翼型空泡周期性流动的数值模拟及机理分析

采用基于正压关系的均质平衡流空化模型和低雷诺数修正的k-ε湍流模式,自行开发了空泡流数值模拟方法和计算软件,对绕翼型空泡的周期性流动现象进行了数值模拟.计算结果与实验数据的对比表明,空泡的宏观特征、流动特性、周期性脱落的斯坦顿数St等与试验结果接近,验证了计算结果的可靠性.空泡在大约一个周期的2/3时间段内成长,并在大约1/3周期时刻发生断裂脱落.这两个特征时间与高速摄像实验结果一致.所取工况对应的组合参数σ/2α=2.865,以翼弦长计算可得St=0.217,与文献的最新试验结果吻合.空泡周期性运动过程中升阻系数也周期性振荡,时均值C<,1>=0.41,C<,d>=0.097,振荡频率与空泡脱落频率一致.对空泡运动过程中流场结构的变化进行了分析,结果表明在大攻角条件下,空泡闭合区后的逆压梯度导致涡的形成及回射流的发展,沿壁面逆向流动的混合介质射流是引起空泡断裂的原因,回射流发展、涡结构变化与空泡非稳态演化过程存在密切的联系,探讨了翼型空泡发生周期性脱落的一些机理.     

绕三维水翼云状空化现象的实验研究

为了研究云状空化阶段空穴发展和脱落的机理,采用实验的方法对绕三维水翼云状空化流动进行了研究.实验在高速水洞中进行,采用高速摄像技术研究了不同空化阶段的空穴形态,并测量了翼型所受的升阻力,并对上述数据进行了频谱分析.结果发现:在云状空化阶段,观测到空穴的产生-发展-脱落-溃灭的准周期性变化;并捕捉到空泡脱落时附着在翼型前...     

Numerical simulation of cavitating flow in 2D and 3D inducer geometries

A computational method is proposed to simulate 3D unsteady cavitating flows in spatial turbopump inducers. It is based on the code FineTurbo, adapted to take into account two‐phase flow phenomena. The initial model is a time‐marching algorithm devoted to compressible flow, associated with a low‐speed preconditioner to treat low Mach number flows. The presented work covers the 3D implementation of a physical model developed in LEGI for several years to simulate 2D unsteady cavitating flows. It is based on a barotropic state law that relates the fluid density to the pressure variations. A modification of the preconditioner is proposed to treat efficiently as well highly compressible two‐phase flow areas as weakly compressible single‐phase flow conditions. The numerical model is applied to time‐accurate simulations of cavitating flow in spatial turbopump inducers. The first geometry is a 2D Venturi type section designed to simulate an inducer blade suction side. Results obtained with this simple test case, including the study of its general cavitating behaviour, numerical tests, and precise comparisons with previous experimental measurements inside the cavity, lead to a satisfactory validation of the model. A complete three‐dimensional rotating inducer geometry is then considered, and its quasi‐static behaviour in cavitating conditions is investigated. Numerical results are compared to experimental measurements and visualizations, and a promising agreement is obtained. Copyright © 2004 John Wiley & Sons, Ltd.     

Numerical simulation of multiphase cavitating flows around an underwater projectile

The present simulation investigates the multiphase cavitating flow around an underwater projectile. Based on the Homogeneous Equilibrium Flow assumption, a mixture model is applied to simulate the multiphase cavitating flow including ventilated cavitation caused by air injection as well as natural cavitation that forms in a region where the pressure of liquid falls below its vapor pressure. The transport equation cavitating model is applied. The calculations are executed based on a suite of CFD code. The hydrodynamics characteristics of flow field under the interaction of natural cavitation and ventilated cavitation is analyzed. The results indicate that the ventilated cavitation number is under a combined effect of the natural cavitation number and gas flow rate in the multiphase cavitating flows.     

Compressible simulations of bubble dynamics with central-upwind schemes

This paper discusses the implementation of an explicit density-based solver, that utilises the central-upwind schemes for the simulation of cavitating bubble dynamic flows. It is highlighted that, in conjunction with the Monotonic Upstream-Centered Scheme for Conservation Laws (MUSCL) scheme they are of second order in spatial accuracy; essentially they are high-order extensions of the Lax–Friedrichs method and are linked to the Harten Lax and van Leer (HLL) solver family. Basic comparison with the predicted wave pattern of the central-upwind schemes is performed with the exact solution of the Riemann problem, for an equation of state used in cavitating flows, showing excellent agreement. Next, the solver is used to predict a fundamental bubble dynamics case, the Rayleigh collapse, in which results are in accordance to theory. Then several different bubble configurations were tested. The methodology is able to handle the large pressure and density ratios appearing in cavitating flows, giving similar predictions in the evolution of the bubble shape, as the reference.     

PANS模型在空化湍流数值计算中的应用

采用一种基于标准k-ε模型改进的局部时均化模型（Partially-Averaged Navier-Stokes Model,PANS）,并应用于空化流动计算。控制不同的模型参数,分别对绕平头轴对称回转体和Clark-Y型水翼的空化流动进行模拟,并与实验结果进行对比。结果表明：PANS模型中未分解湍动能比率fk的取值对预测空化流动的数值计算精度有重要影响,改变fk的取值可实现对不同滤波尺度范围内的求解;随着fk值的减小PANS的预测精度逐步提高,能在相对较大范围内求解较小尺度的湍流运动过程中,预测到湍流运动中强烈的非定常特性;同时可以比较准确地预测空化流场结构和动力特性。     

一种修正的低温流体空化流动计算模型

为了更准确地预测低温流体的空化流动特性, 基于Kubota空化模型, 对蒸发和凝结源项进行修正, 建立了一种考虑热力学效应的空化模型. 分别采用原始和修正的Kubota空化模型, 计算了绕对称回转体液氮的空化流动, 通过与实验结果的比较对修正的空化模型进行了评价. 结果表明, 与原Kubota空化模型比较, 修正的空化模型由于考虑了热力学效应, 计算获得的蒸发量减小, 凝结量增大, 空穴长度减小, 空穴界面形态呈模糊状态.计算结果与实验结果更加一致, 说明修正的空化模型能准确的描述低温流体空化过程的质量传输过程, 能够更准确模拟低温流体中的空化流动特性.      

A high-order nodal discontinuous Galerkin method to solve preconditioned multiphase Euler/Navier-Stokes equations for inviscid/viscous cavitating flows

In this study, a high-order accurate numerical method is applied and examined for the simulation of the inviscid/viscous cavitating flows by solving the preconditioned multiphase Euler/Navier-Stokes equations on triangle elements. The formulation used here is based on the homogeneous equilibrium model considering the continuity and momentum equations together with the transport equation for the vapor phase with applying appropriate mass transfer terms for calculating the evaporation/condensation of the liquid/vapor phase. The spatial derivative terms in the resulting system of equations are discretized by the nodal discontinuous Galerkin method (NDGM) and an implicit dual-time stepping method is used for the time integration. An artificial viscosity approach is implemented and assessed for capturing the steep discontinuities in the interface between the two phases. The accuracy and robustness of the proposed method in solving the preconditioned multiphase Euler/Navier-Stokes equations are examined by the simulation of different two-dimensional and axisymmetric cavitating flows. A sensitivity study is also performed to examine the effects of different numerical parameters on the accuracy and performance of the solution of the NDGM. Indications are that the solution methodology proposed and applied here is based on the NDGM with the implicit dual-time stepping method and the artificial viscosity approach is accurate and robust for the simulation of the inviscid and viscous cavitating flows.     

Dynamics of cavitation–structure interaction

Cavitation–structure interaction has become one of the major issues for most engineering applications. The present work reviews recent progress made toward developing experimental and numerical investigation for unsteady turbulent cavitating flow and cavitation–structure interaction. The goal of our overall efforts is to(1) summarize the progress made in the experimental and numerical modeling and approaches for unsteady cavitating flow and cavitation–structure interaction,(2) discuss the global multiphase structures for different cavitation regimes, with special emphasis on the unsteady development of cloud cavitation and corresponding cavitating flow-induced vibrations,with a high-speed visualization system and a structural vibration measurement system, as well as a simultaneous sampling system,(3) improve the understanding of the hydroelastic response in cavitating flows via combined physical and numerical analysis, with particular emphasis on the interaction between unsteady cavitation development and structural deformations. Issues including unsteady cavitating flow structures and cavitation–structure interaction mechanism are discussed.     

Experiments and modeling of cavitating flows in venturi: attached sheet cavitation

Correlated experimental and numerical studies were carried out to analyze cavitating flows and to describe the two-phase flow structures of attached sheet cavitation in Venturi geometries. New double optical probe measurements were performed and special data processing methods were developed to estimate void ratio and velocity fields for cold water flows.By applying a computational method previously developed in LEGI (Laboratoire des Ecoulements Géophysiques et Industriels, Grenoble, France) based on the code Fine^TM/Turbo and on a barotropic approach, several steady calculations were performed in cold water cavitating flows. Local and global analyzes based on comparisons between experimental and numerical results were proposed.     

Numerical study of unsteady turbulent cavitating flows

The simulation of cavitating flows is a challenging problem both in terms of modelling the physics and developing robust numerical methodologies. Such flows are characterized by important variations of the local Mach number, compressibility effects on turbulence and involve thermodynamic phase transition. To simulate these flows by applying homogeneous models and Reynolds averaged codes, the turbulence modelling plays a major role in the capture of unsteady behaviours. This paper presents a one-fluid compressible Reynolds-Averaged Navier–Stokes (RANS) solver with a simple equation of state (EOS) for the mixture. A special focus is devoted to the turbulence model influence. Unsteady numerical results are given for Venturi geometries and comparisons are made with experimental data.     

Experimental determination of the speed of sound in cavitating flows

This paper presents measurements of the speed of sound in two-phase flows characterized by high void fraction. The main objective of the work is the characterization of wave propagation in cavitating flows. The experimental determination of the speed of sound is derived from measurements performed with three pressure transducers, while the void fraction is obtained from analysis of a signal obtained with an optical probe. Experiments are first conducted in air/water mixtures, for a void fraction varying in the range 0–11%, in order to discuss and validate the methods of measurement and analysis. These results are compared to existing theoretical models, and a nice agreement is obtained. Then, the methods are applied to various cavitating flows. The evolution of the speed of sound according to the void fraction α is determined for α varying in the range 0–55%. In this second configuration, the effect of the Mach number is included in the spectral analysis of the pressure transducers’ signals, in order to take into account the possible high flow compressibility. The experimental data are compared to existing theoretical models, and the results are then discussed.     

Implementation of phase change thermodynamic probability for unsteady simulation of cavitating flows

The aim of this work is to investigate the non‐equilibrium effects of phase change in cavitating flows. For this purpose, the concept of phase change thermodynamic probability is used along with homogeneous model to simulate two‐phase cavitating flows. For simulation of unsteady behaviors of cavitation, which have practical applications, unsteady PISO algorithm based on the non‐conservative approach is utilized. For multi‐phase simulation, single‐fluid Navier–Stokes equations, along with the volume fraction transport equation, are employed. In this paper, phase change thermodynamics probabilities and cavitation model is briefly summarized. Thus, derivation of the cavitation model, starting from the basic thermodynamic equations to the mass and momentum conservation equations at a liquid–vapor two‐phase flow, is presented to explain the numerical model. Unsteady simulations of cavitation around a flat plate normal to flow direction are presented to clarify the accuracy of the model. The accuracy of the numerical results is good, and it is possible to apply this method to more complex geometries. Copyright © 2010 John Wiley & Sons, Ltd.     

Interfacial dynamics‐based modelling of turbulent cavitating flows,Part‐2: Time‐dependent computations

The interfacial dynamics‐based cavitation model, developed in Part‐1, is further employed for unsteady flow computations. The pressure‐based operator‐splitting algorithm (PISO) is extended to handle the time‐dependent cavitating flows with particular focus on the coupling of the cavitation and turbulence models, and the large density ratio associated with cavitation. Furthermore, the compressibility effect is important for unsteady cavitating flows because in a water–vapour mixture, depending on the composition, the speed of sound inside the cavity can vary by an order of magnitude. The implications of the issue of the speed of the sound are assessed with alternative modelling approaches. Depending on the geometric confinement of the nozzle, compressibility model and cavitation numbers, either auto‐oscillation or quasi‐steady behaviour is observed. The adverse pressure gradient in the closure region is stronger at the maximum cavity size. One can also observe that the mass transfer process contributes to the cavitation dynamics. Compared to the steady flow computations, the velocity and vapour volume fraction distributions within the cavity are noticeably improved with time‐dependent computations. Copyright © 2004 John Wiley & Sons, Ltd.     

Local flows of a deformable damageable medium under impact interaction with a cavitating fluid

Local viscoplastic-flow and damage processes in a deformable medium induced by the collapse of dispersed vapor-gas bubbles in the near-wall layer of a cavitating fluid in the presence of propagating shock waves are investigated. The study is based on a generalized model developed for describing nonlinear deformations and flow of damageable media and on the results obtained earlier for local fluid flows induced by limiting transitions of vapor-gas bubbles.     

Reduced-order modeling of three-dimensional unsteady partial cavity flows

An efficient reduced-order modeling to analyze three-dimensional unsteady partial cavity flows is proposed. The proposed approach is based on the boundary element method along with the potential flow assumption. To this end, a novel non-iterative method based on the flow eigenmodes of three-dimensional partial cavity flows is applied. Eigenanalysis and reduced-order modeling for unsteady flows over a three-dimensional hydrofoil with various sections are performed. The results obtained from the present analysis are compared with those reported in the literature to verify the strength of the proposed approach. In order to examine the performance of the introduced algorithm for unsteady cavitating flows, various simulations for several reduced frequencies, hydrofoil geometries and different cavitation numbers are also investigated. Comparison between the obtained results using the novel and conventional methods indicates that the present algorithm works very well with sufficient accuracy. Moreover, it is shown that the proposed method is computationally more efficient than the conventional ones for unsteady sheet cavitation analysis on three-dimensional hydrofoils.     

Numerical simulation of the unsteady behaviour of cavitating flows

A 2D numerical model is proposed to simulate unsteady cavitating flows. The Reynolds‐averaged Navier–Stokes equations are solved for the mixture of liquid and vapour, which is considered as a single fluid with variable density. The vapourization and condensation processes are controlled by a barotropic state law that relates the fluid density to the pressure variations. The numerical resolution is a pressure‐correction method derived from the SIMPLE algorithm, with a finite volume discretization. The standard scheme is slightly modified to take into account the cavitation phenomenon. That numerical model is used to calculate unsteady cavitating flows in two Venturi type sections. The choice of the turbulence model is discussed, and the standard RNG k–εmodel is found to lead to non‐physical stable cavities. A modified k–εmodel is proposed to improve the simulation. The influence of numerical and physical parameters is presented, and the numerical results are compared to previous experimental observations and measurements. The proposed model seems to describe the unsteady cavitation behaviour in 2D geometries well. Copyright © 2003 John Wiley & Sons, Ltd.     

绕栅中水翼空化流动的数值和实验研究

采用数值计算和实验研究的方法研究了绕水翼和栅中水翼的非定常空化流动. 实验采用高速录像技术分别观察了绕水翼和栅中水翼云状空化形态随时间的变化, 测量了升阻力, 并对测量数据进行了频率分析. 计算时空化模型选用了能比较准确描述旋涡空化非定常特性的Kubota模型, 湍流模型采用能准确捕捉流场非定常特性的FBM模型. 计算模型的可靠性用实验结果进行验证. 结果表明, 计算与实验的结果基本一致, 相比绕单个水翼的空化流动, 绕栅中水翼的空穴厚度比较薄, 翼型近壁处的逆压梯度较小, 反向射流的速度较小, 且水汽混合区速度梯度较小, 空穴的脱落周期变长, 平均升阻力系数较小      

质量传输模型在考虑热力学效应空化流动计算中的应用评价

通过二次开发技术，将Merkle、Kunz、Kubota、Singhal四种不同的质量传输模型和液氮物质属性随温度变化函数等引入了计算软件CFX。在考虑热力学效应的条件下，对绕翼型的液氮空化流动进行了数值计算，并与实验结果进行对比分析。结果表明：由于传输方程的物理机制不同，造成各模型的计算结果尤其是对热力学效应影响的描述存在明显的差别。Merkle模型计算得到的压力和温度分布与实验最为接近，质量传输过程能较好地反映温度场变化的影响，从而能较好地反映热力学效应对空化发展的影响；Singhal模型计算得到的结果与实验数据差距最大，其模拟得到的质量传输过程不能很好地反应温度流场的变化的影响。     

空化可压缩流动空穴溃灭激波特性研究

为深入研究空化可压缩流动中空泡/空泡团溃灭过程中激波产生、传播及其与空穴相互作用规律,本文采用数值模拟方法对空化可压缩流动空穴溃灭激波特性展开了研究.数值计算基于OpenFOAM开源程序,综合考虑蒸汽相和液相的压缩性,通过在原无相变两相可压缩求解器的控制方程中耦合模拟空化汽液相间质量交换的源项,实现了对空化流动的非定常可压缩计算.利用上述考虑汽/液相可压缩性的空化流动求解器,对周期性云状空化流动进行了数值模拟,并重点研究了空穴溃灭激波特性.结果表明:上述数值计算方法可以准确捕捉到空穴非定常演化过程及大尺度脱落空泡云团溃灭激波现象,大尺度脱落空泡云团溃灭过程分为3个阶段:(1) U型空泡团形成; (2) U型空泡团头部溃灭; (3) U型空泡团腿部溃灭.在U 型空泡团腿部溃灭瞬间,观察到激波产生,并向上游和下游传播,向上游传播的激波与空穴相互作用,导致水翼吸力面新生的附着型片状空穴回缩,直至完全溃灭.并且空穴溃灭激波存在回弹现象, 抑制了下一周期的空化发展.