
doi: 10.17077/etd.006449
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. Traditional Computational Fluid Dynamics (CFD) methodologies cannot properly predict it due to either insufficient grid resolution that results in underpredicted minimum pressures in the flow, or in well resolved grids that can better predict the pressure but do not consider the duration or the volume of the low pressure events. With proper modeling of unresolved turbulence in the sub-grid scale (SGS), cavitation event rates in the SGS can be computed using the rates of low pressure fluctuating events and their corresponding duration. This thesis presents a cavitation inception model that includes pressure fluctuations at the (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 considering the frequency and duration of unresolved low pressure fluctuations in the SGS. The SGS flow field is modeled as homogeneous isotropic turbulence (HIT), dependent on the unresolved turbulence Taylor scale Reynolds number {Re}_\lambda. Direct numerical simulations (DNS) of HIT up to {Re}_\lambda=240 were performed with a pseudo-spectral code, tracking nuclei with sizes between 0.1 and 150 \mu m 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 experienced by nuclei in HIT was studied, including pressure probability density functions, low-pressure event frequency and duration, and the effect of nuclei size on these parameters. It is found that low-pressure events are more likely as {Re}_\lambda and the nuclei size increase. Solutions of the Rayleigh-Plesset equation along the nuclei trajectories offered cavitation event rates for a defined cavitation criterion. A table providing cavitation rate as a function of {Re}_\lambda, nuclei radius, turbulent kinetic energy dissipation rate, and pressure was generated to use in the prediction of cavitation inception in complex CFD problems. Validation of the model is performed for high {Re}_\lambda HIT turbulence and shear flow behind a backward facing step. As the model uses the nuclei size distribution and concentration, the predicted cavitation frequency depends on the water quality. The model can predict the effect of unresolved pressure fluctuations, typically increasing the cavitation inception number with respect to CFD predictions using the minimum flow pressure to predict inception but can also predict a lower cavitation inception number for highly resolved LES simulations where very low pressure events can be infrequent and of small volume. The model showed satisfactory comparisons with experiments for both HIT and shear flow.
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