A sub-grid scale cavitation inception model

Unresolved pressure fluctuations at the sub-grid scale (SGS) level of large eddy simulation (LES) or Reynolds-averaged Navier-Stokes computations affect cavitation inception predictions, as SGS low pressures are simply ignored. We present a framework to take the unresolved SGS flow into account. Representing the SGS flow as canonical turbulence, in this paper, homogeneous isotropic turbulence (HIT), the pressure fluctuations, and transport and cavitating behavior of nuclei in such turbulence can be evaluated from direct numerical simulations (DNS) and used to create a model of cavitation inception that accounts for SGS fluctuations. To accomplish this, nuclei of different sizes were transported in DNS of HIT using their pressure history to drive the Rayleigh-Plesset equation that simulates bubble dynamics. In this way, expected average cavitation frequencies were tabulated for a range of SGS Taylor scale Reynolds numbers (Re-lambda), nucleus size, turbulent kinetic energy dissipation rate, and mean pressure. The model uses this table to estimate the cavitation event rate in each cell of a computational fluid dynamics solution. Inception can then be predicted by comparing the total cavitation rate with the detection criterion. The model is first assessed on two cases of HIT (at Re-lambda = 240 and 324) by comparing the pressure statistics, which it predicts in LES runs using the SGS cavitation model against the statistics of DNS. Then, a high Re-lambda (1660-1880) HIT flow is simulated using LES, and cavitation events are compared against experimental data. The inception model successfully predicts the inception pressure and the cavitation rates in the flow.