Surface tension for compressible fluids in ALE framework

Corot, Théo; Hoch, Philippe; Labourasse, Emmanuel

doi:10.1016/j.jcp.2020.109247

Cited by 7 publications

(17 citation statements)

References 61 publications

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“…The third and final approach is a homogeneous flow model known as the "one-fluid" formulation, where an equilibrium is assumed to exist between the liquid and the gas phases. This one-fluid formulation has been extensively used in incompressible flow [23][24][25][26], and recently in compressible shock modelling [12,27,28] of liquid-gas systems. For this article, we shall consider the inviscid modelling of a liquid-gas flow via a homogeneous one-fluid method.…”

Section: Introductionmentioning

confidence: 99%

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An All-Mach Number HLLC-Based Scheme for Multi-Phase Flow with Surface Tension

et al. 2021

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This paper presents an all-Mach method for two-phase inviscid flow in the presence of surface tension. A modified version of the Hartens–Lax–van Leer Contact (HLLC) solver is developed and combined for the first time with a widely used volume-of-fluid (VoF) method: the compressive interface capturing scheme for arbitrary meshes (CICSAM). This novel combination yields a scheme with both HLLC shock capturing as well as accurate liquid–gas interface tracking characteristics. It is achieved by reconstructing non-conservative (primitive) variables in a consistent manner to yield both robustness and accuracy. Liquid–gas interface curvature is computed via height functions and the convolution method. We emphasize the use of VoF in the interest of interface accuracy when modelling surface tension effects. The method is validated using a range of test-cases available in the literature. The results show flow features that are in sensible agreement with previous experimental and numerical work. In particular, the use of the HLLC-VoF combination leads to a sharp volume fraction and energy field with improved accuracy.

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Section: Introductionmentioning

confidence: 99%

“…To capture the compressible characteristics in the flow, different solvers are outlined in the literature [1,12,20,[27][28][29]. These comprise the popular Riemann-or Godunov-type schemes [29][30][31] and the semi-implicit projection solvers [32].…”

Section: Introductionmentioning

confidence: 99%

An All-Mach Number HLLC-Based Scheme for Multi-Phase Flow with Surface Tension

et al. 2021

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“…However, for problems that involve small interfacial length scales or topology changes due to liquid breakups, the capillary time scale becomes comparable to the flow time scale, then the surface tension is important and must be rigorously incorporated in the simulation. DNS of compressible interfacial multiphase flows with surface tension is an emerging area, and only a few studies are available in the literature [4,5,6,7,8]. The recent progress on the diffused-interface methods in simulating compressible two-phase flows is reviewed by Saurel and Pantano [9].…”

Section: Introductionmentioning

confidence: 99%

“…A minor drawback of the method is the lack of sufficient treatment for shock capturing, as a result, the numerical oscillations near discontinuities are not sufficiently damped. More recently, Corot et al [8] developed an ALE method for two-phase compressible flows with surface tension. When the interface deformation is small, the interface is tracked based on the Lagrangian framework, while the deformation becomes large, the method switches to the Eulerian representation of the interface and resolves the interface with the VOF method.…”

Section: Introductionmentioning

confidence: 99%

“…The method is accurate but is also more complicated to use due to the addition of the Lagrangian step. The viscous effects are generally ignored in these simulations [4,8]. The present study aims at extending the method of Fuster and Popinet (FP) to enable direct numerical simulation of compressible interfacial multiphase flows with interaction between shock waves and interfaces.…”

Section: Introductionmentioning

confidence: 99%

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Conservative, Consistent All-Mach Method to Simulate Liquid Atomization in Supersonic Flows

Ling

Zhang

2021

ICLASS

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Atomization of bulk liquids subjected to a supersonic flow is essential to applications such as liquid fuel injection in supersonic propulsion systems. Since high-level details are often difficult to measure in experiments, numerical simulation is an important alternative to shed light on the unclear physics. A detailed numerical simulation (DNS) of liquid atomization in supersonic flows will need to rigorously resolve the shock waves, the interfaces, and the interaction between the two. In the present study, a new simulation framework for compressible multiphase flows is proposed. The geometric volume-of-fluid (VOF) method is employed to advect the sharp interfaces. The convection fluxes of density, momentum, and energy are computed based on the VOF flux, to achieve an important mass-momentum-energy consistence. To suppress spurious oscillations near shocks, numerical diffusion is introduced in single-phase regions away from the interface. The contribution of pressure is incorporated using a projection method, so that the method can be used for flows of all Mach numbers. Different compressible interfacial multiphase flow problems, including the two-phase shocktube, Richtmyer-Meshkov instability (RMI), and shock-drop interaction have been used to test the present method. The linear singlemode RMI with finite Weber and Reynolds numbers are simulated. The simulation results agree very well with the linear stability theory, which clearly affirms the capability of the present method in capturing the viscous and capillary effects on shock-interface interaction.

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An ALE‐based finite element strategy for modeling compressible two‐phase flows

Potghan

Jog

2022

Numerical Methods in Fluids

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In this work, we develop a numerical strategy for solving two-phase immiscible compressible fluid flows in a general arbitrary Lagrangian-Eulerian framework.The interpolation functions for the field variables are chosen so as to produce a stable numerical formulation. We model one of the fluids in a Lagrangian setting and use a conforming mesh moving with it which circumvents the need of solving an additional diffusion equation to track or construct the interface. The discontinuity in the pressure field across the interface is accurately modeled using the dummy-node technique. This technique yields a sharp and accurate representation of the interface and in turn a correct computation of the surface tension forces. We present a variational form of the governing equations including the surface tension effect and their exact linearization. Various benchmark examples are presented to illustrate the good performance and good coarse-mesh accuracy of the proposed scheme.

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Surface tension for compressible fluids in ALE framework

Cited by 7 publications

References 61 publications

An All-Mach Number HLLC-Based Scheme for Multi-Phase Flow with Surface Tension

An All-Mach Number HLLC-Based Scheme for Multi-Phase Flow with Surface Tension

Conservative, Consistent All-Mach Method to Simulate Liquid Atomization in Supersonic Flows

An ALE‐based finite element strategy for modeling compressible two‐phase flows

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