Cavity Detachment Research Articles

The characteristics of bubbly shock waves in a cavitating axisymmetric venturi via time-resolved X-ray densitometry

The bubbly shock-driven partial cavitation in an axisymmetric venturi is studied with time-resolved two-dimensional X-ray densitometry. The bubbly shock waves are characterised using the vapour fraction and pressure changes across it, propagation velocity, and Mach number. The sharp changes in vapour fraction measured with X-ray densitometry, combined with high-frequency dynamic pressure measurements, reveal that the interaction of the pressure wave with the vapour cavity dictates the shedding dynamics. At the lowest cavitation number ( $\sigma \sim 0.47$ ), the condensation shock front is the predominant shedding mechanism. However, as $\sigma$ increases ( $\sigma \sim 0.78$ ), we observe an upstream travelling pressure discontinuity that changes into a condensation shock as it approaches the venturi throat. This coincides with the increasing strength of the bubbly shock wave as it propagates upstream, manifested by the increasing velocity of the shock front and the pressure rise across it. Consequently, the Mach number of the shock front increases and surpasses the critical value 1, favouring condensation shocks. Further, at higher $\sigma$ ( ${\sim }0.84\unicode{x2013}0.9$ ), both the re-entrant jet and pressure wave can cause cavity detachment. However, at such $\sigma$ , the pressure wave likely remains subsonic. Hence cavity condensation is not favoured readily. This leads to the re-entrant jet causing the cavity detachment at higher $\sigma$ . The shock front is accelerated as it propagates upstream through the variable cross-section of the venturi. This enhances its strength, favouring cavity condensation and eventual shedding. These observations explain the existence of shock fronts in an axisymmetric venturi for a large range of $\sigma$ .

Numerical study on the cavitation instability from the perspectives of pressure change and hydrodynamics evolution in the cavitating flow over a hydrofoil

The objective of this study is to investigate cavitation instability by analyzing the pressure change and hydrodynamics evolution in the cavitating flow over a hydrofoil. Two-dimensional (2D) simulation results indicate that the multi-peak pressure features are influenced by the position on the hydrofoil surface. The increased cavitation number in a certain range aggravates the oscillation of partial cavitation and promotes the cavity change, then leads to the occurrence of higher peak pressure and more complicated fluctuation frequency. The lift coefficient presents a near-linear increasing trend due to the extended low-pressure area on the suction surface and the suppression on the vortex generation in the stable development stage of sheet cavity. The interaction between the vortex with different directions on the trailing edge dominates the fluctuation of lift coefficient. The differences in three-dimensional (3D) cavitating flows with constant velocity inlet and sinusoidal velocity inlet are the flow separation point distribution and vortex changes. More separation points form in the downstream of the hydrofoil due to more cloud cavity reattachment behaviours for sinusoidal velocity inlet. Furthermore, the sinusoidal velocity inlet promotes a more violent cavity detachment and the large-scale vortex formation, which enhances the fluctuations of pressure change, lift and drag coefficient.

An improved laminar–turbulent transition cavitation model using the IDDES method

Prediction of the detachment positions of sheet cavitation remains an unsolved problem, being not only dependent on local pressure but also closely related to the boundary layer transition. For hydrofoils, traditional cavitation models tend to predict premature cavity detachment positions. In the study reported here, to obtain cavity detachment positions that match experimental results, improvements are made to both turbulence models and cavitation models. A scale-resolving transition turbulence model is established by incorporating transport equations to represent boundary layer transition that are based on the improved delayed detached eddy simulation (IDDES) method. The intermittency γ, representing the probability of turbulence at a specific point in space, is introduced into the homogeneous cavitation model to account for the influence of the laminar–turbulent transition on the sheet cavitation detachment position. Numerical results show that the IDDES-based transition turbulence model combines transition and scale-resolving capabilities. The improved turbulence transition cavitation model proposed here is shown to be able to accurately predict the detachment position of sheet cavitation around two-dimensional hydrofoils and a typical axisymmetric ITTC body.

Experimental investigation of three distinct mechanisms for the transition from sheet to cloud cavitation

The conventional high-speed images of cavitation with a set of X-ray phase contrast images reveal the presence of three different types of mechanisms responsible for large cloud shedding: re-entrant jet mechanism, condensation shock wave mechanism, and collapse-induced pressure wave mechanism. At higher cavitation numbers, the sheet cavity is relatively short and the cavity detachment is a consequence of a re-entrant jet pinching off the cavity from its leading edge. At lower cavitation numbers, the re-entrant jet plays a smaller role in the cavitation instabilities and the primary reason for periodic cloud shedding is the condensation shock mechanism where a void fraction discontinuity propagates upstream until collapsing the entire cavity. If the amount of shed vapour cloud reaches a certain extent, the collapse will emit a pressure wave strong enough to disturb the growing cavity, and subsequently make it detached from the wall. This is the third mechanism observed in the experiments. We point out the inappropriate classification of combining condensation shock and collapse-induced pressure wave mechanisms in the literature, since we identify pronounced differences between them: (i) the pressure increase across the condensation front is very weak (a few kPa) while the amplitude of collapse-induced pressure wave can be hundreds of kPa, (ii) the travelling velocity of the collapse-induced pressure wave within the cavity is much faster than the condensation shock, and (iii) the collapse-induced pressure wave does not result in an obvious discontinuity in void fraction when it propagates through the cavity, in contrary to the condensation shock.

Penetration and ligament formation of viscoelastic droplets impacting on the superhydrophobic mesh

Spraying occurs by the impact of water droplets on the superhydrophobic wire meshes by liquid penetration during the spreading and recoiling. We have shown that adding a small amount of high molecular weight polymer (PEO) alters the ligaments formation and stabilizes them due to its high elasticity. Consequently, it suppresses droplet spray during droplet spreading and recoiling (recoil penetration). In the wide range of the impact velocities, the penetrated ligaments retracted back to the mesh after reaching the maximum length and eventually merged with the droplet on the mesh. The empirical fitting shows that the ligament evolution follows the parallel spring-dashpot model of Kelvin–Voigt. The additive polymer also changes the recoil penetration mechanisms from cavity collapse to cavity detachment due to the higher retraction velocity of the cavity near the mesh that is induced by the upward flow formed by the retraction of the ligaments to the mother droplet. A model based on mass conservation is proposed to calculate the variation of the maximum ligament size.

The structure of near-wall re-entrant flow and its influence on cloud cavitation instability

The so-called ‘re-entrant jet’ is fundamental to periodic cloud shedding in partial cavitation. However, the exact physical mechanism governing this phenomenon remains ambiguous. The complicated topology of the re-entrant flow renders whole-field, detailed measurement of the re-entrant flow cumbersome. Hence, most studies in the past have derived a physical understanding of this phenomenon from qualitative analyses of the re-entrant jet. Thus, quantitative studies are scarce in the literature. In this work, we present a methodology to experimentally measure the re-entrant flow below the vapour cavity in an axisymmetric venturi. The axisymmetry of the flow geometry is exploited to image tracer particles in the near-wall re-entrant flow. The main objective of employing tomographic imaging and subsequent velocimetry is to resolve the thickness and the velocity of the re-entrant flow. Additionally, phase-averaging conditioned on cavity length sheds light on the temporal evolution of re-entrant flow in a shedding cycle. The measured re-entrant film is as thick as sim 1.2 mm for a maximum cavity length of sim 0.9 D_{t}, where D_{t} is the venturi throat diameter. However, the re-entrant film thickness at higher cavitation number is measured to be about 0.5 mm. Further, the re-entrant flow is seen to attain a maximum velocity up to half the throat velocity as the vapour cavity grows in time and the re-entrant flow thickens. We observe that a complex spatio-temporal evolution of re-entrant flow is involved in the cavity detachment and periodic cloud shedding. Finally, we apply the demonstrated methodology to study the evolution of the near-wall liquid flow, below the vapour cavity in different cavity shedding flow regimes. The role of two main mechanisms responsible for cloud shedding, i.e. (i) the adverse-pressure gradient driven re-entrant jet, and (ii) the bubbly shock wave emanating from the cloud collapse are quantitatively assessed. We observe that the thickness of the re-entrant liquid film with respect to the cavity thickness can influence the cavity shedding behaviour. Further, we show that both the mechanisms could be operating at a given flow condition, with one of them dominating to dictate the cloud shedding behaviour.Graphical abstract

Cavity Detachment from a Wedge with Rounded Edges and the Surface Tension Effect

Cavity flow around a wedge with rounded edges was studied, taking into account the surface tension effect and the Brillouin–Villat criterion of cavity detachment. The liquid compressibility and viscosity were ignored. An analytical solution was obtained in parametric form by applying the integral hodograph method. This method gives the possibility of deriving analytical expressions for complex velocity and for potential, both defined in a parameter plane. An expression for the curvature of the cavity boundary was obtained analytically. By using the dynamic boundary condition on the cavity boundary, an integral equation in the velocity modulus was derived. The particular case of zero surface tension is a special case of the solution. The surface tension effect was computed over a wide range of the Weber number for various degrees of cavitation development. Numerical results are presented for the flow configuration, the drag force coefficient, and the position of cavity detachment. It was found that for each radius of the edges, there exists a critical Weber number, below which the iterative solution process fails to converge, so a steady flow solution cannot be computed. This critical Weber number increases as the radius of the edge decreases. As the edge radius tends to zero, the critical Weber number tends to infinity, or a steady cavity flow cannot be computed at any finite Weber number in the case of sharp wedge edges. This shows some limitations of the model based on the Brillouin–Villat criterion of cavity detachment.

Effect of a Boundary Layer on Cavity Flow

Cavity flow past an obstacle in the presence of an inflow vorticity is considered. The proposed approach to the solution of the problem is based on replacing the continuous vorticity with its discrete form in which the vorticity is concentrated along vortex lines coinciding with the streamlines. The flow between the streamlines is vortex free. The problem is to determine the shape of the streamlines and cavity boundary. The pressure on the cavity boundary is constant and equal to the vapour pressure of the liquid. The pressure is continuous across the streamlines. The theory of complex variables is used to determine the flow in the following subregions coupled via their boundary conditions: a flow in channels with curved walls, a cavity flow in a jet and an infinite flow along a curved wall. The numerical approach is based on the method of successive approximations. The numerical procedure is verified considering a body with a sharp edge, for which the point of cavity detachment is fixed. For smooth bodies, the cavity detachment is determined based on Brillouin’s criterion. It is found that the inflow vorticity delays the cavity detachment and reduces the cavity length. The results obtained are compared with experimental data.

Characterization of unsteady cavitating flow regimes around a hydrofoil, based on an extended Schnerr–Sauer model coupled with a nucleation model

The present work is aimed at the numerical spatio-temporal characterization of the unsteady cavitating flow structures on a hydrofoil by means of Proper Orthogonal Decomposition (POD) and Fast Fourier Transform (FFT) techniques. Three different cavitation regimes have been investigated: bubble cavitation, cloud cavitation and supercavitation. The homogeneous mixture approach has been used, in combination with an extended Schnerr–Sauer cavitation model. The accuracy of the numerical predictions has been improved by means of the implementation of a Density Correction Model of the turbulent viscosity, and a simplified Population Balance Modeling (PBM) which solved the spatial distribution and the temporal evolution of the nuclei. In particular, the PBM has led to a reduction of the intensity of the evaporation inside the vapor cavities and a consequent condensation enhancement at the cavity closure and in the wake downstream. This phenomenon mainly impacted on the vapor cavity dynamics during supercavition by facilitating the formation of the re-entrant jet and the vapor cavity detachment. Also, during supercavitation the nuclei density nb exhibited maximum variations of about 35.6% with respect to the inlet nuclei density. As the cavitation number increased, both the intensity and the extension of oscillations significantly reduced, and in bubble cavitation regime nb fluctuated at amplitudes of about 10% of the inlet nuclei density.The characterization of the cavitation regimes revealed that the bubble cavitation regime had a more stable and periodic dynamics highlighted by a higher hydrodynamic efficiency and a reduced root mean square of the lift force. The cloud cavitation and the supercavitation exhibited a more violent bubble detachment which caused stronger oscillations of the vapor cavity as well as the pressure upstream. This was retrieved in an increase of the average drag coefficient of about the 38% due to the presence of vapor cloud transported downstream, which promoted the surge of the flow. The vorticity analysis underlined that the formation of the re-entrant jet and the bubble detachment were promoted by the baroclinic vorticity, while the dilatation vorticity drove the dynamics of the detached clouds, governed by the phase change phenomena. The FFT analysis of the dynamics of the vapor cavity and the pressure upstream led to the detection of the most representative frequencies and Strouhal numbers of each cavitation regimes, in particular (fs=16.6Hz,St=0.355) for bubble cavitation, (fs=10.74Hz,St=0.358) for cloud cavitation, and (fs=8.79Hz,St=0.300) during supercavitation.The POD analysis allowed for the detection of the most relevant cavitating structures, in relation to the vapor cavity fluctuations and their frequency content. Furthermore, the FFT analysis of the temporal eigenfunctions demonstrated that the first POD mode of the liquid volume fraction described the overall unsteady behavior previously detected. Instead, high order POD modes revealed frequency values well above the overall ones of the main flow previously detected.

The dynamics of partial cavity formation, shedding and the influence of dissolved and injected non-condensable gas

In the present study, the experimental set-up of Ganeshet al.(J. Fluid Mech., vol. 802, 2016, pp. 37–78) is used to examine the dynamics of a shedding cavity by examining the vapour production rate of the natural cavity and determining how minimal injection of non-condensable gas can substantially alter the vapour production rate, the resulting cavity flow and the cavity shedding process. The influence of the dissolved gas content on the shedding natural cavity flow is also examined. High-speed visual imaging and cinemagraphic X-ray densitometry were used to observe the void fraction dynamics of the cavity flow. Non-condensable gas is injected across the span of the cavity flow at two locations: immediately downstream of the cavity detachment location at the apex of the wedge or further downstream into mid-cavity. The gas injected near the apex is found to increase the pressure near the suction peak, which resulted in the suppression of vapour formation. Hence, the injection of gas could result in a substantial net reduction in the overall cavity void fraction. Injection at the mid-cavity did less to suppress the vapour production and resulted in less significant modification of both the mean cavity pressure and net volume fraction. Changes in the cavity void fraction, in turn, altered the dynamics of the bubbly shock formation. Variation of the dissolved gas content alone (i.e. without injection) did not significantly change the cavity dynamics.

Numerical investigation of near-wake characteristics of cavitating flow over a circular cylinder

A homogeneous mixture model is used to study cavitation over a circular cylinder at two different Reynolds numbers ($Re=200$and 3900) and four different cavitation numbers (${\it\sigma}=2.0$, 1.0, 0.7 and 0.5). It is observed that the simulated cases fall into two different cavitation regimes: cyclic and transitional. Cavitation is seen to significantly influence the evolution of pressure, boundary layer and loads on the cylinder surface. The cavitated shear layer rolls up into vortices, which are then shed from the cylinder, similar to a single-phase flow. However, the Strouhal number corresponding to vortex shedding decreases as the flow cavitates, and vorticity dilatation is found to play an important role in this reduction. At lower cavitation numbers, the entire vapour cavity detaches from the cylinder, leaving the wake cavitation-free for a small period of time. This low-frequency cavity detachment is found to occur due to a propagating condensation front and is discussed in detail. The effect of initial void fraction is assessed. The speed of sound in the free stream is altered as a result and the associated changes in the wake characteristics are discussed in detail. Finally, a large-eddy simulation of cavitating flow at$Re=3900$and${\it\sigma}=1.0$is studied and a higher mean cavity length is obtained when compared to the cavitating flow at$Re=200$and${\it\sigma}=1.0$. The wake characteristics are compared to the single-phase results at the same Reynolds number and it is observed that cavitation suppresses turbulence in the near wake and delays three-dimensional breakdown of the vortices.

Applications of a curvature correction turbulent model for computations of unsteady cavitating flows

A Curvature Correction model (CCM) based on the original k-ϵ model is proposed to simulate unsteady cavitating flows. The objective of this study is to validate the CCM model and further investigate the unsteady vortex behaviors of cavitating flows around a Clark-Y hydrofoil. Compared with the original k-ϵ model, predicted results are improved in terms of the cavity detachment and hydrofoil fluctuations. Results show that streamline curvature correction of CCM model overcomes the over-predictions of turbulence kinetic energy and eddy viscosity in cavitating vertical region with the original k-ϵ model, which leads to better simulation abilities for the unsteady cavitating flow computations. Based on computations, it is proved that the vortex structure is significantly modified by the transient cavitation, especially with respect to the cavity shedding behaviors. Complex vortex interactions and corresponding cavity shedding process near hydrofoil trailing edge lead to various load frequencies.

Numerical analysis of basic base-ventilated supercavitating hydrofoil sections

A numerical analysis of the inviscid flow over base-ventilated intercepted hydrofoils is presented. The low-order, non-linear boundary element formulation used is described along with the significant issues concerning the modelling of supercavities with this method. The use of transom-mounted interceptors is well established for the manoeuvring and trim control of high-speed vessels. The flow field over a forward-facing step at the trailing edge of a blunt-based hydrofoil section, with consequent cavity detachment from the outer edge of the step, is similar to that of the transom-mounted interceptor operating at high speed with free surface detachment from the outer edge. Due to this similarity, the term ‘intercepted’ hydrofoil is used to describe this arrangement. The results presented show that a number of geometric parameters, in particular thickness, leading-edge radius and trailing-edge slope, have a significant effect on the hydrodynamic performance of base-ventilated intercepted hydrofoils.

Cavity detachment on a hydrofoil with the inclusion of surface tension effects

The non-linear problem of cavity flow past a hydrofoil is considered with taking into account fluid viscosity in the cavity closure region and surface tension, which affect the cavity detachment. The theoretical model is based on the concept of viscous–inviscid interaction between the outer inviscid cavity flow and the inner turbulent separated flow downstream of the cavity. The outer inviscid flow is solved by constructing the complex flow potential, and the wake model is based on the method of integral relationships for separated turbulent flows. The obtained numerical results are compared with experimental data.

Capillary cavity flow past a circular cylinder

Cavity flow past a circular cylinder is considered accounting for the surface tension on the cavity boundary. The fluid is assumed to be inviscid and incompressible, and the flow is assumed to be irrotational. The solution is based on two derived governing expressions, which are the complex velocity and the derivative of the complex potential defined in an auxiliary parameter region. An integral equation in the velocity magnitude along the free surface is derived from the dynamic boundary condition. The Brillouin–Villat criterion is employed to determine the location of the point of flow separation. The cases of zero surface tension and zero cavitation number are obtained as limiting cases of the solution. Numerical results concerning the effects of surface tension and cavitation development on the cavity detachment, the drag force and the geometry of the free boundaries are presented over a wide range of the Weber and the cavitation numbers.

Determination of Cavity Detachment for Sheet Cavitation

Sheet cavitation has been traditionally analyzed with ideal fluid theory that employs the cavitation number as the single parameter. However, characteristics of cavitation can significantly depend on location of cavity detachment. According to known experimental data, this location is influenced by the freestream speed and the body/hydrofoil size. As shown in this paper, it takes place because of the combined effect of the Reynolds number and Weber number. Here, sheet cavitation is considered as a special kind of viscous separation caused by the cavity itself. The viscous-inviscid interaction concept is employed to analyze the entire flow. Validation of the suggested approach is provided for hydrofoils and bodies of revolution. The effects of flow speed, the body size, and its surface wettability are illustrated by comparison of computed cavity length/shape to the known experimental data. The difference between cavity detachment in laminar and turbulent boundary layers is discussed.

Modeling of Unsteady Sheet Cavitation on Marine Propeller Blades

Unsteady sheet cavitation is very common on marine propulsor blades. The authors summarize a lifting‐surface and a surface‐panel model to solve for the unsteady cavitating flow around a propeller that is subject to nonaxisymmetric inflow. The time‐dependent extent and thickness of the cavity were determined by using an iterative method. The cavity detachment was determined by applying the smooth detachment criterion in an iterative manner. A nonzeroradius developed vortex cavity model was utilized at the tip of the blade, and the trailing wake geometry was determined using a fully unsteady wake‐alignment process. Comparisons of predictions by the two models and measurements from several experiments are given.

A BEM for the Prediction of Unsteady Midchord Face and/or Back Propeller Cavitation

A boundary element method (BEM) is used for the numerical analysis of sheet cavitation on a propeller subjected to the non-axisymmetric wakes of marine vehicles. This method is extended in order to treat mixed partial and supercavity patterns on both the face and back of the blades with searched cavity detachment. The convergence of the method is studied. The predicted cavity shapes and forces by the present method agree well with experiments and with those predicted by another numerical method.

Propeller Sheet Cavitation Predictions Using a Panel Method

A boundary element method is used to predict the time-dependent cavitation on a propeller subject to nonaxisymmetric inflow. The convergence of the method is studied. The predicted cavities agree well with those observed in CAPREX, an experiment performed at MIT’s variable pressure water tunnel. The method is modified so that prediction of cavities detaching at mid-chord regions is possible. An algorithm for predicting the cavity detachment location on the blade is described and applied on a blade geometry which exhibits mid-chord cavitation.

Pneumatic Displacement of Subretinal Hemorrhage Without Tissue Plasminogen Activator

Objective To assess the efficacy and complications of intravitreal injection of perfluoropropane gas for displacement of subretinal hemorrhage (SRH), without the use of tissue plasminogen activator. Patients and Methods Pure perfluoropropane gas (0.4-0.5 mL) was injected into the vitreous cavity in 5 patients with SRH involving the fovea because of age-related macular degeneration (4 eyes) or ruptured retinal arterial macroaneurysm (1 eye). The patients were instructed to maintain a prone position. Results Visual acuity ranged from 20/300 to 20/2000 before gas injection. On the day after gas injection, SRH was dramatically displaced in 3 eyes and slightly displaced with a reduction in the thickness of subfoveal hemorrhage in the remaining 2 eyes. Final visual acuity improved in all cases, ranging from 20/15 to 20/220. Three eyes had a final visual acuity of 20/50 or better. Vitreous hemorrhage caused by migration of SRH into the vitreous cavity and retinal detachment each occurred in 1 eye, and both complications were successfully treated by vitrectomy. Conclusions Gas injected into the vitreous cavity can displace SRH without the use of tissue plasminogen activator in some cases. Visual acuity after gas injection may be improved, making this treatment an alternative to evacuation of SRH with vitrectomy.