arXiv subjects

S. Zaleski

Publications and source records attributed to S. Zaleski.

11 recordsLinked to original sources

arXiv2021

A phase inversion benchmark for multiscale multiphase flows

A series of benchmarks based on the physical situation of "phase inversion" between two immiscible liquids is presented. These benchmarks aim at progressing toward the direct numerical simulation of two-phase flows. Several CFD codes developed in French laboratories and using either Volume-of-Fluid or Level-Set interface tracking methods are used to provide physical solutions of the benchmarks, convergence studies and code comparisons. Two typical configurations are retained, with integral scale Reynolds numbers of 13.700 and 433.000, respectively. The physics of the problem are probed through macroscopic quantities such as potential and kinetic energies, or enstrophy. In addition, scaling laws for the temporal decay of the kinetic energy are derived to check the physical relevance of the simulations. Finally the droplet size distribution is probed. Additional test problems are also reported to estimate the influence of viscous effects in the vicinity of the interface.

physics.flu-dyn↗

arXiv2021

A mass-momentum consistent, Volume-of-Fluid method for incompressible flow on staggered grids

The computation of flows with large density contrasts is notoriously difficult. To alleviate the difficulty we consider a discretization of the Navier-Stokes equation that advects mass and momentum in a consistent manner. Incompressible flow with capillary forces is modeled and the discretization is performed on a staggered grid of Marker and Cell type. The Volume-of-Fluid method is used to track the interface and a Height-Function method is used to compute surface tension. The advection of the volume fraction is performed using either the Lagrangian-Explicit / CIAM (Calcul d'Interface Affine par Morceaux) method or the Weymouth and Yue (WY) Eulerian-Implicit method. The WY method conserves fluid mass to machine accuracy provided incompressibility is satisfied. To improve the stability of these methods momentum fluxes are advected in a manner "consistent" with the volume-fraction fluxes, that is a discontinuity of the momentum is advected at the same speed as a discontinuity of the density. To find the density on the staggered cells on which the velocity is centered, an auxiliary reconstruction of the density is performed. The method is tested for a droplet without surface tension in uniform flow, for a droplet suddenly accelerated in a carrying gas at rest at very large density ratio without viscosity or surface tension, for the Kelvin-Helmholtz instability, for a 3mm-diameter falling raindrop and for an atomizing flow in air-water conditions.

physics.comp-ph↗

arXiv2020

PArallel, Robust, Interface Simulator (PARIS)

Paris (PArallel, Robust, Interface Simulator) is a finite volume code for simulations of immiscible multifluid or multiphase flows. It is based on the "one-fluid" formulation of the Navier-Stokes equations where different fluids are treated as one material with variable properties, and surface tension is added as a singular interface force. The fluid equations are solved on a regular structured staggered grid using an explicit projection method with a first-order or second-order time integration scheme. The interface separating the different fluids is tracked by a Front-Tracking (FT) method, where the interface is represented by connected marker points, or by a Volume-of-Fluid (VOF) method, where the marker function is advected directly on the fixed grid. Paris is written in Fortran95/2002 and parallelized using MPI and domain decomposition. It is based on several earlier FT or VOF codes such as Ftc3D, Surfer or Gerris. These codes and similar ones, as well as Paris, have been used to simulate a wide range of multifluid and multiphase flows.

physics.comp-ph↗

arXiv2020

Host-to-Host Airborne Transmission As a Multiphase Flow Problem For Science-Based Social Distance Guidelines

COVID-19 pandemic has strikingly demonstrated how important it is to develop fundamental knowledge related to generation, transport and inhalation of pathogen-laden droplets and their subsequent possible fate as airborne particles, or aerosols, in the context of human to human transmission. It is also increasingly clear that airborne transmission is an important contributor to rapid spreading of the disease. In this paper, we discuss the processes of droplet generation by exhalation, their potential transformation into airborne particles by evaporation, transport over long distances by the exhaled puff and by ambient air turbulence, and final inhalation by the receiving host as interconnected multiphase flow processes. A simple model for the time evolution of droplet/aerosol concentration is presented based on a theoretical analysis of the relevant physical processes. The modeling framework along with detailed experiments and simulations can be used to study a wide variety of scenarios involving breathing, talking, coughing and sneezing and in a number of environmental conditions, as humid or dry atmosphere, confined or open environment. Although a number of questions remain open on the physics of evaporation and coupling with persistence of the virus, it is clear that with a more reliable understanding of the underlying flow physics of virus transmission one can set the foundation for an improved methodology in designing case-specific social distancing and infection control guidelines.

physics.flu-dyn↗

arXiv2020

A geometric vof method for interface resolved phase change and conservative thermal energy advection

We present a novel numerical method to solve the incompressible Navier-Stokes equations for two-phase flows with phase change, using a one-fluid approach. Separate phases are tracked using a geometric Volume-Of-Fluid (VOF) method with piecewise linear interface construction (PLIC). Thermal energy advection is treated in conservative form and the geometric calculation of VOF fluxes at computational cell boundaries is used consistently to calculate the fluxes of heat capacity. The phase boundary is treated as sharp (infinitely thin), which leads to a discontinuity in the velocity field across the interface in the presence of phase change. The numerical difficulty of this jump is accommodated with the introduction of a novel two-step VOF advection scheme. The method has been implemented in the open source code PARIS and is validated using well-known test cases. These include an evaporating circular droplet in microgravity (2D), the Stefan problem and a 3D bubble in superheated liquid. The accuracy shown in the results were encouraging. The 2D evaporating droplet showed excellent prediction of the droplet volume evolution as well as preservation of its circular shape. A relative error of less than 1% was achieved for the Stefan problem case, using water properties at atmospheric conditions. For the final radius of the bubble in superheated liquid at a Jacob number of 0.5, a relative error of less than 6% was obtained on the coarsest grid, with less than 1% on the finest.

physics.comp-ph↗

arXiv2018

Transition in a numerical model of contact line dynamics and forced dewetting

We investigate the transition to a Landau-Levich-Derjaguin film in forced dewetting using a quadtree adaptive solution to the Navier-Stokes equations with surface tension. We use a discretization of the capillary forces near the receding contact line that yields an equilibrium for a specified contact angle $θ_Δ$ called the numerical contact angle. Despite the well-known contact line singularity, dynamic simulations can proceed without any explicit additional numerical procedure. We investigate angles from $15^\circ$ to $110^\circ$ and capillary numbers from $0.00085$ to $0.2$ where the mesh size $Δ$ is varied in the range of $0.0035$ to $0.06$ of the capillary length $l_c$. To interpret the results, we use Cox's theory which involves a microscopic distance $r_m$ and a microscopic angle $θ_e$. In the numerical case, the equivalent of $θ_e$ is the angle $θ_Δ$ and we find that Cox's theory also applies. We introduce the scaling factor or gauge function $ϕ$ so that $r_m = Δ/ϕ$ and estimate this gauge function by comparing our numerics to Cox's theory. The comparison provides a direct assessment of the agreement of the numerics with Cox's theory and reveals a critical feature of the numerical treatment of contact line dynamics: agreement is poor at small angles while it is better at large angles. This scaling factor is shown to depend only on $θ_Δ$ and the viscosity ratio $q$. In the case of small $θ_e$, we use the prediction by Eggers [Phys. Rev. Lett., vol. 93, pp 094502, 2004] of the critical capillary number for the Landau-Levich-Derjaguin forced dewetting transition. We generalize this prediction to large $θ_e$ and arbitrary $q$ and express the critical capillary number as a function of $θ_e$ and $r_m$. An analogy can be drawn between $r_m$ and the numerical slip length.

physics.flu-dyn↗

arXiv2018

A two-phase mixing layer between parallel gas and liquid streams: multiphase turbulence statistics and influence of interfacial instability

The two-phase mixing layer formed between parallel gas and liquid streams is an important fundamental problem in turbulent multiphase flows. The problem is relevant to many industrial applications and natural phenomena, such as air-blast atomizers in fuel injection systems and breaking waves in the ocean. The velocity difference between the gas and liquid streams triggers an interfacial instability which can be convective or absolute depending on the stream properties and injection parameters. In the present study, a direct numerical simulation of a two-phase gas-liquid mixing layer that lie in the absolute instability regime is conducted. A dominant frequency is observed in the simulation and the numerical result agrees well with the prediction from viscous stability theory. As the interfacial wave plays a critical role in turbulence transition and development, the temporal evolution of turbulent fluctuations (such as the enstrophy) also exhibits a similar frequency. In order to investigate the statistical response of the multiphase turbulence flow, the simulation has been run for a long physical time so that time-averaging can be performed to yield the statistically converged results for Reynolds stresses and the turbulent kinetic energy (TKE) budget. An extensive mesh refinement study using from 8 million to about 4 billions cells has been carried out. The turbulent dissipation is shown to be highly demanding on mesh resolution compared to other terms in TKE budget. The results obtained with the finest mesh are shown to be not far from converged results of turbulent dissipation which allow us to obtain estimations of the Kolmogorov and Hinze scales. The computed Hinze scale is significantly larger than the size of droplets observed and does not seem to be a relevant length scale to describe the smallest size of droplets formed in atomization.

physics.flu-dyn↗

arXiv2017

Direct Numerical Simulations of pore competition in idealized micro-spall using the VOF method

Under shock loading, metals have been found to melt and with reflection of the shock wave from the material free surface, cavities nucleate and grow. This process is referred to as micro spall and has been studied experimentally with analytical models describing debris sizes. Measurements during the cavity growth phase are not possible at present and we present here the Direct Numerical Simulation of an idealized problem where we assume an inviscid, incompressible liquid subject to a constant expansion rate with cavities at a vanishing vapour pressure. In order to allow for a time-varying gas volume a free-surface interface condition has been implemented in an existing incompressible multiphase Navier-Stokes solver, PARIS Simulator, using a volume-of-fluid method. The gas flow remains unsolved and is instead assumed to have a fixed pressure which is applied to the liquid through a Dirichlet boundary condition on the arbitrary liquid-gas interface. Gas bubbles are tracked individually, allowing the gas pressure to be prescribed using a suitable equation of state. Simulations with hundreds of bubbles have been performed in a fixed domain under a constant rate of expansion. A bubble competition is observed: larger bubbles tend to expand more rapidly at the demise of smaller ones. The time scale of competition is shown to depend on a modified Weber number.

physics.flu-dyn↗

arXiv1996

Two-dimensional Navier--Stokes simulation of deformation and break up of liquid patches

The large deformations and break up of circular 2D liquid patches in a high Reynolds number (Re=1000) gas flow are investigated numerically. The 2D, plane flow Navier--Stokes equations are directly solved with explicit tracking of the interface between the two phases and a new algorithm for surface tension. The numerical method is able to pursue the simulation beyond the breaking or coalescence of droplets. The simulations are able to unveil the intriguing details of the non-linear interplay between the deforming droplets and the vortical structures in the droplet's wake.

chao-dyn↗

arXiv1996

Two-Dimensional Navier-Stokes Simulation of Breaking Waves

Numerical simulations describing plunging breakers including the splash-up phenomenon are presented. The motion is governed by the classical, incompressible, two-dimensional Navier-Stokes equation. The numerical modelling of this two-phase flow is based on a piecewise linear version of the volume of fluid method. Preliminary results concerning the time evolution of the liquid-gas interface and the vorticity field are given for short waves, showing how an initial steep wave undergoes breaking and successive splash-up cycles.

comp-gas↗

arXiv1995

Investigations of a Two-Phase Fluid Model

We study an interface-capturing two-phase fluid model in which the interfacial tension is modelled as a volumetric stress. Since these stresses are obtainable from a Van der Waals-Cahn-Hilliard free energy, the model is, to a certain degree, thermodynamically realistic. Thermal fluctuations are not considered presently for reasons of simplicity. The utility of the model lies in its momentum-conservative representation of surface tension and the simplicity of its numerical implementation resulting from the volumetric modelling of the interfacial dynamics. After validation of the model in two spatial dimensions, two prototypical applications---instability of an initially high-Reynolds-number liquid jet in the gaseous phase and spinodal decomposition in a liquid-gas system--- are presented.

comp-gas↗