Numerical modelling and flow analysis of a centrifugal pump running as a turbine: Unsteady flow structures and its effects on the global performance

The purpose of this paper is to investigate the flow patterns in a centrifugal pump when it works as a centripetal turbine, with special interest in the unsteady behavior in order to explain the shape of the performance curves. Also, we focus on the determination of the radial thrust and other mechanical loads over a pump‐designed machine. The pump studied is commercial, with single axial suction and a vaneless spiral volute casing. A numerical study has been carried out in order to obtain more information about the flow into the volute and the impeller. A numerical three‐dimensional unsteady simulation has been developed using a commercial code that solves the URANS set of equations with a standard k–ε turbulence model. The results show the non‐axisymmetric flow developed in the volute, responsible for a significant radial thrust; the interaction between the tongue and the impeller, generating force fluctuations; the velocity and pressure distributions inside the impeller; and the exit flow, characterized with post‐rotation and low‐pressure. These flow results allow us to understand the behavior of the machine by comparing it with the pump mode. Complementarily, an experimental study was conducted to validate the numerical model and characterize the pump‐turbine performance curves at constant head. Fast‐response pressure taps and a three‐hole pneumatic pressure probe were employed to obtain a complete data set of non‐stationary and stationary measurements throughout the centrifugal machine. As a result, loss of efficiency or susceptibility to cavitation, detected numerically, was confirmed experimentally. The study demonstrates that the numerical methodology presented here has shown its reliability and possibilities to predict the unsteady flow and time‐mean characteristics of centrifugal pumps working as turbines. In particular, it is shown that the commercial design of the pump allows a reasonable use of the impeller as a turbine runner, due to the suitable adaptation of the inflow distributions to the volute casing. Moreover, the efficiency for the inverse mode is shown to be as high as achieved for the pumping operational mode. In addition, it is concluded that both axial and radial thrusts are controlled, though important unsteady fluctuations—up to 25%—clocked with the blade passing frequency appear beyond the nominal conditions. In that case, a moderate use of the pump as a turbine is recommended in order to minimize risks of fatigue failure of the bearings. Copyright © 2009 John Wiley & Sons, Ltd.     

计算离心泵叶轮流场的扫描流束有限元方法

本文提出一种求解离心式叶轮流场的数值方法，将流动求解区域离散为有限个由流线构成其边界的单元，采用伽辽金法建立的单元方程在一条流束上集合为方程组，流线上的节点坐标亦作为未知量包含在有限元方程中，通过扫描计算，逐步解得流线位置及流动参数。本文应用叶轮的通流理论流动模型，采用扫描流速有限元方法对离心泵叶轮流场进行了计算，并与有关文献作了比较。     

NUMERICAL CALCULATION OF 2D,UNSTEADY FLOW IN CENTRIFUGAL PUMPS: IMPELLER AND VOLUTE INTERACTION

A numerical model is developed for calculating the two-dimensional, unsteady, incompressible and turbulent flow within the rotating impeller and stationary volute of an industrial centrifugal pump. The objective is the investigation and comprehension of the instantaneous behaviour of centrifugal pumps, aiming at the reduction of vibrations, radial forces and hydraulic noise. The computation is performed within a blade-to-blade streamtube for the impeller and a tube normal to the axis of rotation for the volute. The equations to be solved are the unsteady Reynolds-averaged Navier–Stokes equations along with the continuity equation and the unsteady κ–ϵ equations for turbulence modelling. The finite volume method is applied for space discretization and an implicit scheme for time discretization. A multidomain overlapping grid technique is used for matching together the relative flow field calculated within the rotating impeller and the absolute one calculated within the stationary volute. In this way the impeller and volute interaction is directly taken into account. The numerical model is validated for a centrifugal pump of N _q=32 under design flow conditions. Comparisons between calculation and measurements show fairly good agreement.     

离心泵叶轮内密相液固两相湍流的数值模拟

利用作者建立的描述密相液固两相湍流的 KET模型和推导的基本控制方程组 ,在处理壁面边界条件时考虑了颗粒和叶片的相互碰撞作用 ,对离心泵叶轮内密相液固两相流动进行了数值模拟 ,得到了泵叶轮内两相流动的一些规律 ,为液固两相流泵的设计提供了一定的理论依据。     

Internal hydraulic analysis of impeller rounding in centrifugal pumps as turbines

The use of pumps as turbines in different applications has been gaining importance in the recent years, but the subject of hydraulic optimization still remains an open research problem. One of these optimization techniques that include rounding of the sharp edges at the impeller periphery (or turbine inlet) has shown tendencies of performance enhancement.In order to understand the effect of this hydraulic optimization, the paper introduces an analytical model in the pump as turbine control volume and brings out the functionalities of the internal variables classified under control variables consisting of the system loss coefficient and exit relative flow direction and under dependent variables consisting of net tangential flow velocity, net head and efficiency.The paper studies the effects of impeller rounding on a combination of radial flow and mixed flow pumps as turbines using experimental data. The impeller rounding is seen to have positive impact on the overall efficiency in different operating regions with an improvement in the range of 1-3%. The behaviour of the two control variables have been elaborately studied in which it is found that the system loss coefficient has reduced drastically due to rounding effects, while the extent of changes to the exit relative flow direction seems to be limited in comparison. The reasons for changes to these control variables have been physically interpreted and attributed to the behaviour of the wake zone at the turbine inlet and circulation within the impeller control volume.The larger picture of impeller rounding has been discussed in comparison with performance prediction models in pumps as turbines. The possible limitations of the analytical model as well as the test setup are also presented. The paper concludes that the impeller rounding technique is very important for performance optimization and recommends its application on all pump as turbine projects. It also recommends the standardization of the rounding effects over wide range of pump shapes including axial pumps.     

离心风机子午通道内湍流场数值模拟

由进风口－叶轮－无叶扩压器－蜗壳等部件组成的离心风机通道内流分析是非常复杂的，目前还只能是分别计算各部件内的流场，但必须考虑部件间的相互影响。本文采用轴对称Ｎ－Ｓ方程，根据三维叶轮通道计算给出的叶片力分布，求解了考虑叶片力的进风口－叶轮－无叶扩压器组成的子午通道问题，所得结果可用来给出三维叶轮通道计算的进口条件，并可用于优化设计进风口及叶轮前、后盘形状。该方法已得到实践检验。     

PIV measurement of internal flow characteristics of very low specific speed semi-open impeller

Detailed particle-image velocimetry (PIV) measurements of flow fields inside semi-open impellers have been performed to understand better the internal flow patterns that are responsible for the unique performance of these centrifugal pumps operated in the range of very low specific speed. Two impellers, one equipped with six radial blades (impeller A) and the other with four conventional backward-swept blades (impeller B), are tested in a centrifugal pump designed to be operated at a non-dimensional specific speed of n_s=0.24. Complex flow patterns captured by PIV are discussed in conjunction with the overall pump performance measured separately. It is revealed that impeller A achieves higher effective head than impeller B even though the flow patterns in impeller A are more complex, exhibiting secondary flows and reverse flows in the impeller passage. It is shown that both the localized strong outward flow at the pressure side of each blade outlet and the strong outward through-flow along the suction side of each blade are responsible for the better head performance of impeller A.     

离心叶轮机械内部流动的研究进展

随着测量技术及数值算法的不断进步,叶轮机械内部流动研究有了很多新的进展.本文就半个世纪以来离心叶轮机械内部流动的实验及数值模拟研究进行了评述,根据作者掌握的文献,着重在以下几方面展开综述:叶轮内部流动、叶顶间隙泄漏流动、扩压器内部流动及叶轮与扩压器相互作用的非稳态流动等等.文中分别阐述了国内外学者在上述流动研究方面的主要成果,指出了这些研究的特点及其不足,分析了我国在这些领域与国际水平的差距,并结合作者自己的研究工作对离心叶轮机械内流研究提出了建议.      

小型高速离心压气机级内部的三维流场分析

利用三维数值模拟技术对微型燃气轮机中的离心压气机部分进行了数值分析,得到了离心压气机设计转速下的级特性曲线和各通流部件中的流动情况。数值分析表明:设计转速下压气机的级特性非常陡峭;整个特性线范围内离心叶轮基本在亚音速情况下工作,而径向扩压器是在跨音速条件下工作,离心压气机整机的最大流量是由径向扩压器的喉部面积决定的;离心压气机级内部各通流部件之间流动的相互干扰是引起流动分离的重要原因,各通流部件之间流动的相互匹配和协调将决定了离心压气机整机的性能和稳定性。     

An optimization routine on a prediction and selection model for the turbine operation of centrifugal pumps

The paper presents an experimentally validated optimization routine for the turbine-mode operation of radial flow centrifugal pumps. The optimization routine outlined here is designed to be used with prediction (predicting turbine mode characteristics of a pump) and selection (selecting the most appropriate pump for turbine-mode operation) models. The optimization routine improves upon previous uncertainties in prediction, especially in the low specific speed range.The optimization routine is evaluated experimentally for three pumps with specific speeds of 18.2 rpm, 19.7 rpm and 44.7 rpm, and a significant improvement in the accuracy of the turbine predictions with the errors for all the three pumps falling within the ±4% acceptance bands in the full load operating region is found.It is also shown how the optimization routine validates an approach to selection and prediction based on model experiments and classical principles of applied turbomachinery (specific speed-specific diameter or the Cordier/Balje plots). Such an approach is shown to be the most economic in terms of pump mode input variables.The paper recommends the extensive use of the optimization routine in micro hydro and other energy recovery projects involving pumps as turbines and the creation of a database of accurate field results that can be used to improve the routine further.     

Unsteady flow calculation in a radial flow centrifugal pump with spiral casing

The prediction of the two-dimensional unsteady flow established in a radial flow centrifugal pump is considered. Assuming the fluid incompressible and inviscid, the velocity field is represented by means of source and vorticity surface distributions as well as a set of point vortices. Using this representation, a grid-free (Lagrangian) numerical method is derived based on the coupling of the boundary element and vortex particle methods. In this context the source and vorticity surface distributions are determined through the non-entry boundary condition together with the unsteady Kutta condition. In order to satisfy Kelvin's theorem, vorticity is shed at the trailing edges of the impeller blades. Then the vortex particle method is used to approximate the convection of the free vorticity distribution. Results are given for a pump configuration experimentally tested by Centre Technique des Industries Mécaniques (CETIM). Comparisons between predictions and experimental data show the capability of the proposed method to reproduce the main features of the flow considered.     

电动潜油离心泵流道堵塞振动模型研究

电动潜油泵以其独具的特点和优势在油田生产过程中得到了日益广泛的应用,但过高的故障率给油田开发带来效率和经济上的损失。其核心部件离心泵也是故障易发部件,经常出现流道堵塞,严重影响机组的正常运转。本文结合电潜泵机组的工作特性和力学性能,建立了一套潜油离心泵流道堵塞的振动识别模型,并推导了振动模型的运动方程。利用自建的大型实验装置,模拟了该类故障井的实际生产并测得了井口三维振动信号,绘制了信号的时域图和频域图。此外,本文引入小波分析方法对信号进行了细致化分析,研究了此类故障的振动特性并验证了所建模型的可靠性。     

MODELLING AND CALCULATION OF THE TURBULENT BOUNDARY LAYER ON A ROTATING CYLINDER SURFACE WITH STRONG SUCTION 1)

提出了湍流边界层的一种简单、快速计算方法, 用以求解强吸气作用下旋转圆筒表面边界层流动. 首先, 理论分析了同心圆筒间的旋转流体运动, 外筒静止、内筒旋转且为多孔吸气条件. 强吸气情况下旋转流动主要表现为内筒壁面附近的边界层流动, 基于这一事实得到了周向速度分布的解析表达式. 其次, 通过引入新参数扩展Cebeci-Smith代数湍流模型, 使其能考虑流线曲率、壁面吸气、低Reynolds数效应等因素. 针对这些因素的综合影响, 采用解析修正和经验参数对模型进行调整. 同时, 基于Reynolds应力湍流模型的仿真结果, 校准代数湍流模型中的经验参数. 最后, 给出基于广义Cebeci-Smith湍流模型的旋转壁面边界层流动的迭代算法, 该算法适用于需要特殊迭代过程的轴向及周向流动均匀情况. 计算了不同旋转速度和吸气强度组合工况下的边界层流动, 其周向速度和湍流强度分布与基于Reynolds应力湍流模型的计算结果非常接近. 并且表明, 当Reynolds应力湍流模型数值模拟预测内筒边界层为稳定层流时, 该方法也再现了相同初始条件下的层流边界层.     

Flow patterns and boundary conditions for inlet and outlet conduits of large pump system with low head

The flow patterns in the inlet and outlet conduits have a decisive effect on the safe, stable, and highly efficient operation of the pump in a large pumping station with low head. The numerical simulation of three-dimensional （3D） turbulence flow in conduits is an important method to study the hydraulic performance and conduct an optimum hydraulic design for the conduits. With the analyses of the flow patterns in the inlet and outlet conduits, the boundary conditions of the numerical simulation for them can be determined. The main obtained conclusions are as follows： （i） Under normal operation conditions, there is essentially no pre-swirl flow at the impeller chamber inlet of an axial-flow pump system, based on which the boundary condition at the inlet conduit may be defined. （ii） The circulation at the guide vane outlet of an axial-flow pump system has a great effect on the hydraulic performance of the outlet conduit, and there is optimum circulation for the performance. Therefore, it is strongly suggested to design the guide vane according to the optimum circulation. （iii） The residual circulation at the guide vane outlet needs to be considered for the inlet boundary condition of the outlet conduit, and the value of the circulation may be measured in a specially designed test model.     

强吸气旋转圆筒壁面湍流边界层建模及计算

提出了湍流边界层的一种简单、快速计算方法,用以求解强吸气作用下旋转圆筒表面边界层流动.首先,理论分析了同心圆筒间的旋转流体运动,外筒静止、内筒旋转且为多孔吸气条件.强吸气情况下旋转流动主要表现为内筒壁面附近的边界层流动,基于这一事实得到了周向速度分布的解析表达式.其次,通过引入新参数扩展Cebeci-Smith代数湍流模型,使其能考虑流线曲率、壁面吸气、低Reynolds数效应等因素.针对这些因素的综合影响,采用解析修正和经验参数对模型进行调整.同时,基于Reynolds应力湍流模型的仿真结果,校准代数湍流模型中的经验参数.最后,给出基于广义Cebeci-Smith湍流模型的旋转壁面边界层流动的迭代算法,该算法适用于需要特殊迭代过程的轴向及周向流动均匀情况.计算了不同旋转速度和吸气强度组合工况下的边界层流动,其周向速度和湍流强度分布与基于Reynolds应力湍流模型的计算结果非常接近.并且表明,当Reynolds应力湍流模型数值模拟预测内筒边界层为稳定层流时,该方法也再现了相同初始条件下的层流边界层.     

A parametric study for improving the centrifugal pump impeller for use in viscous fluid pumping

Essentially, performance of centrifugal pumps is affected when pumping viscous fluids. In this paper a new idea is proposed to overcome the undesirable effects of viscosity on the pump performance parameters. This idea based on this matter that one specific impeller can be designed, made and installed on the pump for pumping of one fluid with specific viscosity. Therefore a specific pump can be used for pumping of different fluids with different viscosity, by replacement of pump impeller. Replacement of the impeller is more cost effective in comparison to the replacement of the whole of the pump. Passage width and outlet angle of impeller are considered as design variables and the effects of such variables investigated using experimentally validated numerical model. The H–Q, P–Q and η–Q graphs are extracted experimentally for the improved impeller, which show good improvement in comparison with original impeller.     

A novel experimental facility for measuring internal flow of Solid-liquid two-phase flow in a centrifugal pump by PIV

PIV is one of the most effective flow measurement methods, but for solid-liquid two-phase flow in a centrifugal pump with complex internal structure and high speed rotation, many problems exist in the experimental facility design, such as solid particle releasement, synchronization issues among camera, laser and pump impeller, and methods of avoiding introducing bubbles into flow passage, etc. To solve these critical problems, a new experimental facility without agitation was designed for internal solid-liquid two-phase flow test in a centrifugal pump by PIV. The facility was tested by measuring two-phase flow of water-glass beans and water-rape seeds in a centrifugal slurry pump. The new test facility has many obvious advantages, such as the simpler structure without the agitating device, less noise in the test process, less power consumption, less number of particles to get a certain particle volume concentration, and the decrease of the experiment cost. The result shows that the new facility can realize a stable solid-liquid two-phase flow measurement with high reliability in a centrifugal pump.     

高速转动圆盘流动数值模拟研究

重点研究高速离心压气机叶轮与机匣间的间隙流动及其温度分布。研究将离心压气机简化为高速转动圆盘,搭建了相关实验平台,并开展了相应的数值模拟研究。通过改变转动圆盘的转速和轴向进入的冷却流的流量,研究了转速和流量对于间隙内温度和速度分布的影响。结果显示,转速是影响温度变化的最主要因素,转速越大,温度越高;同等幅度的流量变化对温度的影响则较小。研究发现,在实验和模拟对应的大雷诺数条件下,无量纲的速度分布基本不受到圆盘转速、冷却流量和温度场的影响。     

泵喷射推进器性能的变分有限元数值分析

由叶轮机械三元流动两类相对流面理论及相对应的变分原理，应用变分有限元数值计算方法，求解泵喷射推进器的水动力特性。文中通过实际算例，求得推进器上转子和定子的力矩值和推力值，并与实验相比较，两者基本吻合，符合设计要求。