Eulerian models and three-dimensional numerical simulation of polydisperse sprays

International audienceProviding 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 computational costs and may lead to a low level of resolution if not enough numerical parcels are used. Besides, they induce coupling issues due to the different kind of description of the two phases that are involved. A large range of Eulerian models have been recently developed to describe the dispersed liquid phase with a lower cost and an easier coupling with a carrier gaseous phase. Among these models, the multi-fluid model allows a detailed description of polydispersity and size/velocity correlations of droplets of various sizes. It has been studied in depth from a mathematical and numerical point of view and validated through comparisons versus Lagrangian simulations and experimental measurements in 2D and 2D-axisymmetrical configurations. However, the validation in three-dimensional unsteady configurations still remains to be done. In this work, we study the non-evaporating droplet segregation in three-dimensional Homogeneous Isotropic Turbulence (HIT) using a reference Lagrangian spray model versus the Eulerian multi-fluid model. A spectral Direct Numerical Simulation solver is used to describe the evolution of the turbulent carrier phase, whose characteristic properties remain statistically stationary due to a semi-deterministic forcing scheme. We focus on the optimization via a parallel implementation of the multi-fluid model and dedicated numerical methods which demonstrates the ability of the Eulerian DNS model to be used in complex configurations. We provide qualitative comparisons between the Euler-Lagrange and the Euler-Euler descriptions for two different values of the Stokes number based on the initial fluid Kolmogorov time scale, Stokes=0.17 and 1.05. A very good agreement is found between the mesoscopic Eulerian and Lagrangian predictions. We go further with first quantitative comparisons of the segregation effect of the vortices on the spray mass density distribution showing the accuracy and ability of the multi-fluid model to be used in 3D complex configurations from the tracer limit to unity