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.     

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 review of cavitation in hydraulic machinery

This paper mainly summarizes the recent progresses for the cavitation study in the hydraulic machinery including turbopumps, hydro turbines, etc.. Especially, the newly developed numerical methods for simulating cavitating turbulent flows and the achievements with regard to the complicated flow features revealed by using advanced optical techniques as well as cavitation simulation are introduced so as to make a better understanding of the cavitating flow mechanism for hydraulic machinery. Since cavitation instabilities are also vital issue and rather harmful for the operation safety of hydro machines, we present the 1-D analysis method, which is identified to be very useful for engineering applications regarding the cavitating flows in inducers, turbine draft tubes, etc. Though both cavitation and hydraulic machinery are extensively discussed in literatures, one should be aware that a few problems still remains and are open for solution, such as the comprehensive understanding of cavitating turbulent flows especially inside hydro turbines, the unneglectable discrepancies between the numerical and experimental data, etc.. To further promote the study of cavitation in hydraulic machinery, some advanced topics such as a Density-Based solver suitable for highly compressible cavitating turbulent flows, a virtual cavitation tunnel, etc. are addressed for the future works.     

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.     

NUMERICAL SIMULATIONS OF 2D PERIODIC UNSTEADY CAVITATING FLOWS

1. INTRODUCTION Cavitation is a natural phenomenon especially existing in liquids. A cavitating flow generally involves a large number of vapor structures such as bubbles or vortices which are convecting downstream. When they reach high pressure zones, th…     

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...     

Experimental investigation and numerical analysis of unsteady attached sheet- cavitating flows in a centrifugal pump

This paper studies the attached sheet cavitation in centrifugal pumps. A pump casted from Perspex is used as the test subject. The cavitation bubbles were observed in the entrance of the impeller and the drops of the head coefficients were measured under different operating conditions. A Filter-Based Model (FBM), derived from the RNG k – ? model, and a modified Zwart model are adopted in the numerical predictions of the unsteady cavitating flows in the pump. The simulations are carried out and the results are compared with experimental results for 3 different flow coefficients, from 0.077 to 0.114. Under four operating conditions, qualitative comparisons are made between experimental and numerical cavitation patterns, as visualized by a high-speed camera and described as isosurfaces of the vapour volume fraction α_v = 0.1. It is shown that the simulation can truly represent the development of the attached sheet cavitation in the impeller. At the same time, the curves for the drops of the head coefficients obtained from experiments and calculations are also quantitatively compared, which shows that the decline of the head coefficients at every flow coefficient is correctly captured, and the prediction accuracy is high. In addition, the detailed analysis is made on the vapour volume fraction contours on the plane of span is 0.5 and the loading distributions around the blade section at the midspan. It is shown that the FBM model and the modified Zwart model are effective for the numerical simulation of the cavitating flow in centrifugal pumps. The analysis results can also be used as the basis for the further research of the attached sheet cavitation and the improvement of centrifugal pumps.     

Numerical investigation of the effect of rotation on cavitating flows over axisymmetric cavitators

The rotating axisymmetric cavitator is widely applied in underwater vehicles, and its rotational motion affects the cavitating flow over the cavitator. This study focuses on the effect of rotation on the flow structure in the cavity bubble. Unsteady 2-D/3-D numerical simulations of cavitating flows over axisymmetric cavitators are performed using the volume of fraction(VOF) method and the Sauer-Schnerr cavitation model. Firstly, the 2-D simulation of cavitating flow over a circular disk or a cone cavitator is carried out at various cavitation numbers(0.15, 0.175, 0.2, 0.225 and 0.25). The simulated cavity lengths and drag coefficients are compared with the experimental data, the theoretical estimations and the published numerical results. Then the 3-D simulations of cavitating flows over the same axisymmetric cavitators with different rotating speeds are performed using the sliding mesh model(SMM). The effect of rotation on the cavity shape and the internal flow structure is analyzed.     

NUMERICAL SIMULATIONS OF CAVITATING FLOWS

BRIEFINTRODUCTIONOFTHEPAPER :　Thisthesismainlyresearchesonthehydrodynamiccharacteristicsandmechanismfor 3Dcavitatingflowsaroundaxisymmetricbodies ,aswellasthe2Dcavitatingflowsaroundhydrofoils .Anewcavi tatingflowmodel,whichinvolvesviscousandmul ti phaseeffects,isestablishedintwo phaseflowcategory .Accordingtothelocalizedvariationofdensitywithinpredominantlyincompressiblewatermediumandthecharacteristicsofsoundspeedinwater vapormixture ,arelationbetweendensityandpressureisassumed ,in…     

THE WALL EFFECT ON VENTILATED CAVITATING FLOWS IN CLOSED CAVITATION TUNNELS

For ventilated cavitating flows in a closed water tunnel, the wall effect may exert an important influence on cavity shape and hydrodynamics, An isotropic mixture multiphase model was established to study the wall effect based on the RANS equations, coupled with a natural cavitation model and the RNG k-ε turbulent model. The governing equations were discretized using the finite volume method and solved by the Gauss-Seidel linear equation solver on the basis of a segregation algorithm. The algebraic multigrid approach was carried through to accelerate the convergence of solution. The steady ventilated cavitating flows in water tunnels of different diameter were simulated for a conceptual underwater vehicle model which had a disk cavitator. It is found that the choked cavitation number derived is close to the approximate solution of natural cavitating flow for a 3-D disk. The critical ventilation rate falls with decreasing diameter of the water tunnel. However, the cavity size and drag coeflicient are rising with the decrease in tunnel diameter for the same ventilation rate, and the cavity size will be much different in water tunnels of different diameter even for the same ventilated cavitation number.     

NUMERICAL ANALYSIS OF THE INFLUENCE OF THE TIP CLEARANCE FLOWS ON THE UNSTEADY CAVITATING FLOWS IN A THREE- D IMENSIONAL INDUCER

To clarify the influences of the tip clearance flows on the unsteady cavitating flow,the three-dimensional unsteady cavitating flows through both the two-dimensional cascades and the three-dimensional inducer with and without tip clearance are performed numerically.The governing equations for the compressible fluid flow with the DES turbulence model are employed with the assumption of the isentropic process of liquid phase.The evolution of cavities is represented as the source/sink of vapor phase.The basic equations in the curve linear coordinate are solved by the finite difference method.As the results of the three-dimensional cavitating flows through the two-dimensional cascades,the tip clearance flows from the pressure side to the suction side of the blade produces the tip vortex cavitation,which affects the sheet cavitation on the leading edge of the next blade and enhances the blockage effect near the casing than the flows without tip clearance.On the other hand,in the case of the three-dimensional inducer,the large backflow cavitation is observed around the inlet of the inducer,where the cavities are developed on the casing by the tip clearance flows.The large pressure gradient between the non-cavitating pressure side and the cavitating suction side enhances the tip clearance flows.The calculation considering the tip clearance reproduces the developed cavitation region similar to that of experimental visualizations.Additionally,the backflow cavitation rotates with the speed slower than the rotation speed of the inducer.Then,the rotation of backflow cavitation causes the periodic fluctuation of the outlet pressure greater than that of the inlet pressure.     

Some notes on numerical simulation and error analyses of the attached turbulent cavitating flow by LES

In this letter, the attached turbulent cavitating flow around the Clark-Y hydrofoil is investigated by the numerical simulation with special emphasis on error analysis of large eddy simulation(LES) for the unsteady cavitation simulation. The numerical results indicate that the present simulation can capture the periodic cavity shedding behavior and show a fairly good agreement with the available experimental data. Further analysis demonstrates that the cavitation has a great influence on LES numerical error and modeling error. The modeling error and numerical error are almost on the same order of magnitude, while the modeling error often shows a little bit larger magnitude than numerical error. The numerical error and modeling error sometimes can partially offset each other if they have the opposite sign. Besides, our results show that cavitation can extend the magnitudes and oscillation levels of numerical error and modeling error.     

Verification and validation of URANS simulations of the turbulent cavitating flow around the hydrofoil

In this paper, we investigate the verification and validation(VV) procedures for the URANS simulations of the turbulent cavitating flow around a Clark-Y hydrofoil. The main focus is on the feasibility of various Richardson extrapolation-based uncertainty estimators in the cavitating flow simulation. The unsteady cavitating flow is simulated by a density corrected model(DCM) coupled with the Zwart cavitation model. The estimated uncertainty is used to evaluate the applicability of various uncertainty estimation methods for the cavitating flow simulation. It is shown that the preferred uncertainty estimators include the modified Factor of Safety(FS1), the Factor of Safety(FS) and the Grid Convergence Index(GCI). The distribution of the area without achieving the validation at the U v level shows a strong relationship with the cavitation. Further analysis indicates that the predicted velocity distributions, the transient cavitation patterns and the effects of the vortex stretching are highly influenced by the mesh resolution.     

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.     

带空泡运动航行体的附加质量研究

提出了确定带自然空泡运动物体附加质量的方法.这一方法基于在数值水洞中作摇荡运动物体的水动力计算, 包括两个主要步骤:首先采用CFD技术模拟空泡流场,求解水动力;然后根据物体运动方程,由水动力计算出附加质量.研究了带自然空泡圆盘和轴对称细长体的附加质量.计算结果与理论解一致,验证了本文方法的有效性.与切片法相比,本文方法可以更为准确地定量预报带空泡运动轴对称细长体的附加质量.     

PIV analysis and high-speed photographic observation of cavitating flow field behind circular multi-orifice plates

Based on a self-developed hydrodynamic cavitation device with different geometric parameters for circular multi-orifice plates, turbulence characteristics of cavitating flow behind multi-orifice plates, including the effects of orifice number and orifice layout on longitudinal velocity,turbulence intensity, and Reynolds stress, were measured with the particle image velocimetry(PIV) technique. Flow regimes of the cavitating flow were also observed with high-speed photography. The experimental results showed the following:(1) high-velocity multiple cavitating jets occurred behind the multi-orifice plates, and the cavitating flow fields were characterized by topological structures;(2) the longitudinal velocity at each cross-section exhibited a sawtooth-like distribution close to the multi-orifice plate, and each sawtooth indicated one jet issuing from one orifice;(3) there were similar magnitudes and forms for the longitudinal and vertical turbulence intensities at the same cross-section;(4) the variation in amplitude of Reynolds stress increased with an increase in orifice number; and(5) the cavitation clouds in the flow fields became denser with the increase in orifice number, and the clouds generated by the staggered layout of orifices were greater in number than those generated by the checkerboard-type one for the same orifice number. The experimental results can be used to analyze the mechanism of killing pathogenic microorganisms through hydrodynamic cavitation.     

Application of modified κ-ω model to predicting cavitating flow in centrifugal pump

Considering the compressibility of the cavity in the cavitating flow, this paper presents a modified κ-ω model for predicting the cavitating flow in a centrifugal pump, in which the modified κ-ω model and Schnerr-Sauer cavitation model were combined with ANSYS CFX. To evaluate the modified and standard κ-ω models, numerical simulations were performed with these two models, respectively, and the calculation results were compared with the experimental data. Numerical simulations were executed with three different values of the flow coefficient, and the simulation results of the modified κ-ω model showed agreement with most of the experimental data. The cavitating flow in the centrifugal pump obtained by the modified κ-ω model at the design flow coefficient of 0.102, was analyzed. When the cavitation number decreases, the cavity initially generates on the suction side of the blade near the leading edge and then expands to the outlet of the impeller, and the decrease of the total pressure coefficient mainly occurs upstream of the impeller passage, while the downstream remains almost unaffected by the development of cavitation.     

绕扭曲翼型三维非定常空泡脱落结构的数值分析

该文以一种三维扭曲翼型为研究对象,采用均衡流空化模型和基于滤波器的湍流修改模式模拟了绕翼型非定常空化流动。计算结果显示,在一定条件下绕翼型的空泡流动存在两种脱落结构,即主体脱落和二次脱落。进一步的流场分析表明回射流和侧面射流是这两种空泡脱落结构产生的主要原因。计算结果与试验的比较说明,该文采用的数值模拟方法可成功模拟实验观测的空泡脱落现象。     

NUMERICAL SIMULATION OF BUBBLE FLOW INTERACTIONS

Bubble flow interaction can be important in many practical engineering applications. For instance, cavitation is a problem of interaction between nuclei and local pressure field variations including turbulent oscillations and large scale pressure variations. Various types of behaviours fundamentally depend on the relative sizes of the nuclei and the length scales of the pressure variations as well as the relative importance of bubble natural periods of oscillation and the characteristic time of the field pressure variations. Similarly, bubbles can significantly affect the performance of lifting devices or propulsors. We present here some fundamental numerical studies of bubble dynamics and deformation, then a practical method using a multi-bubble Surface Averaged Pressure (DF-Multi-SAP©) to simulate cavitation inception and scaling, and connect this with more precise 3-D simulations. This same method is then extended to the study of two-way coupling between a viscous compressible flow and a bubble population in the flow field.     

混流式水轮机空化流动模拟中的空化模型对比研究

以某水电厂混流式机组为例,在同样的工况下,采用Schnerr-Sauer空化模型和Z-G-B空化模型对其进行空化流动模拟,并与现场真机试验情况进行对比,从而比较各模型的计算效果。结果表明,水轮机叶片背面进水边、出水边附近的大部分区域、水轮机叶片下半段与下环交界处的空化程度较为严重。此外,Schnerr-Sauer空化模型仅适用于空泡数量比较少的情形,且仿真效果不甚理想;而Z-G-B模型的适用范围较广,且效果较好,因此可以在混流式水轮机空化流动模拟中更多地采用。