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.

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.

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.

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.

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.

LES investigation of the tip vortex cavitating flow with special emphasis on the interaction between cavitation and vorticity by a modified cavitation model

Cavitation within the tip vortex(TV)flow remains a challenging issue in the design of high-speed and low-noise hydraulic machinery.In this paper,the TV cavitating flow around an elliptical hydrofoil is calculated by using large eddy simulation(LES)combined with a modified Schnerr-Sauer(S-S)cavitation model.The original S-S cavitation model is modified by taking into account the typical effect of vortex flow.The partial pressure term which can describe the vortex quantitatively and qualitatively is confirmed asρ_(m)ω^(2) x r _(c)^(2) ,and is considered into the R-P equation of the modified S-S cavitation model.Comparison between the numerical and experimental results shows good agreement in the form and evolution of cavities,including attached cavities(AC)and tip vortex cavities(TVC).The vorticity transport equation is utilized to investigate the dynamic mechanisms of the vortex development around the TVC.Further analyses indicate that cavitation in the TV flow influences the pressure in the core of the cavity and the local flow patterns.Typical vortex structures in the TV cavitating flow include TV,secondary vortex(SV)and wake vortex(WV).The direction and magnitude of the rotation effect can be described by axial vorticity which is drawn on the iso-surface of Q=1×105 s−2.The development of the TV cavitating flow can be divided into two stages:Stage I,the development and fusion of TV,SV,stage II,the dissipation of SV.The stretching term dominates the evolution of TV,and the dilatation term is the main reason in the mergence process of SV.

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 simulation unsteady cloud cavitating flow with a filter-based density correction model

In this paper, various turbulence closure models for unsteady cavitating flows are investigated. The filter-based model （FBM） and the density correction model （DCM） were proposed to reduce the turbulent eddy viscosities in a turbulent cavitating flow based on the local meshing resolution and the local fluid density, respectively. The effects of the resolution control parameters in the FBM and DCM models are discussed. It is shown that the eddy viscosity near the cavity closure region can significantly influence the cavity shapes and the unsteady shedding pattern of the cavitating flows. To improve the predictions, a Filter-Based Density Cor-rection model （FBDCM） is proposed, which blends the FBM and DCM models according to the local fluid density. The new FBDCM model can effectively represent the eddy viscosity, according to the multi-phase characteristics of the unsteady cavitating flows. The experimental validations regarding the force analysis and the unsteady cavity visualization show that good agreements with experimental visualizations and measurements are obtained by the FBDCM model. For the FBDCM model, the attached cavity length and the resulting hydrodynamic characteristics are subsequently affected by the detail turbulence modeling parameters, and the model is shown to be effective in improving the overall predictive capability.

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 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.

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.

A PRESSURE-BASED ALGORITHM FOR CAVITATING FLOW COMPUTATIONS

A pressure-based algorithm for the prediction of cavitating flows is presented.The algorithm employs a set of equations including the Navier-Stokes equations and a cavitation model explaining the phase change between liquid and vapor.A pressure-based method is used to construct the algorithm and the coupling between pressure and velocity is considered.The pressure correction equation is derived from a new continuity equation which employs a source term related to phase change rate instead of the material derivative of density Dρ/Dt.This pressure-based algorithm allows for the computation of steady or unsteady,2-D or 3-D cavitating flows.Two 2-D cases,flows around a flat-nose cylinder and around a NACA0015 hydrofoil,are simulated respectively,and the periodic cavitation behaviors associated with the re-entrant jets are captured.This algorithm shows good capability of computating time-dependent cavitating flows.

Measurement and prediction of cavitating flow-induced vibrations

The objective of this paper is to investigate the unsteady cavitation behaviors and the corresponding cavitating flow-induced vibrations. Results are presented for the modified NACA66 hydrofoils made of stainless steel and POM Polyacetate respectively at Re= 6.0×105for various cavitation regimes. The high-speed camera and the single point laser Doppler vibrometer(LDV) are used to observe the transient cavitating flow patterns and measure the vibration velocities. The results showed that the vibration amplitude increases dramatically for the cloud cavitation due to the development of large-scale cloud cavity. The main flow-induced frequencies, which are in accordance with the cavity shedding frequency, decrease with the decrease of the cavitation number. As for the effect of the hydroelastic response on the vibration behavior, the lift coefficient for the POM Polyacetate hydrofoil fluctuates more significantly with a larger mean value than that for the stainless steel hydrofoil. Compared with the vaporous cavity along the suction side of the stainless steel hydrofoil, the cavity for POM Polyacetate hydrofoil appears to be fragmentized. The main vibration frequencies for the POM Polyacetate hydrofoil are larger than that for the stainless steel hydrofoil, with the chaotic hydroelastic response with high frequency.

AN APPROACH IN MODELING TWO-DIMENSIONAL PARTIALLY CAVITATING FLOW

An approach of modeling viscosity, unsteady partially cavitating flows around lifting bodies is presented. By em ploying an one-fluid Navier-Stokers solver, the algorithm is proved to be able to handle two-dimensional laminar cavitating flows at moderate Reynolds numbe r. Based on the state equation of water-vapor mixture, the constructive relatio ns of densities and pressures are established. To numerically simulate the cavi ty wall, different pseudo transition of density models are presumed. The finite-volume method is adopted and the algorithm can be extended to three-dimensional cavitating 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.

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.

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.

Verification and validation of URANS simulations of the turbulent cavitating flow around the hydrofoil

In this paper, we investigate the verification and validation（V＆V） procedures for the URANS simulations of the turbulent cavitating flow around a Clark-Y hydrofoil. The main focus is on the feasibility of various Richardson extrapolation-based uncertainty estimators in the cavitating flow simulation. The unsteady cavitating flow is simulated by a density corrected model（DCM） coupled with the Zwart cavitation model. The estimated uncertainty is used to evaluate the applicability of various uncertainty estimation methods for the cavitating flow simulation. It is shown that the preferred uncertainty estimators include the modified Factor of Safety（FS1）, the Factor of Safety（FS） and the Grid Convergence Index（GCI）. The distribution of the area without achieving the validation at the U v level shows a strong relationship with the cavitation. Further analysis indicates that the predicted velocity distributions, the transient cavitation patterns and the effects of the vortex stretching are highly influenced by the mesh resolution.

Some notes on numerical simulation and error analyses of the attached turbulent cavitating flow by LES

In this letter, the attached turbulent cavitating flow around the Clark-Y hydrofoil is investigated by the numerical simulation with special emphasis on error analysis of large eddy simulation（LES） for the unsteady cavitation simulation. The numerical results indicate that the present simulation can capture the periodic cavity shedding behavior and show a fairly good agreement with the available experimental data. Further analysis demonstrates that the cavitation has a great influence on LES numerical error and modeling error. The modeling error and numerical error are almost on the same order of magnitude, while the modeling error often shows a little bit larger magnitude than numerical error. The numerical error and modeling error sometimes can partially offset each other if they have the opposite sign. Besides, our results show that cavitation can extend the magnitudes and oscillation levels of numerical error and modeling error.