport of phase variables (volume fractions), conserve the total volume of each phase as well as the material volume, but do not conserve the mass of the fluid mixture when densities of two components are different. In this paper, we formulate the phase field theory for mixtures of two incompressible fluids, consistent with the quasi-compressible theory [28], to ensure conservation of mass and momentum for the fluid mixture in addition to conservation of volume for each fluid phase. In this formulation, the mass-average velocity is no longer divergence-free (solenoidal) when densities of two components in the mixture are not equal, making it a compressible model subject to an internal con-straint. In one formulation of the compressible models with internal constraints (model 2), energy dissipation can be clearly established. An efficient numerical method is then devised to enforce this compressible internal constraint. Numerical simulations in confined geometries for both compressible and the incompressible models are carried out using spatially high order spectral methods to contrast the model predictions. Numerical comparisons show that (a) predictions by the two models agree qualitatively in the situation where the interfacial mixing layer is thin; and (b) predictions differ significantly in binary fluid mixtures undergoing mixing with a large mixing zone. The numerical study delineates the limitation of the commonly used incompressible phase field model using volume fractions and thereby cautions its predictive value in simulating well-mixed binary fluids.

scholarly journals A Numerical Study on Stratified Shear Layers With Relevance to Oil-Boom Failure

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
David Kristiansen ◽  
Odd M. Faltinsen
Keyword(s):  
Numerical Model ◽  
Phase Field ◽  
Field Model ◽  
Numerical Study ◽  
Phase Field Model ◽  
Processing Unit ◽  
Stable Model ◽  
Interface Instability ◽  
Two Phase ◽  
Oil Boom

Interface dynamics of two-phase flow, with relevance for leakage of oil retained by mechanical oil barriers, is studied by means of a two-dimensional (2D) lattice-Boltzmann method (LBM) combined with a phase-field model for interface capturing. A multirelaxation-time (MRT) model of the collision process is used to obtain a numerically stable model at high Reynolds number flow. In the phase-field model, the interface is given a finite but small thickness, where the fluid properties vary continuously across a thin interface layer. Surface tension is modeled as a volume force in the transition layer. The numerical model is implemented for simulations with the graphic processing unit (GPU) of a desktop personal computer. Verification tests of the model are presented. The model is then applied to simulate gravity currents (GCs) obtained from a lock-exchange configuration, using fluid parameters relevant for those of oil and water. Interface instability phenomena are observed, and obtained numerical results are in good agreement with theory. This work demonstrates that the numerical model presented can be used as a numerical tool for studies of stratified shear flows with relevance to oil-boom failure.

scholarly journals A ternary Cahn–Hilliard–Navier–Stokes model for two-phase flow with precipitation and dissolution

2020 ◽  
pp. 1-35
Author(s):  
Christian Rohde ◽  
Lars von Wolff
Keyword(s):  
Phase Field ◽  
Stokes Equations ◽  
Solid Phase ◽  
Immiscible Fluids ◽  
Sharp Interface ◽  
Ion Concentration ◽  
Navier Stokes ◽  
Interface Model ◽  
Sharp Interface Model ◽  
Two Phase

We consider the incompressible flow of two immiscible fluids in the presence of a solid phase that undergoes changes in time due to precipitation and dissolution effects. Based on a seminal sharp interface model a phase-field approach is suggested that couples the Navier–Stokes equations and the solid’s ion concentration transport equation with the Cahn–Hilliard evolution for the phase fields. The model is shown to preserve the fundamental conservation constraints and to obey the second law of thermodynamics for a novel free energy formulation. An extended analysis for vanishing interfacial width reveals that in this limit the sharp interface model is recovered, including all relevant transmission conditions. Notably, the new phase-field model is able to realize Navier-slip conditions for solid–fluid interfaces in the limit.

Multiphase Phase-Field Approach for Virtual Melting: A Brief Review

2021 ◽  
Vol 18 (2) ◽  
pp. 102-107
Author(s):  
Arunabha Mohan Roy
Keyword(s):  
Phase Transformations ◽  
Phase Field ◽  
Field Model ◽  
Solid Phase ◽  
Scale Effects ◽  
Phase Field Model ◽  
Short Review ◽  
Nanoscale Material ◽  
Material Parameters ◽  
Field Approach

A short review on a thermodynamically consistent multiphase phase-field approach for virtual melting has been presented. The important outcomes of solid-solid phase transformations via intermediate melt have been discussed for HMX crystal. It is found out that two nanoscale material parameters and solid-melt barrier term in the phase-field model significantly affect the mechanism of PTs, induces nontrivial scale effects, and changes PTs behaviors at the nanoscale during virtual melting.

Sign in / Sign up

Export Citation Format

Share Document