Implementation of a probabilistic surface density volume of fluid approach for spray atomisation

Abstract

Eulerian Stochastic methods in Large Eddy Simulation context have been successfully used in reactive flows. They have been recently applied to spray atomisation, using surface and liquid volume as independent variables. These methods involve the solutions of Stochastic Partial Differential Equations, which are continuous in space and discontinuous in time. The implementation of these equations into a conventional finite volume solver can be challenging due to both the numerical diffusion of the scalar fields and the numerical integration of the stochastic source terms. This work presents the implementation and validation of the Eulerian Stochastic Fields surface/liquid volume atomisation method within the OpenFOAM framework. The paper discusses how algebraic compression methods can be used for the stochastic fields to minimise the numerical diffusion and the effects of the stochastic source term implementation. The model targets a-priori spray atomisation at large Weber numbers, although the implementation recovers the correct solution at low Weber model and captures correctly the capillary effects on liquid–gas interfaces. A turbulent liquid jet is used for validation and discussion of the accuracy and relative cost of the model implementation. The approach is then applied to a multi-hole gasoline direct injector where the agreement with experimental data showcases the capabilities of the solver for realistic injectors and atomisation regimes.