Marc Buffat

• Professor
• Professor (Full) at Claude Bernard University Lyon 1

In the present study, the efficiency of preconditioners for solving linear systems associated with the discretized variable-density incompressible Navier-Stokes equations with semi-implicit second-order accuracy in time and spectral accuracy in space is investigated. The method, in which the inverse operator for the constant-density flow system act...

Linear stability of solid body rotating flows with axisymmetric density variations is addressed analytically. Considering inviscid disturbances, a non trivial dispersion relation is obtained and it is shown that the instability is of Rayleigh-Taylor type in cylindrical frame. The viscous correction is derived, in the limit of large Reynolds numbers...

Linear stability of solid body rotating flows with axisymmetric density variations is addressed analytically. Considering inviscid disturbances, a nontrivial dispersion relation is obtained and it is shown that the instability is of Rayleigh-Taylor type in cylindrical frame. The viscous correction is derived, in the limit of large Reynolds numbers...

To identify laminar/turbulent transition paths in plane Couette flow, a variational formulation incorporating a restricted nonlinear (RNL) system that retains a single streamwise Fourier mode, is used. Considering the flow geometry originally used by Monokrousos et al. (2011) and Duguet et al. (2013) and the same Reynolds numbers Re, we show that i...

The increase of computational resources with the generalization of massively parallel supercomputers benefits to various fields of physics among which turbulence and fluid mechanics, making it possible to increase time and space accuracy and gain further knowledge in fundamental mechanisms. Parametric studies, high fidelity statistics, high resolut...

Massively parallel simulations generate increasing volumes of large data, whose exploitation requires large storage resources, efficient network and increasingly large post-processing facilities. In the coming era of exascale computations, there is an emerging need for new data analysis and visualization strategies. In order to meet these challenge...

The laminar–turbulent transition of a plane channel entrance flow is revisited using global linear optimization analyses and direct numerical simulations. The investigated case corresponds to uniform upstream velocity conditions and a moderate value of Reynolds number so that the two-dimensional developing flow is linearly stable under the parallel...

The interaction between finite-size particles and turbulent channel flow in the absence of gravity is studied by direct numerical simulations (DNS). The study is motivated by DNS observations of a turbulent channel flow with high-density, pointwise particles, that cluster in regions of high streamwise root-mean-square (RMS) acceleration close to th...

Direct numerical simulation of the turbulent flow spatially developing in a plane channel is performed. The channel is long enough for the turbulence to achieve the statistically invariant state in space and time. Spatial evolution of statistical quantities and Reynolds stress budgets are calculated. Results are compared to the canonical flows cons...

The interaction between finite-size particles and turbulent channel flow in the absence of gravity is studied here by direct numerical simulation. The turbulent flow is resolved by an efficient Fourier Chebyshev method, coupled with a direct forcing method for particle tracking. For the volume fraction and particle size we studied here, the presenc...

Massively parallel simulations generate increasing volumes of big data, whose exploitation requires increasingly large storage resources, efficient networking technologies and post-processing facilities. In the coming era of exascale supercomputing, there is an emerging need for new data analysis and visualization strategies. A promising solution c...

This article contains the three contributions of the mini-symposium about MOOCs (Massive Open Online Courses) organized by Violaine Louvet (Institut Camille Jordan, CNRS). The first contribution is from Alain Mille from LIRIS, about the main research questions on this new way of learning. The second one is from Marc Buffat, LMFA. He reviews some op...

Direct numerical simulations of boundary layers transition and their interaction in a very elongated plane channel are presented.Wall-normal velocity perturbations of small amplitude and with a spanwise wavelength of the order of the boundary layer thickness are introduced in one of the boundary layer. They generate steady elongated streaks by a tr...

The transport of solid particles by coherent wall structures is studied here. This phenomenon is present in numerous environmental and engineering flows. The flow above a wall-mounted hemisphere is used for generating hairpin vortices in a laminar boundary layer in a controlled way. By means of direct numerical simulation (DNS) of the fluid flow an...

An efficient parallel spectral method for direct numerical simulations of transitional and turbulent flows is described in this paper. The parallelization is classically based on a bidimensional domain decomposition, but has been specifically developed for a solenoidal Fourier–Chebyshev spectral approximation where in one Fourier direction, the num...

Despite remarkable accomplishment, the classical hydrodynamic stability theory fails to predict transition in wall-bounded shear ow. The shortcoming of this modal approach was found 20 years ago and is linked to the non-orthogonality of the eigenmodes of the linearised problem, de noted by the Orr Sommerfeld and Squire equations. The associated eig...

This work is a continuation of the authors efforts to develop high-order numerical methods for solving elliptic problems with complex boundaries using a fictitious domain approach. In a previous paper, a new method was proposed, based on the use of smooth forcing functions with identical shapes, mutually disjoint supports inside the fictitious doma...

Hydrodynamic cavitation has an important effect on the performance of Diesel injectors. It influences the nature of the fuel spray and the efficiency of the combustion process. In the present study, we investigate numerically the effect of wall roughness in the cavitating and turbulent flow developing inside a Diesel injector. The mixture model bas...

The aim of this article is to solve elliptic partial differential equations (PDEs) using a global spectral approximation in complex physical domain using a ficti- tious domain method. The main idea of the fictitious domain approach consists in immersing the original domain of study into a geometrically bigger and sim- pler one called fictitious dom...

As a consequence of the Helmholtz–Hodge theorem, any divergence-free vector field can be decomposed in two L2-orthogonal, solenoidal vector fields expressed in terms of projections of the velocity and vorticity fields, on an arbitrary direction in space. Based on this type of decomposition and the choice of the wall-normal direction, an efficient s...

Direct numerical simulations (DNS) of incompressible turbulent channel flows coupled with Lagrangian particle tracking are performed to study the characteristics of ejections that surround solid particles. The behavior of particles in dilute turbulent channel flows, without particle collisions and without feedback of particles on the carrier fluid,...

Understanding the pathway of toxic air pollutants from their source is essential to government agencies that are responsible for the public health. CFD remains an expansive tool to evaluate the flow of toxic air contaminants and requires to deal with complex geometry, high Reynolds numbers and large temperature gradients. To perform such simulation...

The inviscid low Mach number compressible flow developing from a plane incompressible vortex with constant density in a bounded domain is studied. A reference solution for this model flow is obtained by two-time scale asymptotic development in the zero Mach number limit. The solution can be decomposed into variations with a slow convective and a fa...

Large eddy simulations (LES) are performed in order to reproduce the generation and the breakdown of a tumbling motion in the simplified model engine [Borée, J., Maurel, S., Bazile, R., 2002. Disruption of a compressed vortex. Phys. Fluids, 14 (7) 2543–2556]. A second-order accurate numerical scheme is applied in conjunction with a mixed finite vol...

Large-eddy simulations (LES) have been performed of a compressed vortex flow undergoing transition to turbulence. The numerical method is based on a finite volume/finite element discretization of the compressible Navier–Stokes equations on unstructured grids and a Roe second-order scheme with MUSCL extrapolation. A particular attention is paid to t...

The objective of this work is to assess the performances of different turbulence models in predicting turbulent diffusion flames in conjunction with the flamelet model.The k– model, the Explicit Algebraic Stress Model (EASM) and the k– model withvaried anisotropy parameter C (LEA k– model)are first applied to the inert turbulent flow over a backwar...

This paper presents numerical simulations of sub-critical flows inside a combustion chamber using both Large Eddy Simulation (LES) and Reynolds-Averaged Navier-Stokes equations (RANS). An experimental setup, “ORACLES”, which is a simplified combustion chamber, is selected to study the flow physics. Simulations are performed on unstructured grids us...

The convective flows which arise in shallow cavities filled with low-Prandtl-number fluids when subjected to a horizontal temperature gradient are studied numerically with a finite element method. Attention is focused on a rigid cavity with dimensions 4×2×1, for which experimental data are available. The three-dimensional results indicate that, aft...

This paper describes the simulation of a compressible turbulent boundary layer with zero pressure gradient, performed using an incompressible low Reynolds k — ε model combined with compressibility modeling. It appears that this model behaves well for such flows.

This paper describes the simulation results of a shock reflection on a flat plate performed using an incompressible low Reynolds k — ε model combined with compressibility modeling. It appears that this model behaves well for such flows.

Simulation of a 24° compression ramp have been performed with a k — ε model. Additional terms to take into account compressibility effects (compressible dissipation, pressure-dilatation correlation) have been introduced in the kinetic energy equation. Wall functions and a low Reynolds model of Lam-Bremhorst are available to modelise the near wall r...

The paper addresses the predictive capabilities of different computational modelling practices which employ various eddy-viscosity models for turbulence, that are based on a linear, a quadratic and two cubic representations of the Reynolds stress tensor in terms of strain and vorticity rates respectively, in the context of a comparative study betwe...

This chapter reviews the simulation of turbulent internal-compressible flows, mainly for the prediction of the aerodynamics inside the combustion chamber of a gas turbine engine.. The averaged Navier-Stokes equations are solved using a mixed finite element/finite volume technique for the mean flow variables. The scalar products and the matrix vecto...

The development of new aeronautic projects require accurate and efficient simulations of compressible flows in complex geometries. It is well known that most flows of interest are at least locally turbulent and that the modelling of this turbulence is critical for the reliability of the computations. A turbulence closure model which is both cheap a...

To improve the prediction of turbulence inside internal combustion engines, a Reynolds stress turbulence model is implemented in the Kiva-II code. After a rapid description of the Launder-Reece-Rodi model (noted LRR), two validation test cases (the plane channel flow and the flow over a backward facing step) are presented. The advantages of a secon...

Two numerical methods, based on high order finite volume formulations and upwind schemes, are used to compute the two- and three-dimensional flow field in a transonic nozzle. The influence of numerical diffusivity, boundary treatment and mesh structure is explored for inviscid and turbulent configurations. First order computations provide significa...

The aim of this work is to present a new numerical method to compute turbulent flows in complex configurations. With this in view, a k-ϵ model with wall functions has been introduced in a mixed finite volume/finite element method. The numerical method has been developed to deal with compressible flows but is also able to compute nearly incompressib...

Two unsteady Euler solvers using high-order upwind finite volume methods are presented and compared. The first uses the Van Leer flux vector splitting on structured moving grids and includes compatibility relations to treat boundary conditions. The second is based on Roe's approximate Riemann solver on fixed unstructured, finite element type meshes...

From our experience in developing large finite element CFD codes for simulating compressible and incompressible complex flows [1, 8], we have learned that the development of such codes (and their evolution) must face three problems: the complexity of the physics, the complexity of the numeric, the large computing time.

Three numerical codes based on high-order finite-volume formulations, with Godunov-type schemes, are described and compared on test cases. Agreements and discrepancies between the results of the three codes are pointed out and analysed.

This paper presents numerical simulations of turbulent flows during the intake and the compression strokes of a model engine. The Favre average Navier-Stokes equations are solved with a k-[epsilon] turbulence model. The numerical procedure uses a time dependent semi-implicit scheme and a finite element method with a moving mesh. Results of 2-D axis...

The aim of this work is to develop a numerical method to compute compressible turbulent flows in complex configurations. With this in view, a k-epsilon turbulent model with wall functions has been introduced in a mixed finite volume/finite element method developed to simulate supersonic flows. A new model for the compressible dissipation has been i...

A precise knowledge of the aerodynamic field around the combustor of an aircraft engine is required to improve its performances. In particular, a low pressure loss and a stable flow around the liner must be obtained. A numerical approach by use of classical stairstep discretization techniques is out of order to describe such a complex domain. To ci...

In this paper a finite element method is presented to predict internal subsonic flows. Using a low-Mach-number approximation, the pressure is decomposed into a mean thermodynamic contribution and a dynamic fluctuation to deal with the complex role of the pressure in internal aerodynamics. A semi-implicit time integration and a finite element method...

The flow occuring in a low Pr number fluid confined in a parallelepipedic box heated from the side is studied with a finite element method. This method is based on a semi-implicit time scheme and uses a space finite element linear interpolation. 2-D results are given for the test cases with emphasis on the mesh size effect and on specific situation...

A numerical approach able to describe the flow around the combustion chamber of a gas turbine engine is discussed. An axisymmetric method is proposed, based on a finite element method which allows a precise description of complex geometries. A two-equation model of turbulence is used with equilibrium laws in the vicinity of the solid boundaries. Th...

The numerical simulation of two and three dimensional natural convection is studied, including the basic equations, the fractional step method, a discrete formulation of the convection step, the discretization of the Stokes solver, and examples. Direct and iterative methods for solving large scale systems are described. The numerical simulation of...

The paper describes a numerical method for solving the time dependent Navier-Stokes equations for incompressible turbulent flows. The method results from a two fractional step implicit scheme for the time discretization and from a finite element approximation for the space discretization. The mean velocity, pressure, enthalpy and two typical turbul...

The flow visualisation technique developed at Ecole Centrale de Lyon (contract no. 017-SRF) has been used for the study of a plume dispersion on a site simulating the experiment field work by CRABOL (contract no. 010-SRF). Very stable situations could be reached by cooling the surface of the model with liquid nitrogen. Quasi-laminar flows were obta...

A numerical method is described for solving the time-dependent Navier-Stokes equations for incompressible viscous fluid flows. The method results from a three step implicit scheme for the time discretization and from a finite element approximation for the space discretization. The typical fractional step method leads to an uncoupling between the no...

Modifications of the optimal control method are introduced for solving a set of Navier-Stokes partial differential equations. A Burgers equation is defined for the nonlinear convective term, along with a simplified equation for the mean turbulent velocity field between two parallel planes to account for the turbulent terms. The shear stress is expr...

The capability to predict air-water drops flows and packing effects is important in the design of hyperbolic natural draft cooling towers. Stationary Navier-Stokes equations with source terms due to air-droplet interaction and packing are solved with the finite element method. (English abstract)

Numerical simulations of turbulence undergoing a compression have been first performed using the classical statistical approach. Different one-point closure k-ε models, usually used for the computation of reciprocating engine flows, appear to be non-equivalent. The lack of reference results for the evaluation of these statistical models for such pe...

We present a parallel multidomain method applied to the industrial solver NATURng for the simulation of transonic turbulent reacting flows on unstructured grids. The strategy is a global coarse-grain parallelism with a domain partitioning and a message-passing model. The subdomains are non-overlapping. The parallel version of the solver implements...

The injection system in Diesel engine has an important effect on the fuel consumption, the combustion process and the pollution emission. The cavitation influences the nature of the fuel spray and the efficiency of the combustion process in Diesel engines. In this study, we investigated numerically the cavitating flow inside a Diesel injector. The...

Documents pédagogiques du cours de dynamique des gaz de l'UFR de Mécanique de l'Université Lyon I : niveau Licence L3 (pour la première partie) et niveau Master M2 (pour la seconde partie). Il ne s'agit pas d'un cours en e-learning, mais d'un support pour un cours en présentiel. Ce cours de dynamique des gaz aborde les sujets suivants: étude des éc...

A numerical model for predicting turbulent flows of thermally compressible fluid is described. Favre's decomposition of the instantaneous velocity and temperature fields leads to averaged mass, momentum and energy conservation equations. The corresponding density weighted second order moments are given by a turbulent viscosity model requiring close...