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…     

AN APPROACH IN MODELING TWO-DIMENSIONAL PARTIALLY CAVITATING FLOW

1. INTRODUCTIONCavitation is a phenomenon that widely occurs in liquids. When the flow leads to the local pressure below the saturation vapor pressure of water (the fluid medium, in our research), usually incipient cavitation firstly occurs on the solid b…     

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.     

回转体空泡流特性研究

利用CFD商业软件F1uent 6．0中的基于Rayleigh-Plesset方程的单一介质可变密度混合模型进行了回转体空泡流特性研究。首先采用二维轴对称求解器进行了不同头体的空泡几何特性研究,及局部空泡阻力特性分析,探索了空泡减阻的机理。然后采用三维求解器进行了非零攻角空泡流及超空泡数值模拟。给出了较易产生空泡的头型,与实验结果符合得较好;得到了零攻角和非零攻角情况下的双空泡及超空泡形态。     

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.     

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 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 turbulence model,and its cavitation behaviors were studied.     

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.     

渠网非恒定流图论原理

基于明渠非恒定流普里斯曼的隐式差分方法,采用矩阵线性变换建立了渠道进出口流量与水深的线性方程。提出了新的渠网非恒定流图论原理,包括适应渠网非恒定流特征的节支关联矩阵A的构建方法及性质分析,基于A的节点连续性矩阵方程和节点水深矩阵方程等。应用矩阵分析方法,推导出渠网非恒定流的节点分析法数学模型,最后给出应用实例。     

带空泡轴对称细长体水动力脉动的实验研究

为了研究带空泡轴对称细长体定常来流下的水动力脉动特性，本文对四种头体模型进行了不同攻角下的空泡水洞实验，记录了水动力系数的时间序列，并对其进行了小波分析。本文运用小波分析方法从水动力脉动频率特征的角度揭示空泡流的脉动特性，是对何友声等(1997)用高速摄影方法研究空泡脉动的补充。     

A SPLIT-CHARACTERISTIC FINITE ELEMENT MODEL FOR 1-D UNSTEADY FLOWS

An efficient and accurate solution algorithm was proposed for 1-D unsteady flow problems widely existing in hydraulic engineering. Based on the split-characteristic finite element method, the numerical model with the Saint-Venant equations of 1-D unsteady flows was established. The assembled finite element equations were solved with the tri-diagonal matrix algorithm. In the semi-implicit and explicit scheme, the critical time step of the method was dependent on the space step and flow velocity, not on the wave celerity. The method was used to eliminate the restriction due to the wave celerity for the computational analysis of unsteady open-channel flows. The model was verified by the experimental data and theoretical solution and also applied to the simulation of the flow in practical river networks. It shows that the numerical method has high efficiency and accuracy and can be used to simulate 1-D steady flows, and unsteady flows with shock waves or flood waves. Compared with other numerical methods, the algorithm of this method is simpler with higher accuracy, less dissipation, higher computation efficiency and less computer storage.     

一种简洁有效的河道平面二维流动数值模型

本文提出了一种简洁有效的河道平面二维流动数值模型。模型采用跟踪河道中心线走向的正交曲线坐标系，曲线网格可用代数方法直接生成。这种河道正交曲线网格较好地适合了河流的形态特征及流动特性，模型基于显式有限差分，利用水面回算消除不稳定性。并使模型在空间和时间上均达到二阶精度。模型采用显式非恒定流渐近迭代法计算河流恒定流场，为了有效地抑制非线性不稳定性发展，二维模型初值由准二维计算结果提供。本文针对弯道水槽试验成果。多体绕流，边池回流和天然山区河流情况，对数值模型进行了测试和验证。结果表明，模型具有较强的模拟复杂流态的能力。     

绕扭曲翼型三维非定常空泡脱落结构的数值分析

该文以一种三维扭曲翼型为研究对象,采用均衡流空化模型和基于滤波器的湍流修改模式模拟了绕翼型非定常空化流动。计算结果显示,在一定条件下绕翼型的空泡流动存在两种脱落结构,即主体脱落和二次脱落。进一步的流场分析表明回射流和侧面射流是这两种空泡脱落结构产生的主要原因。计算结果与试验的比较说明,该文采用的数值模拟方法可成功模拟实验观测的空泡脱落现象。     

超空化水翼流场的DPIV实验研究

该文采用DPIV粒子成像测速系统对绕2D超空化水翼(Tulin翼)的空化流场进行了测量,研究了初生空化阶段,附着型片状空化阶段,空化云以及超空化四个阶段典型流场的速度分布及涡量分布。实验结果表明:在空化发展的四个阶段,相对于主流区域,空化流区域速度明显偏小;在整个流动区域,有两个速度梯度较大的区域,一个是空化区和水体主流区的交界面,一个是翼形表面的边界层区域。在空化发展的四个阶段邻近翼型尾部处均会产生一个大小近似相等的正向涡和一个反向涡,并且正向涡总是处于反向涡的下方,形成一组正向对涡。     

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...     

Compressible effect on the cavitating flow: A numeric study

To understand the effect of the compressibility on the cavitating flow, a compressible, multiphase, single component Reynolds averaged Navier-Stokes(RANS) solver is used to study the cavitating flow on a wedge in the present work. A barotropic equation of status is used. A non-linear model for compressibility in the mixture is adopted to capture the effect of the compressibility within the complex cavitation bubbly mixtures. An unsteady cavitation phenomenon is found in the numerical simulation. The numerical results of local compressibility and Mach number in the bubbly mixture are given. The mechanism responsible for the unsteady shedding of the bubbly mixture is discussed based on the numerical results.     

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.     

长距离输水系统的神经网络模型研究

常规特征线算法在仿真模拟长距离有压输水系统流量调节过渡过程时，存在计算时间较长等不足，故无法很好地满足实时控制和优化调度的需要．本文利用人工神经网络(ANN)所具有的高度非线性全局作用、良好的自适应性及联想记忆功能等优点，将人工神经网络引入到过渡过程的分析中，建立合适的神经网络模型，并通过该模型得出一系列计算成果．该成果与传统算法所得的结果相比较表明，人工神经网络在过渡流的分析中是可行的，并具有明显的优势．     

Three-dimensional large eddy simulation and vorticity analysis of unsteady cavi- taring flow around a twisted hydrofoil

Large Eddy Simulation (LES) was coupled with a mass transfer cavitation model to predict unsteady 3-D turbulent cavitating flows around a twisted hydrofoil. The wall-adapting local eddy-viscosity (WALE) model was used to give the Sub-Grid Scale (SGS) stress term. The predicted 3-D cavitation evolutions, including the cavity growth, break-off and collapse downstream, and the shedding cycle as well as its frequency agree fairly well with experimental results. The mechanism for the interactions between the cavitation and the vortices was discussed based on the analysis of the vorticity transport equation related to the vortex stretching, volumetric expansion/contraction and baroclinic torque terms along the hydrofoil mid-plane. The vortical flow analysis demonstrates that cavitation promotes the vortex production and the flow unsteadiness. In non-cavitation conditions, the streamline smoothly passes along the upper wall of the hydrofoil with no boundary layer separation and the boundary layer is thin and attached to the foil except at the trailing edge. With decreasing cavitation number, the present case has σ= 1.07, and the attached sheet cavitation becomes highly unsteady, with periodic growth and break-off to form the cavitation cloud. The expansion due to cavitation induces boundary layer separation and significantly increases the vorticity magnitude at the cavity interface. A detailed analysis using the vorticity transport equation shows that the cavitation accelerates the vortex stretching and dilatation and increases the baroclinic torque as the major source of vorticity generation. Examination of the flow field shows that the vortex dilatation and baroclinic torque terms increase in the cavitating case to the same magnitude as the vortex stretching term, while for the non-cavitating case these two terms are zero.