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.     

CAVITATING SUPPRESSION OF LOW SPECIFIC SPEED CENTRIFUGAL PUMP WITH GAP DRAINAGE BLADES

This paper aims to clarify the cavitation suppression mechanism of the gap structure impeller based on the analysis of cavitation characteristics in a low specific speed centrifugal pump. In order to obtain reliable and consistent numerical results, some numerical considerations and modeling methodology were demonstrated and researched, and a check of the time and space resolution were also conducted. Hence the predicted cavitation performance of the two centrifugal pumps were investigated and compared with experimental results, and they were in qualitative agreement. It was confirmed that the new gap structure impeller has a very good characteristic of inhibiting cavitation, especially in large flow area, the present numerical method can effectively capture the major internal flow features in the centrifugal pump, through the comparison of the two type impeller flow fields, the cavitation suppression mechanism of the gap impeller may be the combination effects of the small vice blade’s guiding flow and gap tunnel’s auto-balancing of pressure.     

口环间隙泄漏对离心泵空化性能的影响分析

以DG-350型多级离心泵次级叶轮为研究对象,研究了口环间隙对离心泵空化性能产生的影响。通过定常数值模拟,计算出了离心泵的扬程和效率,同时得出了口环与进口段交汇处的速度矢量图、涡量云图和空化区域分布图以及叶轮流道内的空化区域分布图。模拟结果与实验结果的对比分析表明:(1)误差都在实际工程所要求的5%左右,说明计算与模拟结果准确;(2)由于口环与进口段交汇处速度旋涡的存在,使得离心泵的进口段与前口环交汇处区域的压力降低,从而导致了空化现象的发生;(3)随着口环间隙的增大叶轮流道上的空化区域也随之增大,从而减小了流体的过流面积,使流体速度和必须的汽蚀余量增大,NPSHR增大,则叶轮进口处的空化区域也就会增大。     

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...     

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.     

低比转速离心泵空化性能的数值模拟

为了对低比转速离心泵空化发生时的内部气液两相流动进行分析,应用计算流体力学(CFD)软件对比转速为66的离心泵空化性能进行气液两相流场的数值研究。对不同有效空化余量时叶轮内部气泡分布的研究表明,泵在进口压力较高时就已经在叶片的进口背面产生空化初生,临界空化余量和许用空化余量时,气泡在叶片表面和流道内部均有分布,占据了部分叶轮流道,影响叶轮内部能量交换,并可能对泵造成空蚀。对该实型泵进行试验研究,验证了数值计算的精确度。     

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 investigation of unsteady cavitating turbulent flows around twisted hydrofoil from the Lagrangian viewpoint

Unsteady cavitating turbulent flow around twisted hydrofoil is simulated with Zwart cavitation model combined with the filter-based density correction model(FBDCM).Numerical results simulated the entire process of the 3-D cavitation shedding including the re-entrant jet and side-entrant jet dynamics and were compared with the available experimental data.The distribution of finite-time Lyapunov exponent(FTLE) was used to analyze the 3-D behavior of the re-entrant jet from the Lagrangian viewpoint,which shows that it can significantly influence the particle trackers in the attached cavity.Further analysis indicates that the different flow behavior on the suction side with different attack angle can be identified with Lagrangian coherent structures(LCS).For the area with a large attack angle,the primary shedding modifies the flow pattern on the suction side.With the decrease in attack angle,the attached cavity tends to be steady,and LCS A is close to the upper wall.A further decrease in attack angle eliminates LCS A in the boundary layer.The FTLE distribution also indicates that the decreasing attack angle induces a thinner boundary layer along the foil surface on the suction side.     

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.     

Numerical simulation unsteady cloud cavitating flow with a filter-based density correction model简

In this paper, various turbulence closure models for unsteady cavitating flows are investigated. The filter-based model （FBM） and the density correction model （DCM） were proposed to reduce the turbulent eddy viscosities in a turbulent cavitating flow based on the local meshing resolution and the local fluid density, respectively. The effects of the resolution control parameters in the FBM and DCM models are discussed. It is shown that the eddy viscosity near the cavity closure region can significantly influence the cavity shapes and the unsteady shedding pattern of the cavitating flows. To improve the predictions, a Filter-Based Density Cor-rection model （FBDCM） is proposed, which blends the FBM and DCM models according to the local fluid density. The new FBDCM model can effectively represent the eddy viscosity, according to the multi-phase characteristics of the unsteady cavitating flows. The experimental validations regarding the force analysis and the unsteady cavity visualization show that good agreements with experimental visualizations and measurements are obtained by the FBDCM model. For the FBDCM model, the attached cavity length and the resulting hydrodynamic characteristics are subsequently affected by the detail turbulence modeling parameters, and the model is shown to be effective in improving the overall predictive capability.     

Numerical analysis of the unsteady behavior of cloud cavitation around a hydrofoil based on an improved filter-based model

The unsteady cavitation evolution around the Clark-Y hydrofoil is investigated in this paper, by using an improved filter-base model(FBM) with the density correction method(DCM). To improve the prediction accuracy, the filter scale is adjusted based on the grid size. The numerical results show that a small filter scale is crucial for the unsteady simulations of the cavity shedding flow. The hybrid method that combines the FBM and the DCM could help to limit the overprediction of the turbulent viscosity in the cavitation region on the wall of the hydrofoil and in the wake. The large value of the maximum density ratio ? l /? v, clip promotes the mass transfer rate between the liquid phase and the vapor phase, which results in a large sheet cavity length and the vapor fraction rise inside the cavity. The cavity patterns predicted by the improved method are verified by the experimental visualizations. The time-average lift, the drag coefficient and the primary oscillating frequency St for the cavitation number ?= 0.8, the angle of attack, ?= 8o, at a Reynolds number Re= 7 ?105 are 0.735, 0.115 and 0.183, respectively, and the predicted errors are 3.29%, 3.36% and 8.93%. The typical three stages in one revolution are well-captured, including the initiation of the sheet/attached cavity, the growth toward the trailing edge(TE) with the development of the re-entrant jet flow, and the large scale cloud cavity shedding. It is observed that the cloud cavity shedding flow induces the vortex pairs of the TE vortices in the wake and the shedding vortices. The positive vorticity vortex of the re-entrant jet and the TE vortices interacts and merges with the negative vorticity vortex of the leading edge(LE) cavity to produce the shedding flow.     

双吸泵小流量工况下的空化特性研究

为研究双吸泵在小流量工况下叶轮内部空化特性,同时进一步说明小流量工况相比于设计工况时的空化特性差异,结合均质两相流模型和SST k-ω湍流模型,对双吸泵小流量工况和设计工况下的全流道空化流场进行数值模拟,以分析不同流量工况下空化分布与发展情况,以及空化对各叶片载荷造成的影响。研究结果表明:适当减小双吸泵进口流量,有助于改善双吸泵的空化性能;在小流量工况下空化首先发生于叶片吸力面头部靠后盖板附近,而且此处的空泡体积分数最大,这一空化特征同设计工况有所差异;随着NPSH的降低,叶轮内空化不断加强,但是小流量工况下的空化强度始终不及设计工况;不同空化状态会导致叶片吸力面压力的变化,从而表现为叶片表面载荷分布的变化。     

超空化水翼流场的DPIV实验研究

该文采用DPIV粒子成像测速系统对绕2D超空化水翼(Tulin翼)的空化流场进行了测量,研究了初生空化阶段,附着型片状空化阶段,空化云以及超空化四个阶段典型流场的速度分布及涡量分布。实验结果表明:在空化发展的四个阶段,相对于主流区域,空化流区域速度明显偏小;在整个流动区域,有两个速度梯度较大的区域,一个是空化区和水体主流区的交界面,一个是翼形表面的边界层区域。在空化发展的四个阶段邻近翼型尾部处均会产生一个大小近似相等的正向涡和一个反向涡,并且正向涡总是处于反向涡的下方,形成一组正向对涡。     

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.     

基于CFD的离心泵叶轮水力性能优化

离心泵已广泛应用于工农业生产生活中,因此其效率的提升对于满足实际需要和节约能源有着非常重要的意义。为了解决某型号离心泵叶轮出口部位的少量紊流,为该离心泵叶轮添加了5个短叶片,以求减少紊流、改善叶轮出流状况、保护固定导叶,并达到进一步提升效率的目的。将添加短叶片前后的离心泵基于SST模型进行流场模拟,并绘制出Q-η曲线进行比较,然后将设计工况下添加短叶片前后的压力云图、速度流线图与实际试验数据进行比较分析。结果发现,在添加短叶片后,叶轮出口部位的紊流明显减小,液流更加均匀,效率也得到了一定程度的提升。试验结果可为该型号离心泵的优化和效率的进一步提升提供一种新的思路和理论参考。     

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.     

Three-dimensional large eddy simulation and vorticity analysis of unsteady cavi- taring flow around a twisted hydrofoil

Large Eddy Simulation (LES) was coupled with a mass transfer cavitation model to predict unsteady 3-D turbulent cavitating flows around a twisted hydrofoil. The wall-adapting local eddy-viscosity (WALE) model was used to give the Sub-Grid Scale (SGS) stress term. The predicted 3-D cavitation evolutions, including the cavity growth, break-off and collapse downstream, and the shedding cycle as well as its frequency agree fairly well with experimental results. The mechanism for the interactions between the cavitation and the vortices was discussed based on the analysis of the vorticity transport equation related to the vortex stretching, volumetric expansion/contraction and baroclinic torque terms along the hydrofoil mid-plane. The vortical flow analysis demonstrates that cavitation promotes the vortex production and the flow unsteadiness. In non-cavitation conditions, the streamline smoothly passes along the upper wall of the hydrofoil with no boundary layer separation and the boundary layer is thin and attached to the foil except at the trailing edge. With decreasing cavitation number, the present case has σ= 1.07, and the attached sheet cavitation becomes highly unsteady, with periodic growth and break-off to form the cavitation cloud. The expansion due to cavitation induces boundary layer separation and significantly increases the vorticity magnitude at the cavity interface. A detailed analysis using the vorticity transport equation shows that the cavitation accelerates the vortex stretching and dilatation and increases the baroclinic torque as the major source of vorticity generation. Examination of the flow field shows that the vortex dilatation and baroclinic torque terms increase in the cavitating case to the same magnitude as the vortex stretching term, while for the non-cavitating case these two terms are zero.     

微型高速离心泵多工况内部空化特性分析

基于CFX软件和RNG k-ε湍流模型,研究了不同流量和不同进口压力条件下泵内空化流动的特性。通过Rayleigh-Plesset方程均相流动空化模型分析了叶轮内的空泡数与叶轮扭矩随空化系数变化的关系,空化的初生、主要位置和流道的静压变化特性。结果表明:空泡体积随空化系数的减小而增大,空化初生在叶片前缘及附近流道。随着进口压力的减小,诱发空化的低压区主要集中于叶片与流道的中部且压力分布不均匀。各小流量工况下,扭矩变化随着空化系数的减小而减小,在空化系数较大时,不同工况下的扭矩均会有不规则波动且各曲线变化临界点会随着流量的增加逐渐向前移动,但总体变化趋势大致相同。本文研究的微型高速泵内空化流场的特性及空化对泵稳定运行性能的影响可供设计较高运行效率的微型高速离心泵参考。     

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.