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.

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An assessment of the cavitation erosion risk by using a contemporary unsteady Reynolds-averaged Navier–Stokes (URANS) method in conjunction with a newly developed postprocessing procedure is made for an NACA0015 hydrofoil and an NACA0018-45 hydrofoil, without the necessity to compute the details of the actual collapses. This procedure is developed from detailed investigations on the flow over a hydrofoil. It is observed that the large-scale structures and typical unsteady dynamics predicted by the URANS method with the modified shear stress transport (SST) k-ω turbulence model are in fair agreement with the experimental observations. An erosion intensity function for the assessment of the risk of cavitation erosion on the surface of hydrofoils by using unsteady RANS simulations as input is proposed, based on the mean value of the time derivative of the local pressure that exceeds a certain threshold. A good correlation is found between the locations with a computed high erosion risk and the damage area observed from paint tests.

A three-dimensional twisted hydrofoil with an attached cavitaty closely related to propellers was observed with a high-speed camera at the University of Delft Cavitation Tunnel. Reentrant flow coming from the sides of the cavity aimed at the center plane-termed side-entrant flow-collided in the closure region of the cavity, pinching off a part of the sheet resulting in a periodic shedding. The collapse of the remainder of the sheet appears to be a mixing layer at the location of the colliding reentrant flows. Collision of sideentrant jets in the closure region of a cavity is identified as a second shedding mechanism, in addition to reentrant flow impinging the sheet interface at the leading edge. Fig. 7 A close-up of Fig. 6 "marked A… shows the formation of a large spanwise vortex at 2 kHz. As the main sheet collapses, a trail of very small spanwise vortices is created, merging in several distinct larger structures.

An energy conservative method to predict the erosive aggressiveness of collapsing cavitating structures and cavitating flows from numerical simulations Schenke, Sören; van Terwisga, Tom J.C. a b s t r a c tA new technique is proposed in this study to assess the erosive aggressiveness of cavitating flows from numerical flow simulations. The technique is based on the cavitation intensity approach by Leclercq et al. (2017), predicting the instantaneous surface impact power of collapsing cavities from the potential energy hypothesis (see Hammitt, 1963;Vogel and Lauterborn, 1988). The cavitation intensity approach by Leclercq et al. (2017) is further developed and the amount of accumulated surface energy caused by the near wall collapse of idealized cavity types is verified against analytical predictions. Furthermore, two different impact power functions are introduced to compute a weighted time average of the impact power distribution caused by the cavity collapses in cavitating flows. The extreme events are emphasized to an extent specified by a single model parameter. Thus, the impact power functions provide a physical measure of the cavitating flow aggressiveness. This approach is applied to four idealized cavities, as well as to the cavitating flow around a NACA0015 hydrofoil. Areas subjected to aggressive cavity collapse events are identified and the results are compared against experimental paint test results by Van Rijsbergen et al. (2012) and the numerical erosion risk assessment by Li et al. (2014). The model is implemented as a runtime post-processing tool in the open source CFD environment OpenFOAM (2018), employing the inviscid Euler equations and mass transfer source terms to model the cavitating flow.

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.

This study presents a novel physical model to convert the potential energy contained in vaporous cavitation into local surface impact power and an acoustic pressure signature caused by the violent collapse of these cavities in a liquid. The model builds on an analytical representation of the solid angle projection approach by Leclercq et al. ["Numerical cavitation intensity on a hydrofoil for 3D homogeneous unsteady viscous flows," Int. J. Fluid Mach. Syst. 10, 254-263 (2017)]. It is applied as a runtime post-processing tool in numerical simulations of cavitating flows. In the present study, the model is inspected in light of the time accurate energy balance during the cavity collapse. Analytical considerations show that the potential cavity energy is first converted into kinetic energy in the surrounding liquid [D. Obreschkow et al., "Cavitation bubble dynamics inside liquid drops in microgravity," Phys. Rev. Lett. 97, 094502 (2006)] and focused in space before the conversion into shock wave energy takes place. To this end, the physical model is complemented by an energy conservative transport function that can focus the potential cavity energy into the collapse center before it is converted into acoustic power. The formulation of the energy focusing equation is based on a Eulerian representation of the flow. The improved model is shown to provide physical results for the acoustic wall pressure obtained from the numerical simulation of a close-wall vapor bubble cloud collapse.

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