Jean-Luc Estivalezes

A Lagrangian VOF tensorial penalty method for the DNS of resolved particle-laden flows

The direct numerical simulation of particle flows is investigated by a Lagrangian VOF approach and penalty methods of second order convergence in space for incompressible flows interacting with resolved particles on a fixed structured grid. A specific Eulerian volume of fluid method is developed with a Lagrangian tracking of the phase function while the solid and divergence free constraints are ensured implicitly in the motion equations thanks to fictitious domains formulations, adaptive augmented Lagrangian approaches and viscous penalty methods. A specific strategy for handling particle collisions and lubrication effects is also presented. Various dilute particle laden flows are considered for validating the models and numerical methods. Convergence studies are proposed for estimating the time and space convergence orders of the global DNS approach. Finally, two dense particle laden flows are simulated, namely the flow across a fixed array of cylinders and the fluidization of 2133 particles in a vertical pipe. The numerical solutions are compared to existing theoretical and experimental results with success.

Numerical modelling of finite-size particle collisions in a viscous fluid

A general model is presented for short-range hydrodynamic interactions and head-on particle-particle/wall collisions. The model has been embedded in two distinct numerical methods for fully resolved simulation of finite-size particles in a viscous fluid. It accounts for the material properties of the particles and lubrication effects prior to collision that cannot be fully resolved on a fixed grid. We demonstrate that the model is able to reproduce experimental data for the coefficient of restitution of particle-wall collisions over a wide range of Stokes number based on the particle impact velocity. The set of model parameters we selected and more generally the modelling approach we propose can be efficiently used for fully resolved simulations of moderately dense solid-liquid suspensions.

A subgrid computation of the curvature by a particle/level-set method. Application to a front-tracking/ghost-fluid method for incompressible flows

A particle/level-set method is developed to capture the interface between two immiscible phases. No redistance equation is used for the level-set function which is built from an accurate cubic spline interpolation of the markers describing the interface. Mass losses which usually appear with level-set functions are drastically reduced. Interface coupling with the incompressible momentum equation is taken into account thanks to the ghost-fluid method. Indeed, the particles allow an accurate computation of the local interfacial curvatures, and the capillary part of the pressure jump computed across the interface is more accurately evaluated. Results on static drop show a large decrease of spurious currents compared to other methods. Scalar advection validations and convergence studies are carried out as well as tough test-cases involving large density ratios (typically air/water). A better agreement with literature results is shown compared to classical approaches.

Numerical Simulation and Modelling of the Forces Acting on Single and Multiple Non-Spherical Particles

The paper deals with gas-solid turbulent flows carrying non-spherical particles. The main objective of the present paper is to compute the hydrodynamics forces on non-spherical particles as a function of the particle orientation, for different particle shapes and a large range of particle Reynolds number. Two Direct Numerical Simulations at the scale of the particle are used, i.e. a body-fitted approach and a viscous penalty approach, in the case of a uniform flow with a single ellipsoidal particle. Results are compared with several correlations from the literature and a new proposal for the drag coefficient is given. The study is then extended to the case of a lattice of non-spherical particles to measure the pressure drop and to connect it with the drag coefficient.

A Parallel Adaptive Projection Method for Incompressible Two Phase Flows

Direct numerical simulation of high density ratio multiphase flows requires a lot of computational resources. We have developed a parallel algorithm for solving the incompressible Navier-Stokes equation in two-phase flows on an adaptive hierarchy of mesh. The interface between the two fluids is treated by a coupled Level-Set/Ghost-Fluid method; the parallel AMR is handled by the PARAMESH package, which assures good scaling. A robust solver for the variable density pressure equation has been developed, including an AMR levels-based multigrid preconditioner. The code has been applied to the study of the oscillation of a two dimensional liquid sheet sheared by an air flow, and global oscillation frequencies have been computed for a simplified test case. A high resolution computation has been performed to show two dimensional ligament formation and break-up.

Simulation of a Fluidized Bed Using a Hybrid Eulerian-Lagrangian Method for Particle Tracking

The characterisation of fluidized beds still requires specific investigation for understanding and modelling the local coupling between the dispersed phase and the carrier fluid. The aim of this work is to simulate this type of unsteady particle laden flows via Direct Numerical Simulations in order to provide a local and instantaneous description of particle flow interactions and to extract statistical parameters useful for large scale models. A fluidized bed has been studied experimentally by Aguilar Corona ([1]). In this laboratory experiment, 3D tracking of a single bed particle provided Lagrangian properties of the discrete phase motion, while 2D PIV was used to characterize the flow of the continuum phase. This fluidized bed has been simulated during nine seconds in order to compare experimental and numerical results and to obtain some data that experimental studies can’t give.

Novel method to compute drag force and heat transfers for motions around spheres

A viscous penalty method is used to simulate the interaction between spheres and flows with Particle- Resolved Direct Numerical Simulations. An original method has been developed and validated in order to extract from these simulations the hydrodynamic forces and heat transfers on immersed boundaries representing the particles thanks to Aslam extensions [3]. This method is an improvement of a previous work based on Lagrange extrapolations [6, 7]. Comparisons between these two approaches are considered on various incompressible motions such as the flow around an isolated particle at various Reynolds numbers and flows across packed spheres under Faced-Centered Cubic monoand bi-disperse arrangements.

A Priori Study for the Modeling of LES Subgrid Scale Terms in Resolved Scale Multiphase Flows

Modeling accurately the energy transfer across the interface in multiphase flows is difficult. To deal with this phenomenon, the derivation of the governing equations for two-phase flows have been formulated. A priori tests are used in order to evaluate the relative magnitude of unclosed LES specific terms to multiphase flows. There consist in the explicit filtering of 3D Direct Numerical Simulation in order to find LES models appropriated to the different subgrid contributions. In our study, explicit volume filtering and phase weighted filtering have been used in a case of phase separation flow in a cubic closed box between water, the heavier fluid and oil, the lighter fluid, in order to understand the effect of the filtering process on the subgrid contributions.

Analysis of Unsteady Lagrangian and Eulerian Characteristics of a Liquid Fluidized Bed by Direct Numerical Simulation

The characterization of fluidized beds is still a challenging task for macroscopic modeling issues and industrial applications. The macroscopic models require to be fed with parameters or laws that are not well understood or even impossible to estimate as soon as the solid fraction is larger than 0.1. The aim of the present work is to investigate Direct Numerical Simulation [1] of unsteady particle flows in order to solve all the time and space scales of the flow and the particles and to allow for the estimate of unknown macroscopic or stochastic characteristics of the flow. In the DNS, the particles are fully resolved, i.e. the particle diameter is larger than the grid size and to the smallest hydrodynamic scale. A benchmark experimental fluidized bed [2] is simulated and analyzed in terms of macroscopic and Lagrangian characteristics. Comparisons of numerical solutions to measurements are achieved with success.

AN A PRIORI STUDY FOR THE MODELLING OF SUBGRID-SCALE PHENOMENA IN THE INTERACTION BETWEEN A LIQUID SHEET AND A DECAYING TURBULENCE.

Large Eddy Simulation (LES) of one-phase flow is widely used for industrial applications. However, LES of two-phase interfacial flows, i.e. two-phase flows where an interface separates liquid and gas phases, still remains a challenging task. The main issue is development of subgrid-scale models well suited for two-phase interfacial flows. Explicit filtering of 3D Direct Numerical Simulations has been employed to evaluate the order of magnitude of subgrid contributions. Two-phase interfacial flow simulations are carried out with an incompressible flow solver coupled to a ghost-fluid level-set interface capturing method. The originality of this work is the filtering of jump conditions at the interface. Subgrid terms of jump conditions are shown to derive from the filtering of both the pressure gradient term and the viscous term. Conclusions are drawn on the relative importance of the different subgrid scale contributions. These conclusions will contribute to develop subgrid-scale models which take into account the interface-turbulence coupling when LES are performed.Copyright