| An Eulerian/Lagrangian computational procedure was developed for the prediction of cavitation inception by event rate. A cavitation event denotes the process by which a single cavitation nucleus is convected into a region of low pressure, grows explosively to macroscopic size, and collapses when it is convected into a region of higher pressure. Cavitation inception is thus a statistical process and inception is defined by a specific number of events per unit time. 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 literature includes data from a number of nuclei distributions, Reynolds numbers, and geometric scales for this well-behaved flow field. 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 can arise. 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. |
