A phase-field/ALE method for simulating fluid–structure interactions in two-phase flow

Abstract

We present a phase-field/ALE method for simulating fluid-structure interactions (FSI) in two-phase flow. We solve the Navier-Stokes equation coupled with the Cahn-Hilliard equation and the structure equation in an arbitrary Lagrangian Eulerian (ALE) framework. For the fluid solver, a spectral/hp element method is employed for spatial discretization and backward differentiation for time discretization. For the structure solver, a Galerkin method is used in Lagrangian coordinates for spatial discretization and the Newmark-β scheme for time discretization. The mesh is updated from the initial configuration by a harmonic mapping constructed from the velocity of the interface between the fluid and the structure subdomains. To test the accuracy of the phase-field approach of this multi-physics method, we first simulate two-phase co-annular laminar flow in a stationary pipe and compare the results with the analytical solution. To test the accuracy of the FSI solver, we simulate a pipe conveying single-phase flow and compare the results with an existing validated code [1]. Finally, we present two numerical simulations of FSI in two-phase flow, specifically, in a flexible pipe conveying two fluids that induce self-sustained oscillations, and in external cross flow past a circular cylinder that modifies the classical vortex street due to a Kelvin-Helmholtz instability. These three-dimensional simulations demonstrate the capability of the method in dealing with FSI problems in two-phase flow with moving grids as well as its robustness and efficiency in handling different fluids with large contrast in physical properties.

An IB Method for Non-Newtonian-Fluid Flexible-Structure Interactions in Three-Dimensions

“…Since the birth of the IB method, numerous methods for FFSI problems are developped. These include immersed boundary method [Iaccarino and Verzicco (2003); Mittal and Iaccarino (2005)], Arbitrary Lagrangian Eulerian (ALE) [Hughes, Liu and Zimmermann (1981); Donea, Giuliani and Halleux (1982); Yang, Sun, Wang et al (2016)], the lattice Boltzmann [Lallemand and Luo (2003)], fictitious domain [Glowinski, Pan and Periaux (1994a,b)], front tracking [Glimm, Grove, Li et al (1998)], immersed interface [Leveque and Li (1994); LeVeque and Li (1997); Li and Lai (2001)], blob-projection [Cortez (2000)], phase field [Sun, Xu and Zhang (2014); Wick (2016); Zheng and Karniadakis (2016); Mokbel, Abels and Aland (2018)], immersed John et al (2018)] are developping an immersed-boundary lattice-Boltzmann method for viscoelastic fluids including Oldroyd-B and FENE-CR fluids. In their work the motion equations of the solid are solved for by finite difference or finite element methods. In this paper we discuss our recent development of a 3D IB methods for three non-Newtonian fluids: power-law, Oldrod-B [Oldroyd (1950)], and FENE [Peterlin (1961)].…”

A hybrid variational Allen‐Cahn/ALE scheme for the coupled analysis of two‐phase fluid‐structure interaction

“…However, there are very few works on the FSI involving internal flow, which are mainly concerned with the experiments. Some of the recent works based on two‐phase FSI simulations are the works of Calderer et al and Zheng and Karniadakis, where an immersed‐boundary based level‐set approach and a spectral/hp element method‐based phase‐field technique are employed, respectively. The numerical study of Zheng and Karniadakis solves the Cahn‐Hilliard equation for the interface evolution.…”

“…Some of the recent works based on two‐phase FSI simulations are the works of Calderer et al and Zheng and Karniadakis, where an immersed‐boundary based level‐set approach and a spectral/hp element method‐based phase‐field technique are employed, respectively. The numerical study of Zheng and Karniadakis solves the Cahn‐Hilliard equation for the interface evolution. While the high order of the Cahn‐Hilliard equation poses numerical challenges, the second‐order Allen‐Cahn equation is relatively simpler to implement for complex phase‐field FSI modeling in three dimensions using the standard finite element framework.…”

Numerical modeling of fluid–structure interaction between sewage water flow and bar screen to improve the screening process

“…The developments in computational fluid dynamics have made possible the modelling of the FSI problem on a larger scale, such as the bar screen. The arbitrary Lagrangian–Eulerian (ALE) method is a well‐known numerical technique to model and solve the effects of fluid flow on the deformation of structures (Anderson et al ., ; Duarte et al ., ; Liu et al ., ; Clair et al ., ; Zheng and Karniadakis, ). We previously investigated the deformation in the rake system to improve the design of the automatic rake system of the bar screen under conditions of fatigue loading in the screening process (Lee et al ., ).…”