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.     

Investigation of hot-fluid cavitating flow through an obstacle in a pipeline

The results of investigating hot-fluid cavitating flow in a pipe with a local contraction are presented for a broad temperature interval (water from cold to near-boiling) and various cavitation regimes — from the initial (bubble) to the supercavitation regime. Experimental relations for the amplitudes of the fluctuations and the fundamental frequencies are presented for a Venturi tube with various diffusers and for diaphragms of various dimensions. A flow model which takes into account the fluctuations of the vapor pressure in the cavity and, moreover liquid-cavity mass transfer effects is presented. It is shown that for a given flow geometry there is a limiting Jakob number below which the self-oscillating regime is impossible at any cavitation numbers.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.4, pp. 124–133, May–June, 1993.     

Influence of periodic disturbances on inception of cavitation in sharp-edged orifices

The influence of periodic flow disturbances on the onset of cavitation in sharp-edged orifices was determined through a series of experiments. Different amplitudes and frequencies of disturbance were introduced in the flow. The threshold value of cavitation parameter for which transition from attached to cavitating flow took place was shown to depend on the amplitude of the disturbance. Cavitating flow was initiated more spontaneously as the amplitude of disturbance increased. Hysteresis in the flow was, however, observed to decrease. Variations in the frequency of the disturbance did not bring about any significant change in the cavitation parameter at transition. The results are interpreted in terms of the available dwell time for cavitation and the characteristic residence time of the fluid in the sharp-edged orifice and in the pipeline upstream of the orifice.     

Numerical study of choked cavitation in high temperature hydrocarbon liquid jets

A numerical study was conducted on a practical plain orifice injector issuing pressurized high-temperature aviation fuel, in order to simulate injection of fuel after use as a coolant in the active cooling system of a hypersonic vehicle. A three-dimensional unstructured mesh inside the orifice was created using ICEMCFD^TM S/W, and the CFD analysis was performed using FLUENT^TM S/W. A multiphase mixture model was used to simulate cavitating two-phase flow, and the full cavitation model was activated to predict the mechanism and effects of cavitation induced by the high fuel vapor pressures at elevated temperature conditions. The simulation was performed for fuel heated up to 553 K (280 °C) at an upstream pressure (P_inj) of up to 1.0 MPa, and various ambient pressures (P_∞). The results were compared with experimental data, and the simulation was found to predict the discharge coefficient (C_d) with respect to the fuel injection temperature (T_inj) quite well at the given conditions. The CFD analyses for high fuel temperature conditions revealed that the mainstream flow inside the injector separates from the orifice wall at the vena contracta due to the generated fuel vapor cavity, and the attached flow at the end of the cavity separates again to produce a very small recirculation zone. In addition, for a given pressure drop, the sharply decreasing trend of the mass flow rate (or C_d) with increasing T_inj varies depending on P_∞, because the mass flow choking is determined by the relationship between P_∞ and the vapor pressure (P_sat) at T_inj. Finally, C_d with respect to cavitation number was found to follow an almost identical line, even at different P_∞. This confirms that choked cavitation at high fuel temperature conditions depends on the downstream pressure of the orifice, and the effect of cavitation on C_d at high T_inj is well represented by the cavitation numbers, regardless of P_inj, P_∞, and T_inj.     

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.      

Noise generated by cavitating single-hole and multi-hole orifices in a water pipe

This paper presents an experimental study of the acoustical effects of cavitation caused by a water flow through an orifice. A circular-centered single-hole orifice and a multi-hole orifice are tested. Experiments are performed under industrial conditions: the pressure drop across the orifice varies from 3 to 30 bar, corresponding to cavitation numbers from 0.74 to 0.03. Two regimes of cavitation are discerned. In each regime, the broadband noise spectra obtained far downstream of the orifice are presented. A nondimensional representation is proposed: in the intermediate ‘developed cavitation’ regime, spectra collapse reasonably well; in the more intense ‘super cavitation’ regime, spectra depend strongly on the quantity of air remaining in the water downstream of the orifice, which is revealed by the measure of the speed of sound at the downstream transducers. In the ‘developed cavitation’ regime, whistling associated with periodic vortex shedding is observed. The corresponding Strouhal number agrees reasonably well with literature for single-phase flows. In the 'super cavitation’ regime, the whistling disappears.     

围压下自振空化射流冲蚀性能实验研究

自振空化射流是利用瞬态流和水声学原理调制而成的一种新型射流,为研究围压下自激振荡空化射流的冲蚀破碎规律,利用高压釜装置测量了1.0mm出口直径的风琴管自振空化喷嘴在各种射流参数情况下冲蚀铝试样的冲蚀质量,并与同等条件下锥形喷嘴冲蚀效率进行了对比。测量结果表明,冲蚀质量基本与射流压力成正比;存在最优喷距和围压,使得冲蚀效果最佳,在本实验条件,分别为喷嘴出口直径的5～7倍和2MPa左右;相同条件下,自振空化喷嘴冲蚀质量约为同等条件下锥形喷嘴冲蚀的1～2倍,这为自振空化射流提高钻井速度等实际应用提供了实验依据。     

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.     

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.     

Two-phase flow instabilities in a silicon microchannels heat sink

Two-phase flow instabilities are highly undesirable in microchannels-based heat sinks as they can lead to temperature oscillations with high amplitudes, premature critical heat flux and mechanical vibrations. This work is an experimental study of boiling instabilities in a microchannel silicon heat sink with 40 parallel rectangular microchannels, having a length of 15 mm and a hydraulic diameter of 194 μm. A series of experiments have been carried out to investigate pressure and temperature oscillations during the flow boiling instabilities under uniform heating, using water as a cooling liquid. Thin nickel film thermometers, integrated on the back side of a heat sink with microchannels, were used in order to obtain a better insight related to temperature fluctuations caused by two-phase flow instabilities. Flow regime maps are presented for two inlet water temperatures, showing stable and unstable flow regimes. It was observed that boiling leads to asymmetrical flow distribution within microchannels that result in high temperature non-uniformity and the simultaneously existence of different flow regimes along the transverse direction. Two types of two-phase flow instabilities with appreciable pressure and temperature fluctuations were observed, that depended on the heat to mass flux ratio and inlet water temperature. These were high amplitude/low frequency and low amplitude/high frequency instabilities. High speed camera imaging, performed simultaneously with pressure and temperature measurements, showed that inlet/outlet pressure and the temperature fluctuations existed due to alternation between liquid/two-phase/vapour flows. It was also determined that the inlet water subcooling condition affects the magnitudes of the temperature oscillations in two-phase flow instabilities and flow distribution within the microchannels.     

Passive control of cavitating flow around an axisymmetric projectile by using a trip bar

Quasi-periodical evolutions such as shedding and collapsing of unsteady cloud cavitating flow, induce strong pressure fluctuations, what may deteriorate maneuvering stability and corrode surfaces of underwater vehicles. This paper analyzed effects on cavitation stability of a trip bar arranged on high-speed underwater projectile. Small scale water tank experiment and large eddy simulation using the open source software Open FOAM were used, and the results agree well with each other. Results also indicate that trip bar can obstruct downstream re-entrant jet and pressure wave propagation caused by collapse, resulting in a relatively stable sheet cavity between trip bar and shoulder of projectiles.     

Multiphase fluid dynamics and transport processes of low capillary number cavitating flows

To better understand the multiphase fluid dynamics and associated transport processes of cavitating flows at the capillary number of 0.74 and 0.54, and to validate the numerical results, a combined computational and experimental investigation of flows around a hydrofoil is studied based on flow visualizations and time-resolved interface movement. The computational model is based on a modified RNG k-ε model as turbulence closure, along with a vapor-liquid mass transfer model for treating the cavitation process. Overall, favorable agreement between the numerical and experimental results is observed. It is shown that the cavi- tation structure depends on the interaction of the water-vapor mixture and the vapor among the whole cavitation stage, the interface between the vapor and the two-phase mixture exhibits substantial unsteadiness. And, the adverse motion of the interface relates to pressure and velocity fluctuations inside the cavity. In particular, the velocity in the vapor region is lower than that in the two-phase region.     

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.      

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.      

Hydraulic characterization of high temperature hydrocarbon liquid jets

An experimental study has been conducted to investigate the hydraulic characteristics of a plain orifice nozzle issuing pressurized high-temperature liquid hydrocarbon, in order to simulate injection of aviation fuel after being used as coolant in an active cooling system in a hypersonic flight vehicle. The fuel was heated to 553 K (280°C) using an induction heater, at an upstream pressure of up to 1.0 MPa, and injected to atmospheric pressure conditions through a sharp-edged orifice of diameter 0.7 mm and length 4.3 mm. It has been observed that the isothermal lines on the plane of the mass flow rate versus the square root of the pressure drop (ΔP) were clearly affected by increased fuel temperatures, and the discharge coefficient (C_d) decreased sharply with increasing fuel injection temperature (T_inj) above the fuel boiling point of 460 K. The Reynolds number (Re) for three ΔPs with respect to T_inj reached maxima and then began to decrease as T_inj increased for each ΔP case, and the fuel temperature of maximum Re at a given pressure condition increased as ΔP increased. The effects of cavitation on the hydraulic characteristics of the high temperature fuel were explored by representing C_d with respect to three cavitation numbers and dissipation efficiency. The behaviors of C_d showed a clear dependency on cavitation number, and all of the results collapsed to a single curve, regardless of ΔP. In addition, the curve indicated that the C_d characteristics was divided into non-cavitating and cavitating regions by the critical cavitation numbers near the fuel boiling point, and a sharp decrease in C_d was found to be typical in the cavitating region. The relationship between C_d and Re showed that when T_inj exceeded the boiling point the high temperature liquid jets experienced a sharp decrease in C_d at a determined Reynolds number, due to the collapse of the mass flow rate induced by the choked cavitaiton.     

Study of cavitation phenomena based on a technique for visualizing bubbles in a liquid pressurized chamber

In this paper, the influence of nozzle geometry on cavitation and near-nozzle spray behavior under liquid pressurized ambient is studied. For this purpose, eight steel drilled plates, with different diameters and degrees of conicity of their holes, are analyzed. A special near-nozzle field visualization technique, using a test rig pressurized with fuel, is used. Due to the difference in refractive index between liquid and vapor phase, bubbles present at the outlet of the orifice are visualized. The pressure conditions at which bubbles start appearing at the orifice outlet are compared with those at which choked flow appears. The results showed that pressure conditions for inception of cavitation obtained in the visualization tests differs from those seen for choked flow (5–8% in terms of cavitation number). In addition to this, the images taken are analyzed to get the angle of the jet formed by fuel bubbles, showing that it increases significantly for those conditions more prone to cavitate. Furthermore, comparison of bubbles generation when increasing or decreasing backpressure indicates the presence of hysteresis in cavitation inception phenomena.     

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.     

The relation between the high speed submerged cavitating jet behaviour and the cavitation erosion process

In order to accurately and reliably evaluate the cavitation erosion resistance of materials using a cavitating jet generator, the effects of the hydrodynamic parameters and the nozzle geometry on the erosion process were investigated. Since the behaviour of a high speed submerged cavitating jet is also depending on the working conditions; their influence is also discussed based on the evaluation of cavitation erosion process. The erosion rate was used as an indicator for cavitating jet behaviour. Specimens of commercial-purity copper were subjected to high speed submerged cavitating jets under different initial conditions, for certain time periods. The force generated by jet cavitation is employed to initiate the erosion in surface. The tested specimens were investigated with a digital optical microscope and a profilometer. It was found that erosion becomes more pronounced with decreasing cavitation numbers, as well as with increasing exit jet velocities. The nozzle configuration and hydrodynamic parameters have strong influences on the erosion rate, eroded area and depth of erosion. A comparison between the obtained results explains some of the mechanisms involved in cavitation and erosion processes and their relation to the tested parameters. Mathematical expressions which combine these parameters with the erosion rate are obtained. These parameters are very important in order to control the cavitation as a phenomenon and also to control the performance of the cavitating jet generator.     

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.