NUMERICAL SIMULATIONS OF CAVITATING FLOWS

BRIEFINTRODUCTIONOFTHEPAPER :　Thisthesismainlyresearchesonthehydrodynamiccharacteristicsandmechanismfor 3Dcavitatingflowsaroundaxisymmetricbodies ,aswellasthe2Dcavitatingflowsaroundhydrofoils .Anewcavi tatingflowmodel,whichinvolvesviscousandmul ti phaseeffects,isestablishedintwo phaseflowcategory .Accordingtothelocalizedvariationofdensitywithinpredominantlyincompressiblewatermediumandthecharacteristicsofsoundspeedinwater vapormixture ,arelationbetweendensityandpressureisassumed ,in…     

NUMERICAL SIMULATIONS OF 2D PERIODIC UNSTEADY CAVITATING FLOWS

1. INTRODUCTION Cavitation is a natural phenomenon especially existing in liquids. A cavitating flow generally involves a large number of vapor structures such as bubbles or vortices which are convecting downstream. When they reach high pressure zones, th…     

NUMERICAL ANALYSIS OF THE INFLUENCE OF THE TIP CLEARANCE FLOWS ON THE UNSTEADY CAVITATING FLOWS IN A THREE- D IMENSIONAL INDUCER

To clarify the influences of the tip clearance flows on the unsteady cavitating flow,the three-dimensional unsteady cavitating flows through both the two-dimensional cascades and the three-dimensional inducer with and without tip clearance are performed numerically.The governing equations for the compressible fluid flow with the DES turbulence model are employed with the assumption of the isentropic process of liquid phase.The evolution of cavities is represented as the source/sink of vapor phase.The basic equations in the curve linear coordinate are solved by the finite difference method.As the results of the three-dimensional cavitating flows through the two-dimensional cascades,the tip clearance flows from the pressure side to the suction side of the blade produces the tip vortex cavitation,which affects the sheet cavitation on the leading edge of the next blade and enhances the blockage effect near the casing than the flows without tip clearance.On the other hand,in the case of the three-dimensional inducer,the large backflow cavitation is observed around the inlet of the inducer,where the cavities are developed on the casing by the tip clearance flows.The large pressure gradient between the non-cavitating pressure side and the cavitating suction side enhances the tip clearance flows.The calculation considering the tip clearance reproduces the developed cavitation region similar to that of experimental visualizations.Additionally,the backflow cavitation rotates with the speed slower than the rotation speed of the inducer.Then,the rotation of backflow cavitation causes the periodic fluctuation of the outlet pressure greater than that of the inlet pressure.     

Shedding frequency of sheet cavitation around axisymmetric body at small angles of attack

Cavity shedding of cavitating flows around an axisymmetric body belongs to the unsteady cavitating flows in the condition of steady incoming current.The periodic characteristics of unsteady cavitating flows around an axisymmetric body at small angles of attack are investigated experimentally and numerically.The evolution and shedding process of the three-dimensional sheet cavitation are computed numerically by the Reynolds averaged Navier-Stokes equations and the RNG k-?model.The modification approach for eddy viscosity coefficient in the transition area of the two-phase flow is adopted to reproduce the shedding process of cavitating flows.The computed frequency of the cavity shedding coincides with the experimental data for the cases of unsteady cavitating flows around axisymmetric bodies with four headforms.Given the cavitation number,the shedding process of the cavitating flow depends heavily on the headform of the axisymmetric body.If the angle of attack of the axisymmetric body is greater than a critical value,the violent shedding of the sheet cavitation seems to be depressed.     

A review of cavitation in hydraulic machinery

This paper mainly summarizes the recent progresses for the cavitation study in the hydraulic machinery including turbopumps, hydro turbines, etc.. Especially, the newly developed numerical methods for simulating cavitating turbulent flows and the achievements with regard to the complicated flow features revealed by using advanced optical techniques as well as cavitation simulation are introduced so as to make a better understanding of the cavitating flow mechanism for hydraulic machinery. Since cavitation instabilities are also vital issue and rather harmful for the operation safety of hydro machines, we present the 1-D analysis method, which is identified to be very useful for engineering applications regarding the cavitating flows in inducers, turbine draft tubes, etc. Though both cavitation and hydraulic machinery are extensively discussed in literatures, one should be aware that a few problems still remains and are open for solution, such as the comprehensive understanding of cavitating turbulent flows especially inside hydro turbines, the unneglectable discrepancies between the numerical and experimental data, etc.. To further promote the study of cavitation in hydraulic machinery, some advanced topics such as a Density-Based solver suitable for highly compressible cavitating turbulent flows, a virtual cavitation tunnel, etc. are addressed for the future works.     

On the numerical simulations of vortical cavitating flows around various hydrofoils

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

THE WALL EFFECT ON VENTILATED CAVITATING FLOWS IN CLOSED CAVITATION TUNNELS

For ventilated cavitating flows in a closed water tunnel, the wall effect may exert an important influence on cavity shape and hydrodynamics, An isotropic mixture multiphase model was established to study the wall effect based on the RANS equations, coupled with a natural cavitation model and the RNG k-ε turbulent model. The governing equations were discretized using the finite volume method and solved by the Gauss-Seidel linear equation solver on the basis of a segregation algorithm. The algebraic multigrid approach was carried through to accelerate the convergence of solution. The steady ventilated cavitating flows in water tunnels of different diameter were simulated for a conceptual underwater vehicle model which had a disk cavitator. It is found that the choked cavitation number derived is close to the approximate solution of natural cavitating flow for a 3-D disk. The critical ventilation rate falls with decreasing diameter of the water tunnel. However, the cavity size and drag coeflicient are rising with the decrease in tunnel diameter for the same ventilation rate, and the cavity size will be much different in water tunnels of different diameter even for the same ventilated cavitation number.     

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

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.     

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-ε 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 o is the best choice for a given stern wake with a assigned thrust and the minimum force fluctuations.     

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 cav...     

Numerical investigation of the effect of rotation on cavitating flows over axisymmetric cavitators

The rotating axisymmetric cavitator is widely applied in underwater vehicles, and its rotational motion affects the cavitating flow over the cavitator. This study focuses on the effect of rotation on the flow structure in the cavity bubble. Unsteady 2-D/3-D numerical simulations of cavitating flows over axisymmetric cavitators are performed using the volume of fraction(VOF) method and the Sauer-Schnerr cavitation model. Firstly, the 2-D simulation of cavitating flow over a circular disk or a cone cavitator is carried out at various cavitation numbers(0.15, 0.175, 0.2, 0.225 and 0.25). The simulated cavity lengths and drag coefficients are compared with the experimental data, the theoretical estimations and the published numerical results. Then the 3-D simulations of cavitating flows over the same axisymmetric cavitators with different rotating speeds are performed using the sliding mesh model(SMM). The effect of rotation on the cavity shape and the internal flow structure is analyzed.     

Numerical prediction of hydrodynamic cavitating flow structures and their corresponding erosion

Hydrodynamic cavitating flows usually consist of 3-D intense vortical flows that are detached from solid boundaries.Detached vortical flows normally generate he...     

Progress in numerical simulation of cavitating water jets

This paper reviews recent progress made toward modeling of cavitation and numerical simulation of cavitating water jets. Properties of existing cavitation models are discussed and a compressible mixture flow method for the numerical simulation of highspeed water jets accompanied by intensive cavitation is introduced. Two-phase fluids media of cavitating flow are treated as a homogeneous bubbly mixture and the mean flow is computed by solving Reynolds-Averaged Navier-Stokes (RANS) equations for compressible fluid. The intensity of cavitation is evaluated by the gas volume fraction, which is governed by the compressibility of bubble-liquid mixture corresponding to the status of mean flow field. Numerical results of cavitating water jet issuing from an orifice nozzle are presented and its applicability to intensively cavitating jets is demonstrated. However, the effect of impact pressure caused by collapsing of bubbles is neglected, and effectively coupling of the present compressible mixture flow method with the dynamics of bubbles remains to be a challenge.     

带空泡运动航行体的附加质量研究

提出了确定带自然空泡运动物体附加质量的方法.这一方法基于在数值水洞中作摇荡运动物体的水动力计算, 包括两个主要步骤:首先采用CFD技术模拟空泡流场,求解水动力;然后根据物体运动方程,由水动力计算出附加质量.研究了带自然空泡圆盘和轴对称细长体的附加质量.计算结果与理论解一致,验证了本文方法的有效性.与切片法相比,本文方法可以更为准确地定量预报带空泡运动轴对称细长体的附加质量.     

基于高阶和高分辨率格式的自然空泡流数值模拟

基于有限体积通量修正,应用了一类高阶迎风对流格式:二阶迎风格式、二次迎风插值格式、三次迎风插值格式及带TVD限制器的高分辨率格式,对于自然空泡湍流流动的数值计算方法进行了研究.计算模型为轴对称圆盘,计算结果表明所有高阶格式都能有效抑制一阶迎风格式产生的假扩散,并得到了更薄,更"透明"的汽-液界面,其中高分辨率TVD格式最好地捕捉到了空泡界面附近物理量的阶跃特性关键词: 自然空泡;高阶迎风对流格式;汽-液界面     

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.     

The inception cavitating flows over an axisymmetric body with a blunt head-form

The inception cavitating flows around a blunt body are studied based on flow visualizations and velocity field measurements. The main purpose of the present work is to study the incipient cavity evolution and the interplay between the inception cavitation and the local turbulent flows. A high-speed video camera is used to visualize the cavitating flow structures, and the particle image velocimetry(PIV) technique is used to measure the velocity field, the vorticity, and the Reynolds stresses under non-cavitating and inception cavitating flow conditions. It is found that the appearance of visible cavities is preceded by the formation of a cluster of micro-bubbles not attached to the body surface and in a hairpin-shaped vortex structure. During its evolution, the cavity moves downstream with a lower speed. The effect of the incipient cavity is significant on the local vortical structures but slight on the timeaveraged velocity distribution. The mean Reynolds stress distributions in the turbulent shear flow can be substantially altered by the incipient cavities. The presence of the incipient cavities can lead to the production of turbulent fluctuations.     

修正的SST k-ω模型在云状空化流动计算中的应用研究

采用基于Rayliegh-Plesset方程的空化模型及实验结果,评价了修正的SST k-ω湍流模型在云状空化流动计算中的应用。采用不同的修正系数,分别计算了绕Clar k-y型水翼的云状空化流动,获得了随时间变化的空化形态和升、阻力等流场及动力特性。通过与实验结果的对比表明,修正后的模型可以更准确地捕捉云状空化区域的空穴形态和空泡脱落的非定常细节;密度函数中指数n的选取对计算所得的空穴长度、升阻力和主要频谱分布均有影响,并给出了n的合理取值范围,为后续水工模型的空化数值计算提供了参考依据。     

SIMILARITY SOLUTIONS FOR VISCOUS CAVITATING VORTEX CORES

Theoretical analysis of the dynamic behavior of cavitating vortices requires knowledge of the velocity distribution in the vortex core. For that reason an existing similarity model for slender axisymmetric non-cavitating vortex cores has been extended with the viscous boundary conditions for a cavitating vortex. Cavitating similarity solutions exist for a vortex of which both core diameter and circulation grow with the square root of the axial coordinate. Results for this model are presented for varying cavitation numbers and Reynolds numbers. It is shown that viscosity may have a significant influence on the velocity distribution around a cavitating vortex.     

IMPROVEMENT OF BUBBLE MODEL FOR CAVITATING FLOW SIMULATIONS

In the present research,a bubble dynamics based model for cavitating flow simulations is extended to higher void fraction region for wider range of applications.The present bubble model is based on the so-called Rayleigh-Plesset equation that calculates a temporal bubble radius with the surrounding liquid pressure and is considered to be valid in an area below a certain void fraction.The solution algorithm is modified so that the Rayleigh-Plesset equation is no more solved once the bubble radius(or void fraction)reaches at a certain value till the liquid pressure recovers above the vapor pressure in order to overcome this problem.This procedure is expected to stabilize the numerical calculation.The results of simple two-dimensional flow field are presented compared with the existing bubble model.