Robust Numerical Coupling of Pressure and Pressureless Gas Dynamics Equations for Eulerian Spray DNS and LES

Matthieu Boileau (1, 2) , Christophe Chalons (1, 3) , Marc Massot (1, 2)

1 FR3487 - Fédération de Mathématiques de l'Ecole Centrale Paris
2 EM2C - Laboratoire d'Énergétique Moléculaire et Macroscopique, Combustion
3 LMV - Laboratoire de Mathématiques de Versailles

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 since they are able to predict the turbulent dispersion and evaporation. However, the spray system of conservation equations has a convective part which is similar either to gas dynamics Euler equations with a real gas type state law or to the pressureless gas dynamics (PGD), depending on the local flow regime and droplet Stokes number; so they usually involve singularities due to model closure assumptions and require dedicated numerical schemes. The present contribution introduces a new generation of numerical methods based on relaxation schemes which are able to treat both PGD and general gas dynamics as well as to cope in a robust manner with vacuum zones and natural singularities of the resulting system of conservation equations. The approach relies on the coupling between a relaxed model for PGD and a relaxed model for gas dynamics using an energy threshold. The proposed hybrid relaxation scheme and algorithms are validated through comparisons with analytical solutions and other numerical strategies on one-dimensional (1D) and two-dimensional (2D) configurations. They exhibit a very robust behavior and are a very promising candidate for more complex applications since they provide solutions to key numerical issues of the actual Eulerian spray DNS and LES models. Though the energy is considered here as isotropic, the method can be extended to nonequilibrium gas dynamics to describe the spray dynamics with higher accuracy. 1. Introduction. Many industrial devices involve turbulent combustion of a liquid fuel. The transportation sector, rocket, aircraft, or car engines are almost exclusively based on storage and injection of a liquid phase, which is sprayed into a combustion chamber. It is of primary importance to understand and control the physical process as a whole, from the injection into the chamber up to the combustion phenomena. Numerical simulation is now a standard industrial tool to optimize the turbulent combustion process in such devices [11]. Thanks to large eddy simulation (LES), unsteady phenomena such as jet ignition [20] and combustion instabilities [34, 33] can now be accurately predicted in simplified configurations where purely gaseous flames are encountered. Nevertheless, the liquid fuel injection needs special attention in order to properly predict the combustion regimes. It consists in two parts. The first is related to the atomization process near the injector and requires dedicated models and methods. The second part is related to the spray dynamics once the liquid has reached the structure of a polydisperse cloud of droplets; some promising advances

Mots clés: 76T15; 65M08; relaxation schemes; spray equation; 35L67; multifluid models; 76F65; 65Z05; 35L65; large eddy simulation AMS subject classifications 35L60

Domaines: Analyse numérique [math.NA]; Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]; Sciences de l'ingénieur [physics]

Matthieu Boileau, Christophe Chalons, Marc Massot. Robust Numerical Coupling of Pressure and Pressureless Gas Dynamics Equations for Eulerian Spray DNS and LES. SIAM Journal on Scientific Computing, 2015, 37 (1), pp.79-102. ⟨10.1137/130945740⟩. ⟨hal-00906220v2⟩