Lagrangian Point Force regularization for dispersed two-phase flows

Overview & Synopsis

The present paper presents a regularization procedure of the Lagrangian point-particle approach for the simulation of dispersed two-phase flows in a statistical framework. The aim is to regularize the probability presence of a particle, written as a Dirac delta function centered on the particle position in the standard formulation, by a Gaussian like distribution. The associated regularization length scale is obtained by solving additional transport equations in the Lagrangian framework. The regularization itself is then achieved by solving two non-linear diffusion equations. The first diffusion equations allows to spread the field of spatially varying diffusion coefficients required for regularization over the computational mesh. Once this field is defined, regularization of the Lagrangian fields to be projected on the Eulerian grid such as particle density, particle velocity, etc... is performed. These ideas are then tested on simplified one-dimensional test cases. While preliminary results seem encouraging as the dispersed phase fields projected on the Eulerian grid appear much less sensitive to the initial sampling of the spray, further tests on more realistic test cases are necessary to conclude on precision gains with repect to the additional computational expense resulting from the regularization procedure.