The dynamic behaviour of vortex cavitation on marine propellers may cause inboard noise and vibration, but is not well understood. The main goal of the present study is to experimentally analyse the dynamics of an isolated tip vortex cavity generated at the tip of a wing of elliptical planform. Detailed high-speed video shadowgraphy was used to determine the cavity deformations in combination with force and sound measurements. The cavity deformations can be divided in different modes, each of which show a distinct dispersion relation between frequency and wavenumber. The dispersion relations show good agreement with an analytical formulation. Finally, experimental support is given to the hypothesis that the resonance frequency of the cavity volume variation is related to a zero group velocity.

stage. These involve the smooth transport of vapor into the tip vortex, leading harmful implosions away from the propeller surface. The tip vortex cavity dynamics are not directly related to the propeller rotation rate. The excitation of this cavity often leads to high amplitude broadband pressure fluctuations between the fourth and seventh blade rate frequency (Wijngaarden et al. 2005).To better understand the sound production from vortex cavitation, a model for the waves on a tip vortex cavity was developed and was shown to be able to describe the interface dynamics in detail (Pennings et al. 2015). As a result, a condition could be predicted where a cavity resonance frequency could be amplified to produce high amplitude sound, as reported by Maines and Arndt (1997).The part that remains to be validated is a vortex model for the cavity size and cavity angular velocity. It has been shown that a Lamb-Oseen vortex model poorly estimates the cavity size as a function of cavitation number (Pennings et al. 2015). It is possible that overestimation of the vortex peak azimuthal velocity could have led to an overestimation of the cavity size. The main goal of the present study was to configure a simple low-order vortex model, to serve as an input into a vortex cavity wave dynamics model, to describe the tip vortex resonance frequency. It is based on the following steps.1. Model the tip vortex velocity field without cavitation (further referred to as wetted vortex) 2. Model the cavity size as a function of cavitation number based on wetted vortex properties 3. Show the difference in velocity field around a wetted and cavitating vortex 4. Obtain the cavity angular velocity value that gives the best correlation to the tip vortex cavity resonance frequency Abstract Models for the center frequency of cavitatingvortex induced pressure-fluctuations, in a flow around propellers, require knowledge of the vortex strength and vapor cavity size. For this purpose, stereoscopic particle image velocimetry (PIV) measurements were taken downstream of a fixed half-wing model. A high spatial resolution is required and was obtained via correlation averaging. This reduces the interrogation area size by a factor of 2-8, with respect to conventional PIV measurements. Vortex wandering was accounted for by selecting PIV images for a given vortex position, yielding sufficient data to obtain statistically converged and accurate results, both with and without a vapor-filled vortex core. Based on these results, the loworder Proctor model was applied to describe the tip vortex velocity outside the viscous core, and the cavity size as a function of cavitation number. The flow field around the vortex cavity shows, in comparison with a flow field without cavitation, a region of retarded flow. This layer around the cavity interface is similar to the viscous core of a vortex without cavitation.

Marine propellers display several forms of cavitation. Of these, propeller-tip vortex cavitation is one of the important factors in propeller design. The dynamic behaviour of the tip vortex is responsible for hull vibration and noise. Thus, cavitation in the vortices trailing from tips of propeller blades has been studied extensively. Under certain circumstances cavitating vortices have been observed to have wave-like disturbances on the surfaces of vapour cores. Intense sound at discrete frequencies can result from a coupling between tip vortex disturbances and oscillating sheet cavitation on the surfaces of the propeller blades. This research article focuses on the dynamics of vortex cavitation and more in particular on the energy and frequency content of the radiated pressures.

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