Detached-eddy Simulation for Time-dependent Turbulent Cavitating Flows

The Reynolds-averaged Navier-Stokes（RANS）,such as the original k-ω two-equation closures,have been very popular in providing good prediction for a wide variety of flows with presently available computational resource.But for cavitating flows,the above equations noticeably over-predict turbulent production and hence effective viscosity.In this paper,the detached eddy simulation（DES） method for time-dependent turbulent cavitating flows is investigated.To assess the state-of-the-art of computational capabilities,different turbulence models including the widely used RANS model and DES model are conducted.Firstly,in order to investigate the grid dependency in computations,different grid sizes are adopted in the computation.Furthermore,the credibility of DES model is supported by the unsteady cavitating flows over a 2D hydrofoil.The results show that the DES model can effectively reduce the eddy viscosities.From the experimental validations regarding the force analysis,frequency and the unsteady cavity visualizations,more favorable agreement with experimental visualizations and measurements are obtained by DES model.DES model is better able to capture unsteady phenomena including cavity length and the resulting hydrodynamic characteristics,reproduces the time-averaged velocity quantitatively around the hydrofoil,and yields more acceptable and unsteady dynamics features.The DES model has shown to be effective in improving the overall predictive capability of unsteady cavitating flows.

Dynamic mode decomposition and reconstruction of transient cavitating flows around a Clark-Y hydrofoil

The transient cavitating flow around the Clark-Y hydrofoil is numerically investigated by the dynamic mode decomposition with criterion.Based on the ranking dominant modes,frequencies of the first four modes are in good accordance with those obtained by fast Fourier transform.Furthermore,the cavitating flow field is reconstructed by the first four modes,and the dominant flow features are well captured with the reconstructed error below 12%when compared to the simulated flow field.This paper offers a reference for observing and reconstructing the flow fields,and gives a novel insight into the transient cavitating flow features.

Numerical simulation of transient turbulent cavitating flows with special emphasis on shock wave dynamics considering the water/vapor compressibility

The objective of this paper is to investigate the compressible turbulent cavitating flows with special emphasis on shock wave dynamics, with the water/vapor compressibility taken into account. The simulations are performed by solving the compressible, multiphase unsteady Reynolds-averaged Navier-Stokes equations with Saito cavitation model and SST-SAS turbulence model. The compressibility of both the pure water and vapor is considered by employment of the Tait equation of state for water and ideal gas equation of state for vapor. Results are presented for a 3-D NACA66 hydrofoil fixed at ？= 6？ and ？= 1.25 in partial cavitating flows. Cavity collapse induced shock wave formation and propagation, which is closely related to the compressibility characteristics of cavitating flows, are well predicted. Good performance has been obtained for both the cavity evolution process and cavitation induced pressure signals, especially the cavity collapse induced shock wave emission and its interaction with the attached cavity sheet. The pressure peaks in microseconds accompanying the shock wave are captured. The typical quasi-periodic sheet/cloud cavitation evolution is characterized by the following four stages：（1） the growth of the attached cavity sheet,（2） development of re-entrant flow and attached cavity sheet breakup,（3） attached cavity sheet rolling up and cavity cloud shedding, and（4） cloud cavity collapse, shock wave emission and propagation. The cloud cavity collapse induced shock wave dynamics is supposed to be the major origin of cavitation instabilities.

Large eddy simulation of cavitating flows with dynamic adaptive mesh refinement using OpenFOAM

Cavitating flows are dominated by large gradients of physical properties and quantities containing complicated interfacial structures and lots of multi-scale eddies that need to be accurately characterized using a high-resolution mesh.The present work,within OpenFOAM,proposes an effective modeling framework using the large eddy simulation(LES)approach along with the volume of fluid(VOF)method to simulate the two-phase flow system and applies the Schnerr-Sauer model to calculate the mass-transfer rate between water and vapor.The adaptive mesh refinement(AMR)which is a powerful tool for allocating high-resolution grids only to the region of the greatest concern is adopted for improving the solution of interfacial structures.The effect of grid size is firstly investigated and the time-averaged quantities are verified against the experimental data,and then simulations of cavitating flows are successfully achieved to precisely characterize the features of cavitation with automatically and dynamically refining the mesh.As the refinement only takes place in the interfacial region,high-precision simulations can be achieved with limited computational resources,and the method shows promising prospects for modeling of the multi-scale,time-critical and computationally intensive cavitating flows.

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.

ASSESSMENT OF A CENTRAL DIFFERENCE FINITE VOLUME SCHEME FOR MODELING OF CAVITATING FLOWS USING PRECONDITIONED MULTIPHASE EULER EQUATIONS

A numerical treatment for the prediction of cavitating flows is presented and assessed. The algorithm uses the preconditioned multiphase Euler equations with appropriate mass transfer terms. A central difference finite volume scheme with suitable dissipation terms to account for density jumps across the cavity interface is shown to yield an effective method for solving the multiphase Euler equations. The Euler equations are utilized herein for the cavitation modeling, because some certain characteristics of cavitating flows can be obtained using the solution of this system of equations with relative low computational effort. In addition, the Euler equations are appropriate for the assessment of the numerical method used, because of the sensitivity of the solution to the numerical instabilities. For this reason, a sensitivity study is conducted to evaluate the effects of various parameters, such as numerical dissipation coefficients and grid size, on the accuracy and performance of the solution. The computations are performed for steady cavitating flows around the NACA 0012 and NACA 66 （MOD） hydrofoils and also an axisymmetric hemispherical fore-body under different conditions and the results are compared with the available numerical and experimental data. The solution procedure presented is shown to be accurate and efficient for predicting steady sheet- and super-cavitation for 2D/axisymmetric geometries.

A cavitation aggressiveness index within the Reynolds averaged Navier Stokes methodology for cavitating flows

The paper proposes a methodology within the Reynolds averaged Navier Stokes（RANS） solvers for cavitating flows capable of predicting the flow regions of bubble collapse and the potential aggressiveness to material damage. An aggressiveness index is introduced, called cavitation aggressiveness index（CAI） based on the total derivative of pressure which identifies surface areas exposed to bubble collapses, the index is tested in two known cases documented in the open literature and seems to identify regions of potential cavitation damage.

PARTIALLY AVERAGED NAVIER-STOKES METHOD FOR TIME-DEPENDENT TURBULENT CAVITATING FLOWS

Cavitation typically occurs when the fluid pressure is lower than the vapor pressure in a local thermodynamic state,and the flow is frequently unsteady and turbulent.The Reynolds-Averaged Navier-Stokes（RANS）approach has been popular for turbulent flow computations.The most widely used ones,such as the standard k-εmodel,have well-recognized deficiencies when treating time dependent flow field.To identify ways to improve the predictive capability of the current RANS-based engineering turbulence closures,conditional averaging is adopted for the Navier-Stokes equation,and one more parameter,based on the filter size,is introduced into the k-εmodel.In the Partially Averaged Navier-Stokes（PANS）model,the filter width is mainly controlled by the ratio of unresolved-to-total kinetic energy1f.This model is assessed in unsteady cavitating flows over a Clark-Y hydrofoil.From the experimental validations regarding the forces,frequencies,cavity visualizations and velocity distributions,the PANS model is shown to improve the predictive capability considerably,in comparison to the standard k-ε model,and also,it is observed the value of1f in the PANS model has substantial influence on the predicting result.As the filter width1f is decreased,the PANS model can effectively reduce the eddy viscosity near the closure region which can significantly influence the capture of the detach cavity,and this model can reproduce the time-averaged velocity quantitatively around the hydrofoil.

NUMERICAL SIMULATIONS OF CAVITATING FLOWS

A new model, which involves viscous and multi-phase effects, was given to study cavitating flows. A local compressible model was established by introducing a density-pressure function to account for the two-phase flow of water/vapor and the transition from one phase to the other. An algorithm for calculating variable-density N-S equations of cavitating flow problem was put forward. The present method yields reasonable results for both steady and unsteady cavitating flows in 2D and 3D cases. The numerical results of unsteady character of cavitating flows around hydrofoils coincide well with experimental data. It indicates the feasibility to apply this method to a variety of cavitating flows of practical problems.

NUMERICAL SIMULATIONS OF 2D PERIODIC UNSTEADY CAVITATING FLOWS

A two-phase mixture model was established to study unsteady cavitating flows. A local compressible system of equations was derived by introducing a density-pressure function to account for the two-phase flow of water/vapor and the transition from one phase to the other. An algorithm for solving the variable-density Navier-Stokes equations of cavitating flow problem was put forward. The numerical results for unsteady characteristics of cavitating flows on a 2D NACA hydrofoil coincide well with experimental data.

URANS COMPUTATION OF CAVITATING FLOWS AROUND SKEWED PROPELLERS

Cavitating flows around skewed propellers are investigated numerically by means of the unsteady Reynolds Averaged Navier-Stokes （RANS） Equation method. The standard k - c turbulence and the modified Z-G-B cavitation models are employed. A measured nominal wake is used for the inlet velocity boundary condition. Predicted cavitating evolution processes and tip cavity patterns are compared with experimental observations. In addition, the influence of the skew angles on the cavitation and unsteadiness performances of propellers operating in a non-uniform wake is also studied. Results show that the modified Z-G-B cavitation model performs better to simulate the cavitating flow cases studied in this paper. Comparisons demonstrate that the skewed propeller with a skew angle of 20~ is the best choice for a given stern wake with a assigned thrust and the minimum force fluctuations.

LES investigation of cavitating flows around a sphere with special emphasis on the cavitation–vortex interactions

Large eddy simulation(LES)was coupled with a homogeneous cavitation model to study turbulent cavitating flows around a sphere.The simulations are in good agreement with available experimental data and the simulated accuracy has been evaluated using the LES verification and validation method.Various cavitation numbers are simulated to study important flow characteristics in the sphere wake,e.g.periodic cavity growth/contraction,interactions between the cloud and sheet cavitations and the vortex structure evolution.The spectral characteristics of the wake for typical cloud cavitation conditions were classified as the periodic cavitation mode,high Strouhal number mode and low Strouhal number mode.Main frequency distributions in the wake were analyzed and different dominant flow structures were identified for each of the three modes.Further,the cavitation and vortex relationship was also studied,which is an important issue associated with complex cavitating sphere wakes.Three types of cavitating vortex structures alternate,which indicates that three different cavity shedding regimes may exist in the wake.Analysis of vorticity transport equation shows a significant vorticity increase at the cavitation closure region and in the vortex cavitation region.This study provides a physical perspective to further understand the flow mechanisms in cavitating sphere wakes.

INTERFERENCE OF SIDE STRUT WITH THE NATURAL CAVITATING FLOWS AROUND A SUBMERGED VEHICLE IN WATER TUNNEL EXPERIMENTS

To apply the measurements of model experiment in water tunnel to the actual sailing condition, it is necessary to know accurately the strut effect and its rule. In the present work, the corresponding interferences of one-side strut and two-side strut on the natural cavitating flows around a submerged vehicle in water tunnel were investigated numerically, using the homogeneous equilibrium two-phase model coupled with a natural cavitation model. The numerical simulation results show that the strut types have distinct effects on the hydrodynamic properties. For the same given upstream velocity and downstream pressure, the existence of the strut leads to an increment of natural cavitation number, reduces the low-pressure region and depresses the pressure on the vehicle surface near the sides of strut. In the case of given cavitaiton number, the influences of the two-side strut on the drag and lift coefficients are both enhanced along with the increment of attack angle, however the influence of the one-side strut gradually gets stronger on the drag coefficient but weaker on the lift coefficient contrarily. In addition, based on the present numerical results, a correction method by introducing the sigmoidal logistic function is proposed to eliminate the interference from the foil-shaped strut.

APPLICATION OF QUADRATIC AND CUBIC TURBULENCE MODELS ON CAVITATING FLOWS AROUND SUBMERGED OBJECTS

Quadratic and cubic Non-Linear Eddy-Viscosity Models （NLEVMs） at low Reynolds number （Re） correction were introduced into the present Computational Fluid Dynamics （CFD） framework, to provide better numerical treatment about the anisotropic turbulence stress in cavitating flows, which have large density ratio and large-scaled swirling flow structures. The applications of these NLEVMs were carried out through a self-developed cavitation code, coupled with a cavitation model based on the transport equation of liquid phase. These NLEVMs were firstly validated by the benchmark of disk supercavity, and found able to obtain more accurate capture of the hydrodynamic properties than the linear models. One of such models was further applied on the cavitation problem of submerged vehicles. Ultimately, the supercavitating flows around an especially designed underwater vehicle were predicted using the cubic k - e turbulence model, and its cavitation behaviors were studied.

Experimental Investigation on Cavitating Flow Shedding over an Axisymmetric Blunt Body

Nowadays,most researchers focus on the cavity shedding mechanisms of unsteady cavitating flows over different objects,such as 2D/3D hydrofoils,venturi-type section,axisymmetric bodies with different headforms,and so on.But few of them pay attention to the differences of cavity shedding modality under different cavitation numbers in unsteady cavitating flows over the same object.In the present study,two kinds of shedding patterns are investigated experimentally.A high speed camera system is used to observe the cavitating flows over an axisymmetric blunt body and the velocity fields are measured by a particle image velocimetry（PIV）technique in a water tunnel for different cavitation conditions.The U-type cavitating vortex shedding is observed in unsteady cavitating flows.When the cavitation number is 0.7,there is a large scale cavity rolling up and shedding,which cause the instability and dramatic fluctuation of the flows,while at cavitation number of 0.6,the detached cavities can be conjunct with the attached part to induce the break-off behavior again at the tail of the attached cavity,as a result,the final shedding is in the form of small scale cavity and keeps a relatively steady flow field.It is also found that the interaction between the re-entrant flow and the attached cavity plays an important role in the unsteady cavity shedding modality.When the attached cavity scale is insufficient to overcome the re-entrant flow,it deserves the large cavity rolling up and shedding just as that at cavitation number of 0.7.Otherwise,the re-entrant flow is defeated by large enough cavity to induce the cavity-combined process and small scale cavity vortexes shedding just as that of the cavitation number of0.6.This research shows the details of two different cavity shedding modalities which is worthful and meaningful for the further study of unsteady cavitation.

PIV analysis and high-speed photographic observation of cavitating flow field behind circular multi-orifice plates

Based on a self-developed hydrodynamic cavitation device with different geometric parameters for circular multi-orifice plates,turbulence characteristics of cavitating flow behind multi-orifice plates,including the effects of orifice number and orifice layout on longitudinal velocity,turbulence intensity,and Reynolds stress,were measured with the particle image velocimetry(PIV)technique.Flow regimes of the cavitating flow were also observed with high-speed photography.The experimental results showed the following:(1)high-velocity multiple cavitating jets occurred behind the multi-orifice plates,and the cavitating flow fields were characterized by topological structures;(2)the longitudinal velocity at each cross-section exhibited a sawtooth-like distribution close to the multi-orifice plate,and each sawtooth indicated one jet issuing from one orifice;(3)there were similar magnitudes and forms for the longitudinal and vertical turbulence intensities at the same cross-section;(4)the variation in amplitude of Reynolds stress increased with an increase in orifice number;and(5)the cavitation clouds in the flow fields became denser with the increase in orifice number,and the clouds generated by the staggered layout of orifices were greater in number than those generated by the checkerboard-type one for the same orifice number.The experimental results can be used to analyze the mechanism of killing pathogenic microorganisms through hydrodynamic cavitation.

Dynamic Characteristics of High-speed Water-Lubricated Spiral Groove Thrust Bearing Based on Turbulent Cavitating Flow Lubrication Model

The water-lubricated bearings are usually the state of turbulent cavitating flow under high-speed conditions. And the distribution of cavitation bubbles and the interface effect between the two phases have not been included in previous studies on high-speed water-lubricated bearings. In order to study the influence of interface effect and cavitation bubble distribution on the dynamic characteristics of high-speed water-lubricated spiral groove thrust bearings(SGTB).A turbulent cavitating flow lubrication model based on two-phase fluid and population balance equation of bubbles was established in this paper. Stiffness and the damping coefficients of the SGTB were calculated using the perturbation pressure equations. An experimental apparatus was developed to verify the theoretical model. Simulating and experimental results show that the small-sized bubbles tend to generate in the turbulent cavitating flow when at a high rotary speed, and the bubbles mainly locate at the edges of the spiral groove. The simulating results also show that the direct stiffness coefficients are increased due to cavitation effect, and cross stiffness coefficients and damping coefficients are hardly affected by the cavitation effect. Turbulent effect on the dynamic characteristics of SGTB is much stronger than the cavitating effect.

Passive control of cavitating flow around an axisymmetric projectile by using a trip bar

Quasi-periodical evolutions such as shedding and collapsing of unsteady cloud cavitating flow, induce strong pressure fluctuations, what may deteriorate maneuvering stability and corrode surfaces of underwater vehicles. This paper analyzed effects on cavitation stability of a trip bar arranged on high-speed underwater projectile. Small scale water tank experiment and large eddy simulation using the open source software Open FOAM were used, and the results agree well with each other. Results also indicate that trip bar can obstruct downstream re-entrant jet and pressure wave propagation caused by collapse, resulting in a relatively stable sheet cavity between trip bar and shoulder of projectiles.

Cavitation Evolution Around a Twist Hydrofoil by Large Eddy Simulation(LES)with Mesh Adaption

The cavitating flow around a Delft Twist-11 hydrofoil is simulated using the large eddy simulation approach.The volume-of-fluid method incorporated with the Schnerr-Sauer cavitation model is utilized to track the water-vapor interface.Adaptive mesh refinement(AMR)is also applied to improve the simulation accuracy automatically.Two refinement levels are conducted to verify the dominance of AMR in predicting cavitating flows.Results show that cavitation features,including the U-type structure of shedding clouds,are consistent with experimental observations.Even a coarse mesh can precisely capture the phase field without increasing the total cell number significantly using mesh adaption.The predicted shedding frequency agrees fairly well with the experimental data under refinement level 2.This study illustrates that AMR is a promising approach to achieve accurate simulations for multiscale cavitating flows within limited computational costs.Finally,the force element method is currently adopted to investigate the lift and drag fluctuations during the evolution of cavitation structure.The mechanisms of lift and drag fluctuations due to cavitation and the interaction between vorticity forces and cavitation are explicitly revealed.

Generation and Evolution of Cavitation Bubbles in Volume Alternate Cavitation(VAC)

Cavitation generation methods have been used in multifarious directions because of their diversity,and numerous studies and discussions have been conducted on cavitation generation methods.This study aims to explore the generating mechanism and evolution law of volume alternate cavitation(VAC).In the VAC,liquid water is placed in an airtight container with a variable volume.As the volume alternately changes,the liquid water inside the container continues to cavitate.Then,the mixture turbulence model and in-cylinder dynamic grid model are adopted to conduct computational fluid dynamics simulation of volume alternate cavitation.In the simulation,the cloud images at seven heights on the central axis are monitored,and the phenomenon and mechanism of height and eccentricity are analyzed in detail.By employing the cavitation flow visualization method,the generating mechanism and evolution law of cavitation are revealed.The synergistic effects of experiments and high-speed camera capturing confirm the correctness of the simulation results.In the experiment,the volume change stroke of the airtight container is set to 20 mm,the volume change frequency is 18 Hz,and the shooting frequency of the high-speed camera is set to 10000 FPS.The experimental results indicate that the position of the cavitation phenomenon has a reasonable law during the whole evolution cycle of the cavitation cloud.Also,the volume alternation cycle corresponds to the generation,development,and collapse stages of cavitation bubbles.