On the numerical simulations of vortical cavitating flows around various hydrofoils

This paper reviews the numerical models of various cavitating flows around hydrofoils. Numerical models relating to cavitation flows, including mass transfer models and turbulence models, are summarized at first. Then numerical results and analysis of flow characteristics for the cavitating flows around twisted hydrofoils, truncated hydrofoil and tip leakage are discussed respectively. For mean flow fields, Reynolds averaged Navier-Stokes(RANS) simulation associated with a kind of nonlinear turbulence model is found to be an economic and robust numerical approach for different kinds of cavitating flows including cloud cavitation, tip cavitation and tip leakage cavitation. To predict the fluctuations of pressure and velocity, large eddy simulation(LES) and detached eddy simulation(DES) are two effective approaches. Finally, a few open questions are proposed for future research.     

APPLICATION OF QUADRATIC AND CUBIC TURBULENCE MODELS ON CAVITATING FLOWS AROUND SUBMERGED OBJECTS

Quadratic and cubic Non-Linear Eddy-Viscosity Models(NLEVMs) at low Reynolds number correction were introduced into the present Computational Fluid Dynamics(CFD) framework,to provide better numerical treatment about the anisotropic turbulence stress in cavitating flows,which have large density ratio and large-scaled swirling flow structures.The applications of these NLEVMs were carried out through a self-developed cavitation code,coupled with a cavitation model based on the transport equation of liquid phase.These NLEVMs were firstly validated by the benchmark of disk supercavity,and found able to obtain more accurate capture of the hydrodynamic properties than the linear models.One of such models was further applied on the cavitation problem of submerged vehicles.Ultimately,the supercavitating flows around an especially designed underwater vehicle were predicted using the cubic turbulence model,and its cavitation behaviors were studied.     

URANS COMPUTATION OF CAVITATING FLOWS AROUND SKEWED PROPELLERS

Cavitating flows around skewed propellers are investigated numerically by means of the unsteady Reynolds Averaged Navier-Stokes (RANS) Equation method. The standard k-ε turbulence and the modified Z-G-B cavitation models are employed. A measured nominal wake is used for the inlet velocity boundary condition. Predicted cavitating evolution processes and tip cavity patterns are compared with experimental observations. In addition, the influence of the skew angles on the cavitation and unsteadiness performances of propellers operating in a non-uniform wake is also studied. Results show that the modified Z-G-B cavitation model performs better to simulate the cavitating flow cases studied in this paper. Comparisons demonstrate that the skewed propeller with a skew angle of 20 o is the best choice for a given stern wake with a assigned thrust and the minimum force fluctuations.     

组合式水力空化杀灭原水中病原微生物的试验

基于浙江工业大学水力学实验室自主研发的由三角形孔口多孔板和文丘里管构成的组合式水力空化装置,以菌落总数和大肠杆菌作为病原微生物的指示菌,对杭州市区胜利河原水不同体积比水样进行灭菌处理。通过琼脂平板计数法检测菌落总数和大肠杆菌的杀灭率,研究了水力空化对水中菌落总数和大肠杆菌的杀灭效果,分析了文丘里管扩散段的扩散角,三角形孔口多孔板的孔口数量、孔口排列方式,原水体积比以及空化数对菌落总数和大肠杆菌杀灭率的影响。试验结果表明,选取合适的扩散角和原水体积比,适当增加孔口数量,采用交错式孔口排列方式多孔板和降低空化数可以提高菌落总数和大肠杆菌杀灭率。     

Numerical analysis of cavitation cloud shedding in a submerged water jet

Focused on the unsteady behavior of high-speed water jets with intensive cavitation a numerical analysis is performed by applying a practical compressible mixture flow bubble cavitation model with a simplified estimation of bubble radius. The mean flow of two-phase mixture is calculated by unsteady Reynolds averaged Navier-Stokes(URANS) for compressible flow and the intensity of cavitation in a local field is evaluated by the volume fraction of gas bubbles whose radius is estimated with a simplified RayleighPlesset equation according to pressure variation of the mean flow field. High-speed submerged water jet issuing from a sheathed sharp-edge orifice nozzle is treated. The periodically shedding of cavitation clouds is captured in a certain reliability compared to experiment data of visualization observation and the capability to capture the unsteadily shedding of cavitation clouds is demonstrated. The results demonstrate that cavitation takes place near the entrance of nozzle throat and cavitation cloud expands consequentially while flowing downstream. Developed bubble clouds break up near the nozzle exit and shed downstream periodically along the shear layer. Under the effect of cavitation bubbles the decay of core velocity is delayed compared to the case of no-cavitation jet.     

针状突体空化结构的高速摄影观察

应用高速摄影技术在直流式水洞中对针状突体的空化结构进行了试验研究。试验流速为8～40m/s,高速摄影机拍摄速率为20000fps,曝光时间为4μs。观察了不同流速下针状突体后空化云的形态以及随流动的演变情况,及不同掺气量对空化云的影响。此外,还给出针状突体空化区包络线（自由流线）的表达式。     

Large eddy simulation of turbulent attached cavitating flow with special emphasis on large scale structures of the hydrofoil wake and turbulence-cavitation interactions

In this paper, the turbulent attached cavitating flow around a Clark-Y hydrofoil is investigated by the large eddy simulation(LES) method coupled with a homogeneous cavitation model. The predicted lift coefficient and the cavity volume show a distinctly quasi-periodic process with cavitation shedding and the results agree fairly well with the available experimental data. The present simulation accurately captures the main features of the unsteady cavitation transient behavior including the attached cavity growth, the sheet/cloud cavitation transition and the cloud cavitation collapse. The vortex shedding structure from a hydrofoil cavitating wake is identified by the Q- criterion, which implies that the large scale structures might slide and roll down along the suction side of the hydrofoil while being further developed at the downstream. Further analysis demonstrates that the turbulence level of the flow is clearly related to the cavitation and the turbulence velocity fluctuation is much influenced by the cavity shedding.     

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

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The inception cavitating flows over an axisymmetric body with a blunt head-form

The inception cavitating flows around a blunt body are studied based on flow visualizations and velocity field measurements. The main purpose of the present work is to study the incipient cavity evolution and the interplay between the inception cavitation and the local turbulent flows. A high-speed video camera is used to visualize the cavitating flow structures, and the particle image velocimetry(PIV) technique is used to measure the velocity field, the vorticity, and the Reynolds stresses under non-cavitating and inception cavitating flow conditions. It is found that the appearance of visible cavities is preceded by the formation of a cluster of micro-bubbles not attached to the body surface and in a hairpin-shaped vortex structure. During its evolution, the cavity moves downstream with a lower speed. The effect of the incipient cavity is significant on the local vortical structures but slight on the timeaveraged velocity distribution. The mean Reynolds stress distributions in the turbulent shear flow can be substantially altered by the incipient cavities. The presence of the incipient cavities can lead to the production of turbulent fluctuations.     

Progress in numerical simulation of cavitating water jets

This paper reviews recent progress made toward modeling of cavitation and numerical simulation of cavitating water jets. Properties of existing cavitation models are discussed and a compressible mixture flow method for the numerical simulation of highspeed water jets accompanied by intensive cavitation is introduced. Two-phase fluids media of cavitating flow are treated as a homogeneous bubbly mixture and the mean flow is computed by solving Reynolds-Averaged Navier-Stokes (RANS) equations for compressible fluid. The intensity of cavitation is evaluated by the gas volume fraction, which is governed by the compressibility of bubble-liquid mixture corresponding to the status of mean flow field. Numerical results of cavitating water jet issuing from an orifice nozzle are presented and its applicability to intensively cavitating jets is demonstrated. However, the effect of impact pressure caused by collapsing of bubbles is neglected, and effectively coupling of the present compressible mixture flow method with the dynamics of bubbles remains to be a challenge.     

Shedding frequency of sheet cavitation around axisymmetric body at small angles of attack

Cavity shedding of cavitating flows around an axisymmetric body belongs to the unsteady cavitating flows in the condition of steady incoming current.The periodic characteristics of unsteady cavitating flows around an axisymmetric body at small angles of attack are investigated experimentally and numerically.The evolution and shedding process of the three-dimensional sheet cavitation are computed numerically by the Reynolds averaged Navier-Stokes equations and the RNG k-?model.The modification approach for eddy viscosity coefficient in the transition area of the two-phase flow is adopted to reproduce the shedding process of cavitating flows.The computed frequency of the cavity shedding coincides with the experimental data for the cases of unsteady cavitating flows around axisymmetric bodies with four headforms.Given the cavitation number,the shedding process of the cavitating flow depends heavily on the headform of the axisymmetric body.If the angle of attack of the axisymmetric body is greater than a critical value,the violent shedding of the sheet cavitation seems to be depressed.     

RESEARCH ON HYDRODYNAMIC FORCES OF CAVITATING GRID FINS

Hydrodynamic forces and flow pattern of four kinds of cavitating grid fins with cavitation number from 2.5 to 0.25 were simulated numerically with a bubble two phase flow model embodied in the commercial CFD code Fluent 6. 0.Comparison with experimental datum showed that rules of hy drodynamic forces changing with cavitation number were coordinated with experiment, and cavitation made the ratio of lift to resistance decrease. Calculated axial force and chordal pressure center in all wetted condition or those at cavitation number less than 0. 75 agreed well with experiments. Normal force in all wetted condition was less by 20 per cent. The differences between computation and experiment in the total range of cavitation number were mainly because that the inciplent cavitation number in computation was less than that at experiment.     

Numerical analysis of cavitation within slanted axial-flow pump

In this paper, the cavitating flow within a slanted axial-flow pump is numerically researched. The hydraulic and cavitation performance of the slanted axial-flow pump under different operation conditio...     

The direct numerical simulation of pipe flow

The conservative difference scheme and the third-order Runge-Kutta scheme in combination with the the Crank-Nicholson scheme are used to directly simulate the flow field in a pipe with the Reynolds number of 2 600. The flow field, including the velocity distribution and the turbulence intensity, is obtained by the direct numerical simulation. From the calculated results, the ratio of the linear average velocity along the ultrasonic propagation path to the profile average velocity on the pipe cross-section is also obtained in an ultrasonic flow meter. It is concluded that the direct numerical simulation method can be used to study the ratio of the profile-linear average velocity at low Reynolds number conditions in the transition region and to improve the measurement accuracy of the ultrasonic flow meter.     

不同水动力条件下的河流硅藻群落分布机理研究

水体生物种群指标与河流水动力参数之间的关系是水生态的重要研究课题之一。在西江水系柳江河流共设置31个硅藻采样点,来探究表层沉积硅藻在不同水动力条件下的群落结构,着重研究了硅藻与水深、流速和流量等水文变量间的关系。在研究区域共发现硅藻2纲38属264种,通过层状图和排序分析,流速是影响硅藻群落分布最主要的水动力条件,其次才是雷诺数。雷诺数的大小和浮游种类丰度关系紧密,但雷诺数对硅藻种类的影响还有不确定因数。直链藻和小环藻等浮游种类在大江中比小溪中较易出现,同时人工修建的大坝通过改变水动力条件,对藻类的分布产生影响,尤其在水库下游等较极端的湍流条件下,桥弯藻和脆杆藻的丰度明显地增长。     

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.     

A hydrodynamic investigation of brown trout (Salmo trutta) and rainbow trout (Oncorhynchus mykiss) redd selection at the riffle scale

High‐resolution velocity profile measurements were taken over a series of riffles on a gravel‐bed stream using a Pulse Coherent Acoustic Doppler Profiler (PCADP) to quantify the fluid structure of riffles and nests (redds) where brown trout (Salmo trutta) and rainbow trout (Oncorhynchus mykiss) spawned. Velocity profiles were obtained on a highly discretized planometric scale ranging between 20 and 40 cm grid spacings, with vertical observations occurring every 1.6 cm. From the velocity profiles, between 15 000 and 38 000 velocity measurements were obtained over each riffle on any given day of measurement. Velocity profiles were converted to streamwise velocity magnitude, flow depth, Reynolds number, Froude number, shear stress, vertical velocity components and turbulent kinetic energy per unit area to evaluate the spatial structure of the riffles and the spatial structure of redds (pits and tailspills) relative to the surrounding riffle structure. Semi‐variograms were employed to evaluate the persistence of the fluid structure based upon the metrics evaluated. Results showed that discrete velocity observations poorly described the spatial structure of the flow system and poorly correlated with redd locations. Reynolds number analysis identified a relatively consistent fluid property for distances typically 2–3 times the longitudinal length of redds. Turbulent kinetic energy per unit area consistently identified common regions on all riffles studied that corresponded with the location selections for redds where flow was identified as essentially uni‐directional. Froude number was found to be insensitive in predicting the fluid spatial structure in wadeable flow depths and relating it to the fluid structure of redds. Results indicated that a series of metrics at varying spatial scales of turbulence may be necessary to understand the spatial complexity of redd selection. Copyright © 2011 John Wiley & Sons, Ltd.     

带空泡轴对称细长体水动力脉动的实验研究

为了研究带空泡轴对称细长体定常来流下的水动力脉动特性，本文对四种头体模型进行了不同攻角下的空泡水洞实验，记录了水动力系数的时间序列，并对其进行了小波分析。本文运用小波分析方法从水动力脉动频率特征的角度揭示空泡流的脉动特性，是对何友声等(1997)用高速摄影方法研究空泡脉动的补充。     

绕水翼超空化流发展及其旋涡特性的实验研究

为深入了解超空化流场结构特性,利用数字粒子图像测速(DPIV)和高速全流场显示技术,观测了绕hydronautics水翼的超空化流动涡量场。采用空化流场中的空化泡作为示踪粒子来显示流动结构。结果表明:在超空化的不同发展阶段,流动涡量场呈现不同的分布特征:随着空化数的降低,上下涡带逐渐靠拢,并向后延伸、拉直;下涡带随空化区域内汽相和水汽混合相分布的不同而发生明显变化:空穴形成阶段的下涡带基本稳定;在两相共存阶段,汽相和水汽混合相的频繁转换使得下涡带的起始位置和形状发生剧烈的变化;而在超空化完全发展阶段,下涡带又趋于稳定,且起始位置移至水翼后部。在整个超空化阶段,汽相和水汽混合相之间存在着较大的速度梯度;与来流方向相比,垂直于来流方向的速度脉动要大得多。     

NUMERICAL SIMULATION OF FLOW THROUGH ORIFICE ENERGY-DISSIPATORS IN XIAOLANGDI FLOOD-DISCHAR-GE TUNNEL

1.　INTRODUCTIONThe Xiaolangdi project_ a key water conservancy project on the Yellow River_ isbeing built just now. According to the design scheme. three orifice energy-dissipators willbe installed in each flood-discharge tunnel. It is for the first time that orifice energy-dissipators are used in a large-scale hydraulic engineering.As a kind of internal energy-dissipator,orifices have the following advantages:energy dissipation region is shortand easyto control,and the flow pattern is …