ON THE PARTIALLY CAVITATING FLOW AROUND TWO-DIMENSIONAL HYDROFOILS

The steady partially cavitating flow around two-dimensional hydrofoils was simulated numerically by the low-order potential-based boundary integration method. The cavity shape and length are determined for given cavitating numbers in the course of iteration by satisfying the kinematic and dynamic boundary conditions. The re-entrant jet model and the pressure-recovery close model are adopted to replace the high turbulent and two-phase wake forming behind the cavity. The results are compared with the other published numerical ones.     

Numerical modelling of cavities on axisymmetric bodies at zero and non-zero angle of attack

The flow about submerged, fully cavitating axisymmetric bodies at both zero and non-zero angle of attack is considered in this paper. A cavity closure model that relates the point of detachment, the angle that the separating streamline makes with the body and the cavity length is described. The direct boundary element method is used to solve the potential flow problem and to determine the cavity shape. A momentum integral boundary layer solver is included in the formulation so that shear stresses can be incorporated into the drag calculations. The numerical predictions based on the proposed closure model are compared with water tunnel measurements and photographs.     

A numerical method for simulation of attached cavitation flows

A new numerical algorithm for attached cavitation flows is developed. A cavitation model is implemented in a viscous Navier–Stokes solver. The liquid–vapour interface is assumed as a free surface boundary of the computation domain. Its shape is determined with an iterative procedure to match the cavity surface to a constant pressure boundary. The pressure distribution, as well as its gradient along the wall, is taken into account in updating the cavity shape iteratively. A series of computations are performed for the cavitating flows across three kinds of headform/cylinder bodies: conic, ogival and hemispheric heads. A range of cavitation numbers is investigated for each headform/cylinder body. The obtained results are reasonable and the iterative procedure of cavity shape updating is quite stable. The superiority of the developed cavitation model and algorithm is demonstrated. Copyright © 2006 John Wiley & Sons, Ltd.     

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.      

Effect of grain boundary sliding on creep constrained diffusive cavitation

For polycrystalline metals undergoing creep at high temperatures the nucleation, growth and coalescence of grain boundary cavities is investigated, with main focus on the influence of grain boundary sliding. Both the local stress state and the average rate of opening of a cavitating facet can be rather strongly affected by sliding on the grain boundaries emanating from the edges of this facet. A number of numerical solutions of axisymmetric model problems are used to study the combined influence of sliding and cavitation. The time to creep rupture by cavity coalescence is significantly reduced by grain boundary sliding, as is seen by comparison with analyses that disregard sliding. The numerical results are compared with predictions of a set of constitutive relations for creep in polycrystals with grain boundary cavitation.     

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.      

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.     

空化、超空化流动的数值模拟方法研究

基于结构化网格,运用可压缩流N—S方程及k-ε湍流模型对流场进行求解,在低压区域引入一种基于混合密度函数的空化模型对轴对称体的空化、超空化流动进行了数值模拟．通过将半球圆柱的计算结果与实验数据和前人的计算结果进行对比,验证了所发展的数值方法的可靠性．最后,采用非定常的数值方法,研究了钝头体射弹的空化、超空化流动特性,并模拟了其超空泡的发展过程．     

Influence of cavitation on the hydroelastic stability of hydrofoils

This work numerically examines the effect of turbulent and cavitating flow on the hydroelastic response and stability of a hydrofoil. A cantilevered, rectangular, chordwise rigid hydrofoil is modeled as a 2-degrees-of-freedom structure for its spanwise bending and torsional flexibilities. The fluid flow is modeled with the incompressible, Unsteady Reynolds Averaged Navier–Stokes equations using an eddy-viscosity turbulence closure model that is corrected for the presence of cavitation, and with a transport equation based cavitation model. The results show that, in general, massive cavitation tends to: (i) reduce the mean lift, (ii) increase the mean drag, (iii) lower the mean deformations, and (iv) delay static divergence, while unsteady sheet/cloud cavitation promotes flow induced vibrations. Such vibrations and load fluctuations could be as large as (and even greater than) the mean values for cases with unsteady cavitation, so dynamic and viscous fluid–structure models are needed to simulate flexible hydrofoils in cavitating flows. In general, the flow induced vibrations, and hence the drag force, are higher with decreasing stiffness. For small leading edge partial cavitation, increasing foil flexibility increases the maximum cavity length and reduces the cavity shedding frequency; however, the influence of foil flexibility is limited for cases where the maximum cavity length is near or beyond the foil trailing edge, because of the relocation of the center of pressure at the elastic axis, near the mid-chord. The results show that the mean deformations are generally limited by stall, and by the quasi-steady linear theory predictions at the fully-wetted and supercavitating limits. Furthermore, frequency focusing can occur when the cavity shedding frequency is near the fundamental system resonance frequencies, and broadening of the frequency spectrum can occur due to excitation of the sub-harmonics and/or modulation induced by the fluctuating cavities, if the cavity shedding frequency is away from the fundamental system resonance frequencies.     

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.     

深埋隧道地震动力响应的复反应分析

采用高速摄影技术对定常来流中ＮＡＣＡ４４１２翼的不稳定的空泡流形态特征进行了水洞试验研究．试验结果揭示了由于空泡形态断裂而产生的低频脉动现象．这一现象在跨空泡流（Ｔｒａｎｓ－ｃａｖｉｔａｔｉｎｇｆｌｏｗ）情况下尤为明显，常使空泡长度和厚度在大幅范围内拟周期地变动，其频率特性比较稳定，有别于空泡末端局部泡团脱落而产生的脉动     

超空泡航行体转弯运动流体动力特性的数值研究

基于有限体积法,采用两流体多相流模型和SST(Shear Stress Transport)湍流模型,建立了用于求解超空泡航行体转弯运动过程中的三维数值模型,研究了转弯运动条件下通气空泡的形态特征及超空泡航行体的流体动力特性。计算结果表明:在转弯运动过程中空泡产生弯曲变形,空泡轴线与航行体运动轨道基本重合;由于空泡的弯曲变形航行体两侧表面呈现非对称沾湿,利用空化器横向偏转能够避免沾湿区的出现,而且对航行体水平面流体动力有良好的控制作用。     

Une technique de suivi d'interfaces pour la modélisation de la cavitation par poche

A tracking method is presented for the modeling of partial and supercavitation. The velocity and pressure fields in the cavitating flow are computed by a Navier–Stokes solver using a pseudo-compressibility method. The cavity flow is computed from the velocity field by a tracking method based on a volume of fluid technique (VOF). The method is illustrated by several computations, two cases of partial cavitation on a hydrofoil and a case of a cavitating body emerging at a free surface.     

Experimental evaluation of numerical simulation of cavitating flow around hydrofoil

Cavitation in hydraulic machines causes different problems that can be related to its unsteady nature. An experimental and numerical study of developed cavitating flow was performed. Until now simulations of cavitating flow were limited to the self developed “in house” CFD codes. The goal of the work was to experimentally evaluate the capabilities of a commercial CFD code (Fluent) for simulation of a developed cavitating flow. Two simple hydrofoils that feature some 3D effects of cavitation were used for the experiments. A relatively new technique where PIV method combined with LIF technique was used to experimentally determine the instantaneous and average velocity and void ratio fields (cavity shapes) around the hydrofoils. Distribution of static pressure on the hydrofoil surface was determined. For the numerical simulation of cavitating flow a bubble dynamics cavitation model was used to describe the generation and evaporation of vapour phase. An unsteady RANS 3D simulation was performed. Comparison between numerical and experimental results shows good correlation. The distribution and size of vapour structures and the velocity fields agree well. The distribution of pressure on the hydrofoil surface is correctly predicted. The numerically predicted shedding frequencies are in fair agreement with the experimental data.     

基于面元法回转体定长局部空泡的绕流计算

基于面元法 ,通过在回转体和空泡壁面放置源汇 ,对回转体定长局部空泡的绕流问题进行计算和分析 ,并讨论了空泡尾部速度过渡闭合模型对绕流计算的影响。计算结果表明 :本文的方法具有快速收敛的特征 ,第 1次叠代和最终收敛时空泡壁面切向速度的误差不超过 5 % ;随着回转体面元总数N的增加 ,局部空泡的空泡数趋于稳定 ;当回转体线型一定时 ,空泡数将随着局部空泡长度的增大而减小     

High speed digital imaging of cavitating vortices

 Researchers at the Cavitation and Multiphase Flow Laboratory of the University of Michigan worked in conjunction with Princeton Scientific Instruments (PSI) engineers to employ a new digital imaging system in the study of partial attached cavitation. The new high speed solid state system, the Princeton Scientific Ultra Fast Framing Camera (UFFC), was designed for cavitation studies where framing rates of 10⁵–10⁶ frames/s are required to image the detailed mechanisms of cavitating flows. The UFFC, which uses a PSI patented Charge Coupled Device (CCD) array image sensor, was designed to capture 30 frames at a maximum framing rate of 1 million frames/second. In these experiments, a maximum framing rate of 125000 frames per second (8 μs/frame) was used to examine cavitating vortices in the closure region of a partial attached cavity. The vortical structures in the closure region of the attached cavity were imaged, and the evolution and collapse of these flow structures were examined. Relationships between the cavitating vortices size, strength, and collapse time were observed. Received: 15 November 1996/Accepted: 1 December 1997     

可压缩空化流动空穴演化及压力脉动特性实验研究

空化流动具有高度的压缩性,空化流动非定常特性及其流体动力与压缩性密切相关.为研究可压缩空化流动空泡脱落的回射流和激波机制下周期性空穴结构演化及其诱导流体动力特性,本文采用多场同步测试方法对典型云状空化流动进行了实验研究,获得了文丘里管扩张段内部云状空化空穴形态演化及其诱导同步壁面压力脉动信号.并基于数字图像处理技术,对附着型片状空穴和脱落型云状空穴结构演化进行了精细化定量分析.结果表明:可压缩空化流动回射流机制下,空穴演化呈现附着型空穴生长$\!$-$\!$-$\!$回射流产生及发展$\!$-$\!$-$\!$附着型空穴失稳断裂及大尺度空泡云团产生脱落的非定常过程,激波机制下空穴演化具有附着型空穴生长$\!$-$\!$-$\!$激波产生及传播$\!$-$\!$-$\!$附着型空穴失稳断裂及大尺度空泡云团脱落的非定常特征,激波传播时间占空穴脱落周期小于回射流推进.激波与空穴相互作用导致空穴内部含气率瞬间大范围大幅度下降,诱导复杂流体动力.激波传播过程中,空泡内部压力脉动大幅增加,激波前缘诱导压力脉冲,而回射流推进过程中,壁面压力脉动相对平稳,回射流头部存在小幅增加. 不同机制下空穴结构存在显著差异,具有不同的相间质量传输过程.      

Time-dependent hydroelastic analysis of cavitating propulsors

A 3-D potential-based boundary element method (BEM) is coupled with a 3-D finite element method (FEM) for the time-dependent hydroelastic analysis of cavitating propulsors. The BEM is applied to evaluate the moving cavity boundaries and fluctuating pressures, as well as the added mass and hydrodynamic damping matrices. The FEM is applied to analyze the dynamic blade deformations and stresses due to pressure fluctuations and centrifugal forces. The added mass and hydrodynamic damping matrices are superimposed onto the structural mass and damping matrices, respectively, to account for the effect of fluid–structure interaction. The problem is solved in the time-domain using an implicit time integration scheme. An overview of the formulation for both the BEM and FEM is presented, as well as the BEM/FEM coupling algorithm. Numerical and experiment validation studies are shown. The effects of fluid–structure interaction on the propeller performance are discussed.     

收缩扩张管内液氮空化流动演化过程试验研究

本文基于低温空化试验平台研究了收缩扩张流道内液氮非定常空化流动的演化过程. 试验采用高时空分辨率的高速摄像机对77 K液氮在不同空化数σ下空穴结构的演变进行了精细化的分析和研究. 利用试验得到的空穴长度和面积等数据, 定量分析了液氮空化流动的非定常特性与时空演变规律. 研究结果表明: (1)在相似来流速度和温度条件下, 随着空化数的减小, 液氮空化流动呈现四种典型流型, 空穴长度在2.5 h以内为初生空化、空穴长度在2.5 h ~ 7.5 h之间为片状空化、空穴长度在7.5 h ~ 15 h之间为大尺度云状空化, 空穴长度超过15 h为双云状空化, 且在大尺度云状空化和双云状空化阶段均捕捉到了回射流现象; (2)液氮空化流动从初生空化到双云状空化, 脱落空穴的尺度逐渐增大, 空穴面积脉动的幅值和准周期均有所增加. 同时, 在大尺度云状空化与双云状空化阶段, 喉口处堵塞效应对空化流动的影响显著增强; (3)相比于初生空化, 片状空化、大尺度云状空化以及双云状空化中脱落空穴的移动距离依次增加了0.97倍、2.65倍与2.68倍, 溃灭时间依次增加了1.18倍、3.59倍与4.47倍, 但溃灭速度依次减小了0.10倍、0.20倍与0.30倍. 除此之外, 对于双云状空化阶段, 存在两种显著不同的脱落空穴演化过程.