Visualisation and les simulation of cavitation cloud formation and collapse in an axisymmetric geometry

Visualisation and Large Eddy Simulations (LES) of cavitation inside the apparatus previously developed by Franc (2011) for surface erosion acceleration tests and material response monitoring are presented. The experimental flow configuration is a steady-state closed loop flow circuit where pressurised water, flowing through a cylindrical feed nozzle, is forced to turn 90° and then, move radially between two flat plates towards the exit of the device. High speed images show that cavitation is forming at the round exit of the feed nozzle. The cavitation cloud then grows in the radial direction until it reaches a maximum distance where it collapses. Due to the complexity of the flow field, direct observation of the flow structures was not possible, however vortex shedding is inferred from relevant simulations performed for the same conditions. Despite the axisymmetric geometry utilized, instantaneous pictures of cavitation indicate variations in the circumferential direction. Image post-processing has been used to characterize in more detail the phenomenon. In particular, the mean cavitation appearance and the cavity length have been estimated, showing good correlation with the erosion zone. This also coincides with the locations of the maximum values of the standard deviation of cavitation presence. The dominant frequency of the ‘large-scale’ cavitation clouds has been estimated through FFT. Cloud collapse frequencies vary almost linearly between 200 and 2000 Hz as function of the cavitation number and the downstream pressure. It seems that the increase of the Reynolds number leads to a reduction of the collapse frequency; it is believed that this effect is due to the agglomeration of vortex cavities, which causes a decrease of the apparent frequency. The results presented here can be utilized for validation of relevant cavitation erosion models which are currently under development.     

基于动力学模态分解法的绕水翼非定常空化流场演化分析

空化是船舶和水下航行体推进器中经常发生的一种特殊流动现象,它具有强烈的非定常性,空化的发生往往会影响推进器的水动力性能和效率. 为探究绕水翼非定常空化流场结构,本文基于 Schnerr-Sauer 空化模型和 SST $k$-$\omega $ 湍流模型,开展绕二维水翼非定常空化流动数值预报与流场结构分析. 通过将数值预报的空泡形态演变和压力数据与试验结果对比,验证了建立的数值方法的有效性. 并基于动力学模态分解方法对空化流场的速度场进行模态分解,分析了各个模态的流场特征. 结果表明,第一阶模态对应频率为 0,代表平均流场;第二阶模态对应频率约为空泡脱落频率,揭示了空泡在水翼前缘周期性地生长与脱落,第三阶模态对应频率约为第二阶模态的 2 倍,揭示了两个大尺度旋涡在水翼后方存在融合行为. 第四阶模态对应频率约为第二阶模态的 3 倍,具有更高的频率,表征流场中存在一些小尺度旋涡的融合行为. 最后对不同空化数下的空化流场进行了模态分解分析,发现脱落空泡的旋涡结构随着空化数的减小而增大,第二阶模态频率随着空化数的减小而减小.      

ANALYSIS OF UNSTEADY CAVITATION FLOW OVER HYDROFOIL BASED ON DYNAMIC MODE DECOMPOSITION$^{\bf 1)}$

空化是船舶和水下航行体推进器中经常发生的一种特殊流动现象,它具有强烈的非定常性,空化的发生往往会影响推进器的水动力性能和效率. 为探究绕水翼非定常空化流场结构,本文基于 Schnerr-Sauer 空化模型和 SST $k$-$\omega $ 湍流模型,开展绕二维水翼非定常空化流动数值预报与流场结构分析. 通过将数值预报的空泡形态演变和压力数据与试验结果对比,验证了建立的数值方法的有效性. 并基于动力学模态分解方法对空化流场的速度场进行模态分解,分析了各个模态的流场特征. 结果表明,第一阶模态对应频率为 0,代表平均流场;第二阶模态对应频率约为空泡脱落频率,揭示了空泡在水翼前缘周期性地生长与脱落,第三阶模态对应频率约为第二阶模态的 2 倍,揭示了两个大尺度旋涡在水翼后方存在融合行为. 第四阶模态对应频率约为第二阶模态的 3 倍,具有更高的频率,表征流场中存在一些小尺度旋涡的融合行为. 最后对不同空化数下的空化流场进行了模态分解分析,发现脱落空泡的旋涡结构随着空化数的减小而增大,第二阶模态频率随着空化数的减小而减小.     

Numerical analysis of unsteady cavitating turbulent flow and shedding horse-shoe vortex structure around a twisted hydrofoil

Cavitating turbulent flow around hydrofoils was simulated using the Partially-Averaged Navier–Stokes (PANS) method and a mass transfer cavitation model with the maximum density ratio (ρ_l/ρ_v,clip) effect between the liquid and the vapor. The predicted cavity length and thickness of stable cavities as well as the pressure distribution along the suction surface of a NACA66(MOD) hydrofoil compare well with experimental data when using the actual maximum density ratio (ρ_l/ρ_v,clip = 43391) at room temperature. The unsteady cavitation patterns and their evolution around a Delft twisted hydrofoil were then simulated. The numerical results indicate that the cavity volume fluctuates dramatically as the cavitating flow develops with cavity growth, destabilization, and collapse. The predicted three dimensional cavity structures due to the variation of attack angle in the span-wise direction and the shedding cycle as well as its frequency agree fairly well with experimental observations. The distinct side-lobes of the attached cavity and the shedding U-shaped horse-shoe vortex are well captured. Furthermore, it is shown that the shedding horse-shoe vortex includes a primary U-shaped vapor cloud and two secondary U-shaped vapor clouds originating from the primary shedding at the cavity center and the secondary shedding at both cavity sides. The primary shedding is related to the collision of a radially-diverging re-entrant jet and the attached cavity surface, while the secondary shedding is due to the collision of side-entrant jets and the radially-diverging re-entrant jet. The local flow fields show that the interaction between the circulating flow and the shedding vapor cloud may be the main mechanism producing the cavitating horse-shoe vortex. Two side views described by iso-surfaces of the vapor volume fraction for a 10% vapor volume, and a non-dimensional Q-criterion equal to 200 are used to illustrate the formation, roll-up and transport of the shedding horse-shoe vortex. The predicted height of the shedding horse-shoe vortex increases as the vortex moves downstream. It is shown that the shape of the horse-shoe vortex for the non-dimensional Q-criterion is more complicated than that of the 10% vapor fraction iso-surface and is more consistent with the experiments. Further, though the time-averaged lift coefficient predicted by the PANS calculation is about 12% lower than the experimental value, it is better than other predictions based on RANS solvers.     

空化对叶顶间隙泄漏涡演变特性及特征参数影响的大涡模拟研究

利用大涡模拟方法及一个考虑气核效应的欧拉$\!-\!$拉格朗日新空化模型, 对绕NACA0009水翼叶顶间隙泄漏涡(top-leakage vortex, TLV)及其空化流动开展了高精度的模拟, 结果显示数值模拟与实验吻合较好. 在此基础上进一步讨论了不同间隙大小对TLV空化的演变行为及其发生前后TLV强度、气核分布以及切向速度分布等特征参数的变化规律, 分析了TLV空化对TLV演变行为及其特征参数的影响机制. 结果表明, 空化发生后, TLV的强度主要受片空化演变行为的影响, TLV空化对其自身强度的影响较小. 此外, 间隙越小, 片空化越不稳定, TLV的强度也会呈现相应的准周期性波动. 随着间隙的逐渐增大, 片空化强度逐渐减小, 其不稳定性也逐步减弱, TLV强度逐渐恢复至无空化时的水平, 其波动也会逐渐减小. 空化对涡心处气核分布会产生较为明显的影响, 其影响程度取决于空化发生后TLV在空间上的稳定性以及TLV空化的强度. 此外, 空化发生后, TLV半径会在一定程度上增大, 且在空化区域外围形成``类刚体旋转'的切向速度分布特性, 其形成原因主要是空化生长引起的膨胀过程以及流动的黏性作用.      

Numerical analysis of unsteady tip leakage vortex cavitation cloud and unstable suction-side-perpendicular cavitating vortices in an axial flow pump

The objective of this work is to simulate and analyze the formations of three-dimensional tip leakage vortex (TLV) cavitation cloud and the periodic collapse of TLV-induced suction-side-perpendicular cavitating vortice (SSPCV). Firstly, the improved SST k–ω turbulence model and the homogeneous cavitation model were validated by comparing the simulation result with the experiment of unsteady cavitation shedding flow around the NACA66-mod hydrofoil, and then the unsteady TLV cloud cavitation and unstable SSPCV in an axial flow pump were predicted using the improved numerical method. The predicted three-dimensional cavitation structures of TLV and SSPCV as well as the collapsing features show a good qualitative agreement with the high speed photography results. Numerical results show that the TLV cavitation cloud in the axial flow pump mainly includes tip clearance cavitation, shear layer cavitation, and TLV cavitation. The unsteady TLV cavitation cloud occurs near the blade trailing edge (TE) where the shapes of sheet cavitation and TLV cavitation fluctuate. The inception of SSPCV is attributed to the tail of the shedding cavitation cloud originally attached on the suction side (SS) surface of blade, and the entrainment affect of the TLV and the influence of the tip leakage flow at the tailing edge contribute to the orientation and development of the SSPCV. The existence of SSPCV was evidently approved to be a universal phenomenon in axial flow pumps. At the part-load flow rate condition, the SSPCV may trigger cavitation instability and suppress the tip cavitation in the neighboring blade. The cavitation cloud on the SS surface of the neighboring blade grows massively, accompanying with a new SSPCV in the neighboring flow passage, and this SSPCV collapses in a relatively short time.     

Experimental investigation of cavitating structures in the near wake of a cylinder

An experimental investigation of cavitating structures in the near-wake region of a cylinder is presented. From high-speed imaging of this subcritical flow (Reynolds number of 64,000), it is found that inception of cavities occurs in the shear layer. At the developed cavitation condition, the cavities in the separated zone and the free shear layer merge. A distinct spanwise variation in cavitation activity is observed. The non-dimensionalized correlation length at inception varies from close to a non-cavitating value of about 3.5 to about 1 at developed cavitation. The non-dimensionalized length of formation, characterized by crossover of the free shear layer and the wake axis, increases from 1 to 1.8 as the cavitation number is reduced from 85% to 50% of the inception value. A frequency analysis of the cavity dynamics indicates that although the vortex shedding frequency is dominant in the shear layer, there are peaks corresponding to other frequencies in other flow regions. The presence of a sharp peak at 125 Hz, corresponding to a Strouhal number of 0.2, along with a range of frequencies, is also verified independently through measurement of fluctuating pressure at the cylinder surface.     

非定常空化流场结构的实验研究

为深入研究非定常空化流场结构,本文用实验方法研究了绕Clark-Y型水翼的非定常空化流动现象.实验在空化水洞中进行,采用高速摄像技术观测了云状空化阶段的非定常空穴形态,并应用粒子成像测速系统(PIV)对绕水翼空化流场的速度场和涡量场等流动特性进行了同步的实验分析.研究表明:空化现象对流场结构有着重要的影响,在无空化和空...     

CFG桩复合地基沉降影响因素分析

对绕2D水翼无分离流边界层内的初生空化形态进行了实验研究. 采用高速摄像机观测 了空化初生结构的形态，应用2D-LDV测量了空化初生时翼型周围的流动速度分布，并对实 验结果进行了分析. 结果表明：绕水翼无分离边界层内，初生空化结构中空泡伴随 着近壁湍流拟序结构的发生而出现，在初生空化条件下，形成空化涡结构，大量的微空泡产生于发夹 涡结构中，并在涡结构的猝发过程中出现生成---长大---溃灭---反弹---再溃灭的过程. 初生空 化涡结构具有空泡和近壁拟序结构双重特性.     

Research progresses and prospects of unsteady hydrodynamics characteristics for cavitation

空化作为一种重要的复杂水动力学现象,具有明显的三维流动特征与剧烈的非定常特性,在水力机械、船舶推进器、水利工程中广泛存在,且通常会带来不利的影响,长期以来一直是水动力学领域研究的重点与难点课题之一.本文首先从实验测量和数值模拟两个角度,综述了空化水动力学非定常特性研究的发展概况, 分析了当前存在的问题.在空化实验研究中,主要介绍了空化水洞、空化流场测量以及多物理场同步测量等方面所取得的进展.在数值模拟方法中, 对目前的空化模型和湍流模型进行了分类介绍,并重点讨论了大涡模拟、验证和确认等在空化流模拟中的应用.之后以附着型空化为主, 同时兼顾云状空泡、空蚀、涡空化等,梳理了其研究中存在的几个关键科学问题,包括空化演变、空化流动的三维结构、失稳机制、空化不稳定性及其与低频压力脉动的联系、空化与旋涡的相互作用、空化与弹性水翼的流固耦合、空化对尾流场影响等.最后展望了空化水动力学的研究方向和未来发展趋势.     

空化水动力学非定常特性研究进展及展望

空化作为一种重要的复杂水动力学现象,具有明显的三维流动特征与剧烈的非定常特性,在水力机械、船舶推进器、水利工程中广泛存在,且通常会带来不利的影响,长期以来一直是水动力学领域研究的重点与难点课题之一.本文首先从实验测量和数值模拟两个角度,综述了空化水动力学非定常特性研究的发展概况, 分析了当前存在的问题.在空化实验研究中,主要介绍了空化水洞、空化流场测量以及多物理场同步测量等方面所取得的进展.在数值模拟方法中, 对目前的空化模型和湍流模型进行了分类介绍,并重点讨论了大涡模拟、验证和确认等在空化流模拟中的应用.之后以附着型空化为主, 同时兼顾云状空泡、空蚀、涡空化等,梳理了其研究中存在的几个关键科学问题,包括空化演变、空化流动的三维结构、失稳机制、空化不稳定性及其与低频压力脉动的联系、空化与旋涡的相互作用、空化与弹性水翼的流固耦合、空化对尾流场影响等.最后展望了空化水动力学的研究方向和未来发展趋势.      

绕水翼空化流动多尺度数值研究

空化的多尺度效应是一种涉及连续介质尺度、微尺度空化泡以及不同尺度间相互转化的复杂水动力学现象, 跨尺度模型的构建是解析该多尺度现象的关键. 本文基于欧拉-拉格朗日联合算法, 通过界面捕捉法求解欧拉体系下大尺度空穴演化, 通过拉格朗日体系下离散空泡模型求解亚网格尺度离散空泡的运动及生长溃灭. 同时, 通过判断空泡与网格尺度间的关系判定不同尺度空化泡的求解模型. 基于建立的多尺度算法对绕NACA66水翼空化流动进行模拟, 将数值结果与实验进行对比, 验证了数值计算方法的准确性. 研究结果表明, 离散空泡数量与空化发展阶段密切相关, 在附着型片状空穴生长阶段, 离散空泡数量波动较小, 离散空泡主要分布在气液交界面位置; 在回射流发展阶段, 离散空泡逐渐增加并分布在回射流扰动区; 在云状空穴溃灭阶段, 离散空泡数量增多且主要分布在气液掺混剧烈的空化云团溃灭区. 在各空化发展阶段, 离散空泡直径概率密度函数均符合伽玛分布. 空化湍流流场特性对拉格朗日空泡空间分布具有重要影响, 离散空泡主要分布在强湍脉动区、旋涡及回射流发展区域.      

非定常空化流动涡旋运动及其流体动力特性

采用大涡模拟方法对绕水翼云状空化的水动力特性和非定常流场结构进行研究. 基于实验结果对数值方法进行验证,分析空化与流场内部涡旋结构之间的相互作用以及对水翼动力特性的影响. 研究结果表明:大涡模拟方法可以准确模拟绕水翼流动的非定常过程. 在无空化条件下,升阻力系数存在斯特劳哈数St = 0.85 的主频波动,这是由水翼尾部涡旋结构的发展脱落引起的;在云状空化条件下,升阻力系数存在St = 0.34 的高能量密度低频波动,这是由大规模云状空泡团的发展和脱落引起的;云状空化阶段的升阻力系数在St = 0.5~1.5 的范围内都存在较高的波动,这是由于空化现象对水翼尾缘涡旋结构的发展和脱落产生影响,在不同发展阶段,空化现象不同程度地降低尾缘涡旋结构脱落频率.      

Numerical simulation of trajectory and deformation of bubble in tip vortex

According to the behaviors of a bubble in the ship wake flow,the numerical simulation is divided into two stages,quasi-spherical motion and non-spherical motion,based on whether the bubble is captured by the vortex or not.The one-way coupled particle tracking method(PTM) and the boundary element method(BEM) are adopted to simulate these two stages,respectively.Meanwhile,the initial condition of the second stage is taken as the output of the first one,and the entire simulation is connected and completed.Based on the numerical results and the published experimental data,the cavitation inception is studied,and the wake bubble is tracked.Besides,the split of the bubble captured by the vortex and the following sub-bubbles are simulated,including motion,deformation,and collapse.The results provide some insights into the control on wake bubbles and optimization of the wake flow.     

Statistical structure of the velocity field in cavitating flow around a 2D hydrofoil

Transformation of flow turbulence structure with cavitation occurrence, determination of the flow conditions favorable for nucleation of cavitation bubbles, influence of the statistical structure of turbulence on this process and the inverse effect of cavitation on the flow dynamics are challenging problems in modern fluid mechanics. The paper reports on the results of statistical processing of the velocity fields measured by a PIV technique in cavitating flow over a 2D symmetric hydrofoil for four flow conditions, starting from a cavitation-free regime and finishing by unsteady cloud cavitation. We analyze basic information on the statistical structure of velocity fluctuations in the form of histograms and Q-Q diagrams along with profiles of the mean velocity and turbulent kinetic energy. The research reveals that the flow turbulence pattern and distributions of turbulent fluctuations change significantly with the cavitation development. Under unsteady cloud cavitation conditions, the probability density function of the fluctuating velocity has a two-mode distribution, which indicates switching of two alternating flow conditions in a region above the hydrofoil aft part due to periodic passing of cavitation clouds. Behaviors of the mean and most probable velocities unexpectedly appear to be different with a monotonous increase of the incoming flow velocity. This finding must be caused by modification of the skewness coefficient of the fluctuating velocity.     

Mind the gap: a new insight into the tip leakage vortex using stereo-PIV

The tip leakage vortex (TLV), which develops in the clearance between the rotor and the stator of axial hydro turbines, has been studied for decades. Yet, many associated phenomena are still not understood. For instance, it remains unclear how the clearance size is related to the occurrence of cavitation in the vortex, which can lead to severe erosion. Experiments are here carried out on the influence of the clearance size on the tip vortex structure in a simplified case study. A NACA0009 hydrofoil is used as a generic blade in a water tunnel while the clearance between the blade tip and the wall is varied. The 3D velocity fields are measured using Stereo Particle Image Velocimetry (SPIV) in three planes located downstream of the hydrofoil for different values of the upstream velocity, the incidence angle and a large number of tip clearances. The influence of the flow conditions on the structure of the TLV is described through changes in the vortex intensity, core axial flow, vortex center position and wandering motion amplitude. Moreover, high-speed visualizations are used to highlight the vortex core trajectory and clearance flow alteration, turning into a wall jet as the tip clearance is reduced. The measurements clearly reveal the existence of a specific tip clearance for which the vortex strength is maximum and most prone to generating cavitation.     

Axially symmetric cavitation flow at small cavitation numbers

A method for computing the drag coefficient of a body in an axially symmetric, steady-state cavitation flow is presented. A ‘vortex ring’ distribution along the wetted body surface and along the cavity interface is assumed. Since the location of the cavitation interface is unknown a priori, an iterative procedure is used, where, for the first stage, an arbitrary cavitation interface is assumed. The flow field is then solved, and by an iterative process the location of the cavitation interface is corrected. Even though the flow field is governed by the linear Laplace equation, strong non-linearity resulting from the kinematic boundary conditions appears along the cavitation interface. An improved numerical scheme for solving the dual Fredholm integral equations is obtained by formulating high-order approximations to the singular integrals in order to reduce the matrix dimensions. Good agreement is found between the numerical results of the present work, experimental results and other solutions.     

Dispersion modeling by kinematic simulation: Cloud dispersion model

A new technique has been developed to compute mean and fluctuating concentrations in complex turbulent flows (tidal current near a coast and deep ocean). An initial distribution of material is discretized into any small clouds which are advected by a combination of the mean flow and large scale turbulence. The turbulence can be simulated either by kinematic simulation (KS) or direct numerical simulation. The clouds also diffuse relative to their centroids; the statistics for this are obtained from a separate calculation of the growth of individual clouds in small scale turbulence, generated by KS. The ensemble of discrete clouds is periodically re-discretized, to limit the size of the small clouds and prevent overlapping. The model is illustrated with simulations of dispersion in uniform flow, and the results are compared with analytic, steady state solutions. The aim of this study is to understand how pollutants disperses in a turbulent flow through a numerical simulation of fluid particle motion in a random flow field generated by Fourier modes. Although this homogeneous turbulent is rather a “simple” flow, it represents a building block toward understanding pollutant dispersion in more complex flow. The results presented here are preliminary in nature, but we expect that similar qualitative results should be observed in a genuine turbulent flow.     

Vortices and wall shear stresses in asymmetric and symmetric channels with sinusoidal wavy walls for pulsatile flow at low Reynolds numbers

Numerical simulation and flow visualization were performed to study the dynamical behavior of vortices generated in channels with two different geometries, i.e., a periodically converging–diverging channel and serpentine channel, both having sinusoidal wavy walls. This system for pulsatile flow is used to enhance heat and mass transfer in very viscous liquids. The numerical results predict well the dynamical behavior of vortices and agree with the flow visualizations. For both channels, the vortex expands in each furrow of the channel walls during the deceleration phase and shrinks during the acceleration phase, which leads to fluid exchange between the vortex and the mainstream. The time-averaged vortex strength and wall shear stresses increase, as the frequency of fluid oscillation increases under a fixed oscillatory fraction of the flow rate. However, above a certain value of the frequency, they reversely decrease due to viscous effects. This frequency for the serpentine channel is smaller than that for the converging–diverging channel. The channel geometries are found to have an important effect of the flow characteristics.     

Instantaneous and time-averaged flow fields of multiple vortices in the tip region of a ducted propulsor

The instantaneous and time-averaged flow fields in the tip region of a ducted marine propulsor are examined. In this flow, a primary tip-leakage vortex interacts with a secondary, co-rotating trailing edge vortex and other co- and counter-rotating vorticity found in the blade wake. Planar particle imaging velocimetry (PIV) is used to examine the flow in a plane approximately perpendicular to the mean axis of the primary vortex. An identification procedure is used to characterize multiple regions of compact vorticity in the flow fields as series of Gaussian vortices. Significant differences are found between the vortex properties from the time-averaged flow fields and the average vortex properties identified in the instantaneous flow fields. Variability in the vortical flow field results from spatial wandering of the vortices, correlated fluctuations of the vortex strength and core size, and both correlated and uncorrelated fluctuations in the relative positions of the vortices. This variability leads to pseudo-turbulent velocity fluctuations. Corrections for some of this variability are performed on the instantaneous flow fields. The resulting processed flow fields reveal a significant increase in flow variability in a region relatively far downstream of the blade trailing edge, a phenomenon that is masked through the process of simple averaging. This increased flow variability is also accompanied by the inception of discrete vortex cavitation bubbles, which is an unexpected result, since the mean flow pressures in the region of inception are much higher than the vapor pressure of the liquid. This suggests that unresolved fine-scale vortex interactions and stretching may be occurring in the region of increased flow variability.