Tip-vortex cavitation is among the first forms of cavitation to appear around ship propellers. In the present study, the time-resolved three-dimensional flow field around non-cavitating and cavitating tip vortices in the wake of a marine propeller is investigated with tomographic PIV. The advance ratio of the propeller and the Reynolds number of the flow are kept constant, while the cavitation number is varied by changing the pressure inside the cavitation tunnel. The importance of masking the tip-vortex cavities before performing the tomographic reconstruction is firstly demonstrated, followed by a description of the applied masking algorithm. From the three-dimensional velocity vector fields, coherent structures of vorticity are identified using the Q-criterion. Three types of coherent structures are observed to populate the wake of the propeller, i.e. tip vortex, hub vortex, and secondary vortical structures. The secondary vortical structures surrounding the tip vortex appear to be progressively smaller in size and more chaotically-organized for decreasing cavitation number. This can be attributed to the pressure fluctuations induced by the cavity, which strengthen when the cavity size grows.

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The mechanism of bubble capture in a vortical flow is investigated using a Lagrangian bubble tracking method. The motion of bubbles and the factors influencing their movement are examined. Detailed analysis is conducted on the roles played by each force component, such as the lift, added mass, and centrifugal forces, in the bubble capture process. An interesting finding is the identification of the stabilizing effect of the azimuthal lift force on the bubble capture mechanism. Furthermore, a model for capture time based on the radial force balance is also developed, and validated with existing experimental data. These findings, including the force mechanism and capture time model, provide a foundation for understanding the bubble capture process and can potentially inform future studies on tip vortex cavitation inception such as determining the cavitation hotspot.

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Cavitation occurs when the local pressure, induced by high local velocities, drops below the vapor pressure, leading to the formation of vapor bubbles. The subsequent collapse of these bubbles can cause noise, erosion, and vibrations. Recent studies show that cavitation is sensitive to water quality, i.e., the nuclei populations, the chemical composition of water, and the presence of particles. Motivated by investigating the effects of water quality on cavitation, experiments are performed in a dedicated experimental facility. This consists in two co-axial disks that are initially at rest and mutually in contact, in a tank filled with water. The fast diverging movement of the top disk with respect to the bottom one produces a jet flow inside the gap between the disks, which leads to the formation of two counter-rotating vortices. The local pressure drop induced by high flow velocities leads to a phase change. To characterize the phenomenon, two optical techniques are applied, i.e., shadowgraphy and particle image velocimetry (PIV). In performing PIV reconstruction, the sum of correlation enhances the spatial resolution of the velocity vector fields. The pressure field in the region where the vortices occur is obtained from velocity data. The water quality effects on cavitation are investigated by adding salt and using water with an abundance of nuclei inside the tank.@en

Since the industrial revolution the ocean has become noisier. The global increase in shipping is one of the main contributors to this. In some regions, shipping contributed to an increase in ambient noise of several decibels, especially at low frequencies (10 to 100 Hz). Such an increase can have a substantial negative impact on fish, invertebrates, marine mammals and birds interfering with key life functions (e.g. foraging, mating, resting, etc.). Consequently, engineers are investigating ways to reduce the noise emitted by vessels when designing new ships. At the same time, since the industrial revolution (starting around 1760) greenhouse gas emissions have increased the atmospheric carbon dioxide fraction x(CO₂) by more than 100 μmol mol^-1. The ocean uptake of approximately one third of the emitted CO₂ decreased the average global surface ocean pH from 8.21 to 8.10. This decrease is modifying sound propagation, especially sound absorption at the frequencies affected by shipping noise lower than 10 kHz, making the future ocean potentially noisier. There are also other climate change effects that may influence sound propagation. Sea surface warming might alter the depth of the deep sound speed channel, ice melting could locally decrease salinity and more frequent storms and higher wind speed alter the depth of the thermocline. In particular, modification of the sound speed profile can lead to the appearance of new ducts making specific depths noisier. In addition, ice melting and the increase in seawater temperature will open new shipping routes at the poles increasing anthropogenic noise in these regions. This review aims to discuss parameters that might change in the coming decades, focusing on the contribution of shipping, climate change and economic and technical developments to the future underwater soundscape in the ocean. Examples are given, contrasting the open ocean and the shallow seas. Apart from the changes in sound propagation, this review will also discuss the effects of water quality on ship-radiated noise with a focus on propeller cavitation noise.

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Different air phase regimes are formed by controlled air injection in a spatially developing flat plate turbulent boundary layer (TBL). The air is introduced via a slot type injector without the use of a backward-facing step or cavitator upstream of the air injection position. The effect of different incoming liquid flow characteristics on the different regimes is investigated by varying both the liquid freestream velocity and the incoming TBL thickness. The latter is realized through changing the position of the air injection along the length of the water tunnel facility. That resulted in a downstream distance based Reynolds number from 1 to 5 million. Three different air phase regimes are identified under different air flow rates and freestream velocities: the bubbly regime, the transitional, and the air layer regime. The morphological differences of each one are described and quantitative analysis is performed based on the non-wetted area in each condition. The incoming TBL as well as the flow around the air layer are measured with planar particle image velocimetry. The latter enabled the determination of the air layer thickness. In addition, the ratio of the air layer to the incoming boundary layer thickness t_air/δ is also calculated (≈ 0.04 – 0.5). This is a significant dimensionless parameter for scaling, which indicates the extent to which the air layer is embedded within the incoming TBL. Depending on the incoming flow conditions, a two or three branch air layer is formed. The length of the air layer is found to increase with increasing liquid freestream velocities. A good agreement between the air layer length and a half gravity wave predicted by the dispersion relation is found. An increase of the air layer length is observed with a decreasing incoming TBL thickness. This is attributed to a decrease in the local mean velocity at the air–water interface due to the TBL growth. Finally, increasing the incoming TBL thickness delays the onset of the air layer regime.

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A novel cavitation erosion risk model, developed by Schenke et al. ["On the relevance of kinematics for cavitation implosion loads,"Phys. Fluids 31, 052102 (2019)], is applied to compute the cavitation implosion loads. The instantaneous energy balance during the collapse of cavitating structures is considered, where the initial potential energy is first converted into collapse-induced kinetic energy, before it is radiated to the surrounding surface at the final stage of the collapse. In this study, we focus on assessing the cavitation development and the risk of erosion on the blades of propellers operating behind a Ro-Ro container vessel. The presence of the hull contributes to the non-uniformity of the inflow. The consequent variation in velocities and angles of attack leads to the amplification of the cavitation dynamics, especially when the blade passes through the top position. Two designs are investigated that experience cavitation erosion on the pressure side. A statistical filter is used to attenuate low-amplitude implosion loads and identify the extreme events on the blade. The results show a very good correlation with the position of the actual erosion damage on the real propeller blades.

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We propose and analyse an optimization method that uses a machine learning approach to solve multi-objective, constrained propeller optimization problems. The method uses an online learning strategy where explainable supervised classifiers learn the location of the Pareto front and advise search strategies. The classifiers are trained with orthogonal features that capture geometric variation in radial distribution of pitch, skew, camber and chordlength. Based on orthogonal features, the classifiers predict whether or not a design lies on the Pareto front. If the design is predicted to lie on the Pareto front, the method verifies this with an evaluation. If the design is predicted to not lie on the Pareto front with a high confidence level, then the design is ignored. This skipped evaluation reduces the computational effort of optimization. The method is demonstrated on a cavitating, unsteady flow case of the Wageningen B-4 70 propeller with P/D = 1.0 operating in the Seiun-Maru wake. Compared to the classical Non-dominated Sorting Genetic Algorithm — III (NSGA-III) the optimization method is able to reduce 30% of evaluations per generation while reproducing a comparable Pareto front. Trade-offs between suction side, pressure side, tip-vortex cavitation and efficiency are identified from the Pareto front. The non-elitist NSGA-III search algorithm in conjunction with the explainable supervised classifiers also find very diverse solutions. Among the solutions, a design with no pressure side cavitation, low suction side cavitation and reasonable tip-vortex cavitation is found.

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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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This paper introduces a machine learning approach for optimizing propellers. The method aims to improve the computational cost of optimization by reducing the number of evaluations required to find solutions. This is achieved by directing the search towards design clusters with good performance, i.e. high propulsive efficiency and low cavitation. Three types of clusters are expected. The first cluster constitutes designs with performance of interest, i.e. high efficiency and low cavitation. The second cluster constitutes designs with performance not of interest, i.e. low efficiency and high cavitation. The third cluster constitutes designs whose performance cannot be estimated with the Boundary Element Methods (BEM) that we use in this study. In simple cases with single objective optimization to maximize efficiency, these clusters can be identified a-priori with unsupervised classifiers provided that orthogonally independent parameters are used as demonstrated in this paper. For multi-objective constrained optimization, to maximize efficiency and minimize cavitation, for example, supervised classifiers may be required to learn the clusters. Classical design variables such as chordlength, pitch, skew, rake, thickness distribution and camber of hydrofoils cannot be used to identify these clusters because of multicollinearity. Thus, a new orthogonal parametric model is proposed where the parameters are directly derived from the propeller blade mesh. As the blade surface mesh is used as boundary conditions to solve the governing equations, the orthogonal parameters are expected to have a stronger correlation with performance predictions of BEM or Computational Fluid Dynamics (CFD) than classical design variables. We demonstrate that design clusters with good performance can be identified with few BEM evaluations. Furthermore, the method synergizes explainable supervised and unsupervised learning to advice search algorithms and quickly guide them to lucrative regions in the design space. However, reducing the cost of optimization results in a trade-off with completeness of the search; this is also investigated in this paper. The method is demonstrated on a simple fully wetted flow case of the benchmark Wageningen B-4 70 propeller with P/D=1.0, as the geometry and open-water curves are readily accessible allowing back of the envelope verification and validation of our results.

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Following their inception, vortex cavities emanating from stationary wing tips in cavitation tunnels are often observed to grow. These effects are usually attributed to the free and dissolved non-condensable gases in the liquid. However, a detailed mechanism for the cavity's growth is not known. Consequently, the repeatability of vortex cavitation in different flow facilities is generally poor. The main aim of our work is to highlight the contribution of dissolved gases to the cavity's growth, hence addressing water-quality influence in nuclei-depleted conditions. A model is provided for a steady-state diffusion-driven mechanism that transports dissolved gases from the surrounding liquid into the vortex cavitation through a diffusion layer located outside its interface. The model results show that the cavity grows uncontrollably when the dissolved gas concentration in the liquid is saturated or oversaturated relative to its saturation level at ambient pressure conditions (c_∞/c_sat≥1). In addition, it is shown that stable cavity sizes can be achieved when the c_∞/c_sat<1. The predictions in the range 1.04≤c_∞/c_sat≤1.33 are compared with experimental data and infer either of the two geometries for the diffusion layer: (i) a 5μm thin film approximated by a hollow cylinder around the cavity, or (ii) one that evolves like a boundary layer along the axis of the cavity. For the latter modeling approach, the observed length of the cavity was much larger than that required to match with the experimental data, skewing a preference to the thin-film assumption. In the undersaturated regime (c_∞/c_sat=0.14 & 0.39), the proposed model has a qualitative agreement with the data of Briançon-Marjollet and Merle (1996).

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An air layer within a liquid turbulent boundary layer (TBL) is formed by controlled air injection underneath a flat plate. The incoming boundary layer as well as the flow around the air layer were measured with planar particle image velocimetry (PIV). The effect of different incoming liquid flow characteristics on the air layer geometry is investigated by varying both the freestream velocity and the streamwise development length of the TBL. The latter was realized through changing the position of the air injection along the length of the water tunnel facility. Increasing the freestream velocity resulted in an increase of the air layer length, while its maximum thickness remained relatively unaltered. An increase in the TBL development length, had a similarly marginal effect on the resulting maximum air layer thickness but led to a shorter air layer length. The latter could be attributed to a decrease in local mean velocity due to the TBL growth, reflected in a decrease of the air layer to boundary layer thickness ratio (from 0.27 to 0.17). The results of this study are expected to provide insight on the design conditions of an air layer drag reduction system installed in the hull of a ship.

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The Delft Twist 11 Hydrofoil is a common test case for investigating the interaction between turbulence and cavitation modelling in computational fluid dynamics. Despite repeated investigations, results reported for the lift and drag coefficient are accompanied by significant uncertainties, both in experimental and numerical studies. When using scale-resolving approaches, it is known that turbulent fluctuations must be inserted into the domain in order to prevent the flow from remaining laminar around the body of interest, although this has been overlooked until now for the present test case. This work investigates the errors occurring when a laminar inflow is applied for mildly separated or attached flows, by employing the partially averaged Navier–Stokes equations with varying values for the ratio of modelled-to-total turbulence kinetic energy, and with varying grid densities. It is shown that depending on the grid resolution laminar leading edge separation can occur. When turbulent fluctuations are added to the inflow, the leading edge separation is suppressed completely, and the turbulent separation zone near the trailing edge reduces in size. The inflow turbulence has a large effect on the skin friction, which increases with increasing turbulence intensity to a limit determined by the grid resolution. In cavitating conditions the integral quantities are dominated by the shedding sheet cavity. The turbulence intensity has little effect on the pressure distribution, leading to a largely unaffected sheet cavitation, although the shedding behaviour is affected. It is shown that, especially in wetted flow conditions, with scale-resolving methods inflow turbulence is necessary to match the experimental flow field.

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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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Background: Air lubrication techniques have the potential to significantly reduce frictional drag, benefiting sustainable employability of ships. However, these techniques are not yet widely applied in the shipping industry, since a complete understanding of the relevant two-phase flow physics is still lacking. Objective: This article aims to explore the limitations and capabilities of RANS-VoF modelling to numerically model air cavity flows. Methods: Simulations were performed including numerical uncertainty verification and compared to experimental data for an external cavity. To study the effect of reduced eddy-viscosity at the cavity interface, two types of eddy-viscosity correction functions were applied next to a base case, i.e., a power and a Gaussian function. Results: The cavity length and thickness as well as the velocity profiles in the boundary layer just upstream, in the middle and downstream of the external cavity compare well to experimental data. However, in contrast to what was found experimentally, a too strong coupling was found between the computed cavity profile and the air pressure at the nozzle and too much air leaks out of the cavity. For the same nozzle air pressure as in the experiments, similar cavity dimensions were found, but the air flow rate is overestimated by a factor of five. Conclusions: The used methodology is capable of predicting the cavity profile and velocity profiles at different stream-wise locations in the boundary layer around the cavity with respect to experimental findings. However, a mismatch was found in the determination of the required air flow rate for the cavity, which is hypotesized to be mainly caused by the incorrect turbulence modelling around the interface and the advection of a smeared air-water interface in the reattachment zone. This is a direct consequence of the used VoF method. The exact mechanism for air discharge at the cavity closure is still not clear.

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Different variable resolution turbulence modelling approaches (Hybrid, Bridging models and LES) are evaluated for turbulent channel flow at Re_τ=395, for cases using either streamwise periodic boundary conditions or a synthetic turbulence generator. The effect of iterative, statistical and discretisation errors is investigated. For LES, little difference between the different sub-filter modelling approaches is found on the finer grids, while on coarser grids ILES deviates from explicit LES approaches. The results for Hybrid models are strongly dependent on their formulation, and the corresponding blending between the RANS and LES regions. The application of PANS with different ratios of modelled-to-total kinetic energy, f_k, shows that there is no smooth transition in the results between RANS and DNS. Instead a case-dependent threshold which separates two solution regimes is observed: f_k values below 0.2 yield a proper turbulent solution, similar to LES results; higher f_k values lead to a laminar flow due to filtering of the smallest scales in the inverse energy cascade. The application of a synthetic turbulence generator is observed to yield similar performance for all models. The reduced computational cost and increased flexibility makes it a suitable approach to enable the usage of SRS for industrial flow cases which depend on the development of a turbulent boundary layer. It ensures that sufficient large-scale structures develop over the full boundary layer height, thereby negating the problem of relying on the inverse energy cascade for the development of turbulence. Both LES and PANS with turbulence generator yield a better match with the reference data than Hybrid models; of these methods PANS is preferable due to the separation of modelling and discretisation errors.

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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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In the maritime industry, cavitation erosion prediction becomes more and more critical, as the requirements for more efficient propellers increase. Model testing is yet the most typical way a propeller designer can, nowadays, get an estimation of the erosion risk on the propeller blades. However, cavitation erosion prediction using computational fluid dynamics (CFD) can possibly provide more information than a model test. In the present work, we review erosion risk models that can be used in conjunction with a multiphase unsteady Reynolds-averaged Navier-Stokes (URANS) solver. Three different approaches have been evaluated, and we conclude that the energy balance approach, where it is assumed that the potential energy contained in a vapor structure is proportional to the volume of the structure, and the pressure difference between the surrounding pressure and the pressure within the structure, provides the best framework for erosion risk assessment. Based on this framework, the model used in this study is tested on the Delft Twist 11 hydrofoil, using a URANS method, and is validated against experimental observations. The predicted impact distribution agrees well with the damage pattern obtained from paint test. The model shows great potential for future use. Nevertheless, it should further be validated against full scale data, followed by an extended investigation on the effect of the driving pressure that leads to the 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