Experimental study of ventilated cavity flow over a 3-D wall-mounted fence

Ventilated cavity flow over a fixed height 3-D wall-mounted fence is experimentally investigated in a cavitation tunnel for a range of free-stream conditions. The impact of 3-D effects on cavity topology is examined, along with the dependence of the cavitation number and drag on the volumetric flow rate coefficient, fence height based Froude number and vapour pressure based cavitation number. Three different flow regimes are identified throughout the range of cavitation numbers for a particular free-stream condition. Generally, the cavity has a typical re-entrant jet closure the intensity of which is found to increase linearly with increasing Froude number. This increase in re-entrant jet intensity causes an increase in drag with Froude number for constant volumetric flow rate coefficient. At low Froude numbers the closure mechanism transitions from a single to a split re-entrant jet. The parameters used to characterize the cavity topology show a linear dependence on Froude number irrespective of the closure mode. The cavity topology and drag are found to be independent of vapour pressure based cavitation number.     

Flow regime transitions due to cavitation in the flow through an orifice

This paper presents both experimental and theoretical aspects of the flow regime transitions caused by cavitation when water is passing through an orifice. Cavitation inception marks the transition from single-phase to two-phase bubbly flow; choked cavitation marks the transition from two-phase bubbly flow to two-phase annular jet flow.

It has been found that the inception of cavitation does not necessarily require that the minimum static pressure at the vena contracta downstream of the orifice, be equal to the vapour pressure liquid. In fact, it is well above the vapour pressure at the point of inception. The cavitation number [σ = (P₃ − P_v)/(0.5 pV²); here P₃ is the downstream pressure, P_v is the vapour pressure of the liquid, ρ is the density of the liquid and V is the average liquid velocity at the orifice] at inception is independent of the liquid velocity but strongly dependent on the size of the geometry. Choked cavitation occurs when this minimum pressure approaches the vapour pressure. The cavitation number at the choked condition is a function of the ratio of the orifice diameter (d) to the pipe diameter (D) only. When super cavitation occurs, the dimensionless jet length [L/(D - d); where L is the dimensional length of the jet] can be correlated by using the cavitation number. The vaporization rate of the surface of the liquid jet in super cavitation has been evaluated based on the experiments.

Experiments have also been conducted in which air was deliberately introduced at the vena contracta to simulate the flow regime transition at choked cavitation. Correlations have been obtained to calculate the critical air flow rate required to cause the flow regime transition. By drawing an analogy with choked cavitation, where the air flow rate required to cause the transition is zero, the vapour and released gas flow rate can be predicted.     

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.     

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.     

Experiments on unsteady cavitation

 The unsteady behaviour of cloud cavitation is obviously influenced by its internal flow pattern. The main purpose of this work is to investigate such a two phase flow during a cavitation cycle. The tests are carried out with a convergent divergent nozzle. Observations are made by using a classical video set in combination with a stroboscopic light sheet. The use of a double optical probe enables void fraction and velocity to be measured inside the two phase flow structure. Data acquisition is governed by a pressure signal measured near the cavity closures to follow their evolution during the shedding process. Special care has been taken in validating the experimental techniques because they have not been used in such flows. The measurements show an extended reversed flow occurring along the solid surface. It plays a significant function in the vapour cloud shedding process. Received: 11 September 1995 / Accepted: 28 June 1996     

Stokes waves on a cavity surface in a rotating fluid

The axisymmetric flow of an inviscid incompressible fluid rotating about a cavity with constant pressure is considered. Due to the centrifugal force, on the cavity surface waves may exist, in particular, waves with a break in the wave base where the cavity meridional sections form the angle 2/3, i.e. Stokes waves. A method of finding these waves from the boundary-value problem for the fluid velocity potential is described. For an infinite cavity, the dependence of the wave parameters on the cavitation number, calculated using the pressure in the cavity, is given.St. Petersburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 105–110, November–December, 1996.     

Interfacial dynamics‐based modelling of turbulent cavitating flows,Part‐1: Model development and steady‐state computations

The merits of transport equation‐based models are investigated by adopting an enhanced pressure‐based method for turbulent cavitating flows. An analysis of the mass and normal‐momentum conservation at a liquid–vapour interface is conducted in the context of homogeneous equilibrium flow theory, resulting in a new interfacial dynamics‐based cavitation model. The model offers direct interpretation of the empirical parameters in the existing transport‐equation‐based models adopted in the literature. This and three existing cavitation models are evaluated for flows around an axisymmetric cylindrical body and a planar hydrofoil, and through a convergent–divergent nozzle. Although all models considered provide qualitatively comparable wall pressure distributions in agreement with the experimental data, quantitative differences are observed in the closure region of the cavity, due to different compressibility characteristics of each cavitation model. In particular, the baroclinic effect of the vorticity transport equation plays a noticeable role in the closure region of the cavity, and contributes to the highest level of turbulent kinetic energy there. Copyright © 2004 John Wiley & Sons, Ltd.     

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.      

An alternate approach for modelling of transient vaporous cavitation

Simulation of cavitating flow has been a thrust area of research for long period due to its practical and economic importance. The major hurdle in developing a numerical model for such flows is the difficulty in representing the quick phase changes, in general, and the alternate change of flow from single phase to two phase and back, in particular. In this case, instability due to sharp variation of flow characteristics also restricts the development of numerical models. The present study demonstrates the use of a relatively simple formulation for the analysis of flow characteristics in a quasi‐rigid pipeline under abrupt phase changes due to cavitation. A popular scheme—MacCormack scheme—was used for developing a numerical solution for this problem. It uses the conservative form of the governing equations, viz. conservation of mass and momentum, the transport equation and the constitutive relationship. The model can handle variable properties of the water–vapour mixture, which is highly compressible. A newly introduced pressure under‐relaxation method overcomes the numerical instability due to sharp variation of flow characteristics during phase change. The model could predict the instant of occurrence of vapour pressure, duration of persistence of vapour pressure and the rise of pressure due to vapour collapse to satisfactory levels with published data and experimental results. Copyright © 2009 John Wiley & Sons, Ltd.     

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.     

Mass transfer enhancement by capillary waves at a liquid–vapour interface

We present experimental results showing that large amplitude capillary waves at a liquid–vapour interface substantially enhance the interfacial heat and mass transfer. The experiments have been conducted in a circular cylinder that is partially filled with a wetting liquid of low boiling point temperature and pressurized by its vapour. The interfacial capillary waves are sub-harmonically excited by oscillating the circular cylinder at 50 Hz with forcing amplitude A in the direction normal to the liquid surface. The upper part of the test cell containing the vapour is heated to a temperature slightly below the boiling point temperature at the operating pressure. When the interface is at rest, the pressure decrease due to condensation is small. However, in the presence of interfacial capillary waves the rate of pressure decrease is substantial. The results show that the vapour condensation rate with respect to the diffusive vapour flux at an undisturbed interface, which is a Nusselt number, increases with the square of the wave amplitude that is proportional to the forcing amplitude. A model is developed that expresses the pressure variation in terms of Jacob number, the temperature gradient in the liquid at the interface and the capillary wave motion. This model allows extrapolation of the results to other fluids and configurations.     

Effect of the feeding pipeline properties on the nature of cavitation-induced self-oscillations in the presence of a ventilated cavity with a negative cavitation number in the system

Physical modeling of a ventilated cavity with a negative cavitation number has shown that at the same flow rate and head parameters different cavitation-induced self-oscillation patterns can be realized. The generation of these patterns depends on the feeding pipeline parameters. The high-speed videofilming shows that the physics of the process are the same in different frequency regimes, the wave propagation velocity in the jet flow is mainly determined by the cavitation number, and the difference between self-oscillation patterns is characterized by the number of the waves along the cavity length. A method of estimating the self-oscillation frequencies from the given flow geometry and the cavitation number is proposed.     

射流对绕水翼云空化流动抑制机理研究

为理解绕水翼云空化流动的发展机理和探究水翼吸力面开孔射流的影响,采用密度 修正的RNG $k$-$\varepsilon $湍流模型和Schnerr-Sauer空化模型对原始NACA66(mod) 水翼和采用射流后的 水翼的云空化非定常过程进行模拟和对比分析;采用在水翼吸力面近壁区设立监测线的方法对近壁区的流场进行监测,得到 近壁区汽相体积分数、回射流速度、压力及压力梯度的时空分布云图;开展了云空化流场特性的涡动力学分析,进而分析水 翼云空化的发生机理和射流抑制空化的抑制机理. 结果表明:游离型空泡在下游溃灭时产生强烈的局部高压,其向上游传播 导致前缘空穴的一次回缩,而空穴的二次回缩受回射流的影响. 回射流的发展区域受限于较高的压力梯度,高的压力梯度一 直存在,但回射流在一个周期内的首次出现需要时间的积累. 在水翼吸力面射流使得射流孔附近压力升高,弥补了由于空化 和绕流造成的压降,压力梯度增大,抗逆压能力增强,对回射流起到阻挡作用;另一方面,射流使得回射流区域面积和回射 流的强度也有所减小,从而对云空化的发展起到抑制的效果. $Q$准则的涡结构云图相比于汽相体积分数云图能显示复杂的 流动结构,前缘附着型空穴和尾缘游离型空穴内存在旋涡,回射流对空穴存在剪切作用造成空穴脱落. 而射流对空穴和回射 流的剪切和阻挡使云空化发展得到抑制.      

Shadowgraph, Schlieren and interferometry in a 2D cavitating channel flow

Cavitation plays an important role in fuel atomization mechanisms, but the physics of cavitation and its impact on spray formation and injector efficiency are not well documented yet. Experimental investigations are required to support the development and the validation of numerical models and the design of tomorrow??s injectors, in the context of pollutant and fuel consumption reduction. The complexity of modern injectors and the extreme conditions of injection do not facilitate experimental investigations. In this paper, experiments are conducted in a simplified geometry. The model nozzle consists of a transparent 2D micro-channel supplied with a test oil (ISO 4113). Three different optical techniques are proposed to investigate the channel flow, with the pressure drop between upstream and downstream chambers as a parameter. A shadowgraph-like imaging technique allows the observation of cavitation inception and vapor cavities development throughout the channel. The technique also reveals the presence of density gradients (pressure or temperature) in the channel flow. However, this additional information is balanced by difficulties in image interpretation, which are discussed in the paper. In addition, a combination of Schlieren technique and interferometric imaging is used to measure the density fields inside the channel. The three techniques results are carefully analyzed and confronted. These results reveal a wealth of information on the flow, with pressure waves generated by bubble collapses, turbulence in the wake of vapor cavities and bubble survival in flow regions of high pressure. Our results also show that cavitation inception is located in the shear layers between the recirculation zones and the main flow, relatively far from the inlet corner, where the pressure is minimum in average. To explain this behavior, we propose a scenario of cavitation inception based on the occurrence and the growing of instabilities in the shear layers.     

Cylindrical cavity expansion in compressible Mises and Tresca solids

The elastoplastic field induced by quasi-static expansion in steady-state plane-strain conditions of a pressurized cylindrical cavity (cylindrical cavitation) is investigated. Material behavior is modeled by Mises and Tresca large strain flow theories formulated as hypoelastic. Both models account for elastic-compressibility and allow for arbitrary strain-hardening (or softening). For the Mises solid analysis centers on the axially-hydrostatic assumption (axial stress coincides with hydrostatic stress) in conjunction with a controlled error method. Introducing an error control parameter we arrive at a single-parameter-dependent quadrature expression for cavitation pressure. Available results are recovered with particular values of that parameter, and an optimal value is defined such that the cavitation pressure is predicted with high accuracy. For the Tresca solid we obtain an elegant solution with the standard model when no corner develops in the yield surface. Under certain conditions however a corner zone exists near the cavity and the solution is accordingly modified revealing a slight difference in cavitation pressure. Comparison with numerical solutions suggests that the present study establishes cylindrical cavitation analysis on equal footing with existing studies for spherical cavitation.     

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.      

Generation and propagation of pressure waves in supersonic deep-cavity flows

The mechanism behind cavity-induced pressure oscillations in supersonic flows past a deep rectangular cavity is not well understood despite several investigations having been carried out. In particular, the process by which the pressure wave is generated and the path of the pressure wave propagating inside the cavity remains unclear. In the present study, the pressure waves around a deep rectangular cavity over which nitrogen gas flows at a Mach number of 1.7 are visualized using the schlieren method. The length of the cavity is 14.0?mm. The depths of the cavity are selected as 20.0?and 11.7?mm, corresponding to length-to-depth ratios of 0.70 and 1.2, respectively. The pressure waves propagating inside as well as outside the cavity have been successfully visualized using a high-speed camera, and the propagation pattern of these waves is found to be different from that previously predicted by numerical simulation and from those expected in previous oscillation models. In addition, the pressure oscillation near the trailing edge of the cavity is also measured using semiconductor-type pressure transducers simultaneously with the capture of the schlieren images. As a result, the relationship between the shear-layer motion, pressure-wave generation, and pressure oscillation at the trailing edge of the cavity is clarified experimentally.     

Minimal cavitation number and cavity width in plane and axisymmetric channels

This paper presents a study of cavity width behind a body in two-dimensional and axisymmetric channels. Equations are given for calculating the minimal cavitation number and also for calculating the dependence of the cavity width on the cavitation number and on the ratio of the transverse dimensions of the body and the channel.Notation v₀ freestream velocity - v velocity at the cavity boundary - p₀ freestream pressure - p pressure in cavity - fluid density - d body width - D₀ channel width - D width of cavity in channel - D width of cavity in unbounded fluid     

Immersed Boundaries in Large Eddy Simulation of Compressible Flows

Methods to immerse walls in a structured mesh are examined in the context of fully compressible solutions of the Navier–Stokes equations. The ghost cell approach is tested along with compressible conservative immersed boundaries in canonical flow configurations; the reflexion of pressure waves on walls arbitrarily inclined on a cartesian mesh is studied, and mass conservation issues examined in both a channel flow inclined at various angles and flow past a cylinder. Then, results from Large Eddy Simulation of a flow past a rectangular cylinder and a transonic cavity flow are compared against experiments, using either a multi-block mesh conforming to the wall or immersed boundaries. Different strategies to account for unresolved transport by velocity fluctuations in LES are also compared. It is found that immersed boundaries allow for reproducing most of the coupling between flow instabilities and pressure-signal properties observed in the transonic cavity flow. To conclude, the complex geometry of a trapped vortex combustor, including a cavity, is simulated and results compared against experiments.     

Medical applications and bioeffects of extracorporeal shock waves

Lithotripter shock waves are pressure pulses of microsecond duration with peak pressures of 35–120 MPa followed by a tensile wave. They are an established treatment modality for kidney and gallstone disease. Further applications are pancreatic and salivary stones, as well as delayed fracture healing. The latter are either on their way to become established treatments or are currently under investigation. Shock waves generate tissue damage as a side effect which has been extensively investigated in the kidney, the liver, and the gallbladder. The primary adverse effects are local destruction of blood vessels, bleedings, and formation of blood clots in vessels. Investigations on the mechanism of shock wave action revealed that lithotripters generate cavitation both in vitro and in vivo. An increase in tissue damage at higher pulse administration rates, and also at shock wave application with concomitant gas bubble injection suggested that cavitation is a major mechanism of tissue damage. Disturbances of the heart rhythm and excitation of nerves are further biological effects of shock waves; both are probably also mediated by cavitation. On the cellular level, shock waves induce damage to cell organelles; its extent is related to their energy density. They also cause a transient increase in membrane permeability which does not lead to cell death. Administered either alone or in combination with drugs, shock waves have been shown to delay the growth of small animal tumors and even induce tumor remissions. While the role of cavitation in biological effects is widely accepted, the mechanism of stone fragmentation by shock waves is still controversial. Cavitation is detected around the stone and hyperbaric pressure suppresses fragmentation; yet major cracks are formed early before cavitation bubble collapse is observed. The latter has been regarded as evidence for a direct shock wave effect.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.