Application of the Stochastic Field Method to Multi‐Fluid Flow

Abstract

The Stochastic Field Method was originally derived in the field of combustion and firstly applied to a cavitation problem by our group [1]. Randomly distributed variables exist in both combustion and cavitating problems. Calculating strong nonlinear processes using mean values as input, leads to unphysical results. The consideration of the variable's probability density function (PDF) becomes mandatory. The Stochastic Field Method approximates this PDF by samples similar to methods of Lagrangian particles where imaginary particles are introduced to the flow. In contrast to Lagrangian particles methods, these samples are represented by Eulerian fields described by stochastic partial differential equations. This pure Eulerian interpretation makes the method attractive for CFD-codes: A coupling of an Eulerian and a Lagrangian perspective becomes obsolete which results in efficient computation times -especially in the presence of a vast number of bubbles. In contrast to other Eulerian methods, the calculation of an arbitrary PDF is possible at low computational cost. The representation of samples as fields allows the visualization of PDFs within every computational cell. The first implementation into a commercial CFD-Code is presented. In addition, industrial examples, like cavitation in an automotive injection nozzle, are shown.