Unsteady Cloud Cavitation Research Articles

Numerical simulation of unsteady cloud cavitation in an orifice nozzle by a compressible gas-vapor/liquid mixture cavitation model

Abstract Focused on the behaviour of unsteady cloud cavitation in a submerged orifice nozzle, this work presents a numerical investigation by using a compressible gas-vapor/liquid mixture cavitation model. The mean flow of the two-phase mixture is calculated by URANS for compressible fluid and the intensity of cavitation is evaluated by the gas volumetric void fraction considering the effect of fluid compressibility varying with phase change. Water jets issuing from a submerged orifice nozzle are investigated under different cavitation conditions. Computation results are compared with experiment data and the validity of computation is confirmed. The periodical shedding of cavitation clouds is captured reliably. Numerical simulations reveal that a leading cloud principally split by the shear flow and a subsequent cloud detached by the re-entrant jet are successively shed downstream, and they coalesce over the range of approximately x/d ≈ 2∼3. This process is repeated and the flow rate coefficient pulsates periodically under the effect of cavitation clouds.

Active flow control on unsteady cloud cavitation: Insights into jet dynamics

Unsteady cloud cavitation significantly impairs the performance of marine systems. Active flow control method has shown promise in effectively reducing cavitation, yet its specific mechanisms of action require elucidation. This study investigates continuous water injection on a NACA66 (MOD) hydrofoil as an active control against unsteady cloud cavitation. Results show notable reductions in cavitation volume: 52.57 % at a cavitation number of 0.83 and 86.24 % at 1.29. Employing the Lagrangian approach, the study tracks ideal particles to explore the jet's behavior and its interaction with cavitation. The interaction between the jet and cavitation is reciprocal: cavitation draws the jet, which in turn alters the cavitation's structure. The jet's movement is synchronized with the evolution process of cavitating flow, effectively limiting the spread of attached cavitation, disrupting cloud integrity, and encircling scattered clouds to prevent their growth. The analysis identifies the jet's streamwise direction as critical in suppressing cavitation, with the normal direction providing supplementary support, and the spanwise direction having minimal impact. Furthermore, the jet promotes a condensation-dominant state in local flow regions, hindering cavitation growth by altering the water-vapor mass transport process.

Unsteady Cloud Cavitation on a 2D Hydrofoil: Quasi-Periodic Loads and Phase-Averaged Flow Characteristics

We perform large-eddy simulations to study a cavitating flow over a two-dimensional hydrofoil section—a scaled-down profile (1:13.26) of guide vanes of a Francis turbine—using the Schnerr–Sauer cavitation model with an adaptive mesh refinement in intensive phase transition flow areas. In the test case, the guide vane is tilted at an angle of attack of 9° to the direction of the flow, in which the Reynolds number, based on the hydrofoil chord length, equals 1.32×106, thus providing a strong adverse pressure gradient along the surface. The calculated time-averaged turbulence characteristics are compared with those measured by particle image velocimetry to verify that the flow is correctly reproduced in numerical simulations using the procedure of conditional averaging proposed and tested in our previous investigation. A re-entrant jet is identified as the primary source of vapor cloud shedding, and a spectral analysis of the cavitating flow over the profile midsection is conducted. Two characteristic frequencies corresponding to the cases, when an attached cavity detaches completely (as a whole) and two partially from the hydrofoil, are found in the flow. The study reveals that the natural frequency of partial cavity shedding is three times higher than that of full detachments. The examined regime exhibits an oscillatory system with two oscillation zones related to cavitation surge instability and unsteady cloud cavitation resulting from the re-entrant jet. Conditional averaging correlates cavitation structures with pressure distributions, forces, and torque on the guide vane. This modeling approach captures the fine details of quasi-periodic cavitation dynamics, providing insights into unsteady sheet/cloud cavitation and offering a method for developing control strategies.

Experimental study on the mechanism of cavitation-induced ventilation

In this study, the cavitating flow and cavitation-induced ventilation flow around a surface-piercing hydrofoil were investigated to gain in-depth understanding of the interaction mechanism between the vaporous cavity and free surface at low cavitation numbers. Experiments were conducted in a constrained-launching water tank to visualize the cavity using a high-speed camera. Unsteady cloud cavitation and cavitation-induced ventilation at atmospheric pressure were observed and analyzed while piercing the free surface. The flow regime map was summarized at a fixed aspect ratio of ARh = 1.5. Subsequently, a physical model was proposed to predict the maximum depression depth of the water surface (H) at the trailing edge of the hydrofoil. Both the physical model and experimental results reveal that the non-dimensional depth H/c has a linear relation to Fn2 c × Rec × sin2α. Finally, a criterion for cavitation-induced ventilation based on the improved lifting-line theory and a physical model were proposed. A new relation H/Lc ∼ α0.5 was obtained, where Lc is the maximum cavity length. The results of this study can guide the design and application of hydrofoils for ventilation and cavitation processes.

Vapor concentration and bimodal distributions of turbulent fluctuations in cavitating flow around a hydrofoil

The article presents results of a statistical analysis of the original PIV data for the cavitating flow around the 2D symmetric hydrofoil mimicking a guide vane of a Francis turbine which were previously reported in Timoshevskiy et al. (2020). We employ the procedure of statistical vector filtration (Heinz et al., 2004) to eliminate vector outliers from the measured velocity fields, which allows us to retrieve genuine spatial distributions of higher-order statistical moments of velocity fluctuations, and the method of vapor phase detection (Pervunin et al., 2021) to extract time-averaged fields of vapor in the cavitating flow. The spatial distributions of the probability of vapor phase occurrence allowed us to unambiguously distinguish the extension of the flow area occupied by the dispersed phase (cavitation) together with the time-averaged concentration of the vapor phase in the three characteristic regimes of the cavitating flow as well as different features of cavitation evolution, including the location and length of an attached cavity and the place of detachments of cloud cavities in the case of unsteady cloud cavitation. The development of cavitation is also reflected in the fields of higher-order statistical moments of turbulent fluctuations by the example of coefficients of asymmetry and excess. With a transition to unsteady cloud cavitation, the distribution of velocity fluctuations transforms, taking a nonequilibrium shape, with an increase in magnitudes of the asymmetry and excess coefficients over a significant flow area. In a region of the attached cavity, around the place of formation of vapor clouds and downstream, where the cloud cavities are carried away by the flow, the distribution of velocity fluctuations becomes bimodal. Through visual inspection of the raw PIV images, realizations related to two characteristic phases of the cavity oscillation cycle were extracted, providing quasi-phase-averaged data. As a result, the bimodal shape of the distributions in certain areas of the unsteady cavitating flow was demonstrated to be most probably linked with periodic detachments and downstream advection of the vapor clouds as the predominant fundamental process determining the flow structure and dynamics.

Experimental investigation into passive control effect of micro vortex generator at various cavitation conditions

The objective of this study is to discuss a passive control method for different stages of cavitating flows. The passive flow control is implemented using micro delta-shaped vortex generator (mVG) inserted spanwise on the suction side of the NACA66 hydrofoil. A high-speed camera is applied to visualize the cavitating flow structures. The results show that for the inception cavitation, the mVG with different positions can cause different modes of inception cavity. The typical three-dimensional spot cavity, the fingerlike vortex cavity, and the patch cavity are respectively captured at the leading edge of baseline hydrofoil, mVG-1 hydrofoil, and mVG-2 hydrofoil. For the sheet attached cavity, a new cavitation mode is found on the mVG-1 hydrofoil which is the fingerlike vortex cavitation followed by the attached sheet cavity due to the vortex cavitation merging behavior. Furthermore, for the unsteady cloud cavitation, the two mechanisms of cavity quasi-periodic shedding caused by the re-entrant jet and shockwave are analyzed to reveal that the mVG-1 can enhance the instability while the mVG-2 can weaken it.

Dynamic mode decomposition to classify cavitating flow regimes induced by thermodynamic effects

The effect of temperature on the intensity and the dynamics of cavitation is investigated. Experiments of cavitating flows are conducted at various cavitation numbers and temperatures, leading to different cavity intensities and dynamic behaviors. The thermodynamic effects significantly influence the cavitation extent at elevated temperatures (over 58 °C) in water. Three regimes of instability, i.e. the sheet cavitation, the periodic single-cloud cavitation, and the aperiodic multi-clouds cavitation are distinguished based on their temporal-spatial evolutions. Application of DMD and POD decompositions on the velocity fields and gray level snapshots to determine the coherent structures and the various mechanics causing different shedding behaviors are discussed. The coherent structures obtained in cloud cavitation consist of the re-entrant jet and counter-rotating vortex structures, which are more aggressive dynamic behavior and are absent in the sheet cavitation. To inhibit the effects of hydrodynamic cavitation, it is recommended that a temperature range (55 °C–60 °C) of water be avoided in practical applications. Since working under this temperature range has larger potentials of transforming the steady sheet cavitation to unsteady cloud cavitation with the larger cavitation extent and the vigorous vapor cloud shedding.

Numerical Study of Mitigating Cloud Cavitation Shedding Using Biomimetic Protuberant Stripes

Abstract Cloud cavitation usually appears on impeller blades of hydraulic machinery. When unsteady cloud cavitation travels downstream to a high-pressure region and collapses, performance drops and cavitation erosion appears. It is important to develop effective methods to mitigate the undesirable effects. By million years of natural selection, bird feather has presented excellent flow performance. As typical characteristic structure of bird feather, a number of barbs are supported by a central hollow shaft. Under inspiration of bird feathers, we presented a method of passive cavitation control. This method of passive cavitation control uses biomimetic protuberant stripes (PSs) mounted on a NACA66 hydrofoil. The effects of various biomimetic PS arrangements on the cavitation pattern, pressure fluctuation, and hydrodynamic load are numerically studied. Then, the cavitation control mechanism of the biomimetic PS is analyzed in detail. We observe that the biomimetic PSs not only inhibit the shedding of large-scale cloud cavitation but also reduce the cavitation size. Moreover, analysis shows that turbulence velocity fluctuation may be mitigated and boundary layer thickness is reduced with biomimetic PSs, which enhances the flow intensity in the main flow direction.

Statistical analysis of vapor distribution in a cavitation flow based on an ensemble of instantaneous liquid velocity fields

A new method was developed for statistical analysis of ensembles of instantaneous velocity fields measured by PIV in liquid (continuous phase) to determine the distribution of the vapor phase in cavitating flow. The method is based on two main principles: the absence of tracers used for PIV measurements in vapor, and the statistical independence of individual measurements. This allowed establishing an exponential dependence of repeatability of the vapor phase at a certain point of a cavitating flow. Compliance with this theoretical law was verified using the Pearson chi-square test. All theoretical distributions were divided into several groups depending on the time-averaged local vapor content calculated over the entire ensemble of realizations and the probability of a single event. As a result, dimensions of the stationary part of an attached cavity and the place of detachments of cloud cavities from the hydrofoil surface were determined using the new method of statistical analysis for an unsteady cloud cavitation regime.

Systematic Validation Study of an Unsteady Cavitating Flow over a Hydrofoil Using Conditional Averaging: LES and PIV

We present results of Large-eddy simulations (LES) modeling of steady sheet and unsteady cloud cavitation on a two-dimensional hydrofoil which are validated against Particle image velocimetry (PIV) data. The study is performed for the angle of attack of 9° and high Reynolds numbers ReC of the order of 106 providing a strong adverse pressure gradient along the surface. We employ the Schnerr–Sauer and Kunz cavitation models together with the adaptive mesh refinement in critical flow regions where intensive phase transitions occur. Comparison of the LES and visualization results confirms that the flow dynamics is adequately reproduced in the calculations. To correctly match averaged velocity distributions, we propose a new methodology based on conditional averaging of instantaneous velocity fields measured by PIV which only provides information on the liquid phase. This approach leads to an excellent overall agreement between the conditionally averaged fields of the mean velocity and turbulence intensity obtained experimentally and numerically. The benefits of second-order discretization schemes are highlighted as opposed to the lower-order TVD scheme.

Unsteady cloud cavitation mechanisms of liquid nitrogen in convergent–divergent nozzle

An investigation into the shedding mechanism of cloud cavitation is of great importance to understand the cavitation dynamics for cryogenic liquids. In this study, the dynamic processes of liquid nitrogen cavitating flows in a convergent–divergent (C–D) square nozzle under various operating conditions are experimentally investigated. Simultaneous measurements of cavity dynamics and the velocity variations in the cavitation region are implemented by introducing a high-speed camera and laser Doppler velocimetry (LDV). Several cavitation numbers are realized by changing the inflow velocity and thus the throat velocity. The specific shedding characteristics as well as the mechanism of the re-entrant jet and condensation shock are qualitatively analyzed for each case by examining high-speed photographs. In addition, a three-dimensional numerical model based on the large Eddy simulation (LES) is employed to further explore the re-entrant jet/condensation shock-dominated cavity shedding dynamics. The numerical results are in good agreement with the experimental results by comparing the temporal cavitation regime distributions and the velocity variations at the same positions. The velocity of the re-entrant jet at the end of the cavity is about −4 to −5 m/s and decreases along the upstream direction. The re-entrant jet and the condensation shock are found to be the dominant mechanism for the shedding of cloud cavitation when σ = 0.497 and σ = 0.386, respectively. The shedding mechanism revealed by the combined experimental and numerical studies offers a deeper understanding of the unsteady shedding of cloud cavitation for cryogenic fluids.

Numerical analysis of unsteady cloud cavitating flow around a 3D Clark-Y hydrofoil considering end-wall effects

This study employs an incompressible homogeneous flow framework with a transport equation based cavitation model and density corrected Shear Stress Transport (SST) k-ω turbulence model to successfully reproduce the unsteady cavitating flow around a 3D Clark-Y hydrofoil with an end wall. Cavity growth, development, and break-off during the periodic shedding process are adequately reproduced and match experimental observations. The predicted shedding frequency is very close to the experimental value of 43.48 Hz. The existence of an end wall brings about the generation and convection of wall-side cavity. Moreover, large horse-type cavity structure is captured, which agrees with experimental results. Cavities at the closure region easily detach from the main pocket part resulting in a secondary vortical structure. Differences between numerical and experimental lift are observed, however, similar to our previous findings, the experimental lift coefficient appears to correlate with the inverse of the second derivative of the total cavity volume. Based on the analysis of vorticity transportation, compressibility source occupies the highest contribution of vorticity transportation and is significantly higher than other two terms, which serves the promotion effect at the trailing region of growing attached cavity while inhibits the development of vorticity within the leading area.

A modified filter-based model for simulation of unsteady cavitating flows around a NACA66 hydrofoil

Unsteady cavitating turbulent flow around a NACA66 hydrofoil was simulated using a mass transfer cavitation model and a modified filter-based turbulence model in this paper. The modified filter-based turbulence model can accurately predict the pressure coefficient in midplane and shedding frequency of the unsteady cloud cavitation than standard [Formula: see text]–[Formula: see text] model and filter-based turbulence model. The time evolution of transient cavitation cloud structure predicted by the three-turbulence model was compared. The result which was predicted by the modified filter-based turbulence model is in good agreement with the experimental results. The time evolution of re-entrant jet had been analyzed. The instantaneous wall-pressure evolution on the suction surface (SS) predicted by the modified filter-based turbulence model had been analyzed. The cavitation-vortex interaction had been analyzed in this study. The different effects on the cavitation-vortex interaction of the vortex stretching term, vortex dilatation term and baroclinic torque term in the transport equation of vorticity had been discussed.

Some notes on numerical simulation of the turbulent cavitating flow with a dynamic cubic nonlinear sub-grid scale model in OpenFOAM

The accuracy of large eddy simulation (LES) is highly dependent on the performance of sub-grid scale (SGS) model. In the present paper, a dynamic cubic nonlinear sub-grid scale model (DCNM) proposed by Huang et al. is implemented for the simulation of unsteady cavitating flow around a 3-D Clark-Y hydrofoil in OpenFOAM. Its performance in predicting the evolution of cloud cavitation is discussed in detail. The simulation with a linear model, the dynamic Smagorinsky model (DSM), is also conducted as a comparison. The results with DCNM show a better agreement with the available experimental observation. The comparison between DCNM and DSM further suggests that the DCNM is able to predict the backscatter more precisely, which is an important feature in LES. The characteristics of DCNM is analyzed to account for its advantages in the prediction of unsteady cloud cavitation as well. The results reveal that it is the nonlinear terms of DCNM that makes DCNM capture sub-grid scale vortices better and more suitable for studying the transient behaviors of cloud cavitation than DSM.

Numerical Simulation of Cavitation Erosion Aggressiveness Induced by Unsteady Cloud Cavitation

A numerical investigation of the erosion aggressiveness of leading edge unsteady cloud cavitation based on the energy balance approach has been carried out to ascertain the main damaging mechanisms and the influence of the free stream flow velocity. A systematic approach has permitted the determination of the influence of several parameters on the spatial and temporal distribution of the erosion results comprising the selection of the cavitation model and the collapse driving pressure. In particular, the Zwart, Sauer and Kunz cavitation models have been compared as well as the use of instantaneous versus average pressure values. The numerical results have been compared against a series of experimental results obtained from pitting tests on copper and stainless steel specimens. Several cavitation erosion indicators have been defined and their accuracy to predict the experimental observations has been assessed and confirmed when using a material-dependent damaging threshold level. In summary, the use of the average pressure levels during a sufficient number of simulated shedding cycles combined with the Sauer cavitation model are the recommended parameters to achieve reliable results that reproduce the main erosion mechanisms found in cloud cavitation. Moreover, the proposed erosion indicators follow a power law as a function of the free stream flow velocity with exponents ranging from 3 to 5 depending on their definition.

Statistical structure of the velocity field in cavitating flow around a 2D hydrofoil

Transformation of flow turbulence structure with cavitation occurrence, determination of the flow conditions favorable for nucleation of cavitation bubbles, influence of the statistical structure of turbulence on this process and the inverse effect of cavitation on the flow dynamics are challenging problems in modern fluid mechanics. The paper reports on the results of statistical processing of the velocity fields measured by a PIV technique in cavitating flow over a 2D symmetric hydrofoil for four flow conditions, starting from a cavitation-free regime and finishing by unsteady cloud cavitation. We analyze basic information on the statistical structure of velocity fluctuations in the form of histograms and Q-Q diagrams along with profiles of the mean velocity and turbulent kinetic energy. The research reveals that the flow turbulence pattern and distributions of turbulent fluctuations change significantly with the cavitation development. Under unsteady cloud cavitation conditions, the probability density function of the fluctuating velocity has a two-mode distribution, which indicates switching of two alternating flow conditions in a region above the hydrofoil aft part due to periodic passing of cavitation clouds. Behaviors of the mean and most probable velocities unexpectedly appear to be different with a monotonous increase of the incoming flow velocity. This finding must be caused by modification of the skewness coefficient of the fluctuating velocity.

Numerical investigation of unsteady cloud cavitating flow around the Clark-Y hydrofoil with adaptive mesh refinement using OpenFOAM

In this paper, the cavitating flow around a three-dimension Clark-Y hydrofoil is investigated by the large eddy simulation (LES) method coupled with the volume of fluid (VOF) model in OpenFOAM. The simulated results are compared with the experimental data and a reasonable agreement is obtained. The cavitation-vortex interaction is studied with the vorticity transport equation and much stronger baroclinic torque term is observed. The adaptive mesh refinement (AMR) method is adopted for improving the accuracy and efficiency of numerical simulation. Comparing with the results presented by the mesh with fine resolution, even the coarse resolution mesh, with AMR method, can precisely characterize identical complex cavity structures and flow details. The local high pressure induced by the reverse flow and small residual vortex structures are obtained by the coarse resolution mesh with the AMR method. Further analyzes of the variation trend of total grid numbers using the AMR in one typical cycle show that the rates of the cloud cavitation shedding and collapse are faster than that of the attached cavity growth. This research illustrates that the AMR is a potential approach to accurately model multi-scale cavitating flows and to better understand cavitation mechanism on the premise of limited computational costs.

Cavitation control using Cylindrical Cavitating-bubble Generators (CCGs): Experiments on a benchmark CAV2003 hydrofoil

Cavitation often causes a destructive impact on the performance of hydraulic machinery, such as erosive wear, noise and vibrations of the framework and moving parts of marine propellers, pumps, hydraulic turbines and other equipments, which eventually leads to a degradation of overall system effectiveness. The paper reports on an experimental investigation of a passive method of flow control for different cavitation conditions: starting from the cavitation inception, including quasi-steady partial cavitation with shedding of small-scale vortical structures and finishing by unsteady cloud cavitation. The passive flow control was implemented using miniature vortex generators of a cylindrical type referred to as Cylindrical Cavitating-bubble Generators (CCGs) that were placed on the surface of a benchmark CAV2003 hydrofoil. First, we performed high-speed visualization of cavitation on the suction side of the original hydrofoil (without the control element) to find the cavitation inception point near the leading edge and to analyze the spatial structure and time evolution of partial cavities. In order to improve our understanding of the mechanism of cavitating flow unsteadiness and the effect of CCGs on the cavitation dynamics, we also applied a PIV technique to measure the mean flow velocity profiles and a hydroacoustic pressure transducer to record local pressure pulsations in the hydrofoil wake. As a result, this allowed us to determine the influence of CCGs on turbulent structure of the flow at different cavitation regimes and amplitude-frequency spectra of the pressure pulsations associated with attached cavity length oscillations for unsteady flow conditions. It was revealed that, in the case of unsteady cloud cavitation, CCGs were capable to mitigate large-scale cloud cavities. In addition, a substantial decrease in the amplitude of pressure pulsations was registered for the modified hydrofoil (with the control element). In general, CCGs appeared to be quite effective to hinder the cavitation development and to reduce the strength of side- and middle-entrant jets as the primary mechanisms of unsteady cloud cavitation.

Evaluation of mass transport cavitation models for unsteady cavitating flows

Modeling of unsteady cavitating flow is a critical issue in a lot of practical cases. The objective of this paper is to assess the practical applicability of three widely used mass transport cavitation models under RANS framework, including the Kubota model, Kunz model, and Singhal model, for predicting partial sheet cavitating flow around an axisymmetric body with hemispherical head and unsteady cloud cavitating flow around a Clark-Y hydrofoil. The results show that for the axisymmetric cylindrical body, all three cavitation models could generally predict the pressure distributions. The significant differences are found around the closure region of the attached cavity due to the magnitude and distribution of mass transfer rate. For the unsteady cavitating flow along the hydrofoil, the significant differences with different cavitation model are observed in time-averaged and time-dependent concerning the cavity shapes, multiphase structures and the cloud shedding dynamics. The Singhal model coupling the effect between the vorticity distribution and the cavity dynamics agrees best with the experimental measurements.

Experimental investigation of the passive control of unsteady cloud cavitation using miniature vortex generators (MVGs)

The research is aimed at the study of a passive control method to control unsteady cloud cavitation that is characterized by regular shedding of large vapour structures from the solid surface of a cavitating immersible body. The unsteady cloud cavitation is an important subject of research because of its destructive impacts in various industrial applications, including ship propellers and rudders, pumping and hydraulic machinery systems. For this, we placed miniature vortex generators (MVGs) of a cylindrical type on the surface of a benchmark CAV2003 hydrofoil and investigated effects of these MVGs on the spatial structure of unsteady cavitation clouds. We analyzed the temporal and spatial cavity characteristics in comparison with those for the original hydrofoil (without MVGs) by means of high-speed imaging. In addition, we used a hydrophone to register the signal of pressure pulsations in time and thereby derive power spectra of the pressure pulsations. The results showed that the implemented cavitation control method is an effective tool to manage the unsteady behaviour of cloud cavitation and to mitigate the amplitude of pressure pulsations. It was revealed that, with this control approach, the large-scale cavitation clouds appear to be broken and only small-scale cavity structures are shed away from the hydrofoil surface. Moreover, a notable reduction in the cavitation-induced vibrations of the solid surface may be expected.