Invité d'honneur

Gregory Sivashinsky


Henri Berestycki (EHESS et Paris 6)

Roland Borghi (LMA, Marseille)

Bénédicte Cuenot (CERFACS)

Bruno Dubroca (MAB/CELIA)

Josephus Hulshof (Amsterdam)

Guy Joulin (ENSMA Poitiers)

Ash Kapila (RPI)

Jean-Michel Roquejoffre (MIP, Toulouse)

Gregory Sivashinsky (Tel-Aviv)

Titres et résumés des exposés

Gregory I. Sivashinsky
Department of Applied Mathematics
Tel Aviv University
Ramat Aviv, Tel Aviv 69978, Israel

Multiplicity of Detonation Regimes and Deflagration-to-Detonation Transition

The effects of hydraulic resistance on premixed gas combustion in rough tubes and inert porous beds are discussed on the basis of recent research.  It is found that the hydraulic resistance causes a gradual precompression and preheating of the unburned gas adjacent to the advancing deflagration which may lead (after an extended induction period) to a localized thermal explosion triggering an abrupt transition from deflagrative to detonative combustion.
The hydraulic resistance has a profound effect also on the structure and velocity of the well-settled detonation.  At a sufficiently high level of resistance the normal near Chapman-Jouguet-detonation is found to undergo a jumpwise hysteretic transition to a low-velocity detonation driven by the developing pressure diffusivity.  The latter mode may even become subsonic, the phenomenon occasionally observed in porous bed combustion.

Henri Berestycki
EHESS et Université Paris VI
École des Hautes Études en Sciences Sociales
54, bd Raspail
75270 PARIS Cedex 06

The influence of advection on front propagation

Roland Borghi
Laboratoire de Mécanique et d'acoustique, UPR7051 CNRS
31 Chemin Joseph Aiguier
13402 Marseille cedex

Statistical modelling of turbulent premixed combustion : problems of "flame generated turbulence" and non-gradient diffusion.

Turbulent premixed flames are of wide practical interest and their statistical modelling is expected to give access soon to numerical practical predictions of their large scale characteristics. In the case of very fast chemistry and large Reynolds number, the flame brush are composed of wrinkled fluctuating flamelets and it is suspected from a long time that they display "flame generated turbulence" and non-gradient diffusion, both related to the gas expansion. Based on the results of Direct Numerical Simulations of such a flame, the modelling of these two phenomena is discussed in the classical framework of turbulence models. Very simple estimations of the scaling of some terms in the equations are in agreement with the DNS. An additional study of the length scales involved is now needed in order to be able to build a complete model.

Joint work with S.Nishiki and T.Hasegawa, University of Nagoya, Nagoya.

Bénédicte Cuenot
42 Avenue G. Coriolis
31057 Toulouse cedex

Simulation numerique directe et simulation aux grandes echelles de la combustion turbulente.

La combustion turbulente est au coeur de nombreux systèmes industriels: turbines a gaz, moteurs a piston, moteurs fusée,...C'est un phénomène complexe, couplant des processus chimiques, dynamiques et thermodynamiques. L'amélioration des systèmes et la prédiction de leurs performances en termes de rendement, stabilité, bruit, pollution, nécessite la mise en oeuvre de techniques numeriques sophistiquées pour le calcul des foyers.
La simulation numérique directe (SND) est un outil puissant pour la compréhension des phénomenes physiques et permet de developper de nouveaux modèles de combustion turbulentes. Elle est cependant limitée à des géometries simples et de petite taille. Moins précise, la simulation des grandes echelles (SGE) permet, elle, de calculer des foyers complets en géometrie complexe et capture les phénomènes instationnaires.
Après une presentation de la problématique de la simulation de la combustion turbulente, les techniques SND et SGE seront décrites, ainsi que leur mise en oeuvre pratique dans des codes de calcul. A titre d'illustration quelques exemples de simulations seront ensuite detaillés.

Bruno Dubroca
Université Bordeaux 1
33405 Talence cedex

Mathematical and numerical modelling for radiative transfer and coupling with hydrodynamics

In this talk, we discuss a hierarchy of moment model for modelling the  raditiave transfer equation. We begin at low level by considering the microscopic case and its numerical approximation by an entropic S-N method. At high level, the macrocopic case, we consider grey or multi group spectrum models. As these models are very cheap, they can be coupled efficiently with hydrodynamics. Several examples about radiative shock fronts, combustion or aerothermodynamic illustrate this approach.

Joint work with Pierre Charrier and Rodolphe Turpault.

Josephus Hulshof
Department of Mathematical Analysis
Vrije Universiteit Amsterdam
De Boelelann 1081
1081 HV Amsterdam

Near-Equilibrium Flames with radiative transfer

We consider the NEF model in combustion for the propagation of premixed flames, in combination with the Eddington equation for radiative transfer. The Lewis number and the radiative parameters (opacity and Boltzmann number) are coupled to the
inverse of the dimensionless activation energy. Using a three-scale matching argument we examine the limiting travelling wave profiles and their stability properties. We obtain an asymptotic law for the speed of the wave vs. reduced opacity and Boltzmann number, which enlights the Joulin effect.

Joint work with Claude-Michel Brauner (Bordeaux) and Alessandra Lunardi (Parma)

Guy Joulin
Laboratoire de Combustion et Détonique
BP 40109
86961 Futuroscope cedex, France

On  a Galerkin-type approach to wrinkled flames in gravity fields

Joint work with G. Boury

Abstract : postcript file
Abstract : PDF file

Ash K. Kapila
Rensselaer Polytechnic Institute
319 Amos Eaton Hall
110 8th St
Troy, NY 12180, USA

Evolution of detonation provoked by nonuniform initial data: a Sivashinsky problem re-visited

Emergence of a detonation in a homogeneous, exothermically reacting medium can be deemed to occur in two phases.  The first phase processes the medium so as to create conditions ripe for the onset of detonation.  The second phase consists of the actual formation of the detonation wave via chemico-gasdynamic interactions.  This presentation examines the second phase in the context of an idealized medium with simple, rate-sensitive kinetics, for which the preconditioned state is modelled as one with a prescribed temperature nonuniformity.

In a planar, 1-D geometry the problem, for a linear initial temperature profile, was first considered computationally by Sivashinsky in collaboration with Zeldovich, Librovich and Makhviladze.  Since then it has been extensively re-examined, asymptotically and computationally, and we shall describe what it has taught us as to the mechanisms of detonation initiation.

We shall then consider detonation evolution in an annular geometry, inspired by the so-called cook-off experiments on high-energy explosives, and explore how the 1-D results shed light on the 2-D processes.

The results are based on a combination of asymptotic analysis and high-resolution adaptive numerics.

Jean-Michel Roquejoffre
Laboratoire MIP,  Université Paul  Sabatier
118, route de Narbonne, 31062 Toulouse cedex, France

Stability of two-dimensional conical flame fronts

The premixed part of a Bunsen burner flame can be modelled - in a very crude approximation - by  a reaction-diffusion equation in the plane with conical conditions at infinity. This means that  the fresh gases are located in some given cone of the lower half plane. Travelling fronts to such an equation, whose velocity is given by the classical Lewis-Von Elbe formula, can be shown to exist. In this talk, we will discuss different stability results for such fronts.

Joint work with F. Hamel and R. Monneau.

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