Cavitation research with computational fluid dynamics:From Euler-Euler to Euler-Lagrange approach

Unsteady cavitating flow often contains vapor structures with a wide range of different length scales,from micro-bubbles to large cavities,which issues a big challenge to precisely investigate its evolution mechanism by computational fluid dynamics(CFD)method.The present work reviews the development of simulation methods for cavitation,especially the emerging Euler-Lagrange approach.Additionally,the progress of the numerical investigation of hot and vital issues is discussed,including cavitation inception,cloud cavitation inner structure and its formation mechanism,cavitation erosion,and cavitation noise.It is indicated that the Euler-Lagrange method can determine cavitation inception point better.For cloud cavitation,the Euler-Lagrange method can reveal the source of microbubbles and their distribution law inside the shedding cloud.This method also has advantages and great potential in assessing cloud cavitation-induced erosion and noise.With the ever-growing demands of cavitation simulation accuracy in basic research and engineering applications,how to improve the Euler-Lagrange method’s stability and applicability is still an open problem.To further promote the application of this advanced CFD simulation technology in cavitation research,some key issues are to be solved and feasible suggestions are put forward for further work.

Some notes on numerical investigation of three cavitation models through a verification and validation procedure

The present paper investigates the turbulent cavitating flow around the Clark-Y hydrofoil with special emphasis on the influence of cavitation models by verification and validation(V&V)method.RANS solver coupled with the three major cavitation models(i.e.,Zwart-Gerber-Belamri,Schnerr and Sauer and full cavitation model,which are abbreviated to ZGB model,SS model and FC model respectively)is employed in this paper.The results indicate that the three cavitation models can properly reproduce the cavitation evolutions.ZGB model and SS model give better prediction in the overall cavitation patterns.FC model exhibits an obvious under-estimation for the sheet cavity,and the predicted volume fraction is closely related to the turbulent flow.The verification and validation procedure is involved to quantitatively assess the accuracy of these three cavitation models.It is indicated that the V&V procedure is suitable for the unsteady cavitating flow.The errors estimate is robust and conservative within the cavitation region,while gets closer to zero in the no-cavitation region.In addition,ZGB model exhibits the highest overall accuracy among the three models,which further verifies its wide applicability.

Experimental investigation of the flow characteristics of jet pumps for zero flow-ratio conditions

Experimental research was conducted on the performance curves and the cavity evolution for different flow and geometric parameters in jet pumps for zero flow ratio(ZFR)conditions.New pressure ratio,Pr,flow ratio,qr,were used in place of the conventional performance parameters h,q,to characterize the jet pump flow performance.A super cavitation cavity in the jet pump was observed to fill most of the flow channel,which hindered further increases of the flow rate and increased qr to one,thus,created a critical point on the new P_(r)-q_(r)^(2)curve.Before the critical point,P_(r)was proportional to q_(r)^(2)with a coefficient that was much more sensitive to the area ratio than the relative throat length and the diffusion angle.After the critical point,the flow rate reached its maximum,the limiting flow rate,which only depended on the total inlet pressure and the area ratio.The total inlet pressure was proportional to the square of the limiting flow rate with a flow coefficient that was only a quadratic function of the area ratio.

A review of cavitation in tip-leakage flow and its control

The tip-leakage vortex(TLV)cavitation is a challenging issue for a variety of axial hydraulic turbines and pumps from both technical and scientific viewpoints.The flow characteristics of the TLV cavitation were widely studied in the past decades,but the knowledge about the tip-leakage cavitating flow is still limited.The present paper reviews the progresses in the researches of the TLV cavitation,including the numerical methods for the TLV cavitation,the flow characteristics of the TLV,the influences of the TLV cavitation on the local flow field and the control strategies of the TLV cavitation.It is indicated that the non-condensable gas may play an important role in the development of the TLV cavitation,and this fact should be considered during a careful simulation of the TLV cavitation.It is also suggested that the development of the TLV cavitation will significantly influence the distributions of the vorticity and the turbulence kinetic energy.Due to the complexity of the TLV cavitation,it is still an open question how to suppress the TLV cavitation in a simple but effective way.Finally,based on these understandings,some advanced topics for the future work are suggested to further promote the study of the TLV cavitation,for a deeper knowledge about the TLV cavitation.

LES method of the tip clearance vortex cavitation in a propelling pump with special emphasis on the cavitation-vortex interaction

The turbulent cavitating flow around the propelling pump tip clearance is numerically simulated using the large eddy simulation(LES)method coupled with the Zwart-Gerber-Belamri(ZGB)cavitation model to investigate the cavitation-vortex interaction mechanism.The calculated cavitation structures around the blades are in a remarkable agreement with the experimental results.The distributions of the tip clearance vortex under two cavitation conditions are obtained and compared.The results show that the cavitation development enhances the vorticity generation and the flow unsteadiness around the tip clearance of a propelling pump.Vortices are basically located around the cavitation areas,particularly in the tip clearance region,during the cavitation.The relative vorticity transport equation is applied for the cavitating turbulent flows and it is further indicated that the vortex stretching term makes the main contribution in the vortex production,and the baroclinic torque and dilation terms are important source terms for the vorticity generation in the cavitating flow.In addition,the viscous diffusion term and the Coriolis force term are significant in modifying the vorticity field inside the blade tip clearance.

Numerical assessment of the erosion risk for cavitating twisted hydrofoil by three methods

In this paper, the large eddy simulation (LES) method in conjunction with the Zwart cavitation model is adopted for the assessment of the erosion risk on a hydrofoil surface. The numerical results are in good agreement with the experiments. On this basis, three methods, namely the intensity function method (IFM), the time-averaged aggressiveness indicators (TAIs) and the gray level method (GLM), are applied for the assessment of the erosion risk. It is shown that the erosion intensity index of the IFM is extremely sensitive to the artificially selected thresholds, which greatly limits the application of the method. The erosion risk predicted by four indicators in the TAIs does not agree well with the experimental results. Further analysis demonstrates that the GLM using the instantaneous pressure field is relatively satisfactory, which can provide a reasonable assessment of the erosion and is not very sensitive to the artificially selected thresholds. To further improve the accuracy of the GLM for the erosion risk prediction, the time-average pressure field is adopted in the GLM for the erosion evaluation. It is suggested that the erosion assessment by using the time-averaged pressure field is in better agreement with the experimental results when compared with that by using the instantaneous pressure field.

Some notes on numerical simulation of the turbulent cavitating flow with a dynamic cubic nonlinear sub-grid scale model in OpenFOAM

The accuracy of large eddy simulation(LES)is highly dependent on the performance of sub-grid scale(SGS)model.In the present paper,a dynamic cubic nonlinear sub-grid scale model(DCNM)proposed by Huang et al.is implemented for the simulation of unsteady cavitating flow around a 3-D Clark-Y hydrofoil in OpenFOAM.Its performance in predicting the evolution of cloud cavitation is discussed in detail.The simulation with a linear model,the dynamic Smagorinsky model(DSM),is also conducted as a comparison.The results with DCNM show a better agreement with the available experimental observation.The comparison between DCNM and DSM further suggests that the DCNM is able to predict the backscatter more precisely,which is an important feature in LES.The characteristics of DCNM is analyzed to account for its advantages in the prediction of unsteady cloud cavitation as well.The results reveal that it is the nonlinear terms of DCNM that makes DCNM capture sub-grid scale vortices better and more suitable for studying the transient behaviors of cloud cavitation than DSM.

Large eddy simulation of the transient cavitating vortical flow in a jet pump with special emphasis on the unstable limited operation stage

This paper studies the unsteady three-dimensional cavitating turbulent flow in a jet pump.Specifically,thefocus is on the unstable limited operation stage,and both the computational and experimental methods are used.In the experiments,the distribution of the wall pressure,as well as the evolution of cavitation over time,are obtained for a jet pump.Computation is carried out using the large eddy simulation,combined with a mass transfer cavitation model.The numerical results are compared with the experimental results,including the fundamental performances(the pressure ratio h and the efficiencyη),as well as the wall pressure distribution.Both the experimental and computational results indicate that the evolution of the cavitation over time in a jet pump is a quasi-periodic process during the unstable limited operation stage.The annular vortex cavitation inception,development and collapse predicted by the large eddy simulation agree fairly well with the experimental observations.Furthermore,the relationship between the cavitation and the vortex structure is discussed based on the numerical results,and it is shown that the development of the vortex structures in the jet pump is closely related to the evolution of the cavitation.The cavitation-vortex interaction is thoroughly analyzed based on the vorticity transport equation.This analysis reveals that the cavitation in a jet pump dramatically influences the distribution and the production of the vorticity.The process of the annular cavitation inception,development,and collapse involves a significant increase of the vorticity.

Spatial and spectral investigation of turbulent kinetic energy in cavitating flow generated by Clark-Y hydrofoil

In the present paper,the turbulent cavitating flow generated by a Clark-Y hydrofoil is investigated by large eddy simulation(LES)combined with Zwart-Gerber-Belamri(ZGB)cavitation model.In order to shed light on the influence of cavitation on turbulent energy distribution among scales,energy spectrum obtained from the three-dimensional velocity field is firstly applied to turbulent cavitating flow.Spatial and spectral distributions of turbulent kinetic energy are studied for both non-cavitating flow and cavitating flow.Cavitation is found to have a significant effect on the original turbulent flow by inducing more large-scale turbulent structures.The energy spectrum of cloud cavitating flow also experiences a periodic evolution as cavitation develops,and a large amount of turbulent kinetic energy is found to generate as the first shedding,cutoff and second shedding of cavities happen.

URANS simulations of the tip-leakage cavitating flow with verification and validation procedures

In the present paper, the Vortex Identified Zwart-Gerber-Belamri（VIZGB） cavitation model coupled with the SST-CC turbulence model is used to investigate the unsteady tip-leakage cavitating flow induced by a NACA0009 hydrofoil. A qualitative comparison between the numerical and experimental results is made. In order to quantitatively evaluate the reliability of the numerical data, the verification and validation（V＆V） procedures are used in the present paper. Errors of numerical results are estimated with seven error estimators based on the Richardson extrapolation method. It is shown that though a strict validation cannot be achieved, a reasonable prediction of the gross characteristics of the tip-leakage cavitating flow can be obtained. Based on the numerical results, the influence of the cavitation on the tip-leakage vortex（TLV） is discussed, which indicates that the cavitation accelerates the fusion of the TLV and the tip-separation vortex（TSV）. Moreover, the trajectory of the TLV, when the cavitation occurs, is close to the side wall.

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.

基于多重调谐质量阻尼器的苏通大桥抖振位移最优控制的数值模拟（英文）

研究目的:为超大跨度斜拉桥抗风设计与抖振控制提供参考。研究方法:基于ANSYS建立了苏通大桥三维有限元模型,并在MATLAB平台模拟了苏通大桥三维脉动风场。考虑主梁断面气动自激力,进行了苏通大桥抖振时域分析。根据苏通大桥动力特性和抖振时域分析结果,重点分析了多重调谐质量阻尼器(MTMD)用于抖振控制的参数敏感性。考虑MTMD的控制效果、建造费用、施工难度及鲁棒性等因素建立了关于MTMD设计参数的目标函数,并基于一阶优化算法进行目标函数最优解的非线性搜索,据此获得了MTMD在约束条件下的最优设计参数。重要结论:1.苏通大桥侧向抖振位移主要由第一阶侧弯振型控制,竖向抖振位移主要由第一阶竖弯振型控制;2.MTMD的控制效果对设计参数的变化十分敏感,其中质量比和频带宽敏感性更强;3.MTMD的最优设计参数可以通过一阶优化算法获得,并可通过零阶优化算法对优化结果进行验证;4.采用优化后的MTMD设计参数,苏通大桥的抖振响应可以得到明显抑制,且侧向抖振控制效果更加明显。

Temporal and spatial characteristics of monopole acoustic energy dominated by unsteady thermodynamic cavitating flow

The acoustic propagation characteristics of the cavitating flow are essential for the noise suppression, but were not well studied. In the current paper, a new technique concerning the propagation path of the monopole acoustic energy is presented and two typical thermodynamic cavitation modes (the inertial and thermal modes) are selected to investigate the effect of the cavity shedding dynamics on the acoustic propagation path. In the inertial mode, the temporal variation and the spatial distributions of the monopole acoustic energy as well as the divergence of the monopole acoustic pressure are both more powerful and concentrated than that in the thermal mode. The acoustic propagation path in the thermal mode strictly satisfies the feature of the convective amplification, while there exists another propagation direction close to the normal direction of the foil surface in the inertial mode. Furthermore, the occurrence of the normal direction propagation will make the path deviate from the convective direction.

大攻角下仿生水翼非一致流场及空化数值分析

基于座头鲸鳍肢造型的仿生水翼在大攻角下具有优越的流动控制和空化性能,为研究大攻角下仿生水翼绕流机理,该文基于LES和ZGB模型对18°攻角下4L仿生水翼的空化流场进行了数值模拟,结果表明:大攻角下,仿生水翼表面存在非一致流场,其产生于分离涡的展向扩展及凸峰附着流的分割作用,根据分离涡状态将水翼表面流场分为扩张区和收缩区。收缩区内空泡形态较稳定,脱落频率小,存在由附着流汇合引起的小范围回射流;扩张区内存在“U”形空泡及涡结构,其产生于流向涡与回射流的共同作用;非一致流场下水翼表面呈现一定的压力脉动特征,水翼后部压力脉动较小而分区边界处压力脉动较大。

Numerical simulation of multi-scale cavitating flow with special emphasis on the influence of vortex on micro-bubbles

A multi-scale Euler-Lagrange method is applied in the current paper to investigate the characteristics of turbulent cloud cavitating flow around a Clark-Y hydrofoil,in which macroscopic cavitating structures are simulated by volume of fluid(VOF)approach,while micro-scale bubbles are modelled based on Rayleigh-Plesset equation and bubble motion equation.The numerical results are in reasonable agreement with the available experiments,and the transition between multi-scale structures is captured clearly.The evolution of microscopic bubble behaviors is statistically investigated.During one typical cycle,numbers and Sauter mean radius of the bubbles show a similar variation tendency which both sharply spike to their maxima after the breakup of the sheet cavity,and then decrease continuously to their minima before the next breakup.Discrete bubbles are mainly concentrated at the tail of the attached cavity,in front of the cloud cavity and in the region quite close to the hydrofoil suction side.Furthermore,vortices are extracted to account for the micro-scale hydrodynamics.It is found that intense vortices aggravate turbulence fluctuation,thus spalling cavity to generate massive micro bubbles.Meanwhile,the vortices provide microscopic bubbles low pressure and detain them so that numerous bubbles are able to grow.These effects are remarkable after the breakup of attached sheet cavity,owing to the violent vortices generated.On the contrary,when sheet cavity develops,the flow field becomes comparatively stable since the strong vortices travel downstream.Few micro-scale bubbles are produced,and their volume is generally small.