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Application of the Stochastic Field Method to Cavitating Flows in an Injection Nozzle

#### Excerpt

In this paper a fully Eulerian Monte Carlo method called ‘Stochastic Field Method’ (SFM) is applied on cavitating flows in an injection nozzle from the automotive industry. After the successful application to the field of combustion, the Stochastic Field Method is now applied to two phase flow. In the presence of numerous bubbles the method provides advantages in computational speed and statistical convergence compared to the classical Lagrangian-particle Monte Carlo methods. Modeling random processes which are omnipresent in combustion and cavitation requires careful treatment: Unphysical results are obtained, if in a nonlinear process a randomly distributed variable is merely approximated by its average. Thus the whole distribution must be considered. A probability density function (PDF) is used to describe the probabilistic behavior. The corresponding evolution and transport in space is governed by the PDF transport equation. Instead of solving the high dimensional PDF transport equation directly it is less complex to discretely approximate the PDF by random samples. In contrast to other stochastic methods that usually consider these samples as Lagrangian particles, the Stochastic Field Method describes them as fluctuating Eulerian fields. This point of view allows PDF description in a fully Eulerian framework, thus omitting the cumbersome coupling of Eulerian and Lagrangian solvers. The very first application of the Stochastic Field Method to a multi-phase flow was published by our working group. Here, stochastic partial differential equations (SPDEs) describe samples of the disperse phase volume fraction as Eulerian fields. The collective of all samples approximates the probability density function at a considered location. Within the present paper the implementation to a commercial code is discussed. Application to an industrial case namely a cavitating flow within an injection nozzle is presented. Collecting samples of several time steps allows the SFM to visualize the volume fraction’s or bubble size’s distribution within individual computational cells. When applying the Stochastic Field Method to multiphase problems a number of physical aspects have to be considered which require careful analysis. These difficulties are pointed out and discussed.

Introduction
Basics of the Stochastic Field Method
Stochastic Field Method in the Field of Combustion
Application to the Field of Two Phase Flow
Application to a Cavitation Example from Automotive Industry
Conclusion
Acknowledgment
References
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