In this paper, we tackle the modeling and numerical simulation of sprays and aerosols, that is dilute gasdroplet flows for which polydispersity description is of paramount importance. Starting from a kinetic description for point particles experiencing transport either at the carrier phase velocity for aerosols or at their own velocity for sprays as well as evaporation, we focus on an Eulerian high order moment method in size and consider a system of partial differential equations (PDEs) on a vector of successive integer size moments of order 0 to N , N > 2, over a compact size interval. There exists a stumbling block for the usual approaches using high order moment methods resolved with high order finite volume methods: the transport algorithm does not preserve the moment space. Indeed, reconstruction of moments by polynomials inside computational cells coupled to the evolution algorithm can create N -dimensional vectors which fail to be moment vectors: it is impossible to find a size distribution for which there are the moments. We thus propose a new approach as well as an algorithm which is second order in space and time with very limited numerical diffusion and allows to accurately describe the advection process and naturally preserves the moment space. The algorithm also leads to a natural coupling with a recently designed algorithm for evaporation which also preserves the moment space; thus polydispersity is accounted for in the evaporation and advection process, very accurately and at a very reasonable computational cost. These modeling and algorithmic tools are referred to as the EMSM (Eulerian Multi Size Moment) model. We show that such an approach is very competitive compared to multi-fluid approaches, where the size phase space is discretized into several sections and low order moment methods are used in each section, as well as with other existing high order moment methods. An accuracy study assesses the order of the method as well as the low level of numerical diffusion on structured meshes. Whereas the extension to unstructured meshes is provided, we focus in this paper on cartesian meshes and two 2D test-cases are presented: Taylor-Green vortices and turbulent free jets, where the accuracy and efficiency of the approach are assessed.

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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 accurate simulation of the injection of a liquid disperse phase into a gas for automotive engine applications. The original model used a high order moment method in droplet size to resolve polydispersity, with built-in realizability preserving numerical algorithm of high order in space and time, but only dealt with one-way coupling and was restricted to fixed meshes. Extending the approach to internal combustion engine and fuel injection requires solving two major steps forward, while preserving the properties of robustness, accuracy and realizability: 1-the extension of the method and numerical strategy to two-way coupling with stable integration of potential stiff source terms, 2-the introduction of a moving geometry and meshes. We therefore present a detailed account on how we have solved these two issues, provide a series of verification of the proposed algorithm, showing its potential in simplified configurations. The method is then implemented in the IFP-C3D unstructured solver for reactive compressible flows in engines and validated through comparisons with a structured fixed mesh solver. It finally proves its potential on a free spray jet injection where it is compared to a Lagrangian approach and its reliability and robustness are assessed, thus making it a good candidate for realistic injection applications.

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Résumé -Développement d'une tabulation FPI pour la prise en compte de la chimie complexe dans la simulation 3D moteurs -L'objectif de cette étude est d'utiliser une tabulation de la chimie de type FPI (Flame Prolongation of ILDM) pour la simulation 3D de la combustion dans les moteurs. La première difficulté a été d'adapter la méthode à des codes compressibles tout en se limitant à des tailles de tables raisonnables. Pour satisfaire ces contraintes, une nouvelle formulation a été proposée. Elle permet de garder une structure de code basée sur le transport de quelques espèces chimiques tout en assurant la cohérence de l'évolution du système grâce à une équation pour l'avancement de la réaction. Le terme source chimique impliqué dans cette dernière est directement extrait de la tabulation. L'approche retenue permet également d'appliquer la modélisation FPI à des problématiques moteur comme l'utilisation de carburants complexes caractérisés par des chimies détaillées très lourdes ou la combustion fortement diluée. Le modèle proposé, introduit dans le code de simulation moteur IFP-C3D, a été validé sur des configurations homogènes à volume constant et à volume variable contrôlé. Enfin, le modèle complet a été appliqué avec succès à un cas moteur Diesel à injection directe. Abstract -Development of a FPI Detailed Chemistry Tabulation Methodology for Internal Combustion Engines -In this paper, the FPI (Flame Prolongation of ILDM) approach for chemistry tabulation is applied to 3D internal combustion engine simulations. The first issue is to