An Eulerian stochastic field cavitation model coupled to a pressure based solver

Probability density functions (PDF) and the relevant methods have been widely used to describe non-linear phenomena in the realm of turbulence modelling and CFD. In order to solve PDF transport equations, the main trend of previous studies rely on Monte Carlo method with Lagrangian particle tracking. However, as with any Lagrangian based approach, the scalability of the parallelized simulations of such method is less than satisfactory. An Eulerian stochastic field model has been presented recently by Dumond et al. [1] to simulate cavitating flows. Their model uses a fully compressible density based solver. Here we present an adapted version using an iso-thermal cavitation model adopting the homogeneous mixture assumption in a pressure based flow solver which is more relevant to engine simulations. A PDF method is used to represent a distribution of vapour volume fractions, based on which the Eulerian stochastic field (ESF) method is applied to perform a three-dimensional large eddy simulation (LES) of the cavitation phenomena inside an academic fuel injector configuration. The numerical model is based on a volume of fluids approach and coupled with a pressure based solver for the flow field, and is implemented in the framework of the open source C++ toolbox OpenFOAM. The result of the ESF simulation is compared against that from a typical single volume fraction solver for validation. Vortex structures and its correspondence to cavitation are shown, and the behaviour of the PDF at different probe locations at different times are acquired to demonstrate the potential of the ESF model in capturing both transient and stochastically steady cavitation.