Dynamics of Vortex Cavitation

Abstract

This thesis describes the mechanisms with which tip vortex cavitation is responsible for broadband pressure fluctuations on ship propellers. Hypotheses for these are described in detail by Bosschers (2009). Validation is provided by three main cavitation-tunnel experiments, one on a model propeller and two on a stationary wing. These have resulted in a model that can quantify the resonance frequency of a tip vortex cavity based on a limited number of propeller related parameters. Simultaneous measurement of sound and high-speed video recordings of propeller tip-vortex cavitation were performed, in the presence and absence of an upstream wake inflow. In uniform inflow no significant sound production was observed. For conditions of wake inflow a strong tonal sound was measured that decreases in frequency as the cavitation number decreases. In the frequency domain there was a 30 dB increase over a broadband range surrounding the tonal frequency. This tonal sound was directly related to the tip-vortex cavity-diameter oscillations downstream of the wake. The model described in chapter 2, based on a resonance frequency of a tip vortex cavity, accurately describes the dominant sound frequencies. The basis for the model are the dispersion relations of three deformation modes. The relations were found experimentally in the frequency and wave number domain of cavity-diameter fluctuations obtained from high-speed video on a fixed wing. Resonance of the tip vortex cavity occurs at zero group velocity of the volume variation mode (n=0-). This resonance frequency was obtained experimentally while a significant sound source was absent. The quantitative model input for the cavity angular velocity was the single fitted parameter and required validation. Validation was performed by measurement of the flow field of a tip vortex in presence as well as in absence of cavitation. This was achieved by stereo particle image velocimetry in combination with a correlation averaging method. It provided sufficient spatial resolution and accuracy, to show the effect of a tip vortex cavity on the flow field. The tip vortex cavity is surrounded by a region of retarded azimuthal velocity, similar to the viscous core of a vortex without cavitation. The tip-vortex cavity-resonance frequency is underestimated when the measured cavity angular velocity is used. This showed the limits of the dispersion relation model that is based on a potential flow vortex. An empirical closure was proposed to serve as input for the cavity angular velocity. A Proctor vortex model was used to describe the flow field of the tip vortex without cavitation. This model required the vortex circulation, the propeller diameter and an empirical roll-up parameter beta. This model was able to provide the cavity diameter as function of cavitation number. The angular velocity without cavitation at a radius equal to the cavity radius, was used as model input for the cavity angular velocity. This closure of the dispersion relation model was able to describe the dominant sound frequencies as found in the model propeller experiment in a wake inflow.