Frédérique Laurent

CentraleSupélec | ECP · Federation of Mathematics CNRS FR3487

When considering moment methods for the resolution of the free-transport term of the 1-D kinetic equation, the hyperbolic quadrature method of moments (HyQMOM) closure introduced in [12] leads to a globally hyperbolic system of conservation equations. Here, the HLL scheme used for its resolution is first proved to be realizable, i.e., allows comput...

The quadrature method of moments (QMOM) for a one-dimensional (1-D) population balance equation was introduced by R. McGraw (Aerosol Science and Technology, 27, 255-265, 1997) to close the moment source terms. QMOM is defined based on the properties of the monic orthogonal polynomials Qi of degrees i=0,1,…,n that are uniquely defined by the set of...

The quadrature method of moments (QMOM) for a one-dimensional (1-D) population balance equation was introduced by R. McGraw (Aerosol Science and Technology, 27, 255-265, 1997) to close the moment source terms. QMOM is defined based on the properties of the monic orthogonal polynomials Q i of degrees i = 0, 1,. .. , n that are uniquely defined by th...

A solution is proposed to a longstanding open problem in kinetic theory, namely, given any set of realizable velocity moments up to order 2n, a closure for the moment of order 2n+1 is constructed for which the moment system found from the free-transport term in the one-dimensional (1-D) kinetic equation is globally hyperbolic and in conservative fo...

The modulation of turbulence by sub-Kolmogorov particles has been thoroughly characterized in the literature, showing either enhancement or reduction of kinetic energy at small or large scale depending on the Stokes number and the mass loading. However, the impact of a third parameter, the number density of particles, has not been independently inv...

A complete characterisation of the moment space corresponding to the Levermore basis is given here, through constraints on the moments. The necessary conditions are obtained thanks to classical tools, similar to Hankel determinants. In the mono-variate case, it is well-known that these conditions are sufficient. To generalize this result to multi-v...

The modulation of turbulence by sub-Kolmogorov particles has been thoroughly char- acterized in the literature, showing either enhancement or reduction of kinetic energy at small or large scale depending on the Stokes number and the mass loading. How- ever, the impact of a third parameter, the number density of particles, has not been independently...

The second-order realizable ζ moment advection scheme developed in Laurent and Nguyen, (2017) is extended to the case of unstructured grids with cells of arbitrary shape. The necessary modifications to the scheme and the conditions under which the scheme ensures the realizability of the advected moment set are presented. The implementation of the s...

The conditional quadrature method of moments (CQMOM) was introduced by Yuan and Fox (2011) [4] to reconstruct a velocity distribution function (VDF) from a finite set of its integer moments. The reconstructed VDF takes the form of a sum of weighted Dirac delta functions in velocity phase space, and provides a closure for the spatial flux term in th...

The extended quadrature method of moments (EQMOM) for the solution of population balance equations (PBE) is implemented in the open-source computational fluid dynamic (CFD) toolbox OpenFOAM as part of the OpenQBMM project. The moment inversion procedure was designed (Nguyen et al., 2016) to maximize the number of conserved moments in the transporte...

In this paper, we tackle the issue of the accurate simulation of evaporating and reactive polydisperse sprays strongly coupled to unsteady gaseous flows. In solid propulsion, aluminum particles are included in the propellant to improve the global performances but the distributed combustion of these droplets in the chamber is suspected to be a drivi...

The accurate description and robust simulation at relatively low cost of a size polydisperse population of fine particles in a carrier fluid is still a major challenge for many applications. For this purpose, moment methods, derived from a population balance equation, represent a very interesting strategy. However, one of the major issues of such m...

The accurate description and robust simulation, at relatively low cost, of global quantities (e.g. number density or volume fraction) as well as the size distribution of a population of fine particles in a carrier fluid is still a major challenge for many applications. For this purpose, two types of methods are investigated for solving the populati...

High fidelity modeling and simulation of moderately dense sprays at relatively low cost is still a major challenge for many applications. For that purpose, we introduce a new multi-fluid model based on a two-size moment formalism in sections, which are size intervals of discretization. It is derived from a Boltzmann type equation taking into accoun...

The present contribution introduces a fourth-order moment formalism for particle trajectory crossing (PTC) in the framework of multiscale modeling of disperse multiphase flow. In our previous work, the ability to treat PTC was examined with direct-numerical simulations (DNS) using either quadrature reconstruction based on a sum of Dirac delta funct...

The automotive industries have been concerned by the efficiency of combustiion devices and the reduction of pollutant emissions. To get accurate measurements inside an engine numerical simulation is considered as a good alternative to understand two-phase flows and two-phase combustion and to design new combustion chambers. A novel Eulerian moment...

In this paper we propose a new Eulerian modeling and related accurate and robust numerical methods, describing polydisperse evaporating sprays, based on high order moment methods in size. The main novelty of this model is its capacity to describe some geometrical variables of the droplet-gas interface, by analogy with the liquid-gas interface in in...

High fidelity modeling and simulation of moderately dense sprays at relatively low cost is still a major challenge for many applications. For that purpose, we introduce a new multi-fluid model based on a two-size moment formalism in sections, which are size intervals of discretization. It is derived from a Boltzmann type equation taking into accoun...

To assist industrial engine design, 3D simulations are increasingly used as they allow evaluation of a wide range of engine configurations and operating conditions and bring a comprehension of the underlying physics comple-mentary to experiments. While the gaseous flow description has reached a certain level of maturity, the multiphase flow descrip...

Relying on two recent contributions by Massot et al. [SIAM J. Appl. Math. 70 (2010), 3203--3234] and Kah et al. [J. Comput. Phys. 231 (2012), 394--422], where a Eulerian Multi-Size Moment (EMSM) model for the simulation of polydisperse evaporating sprays has been introduced, we investigate the potential of such an approach for the robust and accura...

Modeling the oxidation of soot particles in flames is a challenging topic both from a chemical point of view and regarding the statistical treatment of the evolution of the soot number density function (NDF). The method of moments is widely-used for the statistical modeling of aerosol dynamics in various applications, and a number of different mome...

To assist the industrial engine design process, 3-D computational fluid dynamics simulations are widely used, bringing a comprehension of the underlying physics unattainable from experiments. However, the multiphase flow description involving a liquid fuel jet injected into the chamber is still in its early stages of development. There is a pressin...

In this paper we mathematically characterize through a Lie formalism the local errors induced by operator splitting when solving nonlinear reaction-diffusion equations, especially in the non-asymptotic regime. The non-asymptotic regime is often attained in practice when the splitting time step is much larger than some of the scales associated with...

The accurate simulation of polydisperse sprays strongly coupled to unsteady gaseous flows is a major issue (e.g., for solid rocket motor optimization). The Eulerian multifluid method has proven to account for polydispersity efficiently by describing continuously droplet sizes that are sorted into "fluids," which are coupled to the gas through drag...

The accurate simulation of polydisperse sprays strongly coupled to unsteady gaseous flows is a major issue, e.g. for solid rocket motor optimization. The Eulerian Multi-Fluid method (MF) has proven to account for polydispersity efficiently by describing continuously droplet sizes, that are sorted into “fluids” which are coupled to the gas through d...

The accurate simulation of polydisperse sprays undergoing coalescence in unsteady gaseous flows is a crucial issue. In solid rocket motors, the internal flow depends strongly on the alumina droplet size distribution, which spreads up with coalescence. Yet solving for unsteady two-phase flows with high accuracy on the droplet sizes is a challenge fo...

Kah et al. (2010) and recently developed the Eulerian multi-size moment model (EMSM) which tackles the modeling and numerical simulation of polydisperse multiphase flows. Using a high order moment method in a compact interval, they suggested to reconstruct the number density function (NDF) by entropy maximization, which leads to a unique and realiz...

In solid rocket motors, the distributed combustion of aluminum droplets is suspected to be a driving mechanism of hydrodynamic and thermoacoustic instabilities. The accurate simulation of evaporating bi-component polydisperse sprays, strongly coupled to unsteady gaseous flows, appears as a determining step for future solid rocket motor optimization...

Solid rocket motor flows depend strongly on alumina granulometry, which spreads up with coalescence. Solving droplet sizes in unsteady flows is a modeling and numerical challenge, specially when high loadings generate retrocoupling. As an alternative to Lagrangian approaches, the Eulerian Multi-Fluid model describes polydispersity with size-sorted...

http://ctr.stanford.edu/ResBriefs/2012/

In this work, we are interested in the modeling of spray polydispersion in size as well as size–velocity correlations, which may greatly influence the evaporation and the dynamics of the disperse phase. Vié et al. (2011) proposed a new model called Coupled Size–Velocity Moment method (CSVM), which handles the polydispersion using the NDF reconstruc...

In solid rocket motors, aluminum particles are included in the propellant to improve the global performances but the distributed combustion of these droplets is suspected to be a driving mechanism of hydrodynamic instabilities. So the accurate simulation of reactive polydisperse sprays strongly coupled to unsteady gaseous flows appears as a major i...

Population balance equations (PBE) for a number density function (NDF) arise in many applications of aerosol technology. Thus, there has been considerable interest in the development of numerical methods to find solutions to PBE, especially in the context of spatially inhomogeneous systems where moment realizability becomes a significant issue. Qua...

In this paper, we tackle the numerical simulation of reaction-diffusion equations modeling multiscale reaction waves. This type of problems induces peculiar diffculties and potentially large stiffness which stem from the broad spectrum of temporal scales in the nonlinear chemical source term as well as from the presence of large spatial gradients i...

In this paper, we tackle the modeling and numerical simulation of dilute gas-droplet and gas-particle flows for which polydispersity description is of paramount importance. Starting from a kinetic description for point particle experiencing transport either at the carrier phase velocity for aerosols or at their own velocity for more inertial partic...

http://ctr.stanford.edu/ResBriefs/2011/

The ability to simulate multi-phase flows is of crucial importance for the prediction of engine performance and pollutant emissions. The flow generated by the injection of a liquid inside a combustion chamber being generally very complex, we only focus on Eulerian description of the dispersed phase in the present work. One of the main difficulties...

We tackle the numerical simulation of reaction-di�usion equations modeling multi-scale reaction waves. This type of problems induces peculiar di�culties and potentially large sti�ness which stem from the broad spectrum of temporal scales in the nonlinear chemical source term as well as from the presence of large spatial gradients in the reactive fr...

The accurate simulation of polydisperse sprays strongly coupled to unsteady gaseous flows is a major issue for solid rocket motor optimization and a challenge for both modeling and scientific computing. The Eulerian Multi-Fluid method (MF) has proven to account for polydispersity eficiently, considering conservation equations for moments of the spr...

We tackle the numerical simulation of reaction-diffusion equations modeling multi-scale reaction waves. This type of problems induces peculiar difficulties and potentially large stiffness which stem from the broad spectrum of temporal scales in the nonlinear chemical source term as well as from the presence of large spatial gradients in the reactio...

We tackle the numerical simulation of reaction-diffusion equations modeling multi-scale reaction waves. This type of problems induces peculiar difficulties and potentially large stiffness which stem from the broad spectrum of temporal scales in the nonlinear chemical source term as well as from the presence of large spatial gradients in the reactio...

PDF available at http://www.stanford.edu/group/ctr/Summer/SP10/index.html

Dilute liquid sprays can be modeled at the mesoscale using a kinetic equation, namely the Williams-Boltzmann equation, containing terms for spatial transport, evaporation and fluid drag. The most common method for simulating the Williams-Boltzmann equation uses Lagrangian particle tracking wherein a finite ensemble of numerical ``parcels'' provides...

The accurate simulation of polydisperse sprays encountering coalescence in unsteady gaseous flows is a crucial issue for solid rocket booster optimization. Indeed, the internal flow of the engine depends strongly on the alumina droplet size distribution, which spreads up with coalescence. Yet solving for unsteady two-phase flows with a high dimensi...

This work investigates the issue of describing polydispersivity in an Eulerian framework of a disperse spray with potentially mesh movement. In this perspective, the multi-fluid model and and associated numerical schemes provide robust tools (de Chaisemartin (2009)). However, there is a substantial interest for the development of a method able to a...

Large Eddy Simulation (LES) and Direct numerical Simulation (DNS) of polydisperse evaporating sprays with Eulerian models are very promising tools for high performance computing of combustion applications. They are able to describe the turbulent dispersion and evaporation and properly predict the combustion regimes. However, the spray system of con...

Providing accurate simulations of polydisperse evaporating sprays dynamics in unsteady gaseous flows with large scale vortical structures is both a crucial issue for industrial applications and a challenge for modeling and scientific computing. The usual Lagrangian approaches developed in polydisperse unsteady configurations require tremendous comp...

In this paper we tackle a critical issue in the numerical modeling, by Eulerian moment methods, of polydisperse multiphase systems, constituted of dispersed particles or droplets, a general class of systems which includes aerosols. Their modeling starts at a mesoscopic scale with an equation on the number density function (NDF) of particles/droplet...

In the present contribution, we consider acoustically pulsated free jets with a polydisperse spray injection in an axisymmetrical configuration. The acoustic excitation creates periodical large vortical structures, which are representative of the dynamics of gaseous flows in more complex configurations, and a strong interaction with the injected sp...

In this contribution we propose a general presentation of Eulerian multi-fluid modeling and numerical methods for the simulation of polydisperse evaporating sprays. By spray, we denote a cloud of spherical liquid droplets of various sizes ranging from submicronic scales up to several hundred microns which interact with the carrier gaseous phase and...

The accurate simulation of the dynamics of polydisperse evaporating sprays in unsteady gaseous flows with large scale vortical structures is both a crucial issue for industrial applications and a challenge for modeling and scientific computing. The difficulties encountered by the usual Lagrangian approaches make the use of Eulerian models attractiv...

The accurate simulation of the dynamics of polydisperse evaporating sprays in un- steady gaseous flows with large-scale vortical structures is both a crucial issue for indus- trial applications and a challenge for modeling and scientific computing. The difficulties encountered by the usual Lagrangian approaches make the use of Eulerian models at- t...

The simulation of polydisperse evaporating sprays is both a crucial issue for industrial applications and a challenge for modeling and scientific computing. The usual Lagrangian approaches can lead to a very high computational cost or to a low level of resolution if not enough numerical parcels are used. Besides, they induce coupling difficulties b...

The accurate simulation of the dynamics of polydisperse evaporating sprays in unsteady gaseous flow with large scale vortical structures is both a crucial issue for industrial combustion application and a challenge for modelling and scientific computing. Various appraoches have been developped in order to resolve the dispersed liquid phase starting...

The scope of the present study is Eulerian modeling and simulation of polydisperse liquid sprays undergoing droplet coalescence and evaporation. The fundamental mathematical description is the Williams spray equation governing the joint number density function f(v, u; x, t) of droplet volume and velocity. Eulerian multi-fluid models have already be...

The purpose of this article is the analysis and the development of Eulerian multi-fluid models to describe the evolution of the mass density of evaporating liquid sprays. First, the classical multi-fluid model developed in [Laurent and Massot, Combust. Theor. Model. 5 (2001) 537–572] is analyzed in the framework of an unsteady configuration withou...

An Eulerian multi-fluid model is validated by comparison with experimental measurements in the test case of laminar spray counterflow diffusion flames. Special attention is devoted, both from the modelling and experimental point of view, to the treatment of the droplet distribution tail, characterized by the rare occurrence of relatively large drop...

In this paper, we present a new Eulerian multi-fluid modeling for dense sprays of evaporating liquid droplets which is able to describe droplet coalescence and size polydispersion as well as the associated size-conditioned dynamics. It is an uncommon feature of Eulerian spray models which are required in a number of non-stationary simulations becau...

In this Note, we investigate the numerical analysis of a Eulerian multi-fluid model for the description of vaporizing liquid sprays. The study is conducted in a stationary 1D-configuration without dynamical nor heating effects, where the vaporization process is isolated. The phase space is then reduced to the space and droplet size variables. The c...

Dans cette Note, on considère un modèle de type thermo-diffusif pour décrire la propagation d'une flamme 1D dans un milieu gazeux avec une chimie complexe de type graphe ouvert. On redémontre l'existence d'ondes progressives pour ce type de système en utilisant une nouvelle approche et l'on étudie l'effet du passage à la limite d'une diffusion mass...

A Eulerian multi-fluid model is introduced in order to describe the evolution of polydispersed spray flames. It is rigorously derived from a kinetic level of description and has the capability to take into account droplets interactions, such as coalescence, an uncommon feature of Eulerian models. It is validated, in the case of diluted spray, by co...

In this paper, we investigate the existence of mono-dimensional traveling wave of a coupled thermo-diffusive--kinetic model describing the propagation of a plane flame in a polydisperse spray. We first present the model which bridges the gap between the models used for realistic numerical simulations and the ones used for mathematical studies; it c...

A first attempt at deriving a fully Eulerian model for polydisperse evaporating sprays was developed by Tambour et al with the so-called sectional approach. However, the complete derivation of the sectional ‘multi-fluid' conservation equations from the Boltzmann-type spray equation was never provided, neither was the set of underlying assumptions n...