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.

Effect of compressibility on bubbly cavitating flows

Cavitating bubbly flows can form in separated flows and shear layers leading to local regions high vapor void fraction,and these flows often exhibit periodic shedding of vaporous clouds.Historically,the presence of a liquid re-entrant flow,driven by the kinematics of liquid flow stagnation,has been identified as an important mechanism leading to cavity shedding.However,high local vapor void fractions can also result in a reduced mixture speed of sound and a possible supersonic flow.Our recent findings on different geometries indicate that propagating bubbly shocks in these flows are a primary mechanism of flow instability.In this study,we discuss the effect of compressibility on four geometries,mainly in the generation of propagating bubbly shocks that can influence the cavitation shedding dynamics.In order to elucidate the differences and similarities of the observed cavitation dynamics,and the influence of compressibility,we report observations from a backward facing step,backward facing wedge,NACA0015 hydrofoil,and a bluff body with a wedge cross section.

CAVITATION BEHAVIOR OF A NACA16-012 HYDROFOIL

Numerical and experimental study is carried to investigate the cavitation behavior in the turbulent flow around a NACA16-012 hydrofoil. The Navier-Stokes Equations for compressible fluid are adopted to simulate the overall motion and dynamical characteristics of the cavity flow, while the bubble dynamics is used to calculate the motion and growth of nuclei inside the cavity. Cavitation experiment for the hydrofoil is carried out in a water tunnel of CSS-RC, the phenomenon in the experiment is recorded and analyzed with high speed photographic technique.

Hydrodynamic mechanisms of aggressive collapse events in leading edge cavitation

Transient cavities generated from unsteady leading-edge cavitation may undergo aggressive collapses which are responsible for cavitation erosion.In this paper,we studied the hydrodynamic mechanisms of these events in the leading edge cavitation fonned over a modified NACA0009 hydrofoil using experimental and numerical methods.In the experimental investigation,high-speed visualization(HSV)and paint test are employed to study the behavior of the cavitating flow at σ=1.25,α=5°,U∞=20 m/s.In the numerical part,the same cavitating flow is simulated using an inviscid density-based compressible solver with a barotropic cavitation model.The numerical results are first compared with the experimental HSV to show that the simulation is able to reproduce the main features of the cavitating flow.Then,as the compressible solver is capable of capturing the shock wave upon the collapse of cavities,the location of collapse events with high erosion potential are determined.The location of these collapse events are compared with the paint test results with a qualitatively good agreement.It is clearly observed,in both the experiments and the numerical simulation,that there exists four distinct regions along the hydrofoil with higher risks of erosion:(1)A very narrow strip at the leading edge,(2)an area of accumulated collapses at around 60 percent of the sheet cavity maximum length,(3)an area around the closure line of the sheet cavity with the highest erosion damage,and(4)a wide area close to the trailing edge with dispersed collapse events.A combined analysis of the experimental and numerical results reveals that the small-scale structures generated by secondary shedding are more aggressive than the large-scale cloud cavities(primary shedding).It is also observed that the high risk of cavitation erosion in regions 2 and 3 is mainly due to the collapses of the small cavity structures that are formed around the sheet cavity closure line or the rolling cloud cavity.

原型水泵水轮机过渡过程可压缩空化流动模拟

在模型水泵水轮机空化两相流动模拟研究中,通常不考虑水流压缩性对压力脉动的影响,但在原型水泵水轮机过渡过程计算中,该影响显著。因此,提出了一种可压缩的空化两相流动模拟方法来同时考虑液态水和气液两相中间混合物介质的压缩性。在该模拟方法中,结合液态水的弱可压缩模型和气液两相中间介质的状态方程得到了依据流场压力分布对流体密度进行修正的计算模型。采用该密度修正模型对一个原型水泵水轮机的甩负荷过程进行了模拟,研究首次在机组甩负荷过程转轮高压进口回流涡中捕捉到了空化现象。此外,研究发现,空化和转轮进口回流涡的耦合作用诱发空载工况附近出现了低于5倍额定转频的高幅值压力脉动。

三维小空化数空泡流数值方法

采用均质平衡流空泡模型，引入基于求解液体质量份数输运方程的空泡流模型，提出新的压力密度耦合的压缩性方法和控制气液两相转换的源项，求解汽水混合介质的RANS方程和带低雷诺数修正的kε模型，实现了小空化数（σ=0．2～0．01）下水下航行体的空泡流数值模拟．得到清晰的空泡形态特征与内部结构，以及空泡长度和最大直径随空化数的变化规律，给出航行体运动阻力系数与空化数之间的变化关系．将计算结果与解析结果及实验数据进行比较表明，该方法保证了极小空化数下自然空泡流计算的稳定性与收敛性，提高了空泡形态特性的预报精度．

基于全空化模型的柱塞泵内空化流动数值模拟

针对典型斜盘式轴向柱塞泵工作时出现的空化现象,以某高压柱塞泵为例,建立了柱塞泵配流过程中,气液混合相的连续性控制方程和运动控制方程,推导了基于气液两相流的质量输运控制方程,并对柱塞泵进行了空化流动的数值模拟。仿真结果表明,不同的转速、压差和配流盘结构对柱塞腔内部、配流盘表面以及缸体与配流盘接触处的空化存在影响,且仿真结果与实验检测数据结果是吻合的。

旋成体高速入水可压缩性影响研究

针对目前高速(≥100 m/s)跨水-气体界面多相流数值模拟中空化效应和水介质可压缩性影响等问题,建立一套高速入水数值模拟方法。以旋成体为计算模型,采用剪应力传递(SST)k-ω、标准(Standard)k-ε、重整化群(RNG)k-ε及可实现(Realizable)k-ε4种湍流模型进行数值模拟,得到速度衰减与入水深度随时间变化的结果及入水1 ms时的空泡形态,并与理论解比较。基于SST k-ω湍流模型与文献[15,17]实验开展对比研究,选取入水速度50 m/s、100 m/s、200 m/s、400 m/s、800 m/s进行计算。研究结果表明:采用SST k-ω湍流模型的数值模拟结果与理论解一致性最好,入水速度衰减、空泡发展与实验结果基本一致,证明该方法的有效性;在入水速度≤100 m/s时,液体可压缩性对入水冲击载荷基本没有影响;在入水速度≥200 m/s时,随着入水速度增加,液体可压缩性对入水冲击载荷影响越大,会弱化入水冲击载荷及延缓最大载荷出现的时间;在考虑液体可压缩性时,空泡形态有收缩现象;入水速度越大,入水过程速度衰减越快,加速度值在入水初期较大;在计算模型周围被超空泡包裹的航行阶段,随着入水深度增加,加速度逐渐减小,加速度的变化逐渐平缓。

挤压油膜阻尼器内气液均相流模型

在挤压油膜阻尼器内气穴现象实验研究的基础上，本文对挤压油膜因气穴现象而发生物理特性的变化进行了讨论。以气液均相流模型作为挤压油膜的近似描述，导出了上述模型的密度和粘度与油膜压力之间的关系式。分析了当挤压油膜采用这一可压缩模型时，其压力分布的描述更能与实际接近，对阻尼器的力学特性的预测有重要的参考价值。

阻尼孔水射流空化流动数值模拟

对流场中空化现象进行数值模拟时,需要捕捉空泡生成发展到溃灭的过程以及该过程在流场中发生的位置。以阻尼孔淹没水射流为研究对象进行数值模拟时,考虑到水和水蒸气相变过程中两相具有压缩性,选择使用多相流混合模型并加入带有压缩性的正压方程进行描述。湍流模型选择kOmegaSST模型,对近壁面逆压梯度预测更准确,便于捕捉附着型空化现象。方程求解方法采用PIMPLE算法,在求解过程中每一个时间步内的变量根据情况采用不同的离散方法以达到稳定求解。数值模拟结果表明该方法可以捕捉到喉管处由于速度突变引起压力变化产生的附着空化,同时可以很好捕捉到喷嘴处与下游空泡的产生发展和溃灭过程。

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.

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.

3-D NUMERICAL SIMULATION OF FLOW THROUGH AN ORIFICE SPILLWAY TUNNEL

A Large Eddy Simulation (LES) approach based on the weakly compressible hydrodynamic equation with a single plase fluid model for the cavitation flow has been developed and employed in simulating 3 D unsteady viscous flow through an orifice type spillwy tunnel. The finite volume approach in space and the predictor corrector method in time have been used to the numerical discretization, and the 'Law of wall' is applied at the solid boundary. The velocity, pressure fields and the cavitation phenomenon are obtained, the computational results show that 3 D LES approach can give more realistic flow field prediction of the orifice type spillway tunnel.

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.

Asymptotic Behaviour of Solutions to the Navier-stokes Equations of a Two-dimensional Compressible Flow

In this paper, we are concerned with the asymptotic behaviour of a weak solution to the Navier-Stokes equations for compressible barotropic flow in two space dimensions with the pressure function satisfying p（g） = aglog^d（g） for large g. Here d 〉 2, a 〉 0. We introduce useful tools from the theory of Orlicz spaces and construct a suitable function which approximates the density for time going to infinity. Using properties of this function, we can prove the strong convergence of the density to its limit state. The behaviour of the velocity field and kinetic energy is also briefly discussed.

Investigation on strong nonlinear interactions between underwater explosion and water surface based on compressible multiphase flow with phase transition

The strong nonlinear interactions between underwater explosion and water surface were numerically investigated using a phase transition model based on a four-equation system,which can deal with the complex deformable interface among different phases,including water,air,explosion bubble,and cavitation.The numerical method is verified by comparing the numerical results with experimental results,and good agreements are found.This study considers an ideal sine wave for simulating the shape of water surface.Two examples of different detonation depths of charge are investigated.In each example,the first case is the basic simulation without surface wave,and the other three cases are the simulations with sine waves of different wavelengths.Unique characteristics of the interactions,such as shock wave propagation,explosion bubble expansion,and the generation,development,and collapse of cavitation,are observed in the numerical simulations.By capturing the detailed density and pressure contours during the interaction process,we can better understand the underlying mechanisms of the explosion bubble,cavitation,and surface waves.These numerical results demonstrate that geometric nonlinearity impacts cavitation evolution and the explosion bubble movement mechanism.Additionally,the secondary cavitation phenomenon has been found in the cases without surface wave,and its fundamental physical mechanism is presented in detail.The present results can expand the existing database of multiphase flow in the underwater explosion and provide an insight into the strong nonlinear interaction between the underwater explosion and water surface.

Simulation of Compressible Two-Phase Flows Using a Void Ratio Transport Equation

A compressible and multiphase flows solver has been developed for the study of liquid/gas flows involving shock waves and strong expansion waves leading to cavitation.This solver has a structure similar to those of the one-fluid Euler solvers,differing from them by the presence of a void ratio transport-equation.The model and the system of equations to be simulated are presented.Results are displayed for shock and expansion tube problems,shock-bubble interaction and underwater explosion.Close agreement with reference solutions,obtained from explicit finite volume approaches,is demonstrated.Different numerical methods are additionally displayed to provide comparable and improved computational efficiency to the model and the system of equations.The overall procedure is therefore very well suited for use in general two-phase fluid flow simulations.

湍流作用下可压缩液体中空化泡的动力学特性

以水为工作介质,在综合考虑了液体黏性、表面张力、液体压缩性以及湍流作用等因素的情况下,对孔板水力空化反应器中空化泡动力学行为特性进行了详细数值研究.详细分析了湍流作用、空化泡初始半径、孔板下游恢复压力、管道直径以及孔板直径与管道直径之比对空化泡运动特性及其所形成的压力脉冲的影响规律,发现了一些新现象,如空化泡半径二次生长现象.研究结果可为水力空化反应器的优化设计以及水力空化技术的实际应用提供一定的理论指导与技术支撑。

水下爆炸引起的近自由面空化机理研究

水下爆炸过程中总会伴随有空化的产生,空化运动对于冲击波传播、爆炸气泡脉动以及周围结构物变形与损伤都会产生重要的影响。该文针对水下爆炸引起的近自由面空化现象,采用液-汽-空气-爆炸气体等多相可压缩流体模型,并结合相变转换模型来处理液相与汽相之间物质和热量的交换。该系统的控制方程采用分步法处理,首先利用二阶MUSCL-Hancock重构格式和HLLC近似黎曼求解器来求解齐次双曲型方程,再采用牛顿迭代法求解相变方程。利用一维激波管问题上对计算模型中的相变转换以及激波的捕捉能力进行了数值考核。针对水下爆炸引起的近自由面空化现象,首先在一维平面模型中对空化机理进行了探索,观察到了水中空泡在溃灭过程中出现的明显分层现象;然后利用二维轴对称模型模拟了水下爆炸引起的近自由面空化完整过程,发现在空化的演化过程中会出现涡环及其不断向外扩展的现象,数值模拟获得的空化域形态及其运动过程与试验观测基本一致。从流场中部分测点的压力时程曲线来看,相变模型对于早期冲击波阶段压力载荷的影响较小,而对空泡溃灭阶段的压力载荷有一定的影响。数值模拟结果初步证明了基于相变转换的空化计算模型能够有效预测水下爆炸引起的近自由面空化的产生、发展及其溃灭过程,为水下爆炸空化效应的深入研究提供了重要参考。

可压缩涡流场中空泡运动规律及声辐射特性研究

基于可压缩流体力学基本理论,通过边界积分方程,采用不同表面压力模型,求解空泡在计及可压缩性的涡流场中的运动规律;通过表面离散及坐标变换,采用Kirchhoff动边界积分方程,将空泡表面视为运动变形边界,作为直接噪声源,获得涡流场中空泡运动产生的时域声压分布;分析了涡流场参数对空泡运动规律及声辐射特性的影响.研究结果表明:计及流场可压缩性,空泡的脉动幅度会随时间减弱,辐射声压幅值随之减小;空泡在涡流场中会发生延展、颈缩、撕裂,并在撕裂后子空泡中形成射流;当流场中的压力减小时,空泡运动过程中的最大半径与撕裂前的最大长度逐渐增加,且当流场中压力较小时,空泡撕裂时形成的子空泡增多;空泡辐射声压的指向性较弱,撕裂会使辐射声压产生突变,形成极大峰值;随着涡通量的增大或空泡数的减小,空泡脉动周期及其诱导的辐射声压波动周期随之延长,辐射声压峰值逐渐滞后并减小.本文结果旨在为涡流场中空泡运动规律及声辐射特性的相关研究提供参考.