Correction Methods for Exchange Source Terms in Unstructured Euler-Lagrange Solvers with Point-Source Approximation

This paper provides a preliminary study of two different methods to handle the limitations of the Lagrangian point-force approach in the context of unstructured LES solvers. Large deviations in mass, momentum, and energy exchanges between the gas and liquid phases may occur if the assumptions of the point-force approach are not verified. In particular, the point-force approach considers the particles to be subgrid-scale phenomena but the use of more and more refined grids for the carrier flow allowed by today’s computer power leads to cell sizes of the order or smaller than the particle diameters. Several methods are found in the literature to tackle this problem. However, they are usually suited for structured solvers. In the case of unstructured solvers handling several hundred thousand particles in unsteady flows, such methods are far too expensive. In this work, two original methods adapted for spray calculation in unstructured solvers are implemented and compared: the particle-bursting method, and the multigrid method. In this preliminary study, only the correction on the evaporation model is studied, with drag being neglected. Both methods greatly improve the accuracy of the evaporation model but only the multigrid method is independent of the Eulerian mesh refinement. The results presented show that the two methods are relevant to correct the evaporation source terms when the limits of the point-force model are reached. However, the study should be extended to consider the impact of the methods on the drag model calculation and the effects on the interaction with a reactive gaseous phase.