Eulerian/Lagrangian Analysis for the Prediction of Cavitation Inception

Abstract

An Eulerian/Lagrangian computational procedure was developed for the prediction of cavitation inception by event rate. The event rate is governed by the number distribution of nuclei, the instantaneous pressure field in the flow, the trajectory of the nuclei, and the bubble dynamics. The development of the procedure utilized an experimental database for an axisymmetric headform known as a "Schiebe" body. The demonstration of the method in axisymmetric flows is a necessary prerequisite for application to turbomachinery flows, where the issues of grid resolution of vortices and turbulence modeling are more critical. The carrier-phase flow field was computed using an Eulerian Reynolds-Averaged Navier-Stokes solver. The Lagrangian analysis was one-way coupled to the RANS solution, since at inception, the contributions of mass, momentum, and energy of the microbubbles to the carrier flow are negligible. Probability density functions for measured nuclei populations were inverted to produce a representative population of computational bubbles, whose trajectories and growth were tracked through the flow field. The trajectories were computed using Newton's second law with models for various forces acting on the bubble. The growth was modeled using the Rayleigh-Plesset equation. The important effect of turbulence was included by adding a random velocity component to the mean flow velocity by sampling a Gaussian probability density function with variance proportional to the turbulent kinetic energy at the location of the bubble and by reducing the local static pressure by a value proportional to the turbulent kinetic energy squared. The simulation results indicate agreement with experimentally observed trends and a significant event rate at cavitation numbers above visual inception. The velocity dependence of the inception data is shown to be related to the change in the nuclei population. In this paper, the Eulerian/Lagrangian formulation is presented followed by a discussion of the simulation results of the experiment reported by Meyer, Billet, and Holl (1992).