An analytical and numerical study of cavitation scale effects in high-Reynolds number circular jet flows

by Edge, Brian A.

Since its earliest discovery, cavitation has proved to be a challenging topic for engineers. Engineers often seek to predict the performance of a prototype by building and testing a scale model. Model theory has traditionally worked well for predicting hydrodynamic loads, but predictions of cavitation inception from scale model tests have proved to be quite unreliable. The current theory of cavitation scaling assumes that the dimensionless cavitation number will remain constant between the model and the prototype. Experiments, however, often show that incipient cavitation numbers change significantly with length scale and the properties of the water supply. The problem is further complicated by experimental data which shows that the prototype cavitation number will sometimes increase from the model values, but at other times will decrease. Changes in the cavitation number between the model and the prototype are known as cavitation scale effects. Cavitation inception in circular jets has been the subject of recent experimental studies. These studies have found that jet flows experience significant cavitation scale effects. The data indicates that cavitation number unexpectedly increases with jet diameter. This thesis explores the scale effects associated with cavitation inception and looks to explain the scale effects observed in jet flows. The goal of the thesis is to develop tools which can be used to predict prototype cavitation inception. As a first step, a dimensional analysis of the cavitating jet was completed. This dimensional analysis showed that the cavitation number is a function of at least eight dimensionless parameters. An analysis of these parameters shows that it is not possible to keep all of these parameters constant between the model and prototype. This means that the relative importance of the governing parameters will change with the length scale of the flow. In order to investigate the scale effects further, a numerical code is developed to simulate the response of cavitation nuclei to a fidelity detached-eddy simulaiii tion of a circular jet. The radial growth of cavitation nuclei is governed by the Rayleigh-Plesset equation and the dispersion of the bubbles is governed by a semiempirical equation of motion. This is the first time that an unsteady computational fluid dynamics simulation has been used in combination with the Rayleigh-Plesset equation to simulate cavitation inception. Results of the numerical simulations are consistent with previous experimental data. The scale effects observed in the historical data are confirmed to exist. The results also indicate that the initial nuclei size is the critical parameter for determining whether the incipient cavitation number will increase or decrease with changes in length scale Cavitation scale effects are also investigated from a theoretical perspective. The nonlinear response of nuclei bubbles to an oscillating pressure is investigated. This investigation leads to the development of a scaling law derived from the equilibrium Rayleigh-Plesset equation. The scaling law provides a method to predict the incipient cavitation number for a prototype flow by using the data obtained from a scale model. Unlike prior empirical relations and the current cavitation inception theory, the equilibrium scaling relation can predict and explain opposing trends in historical data. The equilibrium scaling law is validated by comparing with the numerical simulations of the jet flow and by comparing with historical hydrofoil data. These validations show that the equilibrium theory can predict prototype cavitation inception from scale model test data. iv