Statistical modeling of cavitation inception

Cavitation is the phenomenon of bubbles growing when the liquid pressure drops below vapor pressure. Cavitation is mostly undesirable and fluid engineering systems are often designed to avoid it, so proper prediction of the cavitation inception point is important. This thesis presents a cavitation inception model that includes pressure fluctuations at the sub-grid scale (SGS) level in CFD simulations. As turbulence models look to predict the momentum transfer at the resolved scales by approximating the SGS turbulence behavior, the model presented in this thesis seeks to predict the cavitation inception at the SGS level. To this end, the SGS flow field is modeled as homogeneous isotropic turbulence (HIT), dependent on the unresolved turbulence Taylorscale Reynolds number Re_λ. Direct numerical simulations (DNS) of HIT up to Re_λ = 240 were performed, tracking nuclei with sizes between 0.1 and 150 μm and solving the Rayleigh-Plesset equation on the time histories of the nuclei to predict bubble cavitation rates at different absolute pressures. The behavior of the pressure on the nuclei in HIT was studied, including pressure probability density functions, low-pressure event frequency and duration, and effect of nuclei size on these parameters. It is found that low-pressure events are more likely as Re_λ and the nuclei size increase. A table providing cavitation rate as a function of Re_λ, nuclei radius, turbulent kinetic energy dissipation rate, and pressure was generated to use for predicting cavitation inception in complex CFD problems. The model can predict the effect of unresolved pressure fluctuations, which typically increases the cavitation inception number when compared to CFD predictions that use the minimum flow pressure to predict inception, but it can also predict a lower cavitation inception number for highly resolved LES simulations where very low pressure events are rare and small in volume. The model was tested for high Re_λ HIT turbulence and a backward facing step, showing satisfactory comparisons with experiments.