Propeller cavitation erosion prediction at an early design stage is becoming more and more important since it is one of the key constraints in the search for maximum propeller efficiency. Despite the experience from model tests, cavitation erosion research on actual ship scale is very limited. In this study, an attempt is made to assess the erosion risk on the blades of a full-scale steerable thruster of a tug boat. Pressure side cavitation was detected on board for three different propeller designs. For the first time, a cavitation erosion analysis is performed on ship-scale, using a rigorous potential energy approach, which accounts for the focusing of the potential energy at the collapse center during the cavity collapse. A full sensitivity study has been performed for the blade surface accumulated energy. The erosion model shows the erosion risk for different propeller designs applied on the vessel, and different operating conditions, by looking at the surface specific energy on the blade. The erosion analysis shows locations of high erosion risk that show a good resemblance with the actual damage locations on the real blades.

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Predicting the cavitation impact loads on a propeller surface using numerical tools is becoming essential, as the demand for more efficient designs, stretched to the limit, is increasing. One of the possible design limits is governed by cavitation erosion. The accuracy of estimating such loads, using a URANS approach, has been investigated. We follow the energy balance approach by (Schenke and van Terwisga, 2019), (Schenke et al., 2019), where we take account of the focusing of the potential energy into the collapse center before it is radiated as shock wave energy in the domain. In complex flows, satisfying the total energy balance, when reconstructing the radiated energy, has always been an issue in the past. Therefore, in this study, we investigate different considerations for the vapor reduction rate, in order to minimize the numerical errors, when estimating the local surface impact power. We show that when the vapor volume reduction rate is estimated using the mass transfer source term, then all the energy is conserved and the total energy balance is satisfied. The model is verified on a single cavitating bubble collapse, and it is further validated on a model propeller test case. The obtained surface impact distribution agrees well with the experimental paint test results, illustrating the potential for practical use of our fully conservative method to predict cavitation implosion loads on propeller blades.

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Cavitation erosion is a problem in the design of a wide range of fluid machinery involving liquid flows. Ship propellers, rudders, hydro pumps and turbines or diesel injectors are some of the most prominent examples. Cavitation occurs at locations of high local flow velocity, where the pressure may drop so low that the liquid phase vaporizes. The violent collapse of cavitating structures in regions of pressure recovery can result in high pressure loads and severe damage of such devices. Erosive cavitation is typically encountered when the hydrodynamic efficiency of fluid machinery is optimized. In order to find an appropriate balance in the design trade-off between hydrodynamic efficiency and the risk of cavitation erosion damage, there is a need for computational tools that can predict the risk of cavitation erosion in the early design and optimization process. The prediction of cavitation erosion risk using Computational Fluid Dynamics (CFD), however, is a major challenge because the local erosion damage is the result of extreme pressure loads forming at the final stage of cavity collapses at extremely small scales in both space and time. Due to limited computational resources, such small scales can usually not be resolved for flow problems relevant to engineering applications...@en

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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A 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.

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The erosive aggressiveness of idealized cavities collapsing on a flat surface is investigated by numerical simulation, employing the cavitation intensity approach by Leclercq et al (2017) as a measure of the local energy impact rate. We propose a more straight forward formulation of the cavitation intensity model and verify that it satisfies energy conservation requirements for the accumulated surface energy. Based on the cavitation intensity model, statistical aggressiveness indicators are proposed. The indicators account for the rapidness and frequency of the collapse events. The aggressiveness indicators are further applied to a NACA0015 hydrofoil surface.@en

Recent studies have indicated that mass transfer models are able to correctly reflect the sheet cavitation dynamics of inertia driven flows, given that the mass transfer model constants governing the source term magnitude are sufficiently large (Koukouvinis and Gavaises 2015) and that enough temporal resolution is provided (Schenke and Van Terwisga 2017). The inertia driven dynamics, characterised by cavity collapse time, shedding frequencies and local pressure impact frequencies, were shown to be insensitive to variations of the mass transfer coefficients in this limit. This study focuses on an inviscid cavitating flow around a NACA0015 hydrofoil. The flow dynamics are driven by the re-entrant jet as the main mechanism of cavity shedding. A threshold of mass transfer magnitude, temporal and spanwise spatial resolution is identified, beyond which the frequency of local pressure impacts is model parameter independent. Although the excact values of peak pressure loads remain time step size, grid size and model parameter dependent, the sheet cavitation dynamics are considered as well resolved in this regime as far as shedding frequency and characteristic cavity collapse time are concerned. The results are compared to experimental results by Van Rijsbergen et al. (2012). Based on this, the study further focuses on the mechanism of vorticity generation and vorticity break-up, causing potentially erosive cavitating structures such as horseshoe cavities (Dular and Petkovˇsek 2015).@en

The effect of finite mass transfer rate in combination with temporal resolution on the dynamics of caviting flows is subject of this study. It will be shown that global flow quantities exhibit convergent behaviour with respect to mass transfer rate and time step size in incompressible pressurebased simulation of cavitating flows. It is concluded that large mass transfer rates are required in combination with sufficiently small time steps to focus the local phase transition process to time intervals which are small with respect to both the time scale of the flow (Sezal 2009) and the characteristic cavity collapse time. Koukouvinis & Gavaises (2015) as well as Bhatt et al (2015) came to similar conclusions. The effect of finite mass transfer is demonstrated by numerical studies of an isolated bubble collapse and a cavitating wedge flow. It is further shown how a conventional finite mass transfer approach must be modified to achieve homogeneous equilibrium states as given by an arbitrary barotropic equation of state in the presence of advective density change.@en

One of the key aspects classifying the various approaches in numerical simulation of cavitating flows is the equilibrium flow assumption. It states that internal processes in the flow always occur instantaneously compared to the time scale of the flow (s. Sezal (2009)). As a consequence, the density-pressure trajectory in a barotropic flow may follow a unique curve. Contrary to the equilibrium flow assumption, one may assume that the time to achieve a new state is governed by the magnitude of a finite mass transfer source term in a volume fraction transport equation (s. Asnaghi et al. (2015)). In this case, the set of possible density-pressure states is not predefined, but strongly depends on the rate at which pressure changes. Although it has been pointed out by Koukouvinis and Gavaises (2015) that the equilibrium assumption for a barotropic flow would theoretically be mimicked by the mass transfer model if the finite transfer rate tended to infinity, the model parameters triggering the finite transfer rate are generally considered as empirical (s. Frikha et al. (2008)). In this paper, effects of the finite mass transfer rate with special focus on condensation will be studied in detail. First, a cavity collapse will be considered to demonstrate how the finite transfer source term must be modified to satisfy the equilibrium flow assumption. Second, a single bubble collapse is studied numerically and effects of the finite mass transfer rate will be discussed.@en