Sheet Cavitation Research Articles

A computational investigation of noise spectrum due to cavitating and non-cavitating propellers

In this article, noise spectrum of marine propellers is investigated in uniform flow under non-cavitating and cavitating conditions. New results are presented for this research field. Hydrodynamic performance of both non-cavitating and cavitating marine propellers is first analyzed by viscous and potential based flow solvers. In viscous solver, sheet cavitation on propeller blades is simulated with Schnerr–Sauer cavitation model based on Rayleigh Plesset equation using volume of fluid approach. Numerical hydrodynamic results based on viscous solver is compared with potential solver and then validated with experimental data of benchmark David Taylor Model Basin 4119 model propeller. Later, noise spectrum of model propellers is predicted by a hybrid method which combines Reynolds-averaged Navier Stokes and Ffowcs Williams Hawkings equations. Computed noise spectrum is compared with other numerical studies in the literature for the selected model propeller. In addition, hydrodynamic and hydroacoustic pressures are compared in near field to show reliability of numerical solution. Effects of blade number on hydrodynamic performance and noise spectrum are also investigated. Numerical results indicated that as blade number increases, propeller noise level decreases for different loading conditions due to decreased blade loading (circulation) per blade. However, propeller efficiency increases as blade number decreases.

Numerical Prediction of the Pumpjet Propulsor Tip Clearance Vortex Cavitation in Uniform Flow

Previous studies show that the tip clearance loss limits the improvement of pumpjet propulsor (PJP) performance, and the tip clearance flow field is the most complicated part of PJP flow. In this work, the non-cavitation and cavitation hydrodynamic performances of PJP with a tip clearance size of 1 mm are obtained by using the detached-eddy simulation (DES). At constant oncoming velocity, cavitation first occurs on the duct and then disappears with the decrease of the advance ratio. The rotor blade cavitation occurs at the low advance ratio and comprises tip clearance cavitation, tip leakage cavitation, and blade sheet cavitation. In the rotor region, the typical vortices include tip separation vortex, tip leakage vortex, trailing edge shedding vortex, and blade root horseshoe vortex. Combined with the pressure distribution, both the Q and λ2 criteria give reliable results of vortex identification. The cavitation causes an expansion of tip leakage vortex in the circumferential direction and decreases the intensities of tip separation vortex in the whole tip clearance area and tip leakage vortex in the cavitation area, and enhances the strength of tip leakage vortex in the downstream non-cavitation area.

Investigation of Cavitation Noise in Cavitating Flows around an NACA0015 Hydrofoil

To provide theoretical basis for cavitation noise control, the cavitation evolution around a hydrofoil and its induced noise were numerically investigated. A modified turbulence model and Zwart cavitation model were employed to calculate the flow field and predict the cavitation phenomenon accurately. Then, the acoustic analogy method based on the Ffowcs Williams-Hawking (FW-H) equation was applied to analyze the cavitation-induced noise. Seven cavitation numbers were selected for analysis. Acoustic power spectral density (PSD) and acoustic pressure were investigated to establish the relationship between cavitation number and their acoustic characteristics. It was indicated that as cavitation number decreases, cavitation cycle length gets shorter and the magnitude of acoustic power spectral density increases dramatically. One peak value of acoustic power spectral density induced by the extending and retracting of leading-edge cavitation can be obtained under sheet cavitation conditions, while under cloud cavitation, two peak values of acoustic power spectral density can be obtained and are induced by superposition from leading-edge cavitation and trailing vortex.

Effect of obstacle position on attached cavitation control through response surface methodology

The span-wise obstacle on the suction surface of a hydrofoil has been verified to be an effective passive control method for cloud cavitation. The position of obstacle significantly influences the performance of cavitation control. In this research, we investigated the effect of obstacle position on attached cavitation control on the suction surface of a NACA0015 hydrofoil through response surface methodology. The cavitation types covered from sheet cavitation to partial and transitional cavity oscillations. We derived regression equations and built response surfaces to illustrate the quantitative relationship between individual factors (obstacle position, cavitation number, and angle of attack) and cavitation dynamic response parameters (cavity length, acoustic intensity, and energy flux). Sheet cavitation was effectively suppressed because the obstacle increased the pressure at the near-wall region. However, the obstacle would induce a shear cavitation when its position was too close to the leading edge of the hydrofoil. Under partial cavity oscillation conditions, the obstacle was consistently performed well in cloud cavitation control. The cavitation dynamic response parameters significantly decreased. Under transitional cavity oscillation conditions, the obstacle cannot suppress the cavitation because the transitional cavity oscillation was likely a system-inherent instability. This research is beneficial for a comprehensive understanding of cavitation control mechanism using an obstacle and for further industrial application of obstacle in hydraulic machinery to control cavitation.

Visual experiment and numerical simulation of cavitation instability in a high-speed inducer

Cavitation instabilities in a high-speed inducer at a design flow rate were investigated for different cavitation numbers in numerical simulations and visual experiments. On the basis of a shear stress transport k–ω turbulence model and Zwart–Gerber–Belamri cavitation model, the transient cavitating flow in a high-speed centrifugal pump with an inducer is numerically simulated using ANSYS-CFX 15.0 software. Visual experiments were carried out to capture the evolution of cavitating flow in the inducer by using a high-speed camera. The performance and cavitation characteristic curves from numerical simulation agree with those from experiment. With a decreasing cavitation number, the cavitation development in the high-speed inducer goes through incipient cavitation, developing cavitation, critical cavitation, and deteriorated cavitation and presents vortex cavitation, sheet cavitation, cloud cavitation, backflow cavitation, and a cavitation surge. The region having a high vapor volume fraction basically coincides with the region of low local pressure at the same cavitation number. The position of largish blade loading on the inducer changes with the development of cavitation. A cavitation surge as one type of cavitation instability appears in the inducer at lower cavitation numbers. The drop or rise of the head coefficient is affected by an increasing or decreasing cavitation area in the cycle of a cavitation surge.

An innovative propeller with experimental and sea trial verifications

An end plate propeller (ENDP) shaped by a diffused endplate bent to the pressure side is proposed in the paper. The ENDP differs from a contracted and loaded tip (CLT) propeller, and possess remarkable performance in terms of cavitation, efficiency, vibration, and noise comparing with that of CLT and conventional propeller, particularly operating at inclined shaft condition. According to experiments conducted in the cavitation tunnel of National Taiwan Ocean University, it is observed that the diffused endplate can effectively restrain tip vortex cavitation, and eliminate tip-plate cavitation typically found on the outer surface of the tip-plate of a CLT propeller. The optimal diameter of the ENDP is smaller than that of a conventional propeller; thus, the ENDP is more suitable for ships with small stern space. Besides, the thrust of the ENDP is contributed much more from its pressure side, therefore, the cavitation on the back is reduced, and the efficiency is increased. Sea trials using a yacht with the ENDP were carried out and the results show that vibrations due to the sheet cavitation at blade-rate frequencies by the ENDP are significantly decreased in comparison with those of conventional propeller, and overall broad-band amplitude caused by the tip vortex cavitation by the ENDP at high frequencies are nearly disappeared.

Analysis of sheet cavitation with bubble/bubble interaction models

A new cavitation model based on bubble/bubble interactions has been recently proposed by the authors Adama Maiga, Coutier-Delgosha, and Buisine [“A new Cavitation model based on bubble-bubble interactions,” Phys. Fluids 30, 123301 (2018)]. It includes all nonlinear interaction terms between two bubbles, and the only input is the local velocity divergence, while the classical Rayleigh-Plesset or Gilmore models only take into account the linear interaction terms and require the local pressure evolution. In this previous publication, the model has been validated against cases of single bubbles growths and collapses. In the present paper, the same model is applied to configurations of high-speed cavitating flow on a Venturi profile and a two-dimensional foil section, where experiments based on X-ray imaging have been recently conducted. Based on the flow velocity fields available in the two cases, the local velocity divergence is calculated, and a one-dimensional mean divergence evolution from the leading edge to the wake of the cavity is extracted and used as an input for the model validation. The evolutions of the biggest bubble and the volume of vapor are both found in good agreement with the experiments. A typical velocity divergence evolution is then defined, and our model is compared to the modified Rayleigh-Plesset equation that includes the interactions between multiple bubbles. It confirms that the radius evolution of the biggest bubble is systematically better estimated by the new model due to its capability to continuously take into account the interactions of big bubbles with smaller bubbles. Eventually, the model is used to investigate the scale effect, by applying 6 different time scales of cavitation development covering more than 5 orders of magnitude. It is shown that the bubble size does not vary proportionally to the scale, but according to a law that is empirically determined.

Shedding frequency in cavitation erosion evolution tracking

Cavitation erosion is a concern for most hydraulic machinery. An especially damaging type of cavitation is cloud cavitation. This type of cavitation is characterized by a growth-collapse cycle in which a group of vapor bubbles first grows together in a low-pressure region and then collapses almost simultaneously when the pressure recovers. Measuring the frequency of these collapse events is possible by acoustic emission (AE), as demonstrated in this study, in which a cavitation tunnel is utilized to create cloud cavitation in the vicinity of a sample surface. These samples were equipped with AE sensors, and the initially high frequency AE signal was demodulated to detect the relatively low frequency cloud cavitation shedding. It was found that when the cavitation number is increased, AE successfully detects the changes in this frequency, confirmed by comparing the results to video analysis and to simulations from literature. Additionally, the frequency increases when cavitation erosion progresses, thus providing means to track the erosion stage. It is concluded that the presented method is suitable for both detecting the transition from cloud to sheet cavitation and the erosion evolution in the experimental cavitation tunnel. The method could probably be extended to non-intrusive hydraulic machine monitoring, as this type of cloud cavitation is common in hydrofoils.

Attached cavitation in laminar separations within a transition to unsteadiness

Attached sheet cavitation is usually observed in turbulent water flows within small laminar separation bubbles which can provide favorable conditions for inception and attachment of cavities. In the present study, viscous silicone oils are used within a small scale Venturi geometry to investigate attached cavitation into laminar separated flows for Reynolds numbers from 346 to 2188. Numerical simulations about single phase flows are performed with steady simulations for a Reynolds number range Re ∈ [50; 1400] and with unsteady simulations for Re ∈ [1000; 2000]. They reveal the emergence of two large laminar boundary layer separations downstream of the Venturi throat in addition to low pressure zones which can possibly induce both degassing or cavitation features. Experiments are performed with high-speed photography, and several multiphase dynamics are observed in these viscous flows, which are considered as quasisteady flows at low Reynolds numbers Re ≤ 1400. Degassing phenomenon with air bubble recirculation has been first observed at pressures far above liquid vapor pressure whereas typical attached cavities have been identified for low pressure conditions as “band” and “tadpole” cavities into the different separations of the laminar flows. For higher Reynolds numbers, a flow regime transition can be noticed in the wake of well-developed gas structures, characterized by wake instabilities, causing vortex cavitation above a critical Reynolds number associated with the bubble width Recb≃616. This regime transition can possibly occur either quasicontinuously in the wake of an attached “band” vapor cavity or intermittently behind a recirculating air bubble generated with degassing. This last phenomenon is associated in our study to classical “patch” cavitation.

Control effect of micro vortex generators on attached cavitation instability

The control effect of micro-vortex generators (VGs) on the instability of attached cavitation was investigated in a series of experiments. The micro-VGs, located at the leading edge of a NACA0015 hydrofoil, were used to alter the near-wall flow and control the attached cavitation dynamics. The effect of the nondimensional height of micro-VGs on the nondimensional cavity length was quantitatively evaluated by regression equations through response surface methodology. The micro-VGs increased the nondimensional cavity length. The counter-rotating streamwise vortices induced by micro-VGs had a rectifying effect on the near-wall flow and withstood the flow disturbance in the spanwise direction. Additionally, the micro-VGs partially suppressed Rayleigh–Taylor instability and Kelvin–Helmholtz instability arising from reverse flow underneath the cavity. Under a partial cavity oscillation (PCO) condition, the growth of sheet cavitation was highly two-dimensional in the spanwise direction, and the cloud cavity shedding had a strict periodicity with a smaller Strouhal number (St) than for the smooth hydrofoil. The shedding cloud cavity was captured in a single spanwise vortex core, which was advected toward the trailing edge of the hydrofoil. The transition from PCO to transitional cavity oscillation (TCO) occurred when the cavity length was larger than 0.8 of chord length. Under the TCO condition, the concave cavity closure line of sheet cavitation on the hydrofoil showed perfect symmetry and the St was nearly constant. As a result of our investigation, the micro-VGs have high potential to manipulate and control the attached cavitation dynamics.

Experimental Study on Influences of Surface Materials on Cavitation Flow Around Hydrofoils

In order to resist on the cavitation erosion, many researchers try to change the solidity and tenacity of the coatings, but ignore the influence of surface characteristics of materials on cavitation flow and the interaction with each other. In this paper, high speed visualization system is used to observe the cavitation flow patterns in different stage. After comparing the characteristics of cavitation flow around hydrofoils made of aluminum (Foil A), stainless steel (Foil B) and the hydrofoil painted with epoxy coating (Foil C), the study shows that material has a significant effect on the cavitation flow. Firstly, when the incipient cavitation occurs, cavitation number of Foil A is highest among three hydrofoils, generating horseshoe vortex randomly. For Foil B and Foil C, it shows in the form of free bubbles. When the sheet cavitation occurs, Foil A has the highest cavitation number and shortest period, which is contrary to Foil C. And cavity consists of lots of small finger-like cavities. For Foil B and Foil C, it both constitutes with many bubbles. Compared with the high-density and small-scale cavities over surface of Foil C, the cavity of Foil B has larger scale and less density, which causes a minimal scope of influence of the re-entrant jet and strong randomness. When the cloud cavitation occurs, Foil C has the lowest cavitation number and shortest period. Secondly, compared with aluminum, both of stainless steel and epoxy coating restrains the occurrence and development of cavitation, and stainless steel and epoxy coating performs better than aluminum. For inception and sheet cavitation, stainless steel performs better than epoxy coating and aluminum. For cloud cavitation, epoxy coating performs better than stainless steel and aluminum. The objective of this paper is applied experimental method to investigate the effect of surface materials on cavitation around Clark-Y hydrofoils.

Numerical Investigation into the Effect of Sound Speed in Attached Cavitation on Hydrofoil Modes of Vibration

It has been found recently that the dynamic behavior of a cavitating hydrofoil is different from that in pure water in that, not only are the natural frequencies different, but the mode shapes may also change. In order to elucidate the mechanism behind this phenomenon, finite element simulations were carried out based on acoustic–structure coupling equations. It was found that the structure and acoustic modes exhibit mode transitions with the variation of the sound speed in the cavity. Further, the mode transition was caused by coupling of the structure with the acoustic modes, which was induced by the vapor mode. The amplitude of the vibration near the mode transition point was high and the mode shape was easily excited. Moreover, with the change of the sound speed in the cavity, the different distributions of the acoustic pressure mode resulted in different structure mode shapes, even on the same transition line. Considering this, a sheet cavitation was simulated by a small change of the void fraction to 0.999 and the sound speed from 343 to 275 m/s to obtain good agreement with the experimental data. Both results showed that the second bending mode under cavitation conditions became a bending–torsion coupled mode.

A Fast Method to Predict the Cavitation Volume on Two-Dimensional Sections

The paper presents a simplified prediction method to estimate cavitation-induced pressure fluctuations by marine propellers in a nonuniform wake field. It is realized by a very fast calculation of the cavitation volume variation. The sheet cavitation volume is represented by the cavitation area in a two-dimensional section, which is the vapor area inside the cavity contour. The variation of the cavitation area on a two-dimensional blade section has been simplified to a relation in quasi-steady condition with only a limited number of nondimensional parameters. This results in a fast method to predict the cavitation area of a blade section passing a wake peak, using a precalculated database. Application of this method to the prediction of cavitation-induced pressure fluctuations shows to be effective. This makes optimization of propeller sections for minimum cavitation-induced pressure fluctuations feasible.

Cavitation Evolution around a NACA0015 Hydrofoil with Different Cavitation Models Based on Level Set Method

Cavitation is a complex multiphase flow phenomenon that is usually involved in marine propulsion systems, and can be simulated with a couple of methods. In this study, three widespread cavitation models were compared using experimental data and a new modified simulation method. The accuracy of the three cavitation models was evaluated regarding their steady and unsteady characteristics, such as the flow field, re-entrant jet, vortex-shedding, and so on. Based on the experimental data and numerical results, the applicability of different cavitation models in different conditions was obtained. The Kunz model can accurately capture both the adverse pressure gradient and the action of the re-entrant jet in sheet cavitation, while the full cavitation model (FCM) has an accurate prediction for the flow field structure and the shedding characteristic of cloud cavitation. Through comparing the results, the optimal selection of cavitation models for further study at different conditions was obtained.

Dynamic Behaviors of Re-Entrant Jet and Cavity Shedding During Transitional Cavity Oscillation on NACA0015 Hydrofoil

Transitional cavity shedding is known as the stage of attached cavitation with high instability and distinct periodicity. In this study, we experimentally investigated the dynamic characteristics of transitional cavity (0.8≤L/c<1) shedding on NACA0015 hydrofoil with high-speed video observation and synchronous pressure measurement. In the partial cavity (0.4<L/c<0.8) oscillation, the sheet cavitation grew along the chord with good spanwise uniformity, and the middle-entrant jet played a dominant role in cavity shedding. Meanwhile, in the transitional cavity oscillation, the previous shedding cavity exhibited a prohibitive effect on the growth of sheet cavitation on the hydrofoil, resulting in concave cavity closure line. Moreover, two symmetrical side-entrant jets originated at the near-wall ends and induced the two-stage shedding phenomenon. The aft and fore parts of the sheet cavitation shed separated as different forms and eventually merged into the large-scale cloud cavity.

Numerical prediction of sheet cavitation on marine propellers using CFD simulation with transition-sensitive turbulence model

One of the big challenges, yet to be addressed, in the numerical simulation of cavitating flow on marine propellers is; the existence of laminar and turbulence transition flows over the propeller’s blades. The majority of previous studies employed turbulence models that were only appropriate for fully turbulent flows. These models mostly caused high discrepancies between numerical predictions and experimental measurements especially at low rotational speeds where, Reynolds number decreases and laminar and transient flows exist. The present paper proposes a complete and detailed procedure for the CFD simulation of cavitating flow on marine propellers using the ‘K-Kl-ω’ transition-sensitive model. Results are obtained using ‘ANSYS FLUENT 16’. The propeller under consideration is the ‘INSEAN E779A’ propeller model. The fully turbulent standard ‘k-ε’ model is also adopted for comparison. Obtained results, based on both turbulence models, are validated by comparison with experimental data available in the literature. Predictions based on the ‘K-Kl-ω’ transition-sensitive model are found to be in better agreement with experiments at lower rotational speeds i.e. at low Reynolds numbers.

An improved Mesh Adaption and Refinement approach to Cavitation Simulation (MARCS) of propellers

This paper presents the improvements of cavitation modelling for marine propellers particularly developing tip vortex cavitation. The main purpose of the study is to devise a new approach for modelling tip vortex cavitation using Computational Fluid Dynamics (CFD) methods with commercial software, STAR-CCM+. The INSEAN E779A model propeller was used for this study as a benchmark propeller. Utilizing this propeller, firstly, validation studies were conducted in non-cavitating conditions together with grid and time step uncertainty studies. Then, the cavitation was simulated on the propeller using a numerical cavitation model, which is known as the Schnerr–Sauer model, based on the Rayleigh-Plesset equation. While a Reynolds Averaged Navier Stokes (RANS) model was used for open water simulations, Detached Eddy Simulations (DES) and Large Eddy Simulations (LES) models were preferred for cavitation simulations to capture the cavitation and evaluate its effect on propeller performance accurately. Although the comparison with the benchmark experimental data showed good agreement for the thrust and torque coefficients as well as sheet cavitation pattern, tip vortex cavitation could not be adequately simulated using the existing method. After an evaluation of the interaction between cavitation modelling and generated meshes, two techniques, which involved volumetric control and adaptive mesh refinement, were used in combination on the region where the tip vortex cavitation is likely to occur. The first technique, which is called a ‘volumetric control method’, was developed using spiral geometry around the propeller tip region to generate a finer mesh for capturing tip vortex cavitation. Although this method gave better tip vortex cavitation extension than the method without any mesh refinement or with tube refinement, it still required to be improved to extend the tip vortices further into the propeller slipstream. The second method, which is called ‘adaptive mesh refinement’, was introduced using the pressure distribution data from the results of the ‘volumetric control method’. This improved approach, which is called “Mesh Adaption and Refinement for Cavitation Simulation (MARCS)”, has been successfully applied to simulate the tip vortices trailing from the blades of the INSEAN E779A propeller as demonstrated in the paper. The results of the simulations showed an excellent agreement with the experiments in the open literature by tracking the tip vortex cavitation along this propeller's slipstream.

Analysis of influence of cavity content on flow pulsations

Assumptions on the cavity content have an insignificant influence on predictions of time-average characteristics of sheet cavitation. However, cavity pulsation can substantially depend on this content because of compressibility of gas-liquid mixtures within the cavities. Compressibility is predetermined by the local sound speed that sharply depends on void fraction and pressure within the cavities. This speed can be indeed very small, whereas used in many CFD solvers definitions of the mixture density as a linear combination of component densities can lead to enormous overestimation of this speed and, as a result, to underestimation of pulsations of cavity volume and of body lift and drag. This paper provides numerical analysis of the influence of cavity content on pulsations and compares the results with experimental data for a specially designed hydrofoil.

An Improved Numerical Computation of Hull Pressure Fluctuations Due to Unsteady Sheet Cavitation of a Propeller

An operating propeller is the main source of vibration on the ship hull, especially on the stern. In this article, an improved numerical scheme is presented to predict the pressure fluctuations on the ship hull due to the unsteady sheet cavitation of a propeller. The calculated results are compared with the published results and experimental data carried out in the hydrodynamics and cavitation tunnel of Hamburgische Schiffbau-Versuchsanstalt to verify the improvement. The present method is based on a two-cycle iterating scheme which satisfies the boundary integral equation in time domain. The hull pressure fluctuations calculated by the first-cycle iterations are treated as the initial values for the second-cycle iterations. The solid angles of the elements will deviate from the standard value, .5, as the dramatic variation in geometry appears, and accumulate numerical errors in the calculating process. During the second-cycle iterations, a filter based on the solid angles on hull elements is proposed to minimize the iterating error. A container ship is treated as the computing sample in this study, and evidence is offered regarding the 16% improvement achieved by the present method. 1. Introduction A propeller operating in a nonuniform wake field in the ocean is one of the prime sources of vibration and noise affecting the ship. The prediction of hull pressure fluctuations caused by propellers is an important consideration for many vessels and worthy of being researched. Hull pressure fluctuation caused by the marine propeller has been widely investigated since the 1980s. Huse and Guoqiang (1982) developed a semi-empirical prediction method, in which the cavitation volume on the propeller blade surface can be estimated using experimental data. Breslin et al. (1982) proposed a model based on the potential flow theory, which simulates the ship hull by means of a simple panel method and the propeller by means of a lifting surface vortex lattice method. Kinns and Bloor (2004) used an acoustic boundary element (BE) model to simplify the problem of hull vibration excitation due to propeller sources and dipoles. The convergence of results for a cruise liner model was demonstrated with different element distributions. Kehr and Kao (2004) derived the incident blade rate pressure induced by unsteady sheet cavitation (monopole) and unsteady forces (dipole) of an operating propeller, for calculating the hull pressure fluctuations. Brouwer (2005) applied a stationary set of rings of monopole and dipole sources in the frequency domain to solve the propeller-induced noise and vibrations. Lee et al. (2006) integrated computational fluid dynamics (CFD) and the finite difference method for the computation of propeller-induced hull vibration. It was recommended that the phase difference of the propeller-induced pressure should be considered for preventing overprediction. Kao and Kehr (2006) developed a time domain iteration method to calculate the hull pressure fluctuations induced by the operating propeller. The phase difference is included in the iterating scheme, and the computation is robustly convergent. Seol and Moon (2009) derived the governing equation of pressure fluctuation induced by sheet cavitation according to the Ffowcs Williams approach. In the study by van Wijngaarden (2011), a potential flow boundary element method (BEM) with measured hull pressure data as input was applied to solve the hull pressure fluctuations, and the model experiments were also carried out. It was concluded that the computed hull pressure fluctuations due to non-cavitating propellers is reasonably accurate compared with the experimental data. Kehr and Kao (2011) calculated the pressure fluctuations on ship hull due to propeller sheet cavitation by using the method presented in Kao and Kehr (2006). The numerical result is higher than the experimental data provided by the hydrodynamics and cavitation tunnel (HYKAT) of HSVA (Wiemer 1999) by approximately 27%. The pressure fluctuations on ship stern induced by cavitating propellers were solved by Kanemaru and Ando (2011) with a surface panel method. The maximum amplitude appears in the first blade frequency and overestimates the experimental data by about 30%. Kim et al. (2012) predicted the hull pressure fluctuations induced by marine propeller sheet cavitation, and the Doppler effect was considered at the same time. Wei and Wang (2013) employed CFD to simulate the propulsion of a submarine. The finite element method and BEM were then combined to solve the submarine's structure and acoustic responses under the propeller excitations. The matched-field inversion technique applied in Lee et al. (2014) uses the fluctuating hull pressure field measured by receivers and the acoustic field calculated by BEM to define the sheet cavitation noise, source strengths, source positions, and number of sources. The equivalent source model for the propeller can result in more accurately extrapolated hull pressure distribution. In Wei et al. (2016), the unsteady forces of a submarine propeller were predicted by CFD, and the hull pressure fluctuations due to the non-cavitation propeller were calculated by the method proposed in Kao and Kehr (2006).

Large eddy simulation of tip leakage cavitating flow focusing on cavitation-vortex interaction with Cartesian cut-cell mesh method

In the present paper, flow configurations of cavitating flow around a straight NACA0009 foil with a gap between the foil tip and sidewall are investigated numerically by large eddy simulation (LES) coupled with Zwart-Gerber-Belamri (ZGB) cavitation model. A Cartesian cut-cell method is used for mesh generation, which is of good orthogonality and high quality. A good agreement is obtained between simulation and experiment. Two influencing factors on vorticity distributions, the interaction between different vortices and the occurrence of cavitation, are discussed in detail based on the numerical results. A series of Ω- shaped loops are observed during the development of the induced vortex, which is a result of the instability of vortex pair. This finding may provide a new viewpoint to control the evolution of tip-leakage vortex (TLV) cavitation. Moreover, it is found that the dilatation term plays a much more important role in the evolution of TLV cavitation compared with that in sheet cavitation.