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Eulerian Models for the Description of Polydisperse Sprays: From Fundamental Issues to Industrial Applications and HPC

AMS Seminar Series

Speaker: Marc Massot, Centre de Mathématiques Appliquées, Ecole Polytechnique

Presentation

Abstract

The modeling and simulation of multiphase reacting flows covers a large spectrum of applications ranging from combustion in automobile and aeronautical engines to atmospheric pollution as well as biomedical engineering. In the framework of this seminar, we will mainly focus on a disperse liquid phase carried by a gaseous flow field which can be either laminar or turbulent; however, this spray can be polydisperse, that is constituted of droplets with a large size spectrum. Thus, such flows involve a large range of temporal and spatial scales, which have to be resolved in order to capture the dynamics of the phenomena and provide reliable and eventually predictive simulation tools. Even if the power of the computer resources regularly increases, such very stiff problems can lead to serious numerical difficulties and prevent efficient multi-dimensional simulations. The purpose of the presentation is to introduce to the Eulerian modeling of polydisperse evaporating spray for various applications, that is the disperse liquid phase carried by a gaseous flow field is modeled by `fluid" conservation equations. Such an approach is very competitive for real applications since it has strong ability for optimization on parallel architectures and leads to an easy coupling with the gaseous flow field resolution. We will show that all the necessary steps in order to develop a new generation of computational code have to be designed at the same time with a high level of coherence: mathematical modeling through Eulerian moment methods, development of new dedicated stable and accurate numerical methods, implementation of optimized algorithms as well as verification and validations of both model and methods using other codes and experimental measurements. We will introduce both a new class of models and their mathematical analysis for the direct numerical simulation of spray dynamics, even in the presence of coalescence and break-up, as well as a set of dedicated numerical methods and prove that such an approach has the ability, once validated, to lead to high performance computing on parallel architectures. If we have time, we will finally present a synthesis of recent contributions, which aim at: 1- on the one side transferring the proposed models into identified codes for industrial applications in the fields of solid propulsion, aeronautical and automotive engines, 2- on the other side extending the previous work to turbulent flows, where some scales cannot be resolved and have to be modeled, and where some dedicated numerical methods have to be designed, 3- proposing a unified description for the separated and disperse phase modeling in the framework of fuel injection.

Biography

Photo of Marc Massot
Marc Massot obtained his Ph.D. in Applied Mathematics from Ecole Polytechnique in 1996. After a year at Yale University, Department of Mechanical Engineering, he obtained a CNRS position in the Applied Mathematics Laboratory of the University of Lyon, where he stayed until 2005. He was offered an Associate Professor position at Ecole Centrale Paris when he installed a mathematics team in the EM2C mechanical engineering laboratory. He was Visiting Professor at the Center for Turbulence Research at Stanford University in 2011-2012 and created and chaired the Fédération de Mathématiques de l’Ecole Centrale Paris between 2013 and 2016. He initiated the Computing Center (Mésocentre) of Ecole Centrale Paris in 2010, of which he was the deputy director until 2016 and he is scientific adviser at ONERA DEFA and scientific collaborator at Maison de la Simulation since 2013. Full Professor since 2011, he has been recruited on a full Professor position at Ecole Polytechnique, Centre de Mathématiques Appliquées in 2017 and co-chairs the Initiative HPC@Maths. His main fields of research are mathematical modeling and numerical analysis, analysis of PDEs and dynamical systems for multi-scale systems, scientific computing and high performance computing with applications in combustion, two-phase flows, plasma physics and biomedical engineering.