Localization in an Acoustic Cavitation Cloud

Using a nonlinear sound wave equation for a bubbly liquid in conjunction with an equation for bubble pulsation, we theoretically predict and experimentally demonstrate the appearance of a gap in the frequency spectrum of a sound wave propagating in a cavitation cloud comprising bubbles. For bubbles with an ambient radius of 100μm, the calculations reveal that this gap corresponds to the phenomenon of sound wave localization. For bubbles with an ambient radius of 120 μm, this spectral gap is related to a forbidden band of the sound wave. In the experiment, we observe the predicted gap in the frequency spectrum in soda water. However, in tap water, no spectral gap is present because the bubbles are much smaller than 100μm.

Numerical Investigation of the Angle of Attack Effect on Cloud Cavitation Flow around a Clark-Y Hydrofoil

Cavitation is a prevalent phenomenon within the domain of ship and ocean engineering,predominantly occurring in the tail flow fields of high-speed rotating propellers and on the surfaces of high-speed underwater vehicles.The re-entrant jet and compression wave resulting from the collapse of cavity vapour are pivotal factors contributing to cavity instability.Concurrently,these phenomena significantly modulate the evolution of cavitation flow.In this paper,numerical investigations into cloud cavitation over a Clark-Y hydrofoil were conducted,utilizing the Large Eddy Simulation(LES)turbulence model and the Volume of Fluid(VOF)method within the OpenFOAM framework.Comparative analysis of results obtained at different angles of attack is undertaken.A discernible augmentation in cavity thickness is observed concomitant with the escalation in attack angle,alongside a progressive intensification in pressure at the leading edge of the hydrofoil,contributing to the suction force.These results can serve as a fundamental point of reference for gaining a deeper comprehension of cloud cavitation dynamics.

The influence of surface roughness on cloud cavitation flow around hydrofoils

The aim of this study is to investigate experimentally the effect of surface roughness on cloud cavitation around Clark-Y hydrofoils. High-speed video and particle image velocimetry(PIV) were used to obtain cavitation patterns images(Prog. Aerosp. Sci. 37: 551–581, 2001), as well as velocity and vorticity fields. Results are presented for cloud cavitating conditions around a Clark-Y hydrofoil fixed at angle of attack of α = 8? for moderate Reynolds number of Re = 5.6 × 10~5. The results show that roughness had a great influence on the pattern, velocity and vorticity distribution of cloud cavitation. For cavitating flow around a smooth hydrofoil(A) and a rough hydrofoil(B), cloud cavitation occurred in the form of finger-like cavities and attached subulate cavities, respectively. The period of cloud cavitation around hydrofoil A was shorter than for hydrofoil B.Surface roughness had a great influence on the process of cloud cavitation. The development of cloud cavitation around hydrofoil A consisted of two stages:(1) Attached cavities developed along the surface to the trailing edge;(2) A reentrant jet developed, resulting in shedding and collapse of cluster bubbles or vortex structure. Meanwhile, its development for hydrofoil B included three stages:(1) Attached cavities developed along the surface to the trailing edge, with accumulation and rotation of bubbles at the trailing edge of the hydrofoil affecting the flow field;(2) Development of a reentrant jet resulted in the first shedding of cavities. Interaction and movement of flows from the pressure side and suction side brought liquid water from the pressure side to the suction side of the hydrofoil, finally forming a reentrant jet. The jet kept moving along the surface to the leading edge of the hydrofoil, resulting in large-scale shedding of cloud bubbles. Several vortices appeared and dissipated during the process;(3) Cavities grew and shed again.

Effect of leading edge roughness on cavitation inception and development on thin hydrofoil

The cavitation incipience and development of water flow over a thin hydrofoil placed in the test section of high-speed cavitation tunnel were investigated.Hydrofoils with smooth and rough leading edge were tested for different upstream velocities and incidence angles.The observations clearly revealed that cavitation incipience is enhanced by roughness at incidence angle below 2°.This is in line with the former reports,according to whose roughness element decreases the wettability and traps a larger amount of gas.As a result,surface nucleation is enhanced with an increased risk of cavitation.Surprisingly,for higher incidence angles(>3°),it was found that cavitation incipience is significantly delayed by roughness while developed cavitation is almost the same for both smooth and rough hydrofoils.This unexpected incipience delay is related to the change in the boundary layer structure due to roughness.It was also reported a significant influence of roughness on the dynamic of developed cavitation and shedding of transient cavities.

Investigation on the dynamic behavior of cloud cavitation around a flexible hydrofoil

The objective of this paper is to investigate the dynamic behavior of cloud cavitating flow around a flexible hydrofoil with experimental and numerical methods.The tightly coupled fluid-structure interaction(FSI)modeling is applied and validated with the experimental data.The Q-criterion andω-criterion are applied to illustrate the interaction between the vortex structures and cavities.The flexibility is seen to result in nose-up twist deformation,causing a reduction of the shedding frequency from an increase in the attached cavity length.Due to the flexibility,the fluctuation of load coefficients of the flexible hydrofoil is larger than that of the rigid hydrofoil.Moreover,the re-entrant jet propagation speed of the flexible hydrofoil is greater than that of the rigid hydrofoil.The shed cloud cavity is observed to be uniform along the flexible hydrofoil span under the combined influence of the strong vibration and the gap flow.

Large eddy simulation of cloud cavitation and wake vortex cavitation around a trailing-truncated hydrofoil

The cavitation has received considerable attention for decades because of its negative influence on the performance and the safety of the hydraulic machinery.In this study,a large eddy simulation is carried out to numerically investigate the unsteady cavitating flow around a trailing-truncated NACA 0009 hydrofoil for determining the underlying physical mechanisms.Two types of cavitation morphologies are identified:The large-scale bubble cluster and the von Kármán vortex cavity,named as the cloud cavitation and the wake vortex cavitation,respectively.It is shown that the velocity profiles obtained over the hydrofoil suction surface are in good agreement with the experimental data,indicating the accuracy of the current simulation.The dynamic evolution of the sheet/cloud cavity is also well reproduced,covering the sheet cavity breakup,the sheet/cloud transformation,and the collapse of the cloudy bubble cluster.The wake-vortex cavitation is caused by the blunt geometry at the hydrofoil trailing edge,where pairs of vortex cavities are induced.Both the cloud and vortex cavities significantly affect the lift oscillation,which makes it difficult to decompose the components.The fundamental shedding mechanisms of the wake vortex cavitation are discussed based on the finite-time Lyapunov exponent field.Specifically,the suction-side bubble grows and squeezes the giant pressure bubble away from the trailing edge.After the pressure bubble detaches,a new counterclockwise vortex or a new bubble appears at the pressure side,thus lifting the ridge towards the suction trailing edge and generating a strong vortex eye that pinches off the trailing portion of the suction-side bubble.

Numerical analysis of the unsteady behavior of cloud cavitation around a hydrofoil based on an improved filter-based model

The unsteady cavitation evolution around the Clark-Y hydrofoil is investigated in this paper, by using an improved filter-base model（FBM） with the density correction method（DCM）. To improve the prediction accuracy, the filter scale is adjusted based on the grid size. The numerical results show that a small filter scale is crucial for the unsteady simulations of the cavity shedding flow. The hybrid method that combines the FBM and the DCM could help to limit the overprediction of the turbulent viscosity in the cavitation region on the wall of the hydrofoil and in the wake. The large value of the maximum density ratio ρ1 /ρv, clip promotes the mass transfer rate between the liquid phase and the vapor phase, which results in a large sheet cavity length and the vapor fraction rise inside the cavity. The cavity patterns predicted by the improved method are verified by the experimental visualizations. The time-average lift, the drag coefficient and the primary oscillating frequency St for the cavitation number σ= 0.8, the angle of attack, α= 8°, at a Reynolds number Re= 7×10^5 are 0.735, 0.115 and 0.183, respectively, and the predicted errors are 3.29%, 3.36% and 8.93%. The typical three stages in one revolution are well-captured, including the initiation of the sheet/attached cavity, the growth toward the trailing edge（TE） with the development of the re-entrant jet flow, and the large scale cloud cavity shedding. It is observed that the cloud cavity shedding flow induces the vortex pairs of the TE vortices in the wake and the shedding vortices. The positive vorticity vortex of the re-entrant jet and the TE vortices interacts and merges with the negative vorticity vortex of the leading edge（LE） cavity to produce the shedding flow.

Periodical shedding of cloud cavitation from a single hydrofoil in high-speed cryogenic channel flow

In order to explain criteria for periodical shedding of the cloud cavitation, flow patterns of cavitation around a piano-convex hydrofoil were observed using a cryogenic cavitation tunnel of a blowdown type. Two hydrofoils of similarity of 20 and 60 mm in chord length with two test sections of 20 and 60 mm in width were prepared. Working fluids were water at ambient temperature, hot water and liquid nitrogen. The parameter range was varied between 0.3 and 1.4 for cavitation number, 9 and 17 m/sec for inlet flow velocity, and -8° and 8° for the flow incidence angle, respectively. At incidence angle 8°, that is, the convex surface being suction surface, periodical shedding of the whole cloud cavitation was observed on the convex surface under the specific condition with cavitation number and inlet flow velocity, respectively, 0.5, 9 m/sec for liquid nitrogen at 192℃ and 1.4, 11 m/sec for water at 88℃, whereas under the supercavitation condition, it was not observable. Periodical shedding of cloud cavitation occurs only in the case that there are both the adverse pressure gradient and the slow flow region on the hydrofoil.

Numerical investigation of unsteady sheet/cloud cavitation over a hydrofoil in thermo-sensitive fluid

The sheet/cloud cavitation is of a great practical interest since the highly unsteady feature involves significant fluctuations around the body where the cavitation occurs. Moreover, the cavitating flows are complicated due to the thermal effects. The present paper numerically studies the unsteady cavitating flows around a NACA0015 hydrofoil in the fluoreketone and the liquid nitrogen with particular emphasis on the thermal effects and the dynamic evolution. The numerical results and the experimental measurements are generally in agreement. It is shown that the temperature distributions are closely related to the cavity evolution. Meanwhile, the temperature drop is more evident in the liquid nitrogen for the same cavitation number, and the thermal effect suppresses the occurrence and the development of the cavitating flow, especially at a low temperature in the fluoroketone. Furthermore, the cavitating flows are closely related to the complicated vortex structures. The distributions of the pressure around the hydrofoil is a major factor of triggering the unsteady sheet/cloud cavitation. At last, it is interesting to find that one sees a significant thermal effect on the cavitation transition, a small value of σ/2ɑ is required in the thermo-sensitive fluids to achieve the similar cavitation transition that occurs in the water.

A hybrid RANS/LES model for simulating time-dependent cloud cavitating flow around a NACA66 hydrofoil

Cloud cavitating flow is highly turbulent and dominated by coherent large-scale anisotropic vortical structures. For the numer- ical investigation of such a class of flow, large eddy simulation （LES） is a reliable method but it is computationally extremely costly in engineering applications. An efficient approach to reduce the computational cost is to combine Reynolds-averaged Navier-Stokes （RANS） equations with LES used only in the parts of interest, such as massively separated flow regions. A new hybrid RANS/LES model, the modified filter-based method （FBM）, is proposed in the present study which can perform RANS or LES depending on the numerical resolution. Compared to the original FBM, the new method has three modifications： the state-of-the-art shear stress transport （SST） model replaces the k-c model as a baseline RANS model. A shielding function is introduced to obviate the switch from RANS to LES occurring inside the boundary layer. An appropriate threshold controlling the switch from RANS to LES is added to achieve an optimal predictive accuracy. The new model is assessed for its predictive capability of highly unsteady cavitating flows in a typical case of cloud cavitation around a NACA66 hydrofoil. The new mod- el results are compared with data obtained from the Smagorinsky LES and SST model based on the same homogeneous Zwart cavitation model. It is found that the modified FBM method has significant advantages over SST model in all aspects of pre- dicted instantaneous and mean flow field, and its predictive accuracy is comparable to the Smagorinsky LES model even using a much coarser grid in the simulations.

Effect of water injection on the cavitation control:experiments on a NACA66(MOD)hydrofoil

The objective of this work is to investigate experimentally controlling cavitating flow over NACA66(MOD)hydrofoils by means of an active water injection along its suction surface.The continuous water vertically jets out of the chamber inside the hydrofoil through evenly distributed surface holes.Experiments were carried out in cavitation water tunnel.using high-speed visualization technology and the particle image velocimetry(PIV)system to study the sheetlcloud cavity behaviors.We studied the effects of this active control on cavity evolution with four kinds of jet flow at two different jet positions.We analyzed the effect of water injection on the mechanism of the cavitating flow control.The results were all compared with that for the original hydrofoil without jet and show that the active jet can effectively suppress the sheet/cloud cavitation characterized by shrinking the attached cavity size and breaking the large-scaled cloud sheding vortex cavity into small-scaled ones.The optimum effectiveness of cavitation suppression is affected by the jet flow rates and jet positions.The water injection at flow rate coefficient 0.0245 with the jet position of 0.45C reduces the maximum sheet cavity length by 79.4%and the cavity shedding is diminished completely,which gives the most superior effect of sheet cavitation suppression.The jet blocks the re-entrant jet moving upstream and weakens the power of re-entrant jet and thus restrains the cavitation development effectively and stabilizes the flow field.

Numerical analysis of cavitation shedding flow around a three-dimensional hydrofoil using an improved filter-based model

The cavitation shedding flow around a 3-D Clark-Y hydrofoil is simulated by using an improved filter-based model （FBM） and a mass transfer cavitation model with the consideration of the maximum density ratio effect between the liquid and the vapor. The unsteady cloud cavity shedding features around the Clark-Y hydrofoil are accurately captured based on an improved FBM model and a suitable maximum density ratio. Numerical results show that the predicted cavitation patterns and evolutions compare well with the experimental visualizations, and the prediction errors of the time-averaged lift coefficient, drag coefficient and Strouhal number St for the cavitation number o- = 0.8, the angle of attack a= 8°at a Reynolds number Re = 7 x 10^5 are only 3.29%, 2.36% and 9.58%, respectively. It is observed that the cavitation shedding flow patterns are closely associated with the vortex structures identified by the Q- criterion method. The predicted cloud cavitation shedding flow shows clearly three typical stages： （1） Initiation of the attached sheet cavity, the growth toward the trailing edge. （2） The formation and development of the re-entrant jet flow. （3） Large scale cloud cavity sheds downstream. Numerical results also indicate that the non-uniform adverse pressure gradient is the main driving force of the re-entrant jet, which results in the U-shaped cavity and the 3-D bubbly structure during the cloud cavity shedding.

Cavitation shedding dynamics around a hydrofoil simulated using a filter-based density corrected model

The unsteady turbulent cloud cavitation around a NACA66 hydrofoil was simulated using the filter-based density corrected model(FBDCM). The cloud cavitation was treated as a homogeneous liquid-vapor mixture and the effects of turbulent eddy viscosity were reduced in cavitation regions near the hydrofoil and in the wake. The numerical results(in terms of the vapor shedding structure and transient pressure pulsation due to cavitation evolution) agree well with the available experimental data, showing the validity of the FBDCM method. Furthermore, the interaction of vortex and cavitation was analyzed based on the vorticity transport equation, revealing that the cavitation evolution has a strong connection with vortex dynamics. A detailed analysis shows that the cavitation could promote the vortex production and flow unsteadiness by the dilatation and baroclinic torque terms in the vorticity transport equation.

NUMERICAL SIMULATION OF SPHERICAL, CYLINDRICAL AND AXIAL BUBBLE CLOUDS COLLAPSE

The nonlinear dynamics of a spherical, cylindrical and axial cloud of cavitation bubbles were numerically simulated in order to learn more about the physical phenomena occurring in the cloud cavitation. The simulations employed the fully nonlinear continuum mixture equations coupled with the Gilmore equation for the dynamics of bubbles by considering the compressibility of liquid. A set of the Navier-Stokes equations was solved for the gas inside a spherical bubble, considering heat transfer through the gas inside the bubble and the liquid layer. The flow field around the cylindrical and axial cloud was obtained by solving the Navier-Stokes equations using a finite volume method and a dynamic layering mesh scheme. The calculated strength of shock wave in the liquid around the cloud was of the order of 1 ×10^6 Pa and the propagation of this shock wave lasted for l0 p.s. The conducted investigations illustrate that the shock wave propagates before the cloud has completely collapsed. A good agreement with experimental data was observed.

On the numerical simulations of vortical cavitating flows around various hydrofoils

This paper reviews the numerical models of various cavitating flows around hydrofoils. Numerical models relating to cavitation flows, including mass transfer models and turbulence models, are summarized at first. Then numerical results and analysis of flow characteristics for the cavitating flows around twisted hydrofoils, truncated hydrofoil and tip leakage are discussed respectively. For mean flow fields, Reynolds averaged Navier-Stokes（RANS） simulation associated with a kind of nonlinear turbulence model is found to be an economic and robust numerical approach for different kinds of cavitating flows including cloud cavitation, tip cavitation and tip leakage cavitation. To predict the fluctuations of pressure and velocity, large eddy simulation（LES） and detached eddy simulation（DES） are two effective approaches. Finally, a few open questions are proposed for future research.

Bubbly shock propagation as a mechanism of shedding in separated cavitating flows

Stable attached partial cavitation in separated flows can transition to cloud shedding, and the mechanism of transition has been attributed to the presence of a re-entrant liquid jet. Our findings have revealed the presence of propagating bubbly shock waves as an alternative dominant mechanism of shedding when the compressibility of the bubbly mixture is appreciable. In the present paper, we discuss dynamics associated with these bubbly shock waves, interaction of shock waves with obstacles in their path, and means to manipulate their properties to control the shedding process by non-condensable gas injection.

Numerical investigations of the transient cavitating vortical flow structures over a flexible NACA66 hydrofoil

In this paper,the cavitating flow over a flexible NACA66 hydrofoil is studied numerically by a modified fluid-structure interaction strategy with particular emphasis on understanding the flow-induced vibration and the cavitating vortical flow structures.The modified coupling approaches include(1)the hydrodynamic solution obtained by the large eddy simulation(LES)together with a homogenous cavitation model,(2)the structural deformation solved with a cantilever beam equation,(3)fluid-structural interpolation and volume mesh motion based on the radial basis functions and greedy algorithm.For the flexible hydrofoil,the dominant flow-induced vibration frequency is twice of the cavity shedding frequency.The cavity shedding frequency is same for the rigid and flexible hydrofoils,demonstrating that the structure vibration is not large enough to affect the cavitation evolution.The predicted cavitating behaviors are strongly three-dimensional,that is,the cavity is(a)of a triangular shape near the hydrofoil tip,(b)of a rectangular shape near the hydrofoil root,and(c)with a strong unsteadiness in the middle of the span,including the attached cavity growth,oscillation and shrinkage,break-off and collapse downstream.The unsteady hydroelastic response would strongly affect the cavitation shedding process with small-scale fragments at the cavity rear part.Furthermore,three vortex identification methods(i.e.,the vorticity,the Q-criteria and the Ω method)are adopted to investigate the cavitating vortex structures around the flexible hydrofoil.It is indicated that the cavity variation trend is consistent with the vortex evolution.The vortex structures are distributed near the foil trailing edge and in the cavitation region,especially at the cavity-liquid interface.With the transporting downstream the shedding cavities,the vortices gradually increase in the wake flows.

Spatial and spectral investigation of turbulent kinetic energy in cavitating flow generated by Clark-Y hydrofoil

In the present paper,the turbulent cavitating flow generated by a Clark-Y hydrofoil is investigated by large eddy simulation(LES)combined with Zwart-Gerber-Belamri(ZGB)cavitation model.In order to shed light on the influence of cavitation on turbulent energy distribution among scales,energy spectrum obtained from the three-dimensional velocity field is firstly applied to turbulent cavitating flow.Spatial and spectral distributions of turbulent kinetic energy are studied for both non-cavitating flow and cavitating flow.Cavitation is found to have a significant effect on the original turbulent flow by inducing more large-scale turbulent structures.The energy spectrum of cloud cavitating flow also experiences a periodic evolution as cavitation develops,and a large amount of turbulent kinetic energy is found to generate as the first shedding,cutoff and second shedding of cavities happen.

Flow structures and hydrodynamics of unsteady cavitating flows around hydrofoil at various angles of attack

This paper investigates the unsteady structures and the hydrodynamics of cavitating flows. Experimental results are presented for a Clark-Y hydrofoil fixed at ？= 0？, 5？ and 8？, for various cavitation numbers, from subcavitating flow to supercavitation. The high-speed video camera and the particle image velocimetry（PIV） are applied to observe the transient flow structures. Statistics of the cavity lengths, the velocity and vorticity distributions, as well as the turbulent intensities are presented to quantify the unsteady process. Meanwhile, the dynamic measurement system is used to record the dynamic characteristics. The experimental results show that the flow structures and the hydrodynamics of the cavitation vary considerably with various combinations of angles of attack and cavitation numbers. Under various conditions, the cavitation can be generally grouped as the inception cavitation, the sheet cavitation, the cloud cavitation and the supercavitation. The cloud cavitation exhibits noticeable unsteady characteristics. Experimental evidence indicates that the hydrodynamics are clearly affected by the cavitating flow structures, the amplitude of the load fluctuation is much higher in the cloud cavitating cases.

Numerical simulation of multi-scale cavitating flow with special emphasis on the influence of vortex on micro-bubbles

A multi-scale Euler-Lagrange method is applied in the current paper to investigate the characteristics of turbulent cloud cavitating flow around a Clark-Y hydrofoil,in which macroscopic cavitating structures are simulated by volume of fluid(VOF)approach,while micro-scale bubbles are modelled based on Rayleigh-Plesset equation and bubble motion equation.The numerical results are in reasonable agreement with the available experiments,and the transition between multi-scale structures is captured clearly.The evolution of microscopic bubble behaviors is statistically investigated.During one typical cycle,numbers and Sauter mean radius of the bubbles show a similar variation tendency which both sharply spike to their maxima after the breakup of the sheet cavity,and then decrease continuously to their minima before the next breakup.Discrete bubbles are mainly concentrated at the tail of the attached cavity,in front of the cloud cavity and in the region quite close to the hydrofoil suction side.Furthermore,vortices are extracted to account for the micro-scale hydrodynamics.It is found that intense vortices aggravate turbulence fluctuation,thus spalling cavity to generate massive micro bubbles.Meanwhile,the vortices provide microscopic bubbles low pressure and detain them so that numerous bubbles are able to grow.These effects are remarkable after the breakup of attached sheet cavity,owing to the violent vortices generated.On the contrary,when sheet cavity develops,the flow field becomes comparatively stable since the strong vortices travel downstream.Few micro-scale bubbles are produced,and their volume is generally small.