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

Abstract (Summary)

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.
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Bibliographical Information:

Advisor:

School:Pennsylvania State University

School Location:USA - Pennsylvania

Source Type:Master's Thesis

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ISBN:

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