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About this book

This book presents a snapshot of the state-of-art in the field of turbulence modeling, with an emphasis on numerical methods. Topics include direct numerical simulations, large eddy simulations, compressible turbulence, coherent structures, two-phase flow simulation and many more. It includes both theoretical contributions and experimental works, as well as chapters derived from keynote lectures, presented at the fifth Turbulence and Interactions Conference (TI 2018), which was held on June 25-29 in Martinique, France. This multifaceted collection, which reflects the conference´s emphasis on the interplay of theory, experiments and computing in the process of understanding and predicting the physics of complex flows and solving related engineering problems, offers a timely guide for students, researchers and professionals in the field of applied computational fluid dynamics, turbulence modeling and related areas.

Table of Contents


Keynote Lectures


Fluid-Structure Interactions in Discrete Mechanics

The primary objective of discrete mechanics is to unify various laws from different areas of physics, such as fluid mechanics and solid mechanics. The same objective was also pursued by continuum mechanics, but the latter has not been entirely successful in accomplishing it. The Galilean invariance and the principle of equivalence make it possible to rewrite the law of dynamics as an equality between accelerations, the one undergone by the medium and the external accelerations applied to it. The derivation of the equation of discrete motion leads to writing the acceleration as a Hodge-Helmholtz decomposition, i.e. the sum of a gradient of a scalar potential and the rotational of a vector potential. By choosing the acceleration as being a primary variable, we can express the velocity and the displacement simply as quantities that accumulate over time. Potentials represent energies per unit mass and are also stored over time. The resulting formulation is able to describe the motion and dynamics of complex media, that can be both fluid and solid, under large deformations and large displacements. Two examples of fluid-structure coupling, an analytical solution and a numerical solution used for a benchmark, are presented here. They show the ability of the model to reproduce the behavior of interacting fluid and solid media.
Jean-Paul Caltagirone, Philippe Angot

HPC and Data: When Two Becomes One

As claimed for many years, High Performance Computing (HPC) and high performance numerical simulation are necessary tools for fundamental science and engineering. Big data and artificial intelligence are some newcomers in the landscape, but not that new, especially in science. Finally, open data and open science are becoming now mandatory for trustable and reproducible science.
This paper presents the recent evolution of HPC with the spectacular arising of AI. HPC and AI share at least one common point: Data. Many HPC communities are struggling with data, whether they are coming from simulation and wait to be analyzed, or coming from large instruments (experiments, observatories) and wait to be treated.
Data was not a major focus in the last decades for HPC community but it reshapes HPC paradigms by introducing data as a “scientific pillar”.
We will first present the current HPC context and how AI changed the current HPC landscape. We will then focus about data use in HPC and how AI can improve HPC simulations. We will also present the concept of FAIR data and why this concern shall be treated soon and embraced by HPC and AI community. We will finally conclude on the data issue and present our point of view regarding the future evolution of HPC market.
Christophe Calvin, France Boillod-Cerneux

LES of the Flow Past a Circular Cylinder Using a Multiscale Discontinuous Galerkin Method

The variational multiscale (VMS) approach based on a modal discontinuous Galerkin (DG) method is used to perform LES of the sub-critical flow past a circular cylinder at Reynolds numbers \(20\,000\) and \(140\,000\), based on the cylinder diameter. The potential of using p-adaption in combination with DG-VMS is illustrated for the case at \(Re=140\,000\) by considering a non-uniform distribution of the polynomial degree based on a recently developed error estimation strategy [15].
Marta de la Llave Plata, Fabio Naddei, Vincent Couaillier

A Volume-of-Fluid Dual-Scale Approach for Simulating Turbulent Liquid/Gas Interactions

Advances to a dual-scale modeling approach (Gorokhovski and Herrmann, 2008) are presented to describe turbulent phase interface dynamics in a Large Eddy Simulation spatial filtering context. Spatial filtering of the governing equations to decrease the burden of Direct Numerical Simulation introduces several sub-filter terms that require modeling. Instead of developing individual closure models for the interface associated terms, the dual-scale approach uses an exact closure by explicitly filtering a fully resolved realization of the phase interface. This resolved realization is maintained on a high-resolution over-set mesh using a Refined Local Surface Grid approach (Herrmann, 2008) employing an un-split, geometric, bounded, and conservative Volume-of-Fluid method (Owkes and Desjardins, 2014). Advection of the phase interface on this DNS scale requires a reconstruction of the fully resolved interface velocity. This velocity is the sum of the filter scale velocities, readily available from an LES solver, and sub-filter velocity fluctuations. These fluctuations can be due to sub-filter turbulent eddies, which can be reconstructed on-the-fly using a local fractal interpolation technique (Scotti and Meneveau, 1999) to generate time evolving sub-filter velocity fluctuations. In this work, results from the dual-scale LES model are compared to DNS results for four different realizations of a unit density and viscosity contrast interface in a homogeneous isotropic turbulent flow at infinite Weber number. Introduction of a sub-filter turbulent velocity reconstruction in a passive scalar context is the first step towards use of a dual-scale model for multiphase applications.
Dominic Kedelty, James Uglietta, Marcus Herrmann

Influence of Particle Anisotropy and Motility on Preferential Concentration in Turbulence

The simplest numerical framework to study turbulent particle dispersion assumes that particles can be modeled as point-like spheres brought about by the flow. In spite of its simplicity, this framework has led to significant advancements in the study of particle-turbulence interactions. In this paper we examine how particle dispersion in dilute turbulent suspensions changes when particles are non-spherical (elongated) and may actively move within the fluid (motile). In particular, we show how elongation and motility add to particle inertia to modulate preferential concentration. Results for particles suspended in wall-bounded turbulence are presented to highlight effects on wall accumulation and segregation, which represent the macroscopic manifestation of preferential concentration.
Cristian Marchioli, Harshit Bhatia, Diego Dotto

Reference Solutions and URANS Model Characterization for Turbulent Forced Convection Around Heated Square Cylinders

Reference solutions for the turbulent forced convection of air around heated square cylinders at high Reynolds numbers (\(Re\ge 10^4\)) are set-up from a bibliographical synthesis of about twenty experiments. These reference solutions concern the flow dynamics and heat transfer. We particularly focus on the local Nusselt number around the obstacle. These solutions are used to identify the URANS models that are the most adequate to reproduce the flow physics and heat transfer in this configuration. Different versions of the k-\(\epsilon \) and k-\(\omega \) models are tested. The k-\(\omega \) SST model is shown to be the most accurate to evaluate the flow dynamics and heat transfer: its accuracy is equivalent to that obtained by 3D LES and high performance computing.
Xavier Nicolas, Hua Sun, Yannick Sommerer

A Convergence Study of the One-Fluid Formulation in a Phase Inversion Application at Moderate Reynolds and Weber Numbers

As a consequence of the remarkable advances in computational sciences realized over the past decades, complex physical processes can now be simulated. To insure fidelity and accuracy, precise convergence criteria must be satisfied. While efforts have been dedicated towards the validation of the computational tools specialized in two-phase flows, there remains a number of open questions. One of them is whether numerical solvers build upon the one-fluid formulation are able to converge integral quantities. This includes enstrophy, to which the boundary layers that develop in the interface vicinity contribute the most. A subsequent question is whether the lack of convergence of the aforementioned quantity affects lower order statistics, chief among them the surface area density. The presented work examines these questions in the context of the phase inversion configuration [1, 2]. Moderate Reynolds and Weber numbers are selected so as to guarantee proper resolution of the single-phase flow. The simulations are performed using Basilisk, a recently developed tree-based software using adaptive meshes.
Taraneh Sayadi, Stéphane Zaleski, Stéphane Popinet, Vincent Le Chenadec, Stéphane Vincent

Finite-Volume Filtering in Large-Eddy Simulations Using a Minimum-Dissipation Model

Large-eddy simulation (LES) seeks to predict the dynamics of the larger eddies in turbulent flow by applying a spatial filter to the Navier-Stokes equations and by modeling the unclosed terms resulting from the convective non-linearity. Thus the (explicit) calculation of all small-scale turbulence can be avoided. This paper is about LES-models that truncate the small scales of motion for which numerical resolution is not available by making sure that they do not get energy from the larger, resolved, eddies. To identify the resolved eddies, we apply Schumann’s filter to the (incompressible) Navier-Stokes equations, that is the turbulent velocity field is filtered as in a finite-volume method. The spatial discretization effectively act as a filter; hence we define the resolved eddies for a finite-volume discretization. The interpolation rule for approximating the convective flux through the faces of the finite volumes determines the smallest resolved length scale \(\delta \). The resolved length \(\delta \) is twice as large as the grid spacing h for an usual interpolation rule. Thus, the resolved scales are defined with the help of box filter having diameter \(\delta = 2h\). The closure model is to be chosen such that the solution of the resulting LES-equations is confined to length scales that have at least the size \(\delta \). This condition is worked out with the help of Poincarés inequality to determine the amount of dissipation that is to be generated by the closure model in order to counterbalance the nonlinear production of too small, unresolved scales. The procedure is applied to an eddy-viscosity model using a uniform mesh.
Roel Verstappen

Contributed Papers


Simulation of a Particulate Flow in 3D Using Volume Penalization Methods

We are concerned with modelling a particulate flow in a three-dimensional domain. The particles are assumed to be rigid, allowing us to describe their motion using the Newton laws. As we aim to take into account complex shapes for the solid inclusions, we adopt volume penalization methods. Those methods allow us to extend the fluid problem inside the solid domain by assimilating the particle as a porous medium. The homogeneous fluid flow is governed by the incompressible Navier-Stokes equations. The whole problem is solved with a projection-correction method using finite volumes and a staggered mesh to ensure the inf-sup condition for the stability. Regarding the transport of the particles, a marker-based front tracking method is used for the fluid-solid interface, as well as a collision strategy. Both penalization methods are studied and compared in the context of particulate flows.
Philippe Angot, Léa Batteux, Jacques Laminie, Pascal Poullet

Simulation of a Confined Turbulent Round Jet at Moderate Reynolds Number

The objective of this study is to numerically simulate the turbulent flow of a confined round jet at moderate Reynolds number, which is representative, in a first step, of an available experiment characterizing a problem of pollutant transport in a confined medium.
Georges Halim Atallah, Emmanuel Belut, Sullivan Lechêne, Benoît Trouette, Stéphane Vincent

Effect of Very-Large-Scale Motions on One- and Two-Point Statistics in Turbulent Pipe Flow Investigated by Direct Numerical Simulations

Very-large-scale motions appear in the bulk region of turbulent pipe flow. They become increasingly energetic with the Reynolds number and interact with the near-wall turbulence. These structures appear either in the shape of positive (high-speed) or negative (low-speed) streamwise velocity fluctuation. The impact of the sign of the structures on the pipe flow turbulence is analysed in this study by means of conditionally averaged one- and two-point statistics, using data from direct numerical simulations of turbulent pipe flow in a flow domain of length \(L=42R\) and friction Reynolds numbers of \(180 \le Re_\tau \le 1500\). Conditionally averaged two-point velocity correlations reveal that low-speed motions are longer and more energetic than their high-speed counterparts. The latter are predominately responsible for the Reynolds number dependency of turbulence statistics in the vicinity of the wall, which is in good agreement with observations of the so-called amplitude modulation in wall-bounded turbulence.
Christian Bauer, Claus Wagner

Large Eddy Simulation of Turbulent Heat Transfer in Pipe Flows of Temperature Dependent Power-Law Fluids

Heat transfer in turbulent forced convection of power-law fluids, in a heated horizontal pipe at isoflux conditions, is analyzed by large eddy simulations (LES), with an extended Smagorinsky model. A temperature dependent fluid is studied at various Pearson numbers (\(0\!\le \!Pn\!\le \!5\)), for two power law indices (\(n\!=\!0.75\) and 1), at Reynolds and Prandtl numbers \(Re_s\!=\!4000\) and \(Pr_s\!=\!1\). The LES predictions are validated through comparisons with the literature at \(Pn\!=\!0\). They allow a better understanding of the physical mechanisms involved in the non-Newtonian temperature dependent fluid flows: with increasing Pn, the relative viscosity is reduced close to the wall and enhanced towards the pipe center, reducing the turbulent fluctuations and heat transfer in the bulk and, as a consequence, the friction factor and Nusselt number.
Paulin Sourou Ganmbode, Meryem Ould-Rouiss, Xavier Nicolas, Paolo Orlandi

The Flow Around a Surface Combatant at 10 Static Drift: Assessment of Turbulence Models

This paper presents a computational study of the flow around the DTMB 5415 at \(10^\circ \) static drift. Two RANS (Reynolds Averaged Navier-Stokes) turbulence models, as the isotropic k-\(\omega \) SST and the non linear anisotropic EARSM (Explicit Algebraic Reynolds Stress Model) and one hybrid RANS-LES model, the DES (Detached Eddy Simulation) based on the k-\(\omega \), are used with the flow solver ISIS-CFD. All numerical results are compared to experimental data. The numerical results show that the DES model is the one turbulence model that able to predict correctly the behavior of the flow in the core of the SDTV (Sonar Dome Tip Vortex), and particularly the high level of the turbulence kinetic energy.
Emmanuel Guilmineau, Michel Visonneau, Ginevra Rubino

Experiments and Large Eddy Simulations on Particle Interaction with a Turbulent Air Jet Impacting a Wall

Experiments and large eddy simulations are carried out to study the interaction of spherical particles with a turbulent air jet impacting a wall. The context is that of the dynamical air curtains used to separate a contaminated ambiance with passive or inertial particles from a clean ambiance. In the present study, the jet and particle Reynolds numbers and the jet and turbulence Stokes numbers are respectively equal to \(Re_{j}=13500\), \(0.7\le Re_{p} \le 3.5\), \(0.02\le St_j \le 0.35\) and \(0.1\le St_t \le 1\): they mainly concern passive particles. The rate of the particles that cross the air jet is analyzed according to the particle size, for two particle injection heights. A non-monotonic passing rate of the particles through the jet with respect to the particle size is observed in the experiments.
Syphax Ikardouchene, Xavier Nicolas, Stéphane Delaby, Meryem Ould-Rouiss

A Review of Geometrical Interface Properties for 3D Front-Tracking Methods

Modeling and simulating multiphase flows still remain an exciting and stimulating scientific challenge. Many approaches were developed to describe the topological evolution of the interface. This paper remains in the domain of the Front-Tracking method [8, 10], in which, in addition to the use of an Eulerian mesh to solve the Navier-Stokes equations, a Lagrangian interfacial mesh of surface elements (triangles in 3D) explicitly describes the evolution of the interface. Whatever the method used, getting the interfacial capillary, mass or energy transfers is crucial for the study of multiphase flows. A comparison is done between different techniques [7, 10] used to get the geometrical properties of the 3D front-tracking objects, such as the surface tension forces, mean curvatures and normal vectors, which are essential for the modeling and understanding of multiphase flows.
Désir-André Koffi Bi, Mathilde Tavares, Éric Chénier, Stéphane Vincent

Soft-Sphere DEM Simulation of Coarse Particles Transported by a Fully Developed Turbulent Gas Vertical Channel Flow

The main focus of the present study is to evaluate the accuracy of the soft-sphere method to represent the particle-particle and the particle-wall collision effect in dilute rapid particulate flow. At this aim, 3D soft-sphere Discrete Element Method (DEM) simulation results are presented for frictionless elastic and inelastic particles, for different sizes and mean solid volume fractions, transported in a fully developed vertical channel flow. The effect on particle statistics of the friction during particle-wall collisions is analyzed. Profiles of time-averaged quantities are assessed and well agree with simulation results available from the literature, obtained by using the hard-sphere model.
Ainur Nigmetova, Yann Dufresne, Enrica Masi, Vincent Moureau, Olivier Simonin

Rod-Bundle Thermalhydraulics Mixing Phenomena: 3D Analysis with Cathare-3 of ROSA-2/LSTF Experiment

Cathare-3 is the new version of the French Thermal-hydraulic code for the safety analysis of nuclear reactors, its 3D module is mainly used to model the reactor vessel with a “porous” medium approach of two-fluid six equations model. Therefore, the balance equations are established using a double-averaged method: first, a time-average, and then, space-average. Optional terms can be added in momentum and energy balance equations to model turbulent diffusion and dispersion effects. These terms have an impact on core simulations at subchannel scale. So, the Cathare team have established models for these terms in rod bundle geometry and had validated them on various experiments. The presented simulations are a 3D modeling of the core of the ROSA-2/LSTF experiment using Cathare-3 3-D module with a radial nodalization of one mesh per rod. A phase of core uncovering during which the rod temperatures in the dry zone increase is observed in an experimental test and experimental evolutions of rods and gas temperatures are compared with Cathare-3 calculations with and without the turbulent terms.
Raphaël Préa, Anouar Mekkas

Sensitivity of Approximate Deconvolution Model Parameters in a Posteriori LES of Interfacial Turbulence

The current state of the art of large eddy simulation of immiscible two-phase flows suffers from the lack of appropriate closure models for subgrid scale (SGS) contributions of interfacial physics. In this study, we extend the Approximate Deconvolution Model [1] to the two-phase LES with volume of fluid method (ADM-VOF) to account for all the SGS terms appearing in spatially-filtered governing equations of incompressible interfacial flows. Following the central concept of the ADM, the subgrid surface tension force and interfacial transport terms as well as the subgrid stress tensor are reconstructed by approximating the inverse of filter operation. Accordingly, the filtered Navier-Stokes equations as well as the filtered VOF equation are closed and solved using the two-phase finite volume solver in OpenFOAM. In our recent investigation [2], the ADM-VOF formulation is developed into details, and employed for an a posteriori LES on the phase inversion benchmark problem. In the present study, the sensitivity of the simulation results to the ADM parameters such as size and type of filter kernels as well as the approximation order of the inverse filter are investigated. The results clearly reveal the potentials of the structural approach of ADM-VOF for large eddy simulation of interfacial turbulence where functional SGS closures are almost impractical.
Mahdi Saeedipour, Stéphane Vincent, Stefan Pirker

Time-Resolved High-Density Particle Tracking Velocimetry of Turbulent Rayleigh-Bénard Convection in a Cubic Sample

A newly developed high-density particle tracking velocimetry (HD-PTV) technique is introduced and validated on a synthetic data set. Further, Lagrangian velocities in turbulent Rayleigh-Bénard Convection (RBC) are determined based on particle images measured in a cubic sample filled with water with a Prandtl number Pr\(\,=\,\)6.9 and a Rayleigh number of Ra\(\,=\,\) \(1.0\cdot 10^{10}\). It is shown that the new technique allows to resolve not only a three-dimensional (3D) large-scale circulation in a diagonal plane of the sample but also the secondary flow structures developing in the corners of the perpendicular plane.
Daniel Schiepel, Sebastian Herzog, Claus Wagner

Sub-grid Deconvolution Approach for Filtered Two-Fluid Models and the Application to Fluidized Gas-Particle Suspensions

In our prior study [9], an a-priori analysis on the spatially-filtered two-fluid model (TFM) was presented for turbulent gas-solid flows, where the unresolved terms were modeled by an approximate deconvolution model (ADM). With such an approach, an approximation of the unfiltered solution is obtained by repeated filtering allowing the determination of the RSFS (resolved sub-filter scales) contribution of unclosed terms of the filtered equations directly. In the present study, this ADM-TFM approach is implemented in an a-posteriori manner for the coarse grid simulation of unbounded fluidization of Geldart type A particles. The ADM-TFM predictions of the domain averaged slip are in fairly good agreement with the fine grid reference case previously published in literature [3] and do not show a notable grid-dependency. Compared to TFM simulations using the same grid resolution, the ADM-TFM approach does only require marginally more computational resources but yields considerably better agreement with the fine grid data.
Simon Schneiderbauer, Mahdi Saeedipour

A Front-Tracking Method for Multiphase Flows with a Sharp Interface Representation

A front-tracking method is developed with specific algorithms for handling volume conservation and arbitrary shape interfaces. We propose a marker advection method which takes into account the jump relation in order to deal with the jump of the physical discontinuities at the interface for two-phase flow simulations. A comparison to different interface tracking approaches is carried out on a rising bubble test case in order to show the ability of our conservative front-tracking method to describe interfaces with high accuracy.
Mathilde Tavares, Désir-André Koffi Bi, Eric Chénier, Stéphane Vincent

Bayesian Estimation of Turbulent Flow Intermittency

Most of stochastic models for dissipation contain an intermittency parameter which is assumed to be an universal constant. However, a review of the literature reveals a very large range of values for this parameter. We present a model for dissipation with random intermittency and investigate the validity of this model on sample datasets from the Johns Hopkins Turbulence Database and a Sonic anemometer measurement.
Adaté Tossa, Didier Bernard, Richard Emilion

Lagrangian Scheme for Scalar Advection-Diffusion. Application to Pollutant Transport

A Lagrangian scheme devoted to the approximation of advection term in advection-diffusion equation (ADE) is proposed to deal with large values of Péclet number. Advection and diffusion of circular concentration in a vortex flow are considered for validation purpose. The Lagrangian scheme reduces the numerical diffusion to almost computer error and provides better results than other Eulerian classical schemes of the literature. The injection of a pollutant in a cavity is finally illustrated.
Benoît Trouette, Georges Halim Atallah, Stéphane Vincent

Spreading Time of Liquid Droplets Impacting on Non-wetting Solid Surfaces

The spreading time that a droplet takes to reach its maximum spreading state is a parameter of paramount importance. We study the impact of a liquid droplet on a super-hydrophobic surface. A contact angle of \(\theta =170^{\circ }\) is used as the numerical input for the non-wetting property of the surface. Numerical simulations to understand the effects of initial impact conditions on spreading time of liquid droplets onto solid surfaces are conducted in a regime where \(1<We<300\) and \(1<Re<300\). We demonstrate that the spreading time \(t_{max} \) is jointly determined by the inertial, capillary and viscous forces. The spreading time \(t_{max}\) decreases exponentially with the increase of the impact velocity \(V_{0}\) and surface tension \(\sigma \). Regarding the influences of dynamical viscosity on spreading time, the effects of dynamic viscosity is secondary at low Weber numbers (\(We<5\)), while in a moderate Weber number regime (\(5<We<300\)), the effects of dynamic viscosity should be taken into account. Finally, in our study, we successfully scale the dimensionless spreading time in the form as \(t_{max}^{*}/Re^{1/5} \sim WeRe^{-2/5}\).
Yang Xu, Stéphane Vincent, Q.-C. He, H. Le-Quang


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