Optimization on the impeller of a low-specific-speed centrifugal pump for hydraulic performance improvement

In order to widen the high-efficiency operating range of a low-specific-speed centrifugal pump, an optimization process for considering efficiencies under 1.0Q_d and 1.4Q_d is proposed. Three parameters, namely, the blade outlet width b_2, blade outlet angle β_2, and blade wrap angle φ, are selected as design variables. Impellers are generated using the optimal Latin hypercube sampling method. The pump efficiencies are calculated using the software CFX 14.5 at two operating points selected as objectives. Surrogate models are also constructed to analyze the relationship between the objectives and the design variables. Finally, the particle swarm optimization algorithm is applied to calculate the surrogate model to determine the best combination of the impeller parameters. The results show that the performance curve predicted by numerical simulation has a good agreement with the experimental results. Compared with the efficiencies of the original impeller, the hydraulic efficiencies of the optimized impeller are increased by 4.18% and 0.62% under 1.0Q_d and 1.4Q_d, respectively. The comparison of inner flow between the original pump and optimized one illustrates the improvement of performance. The optimization process can provide a useful reference on performance improvement of other pumps, even on reduction of pressure fluctuations.     

Multi-point optimization on meridional shape of a centrifugal pump impeller for performance improvement

A wide operating band is important for a pump to safely perform at maximum efficiency while saving energy. To widen the operating range, a multi-point optimization process based on numerical simulations in order to improve impeller performance of a centrifugal pump used in nuclear plant applications is proposed by this research. The Reynolds average Navier Stokes equations are utilized to perform the calculations. The meridional shape of the impeller was optimized based on the following four parameters; shroud arc radius, hub arc radius, shroud angle, and hub angle as the design variables. Efficiencies calculated under 0.6Q _d, 1.0Q _d and 1.62Q _d were selected as the three optimized objectives. The Design of experiment method was applied to generate various impellers while 35 impellers were generated by the Latin hypercube sampling method. A Response surface function based on a second order function was applied to construct a mathematical relationship between the objectives and design variables. A multi-objective genetic algorithm was utilized to solve the response surface function to obtain the best optimized objectives as well as the best combination of design parameters. The results indicated that the pump performance predicted by numerical simulation was in agreement with the experimental performance. The optimized efficiencies based on the three operating conditions were increased by 3.9 %, 6.1 % and 2.6 %, respectively. In addition, the velocity distribution, pressure distribution, streamline and turbulence kinetic energy distribution of the optimized and reference impeller were compared and analyzed to illustrate the performance improvement.     

Impeller inlet geometry effect on performance improvement for centrifugal pumps

This research treats the effect of impeller inlet geometry on performance improvement for a boiler feed pump, who is a centrifugal pump having specific speed of 183 m·m³min⁻¹·min⁻¹ and close type impeller with exit diameter of 450 mm. The hydraulic performance and cavitation performance of the pump have been tested experimentally. In order to improve the pump, five impellers have been considered by extending the blade leading edge or applying much larger blade angle at impeller inlet compared with the original impeller. The 3-D turbulent flow inside those pumps has been analyzed basing on RNG k-ɛ turbulence model and VOF cavitation model. It is noted that the numerical results are fairly good compared with the experiments. Based on the experimental test and numerical simulation, the following conclusions can be drawn: (1) Impeller inlet geometry has important influence on performance improvement in the case of centrifugal pump. Favorite effects on performance improvement have been achieved by both extending the blade leading edge and applying much larger blade angle at impeller inlet; (2) It is suspected that the extended leading edge have favorite effect for improving hydraulic performance, and the much larger blade angle at impeller inlet have favorite effect for improving cavitation performance for the test pump; (3) Uniform flow upstream of impeller inlet is helpful for improving cavitation performance of the pump. This paper was presented at the 9^th Asian International Conference on Fluid Machinery (AICFM9), Jeju, Korea, October 16–19, 2007.     

Numerical simulations and surrogate-based optimization of cavitation performance for an aviation fuel pump

We used computational modeling to investigate the cavitation performance of an aviation fuel pump, and optimize structural parameters using the surrogate-based method. In the numerical simulation, a rotation-curvature correction was adapted to the k-ε turbulence model, and a four-component surrogate fuel was selected to reproduce the physical properties of the China RP-3 kerosene. Then the performance of the aviation fuel pump was predicted. In the optimization, based on the series of the numerical results, Surrogate-based analysis and optimization (SBAO) was used to optimize the structural parameters of the fuel pump (the variation of the outlet blade angle for the inducer △β _b1 and the variation of the inlet blade angle for the impeller △β _b2). The results show that the prediction of cavitation performance agrees well with the experimental data. The results show that cavitation areas are mainly distributed in the inlet of the inducer. The volume of cavities grows with the decreasing NPSHa. The head of the fuel pump has a sudden head-drop when NPSHa ≤ 5.64 m. Furthermore, the surrogate-based approach is available in structural optimization of the fuel pump. The cavitation performance of the optimized pump improved about 22 % with a little drop of head coefficient when △β _b1 = 4.33° and △β _b2 = 3.24°. The numerical approach employed in this paper can accurately predict the cavitating flow of the high rotating speed fuel pump and the surrogate-based method is available in the structural optimization for a better cavitation performance.

     

Cavitation optimization for a centrifugal pump impeller by using orthogonal design of experiment

Cavitation is one of the most important performance of centrifugal pumps. However, the current optimization works of centrifugal pump are mostly focusing on hydraulic efficiency only, which may result in poor cavitation performance. Therefore, it is necessary to find an appropriate solution to improve cavitation performance with acceptable efficiency. In this paper, to improve the cavitation performance of a centrifugal pump with a vaned diffuser, the influence of impeller geometric parameters on the cavitation of the pump is investigated using the orthogonal design of experiment(DOE) based on computational fluid dynamics. The impeller inlet diameter D_1, inlet incidence angle Δβ, and blade wrap angle φ are selected as the main impeller geometric parameters and the orthogonal experiment of L_9(3*3) is performed. Three-dimensional steady simulations for cavitation are conducted by using constant gas mass fraction model with second-order upwind, and the predicated cavitation performance is validated by laboratory experiment. The optimization results are obtained by the range analysis method to improve cavitation performance without obvious decreasing the efficiency of the centrifugal pump. The internal flow of the pump is analyzed in order to identify the flow behavior that can affect cavitation performance. The results show that D_1 has the greatest influence on the pump cavitation and the final optimized impeller provides better flow distribution at blade leading edge. The final optimized impeller accomplishes better cavitation and hydraulic performance and the NPSHR decreases by 0.63 m compared with the original one. The presented work supplies a feasible route in engineering practice to optimize a centrifugal pump impeller for better cavitation performance.     

Application of different surrogate models on the optimization of centrifugal pump

An optimization process for impellers was carried out based on numerical simulation, Latin hypercube sampling (LHS), surrogate model and Genetic algorithm (GA) to improve the efficiency of residual heat removal pump. The commercial software ANSYS CFX 14.5 was utilized to solve the Reynolds-averaged Navier-Stokes equations by using the Shear stress transport turbulence model. The impeller blade parameters, which contain the blade inlet incidence angle Δβ, blade wrap angle φ, and blade outlet angle β ₂, were designed by random sample points according to the LHS method. The efficiency predicted under the design flow rate was selected as the objective function. The best combination of parameters was obtained by calculating the surrogate model with the GA. Meanwhile, the prediction accuracies of three surrogate models, namely, Response surface model (RSM), Kriging model, and Radial basis neural network (RBNN), were compared. Results showed that the calculated findings agree with the experimental performance results of the original pump. The RSF model predicted the highest efficiency, while the RBNN had the highest prediction accuracy. Compared with the simulated efficiency of the original pump, the optimization increased efficiency by 8.34% under the design point. Finally, the internal flow fields were analyzed to understand the mechanism of efficiency improvement. The optimization process, including the comparison of the surrogate models, can provide reference for the optimization design of other pumps.     

非设计工况下斜流泵叶轮进出口环量变化分析

基于RNG k-ε湍流模型对斜流泵内部三维流场进行了数值计算,重点针对非设计工况下的斜流泵叶轮进出口环量分布特征进行了分析。研究结果显示,在设计点附近的叶轮进口环量受叶片进口边影响较大,不同采样线的环量分布具有一定差异,小流量工况下受到叶轮进口回流的影响,不同采样线的环量分布趋于一致。叶轮出口环量分布受采样线位置影响较小,在设计流量点时,叶轮出口呈等环量分布。在小流量工况点,受到叶轮出口回流的影响,叶轮出口外缘处的环量数值显著增大。通过研究还发现,从叶轮出口流道通过轮毂一侧回流进入叶轮的流体微团具有与叶轮旋转方向相反的圆周速度分量,其环量数值甚至低于同工况下的叶轮进口环量值。     

High-efficiency design optimization of a centrifugal pump

Design optimization of a backward-curved blades centrifugal pump with specific speed of 150 has been performed to improve hydraulic performance of the pump using surrogate modeling and three-dimensional steady Reynolds-averaged Navier-Stokes analysis. The shear stress transport model was used for the analysis of turbulence. Four geometric variables defining the blade hub inlet angle, hub contours, blade outlet angle, and blade angle profile of impeller were selected as design variables, and total efficiency of the pump at design flow rate was set as the objective function for the optimization. Thirty-six design points were chosen using the Latin hypercube sampling, and three different surrogate models were constructed using the objective function values calculated at these design points. The optimal point was searched from the constructed surrogate model by using sequential quadratic programming. The optimum designs of the centrifugal pump predicted by the surrogate models show considerable increases in efficiency compared to a reference design. Performance of the best optimum design was validated compared to experimental data for total efficiency and head.     

大型立式轴流泵叶片进口流场及其对水泵影响研究

分析各因素对大型立式轴流泵叶片进口流态的影响,研究该断面流场的形成机理。提出叶栅对进口流态反作用和相互自动调整的观点,即如果叶栅来流非均匀轴向,叶栅过流特性会反过来影响来流流态并调整达到平衡。结果表明,立式轴流泵叶片进口流场既非轴向,又非均匀,不符合常规假设。用五孔探针实测叶轮直径D=1.64m轴流泵叶片进口流场,证明了理论分析的正确性。分析叶片进口流态对水泵性能、导轴承偏磨和间隙气蚀的影响,提出改善流态的方法。成果对改进轴流泵及其进水流道设计理论和方法,提高运行性能具有重大意义。     

The characteristics investigation under the unsteady cavitation condition in a centrifugal pump

Numerical simulation and experimental method are combined to investigate the pump inlet and outlet pressure fluctuations, the vibration characteristics and the internal flow instabilities under the unsteady cavitation condition in a centrifugal pump. It is found that the unsteady cavitation starts to generate as the NPSHa is lower than 5.93 m. Apparent asymmetric and uneven cavity volume distribution on each blade and in the impeller can be observed as the NPSHa decreases from 4.39 m to 1.44 m, which includes the cavitation develops from cavitation surge, rotating cavitation to asymmetric cavitation. The flow vortexes in each blade channel are produced in the cavity trailing edges by the shedding and collapse of cavitation, which interfere with each other and aggravate the flow instabilities. The dominant frequencies of the pump inlet and outlet pressure fluctuations are the shaft frequency and blade passing frequency under the unsteady cavitation conditions, respectively. Broadband pulses are obtained from both the pump inlet and outlet pressure pulsations, which results from the random shedding and collapse of unsteady cavitation bubbles. Obvious corresponding relationship between the root mean squares of the vibration measured in different positions and the suction performance curve is found under both the non-cavitation and unsteady cavitation conditions.

     

Numerical investigation of two-phase flow characteristics in multiphase pump with split vane impellers

Multiphase pump is a cost-effective option for subsea oil and gas field development. The ability to handle different inlet gas volume fractions (GVFs) especially high inlet GVF is critical to the development of pump performance. In this study, the two-phase flow characteristics in normal impeller and split vane impeller at different inlet GVFs were investigated by steady numerical simulations. The gas distribution on blade-to-blade plane and meridional flow channel at different inlet GVFs were analyzed and compared. Gas accumulation area and movement characteristics of the gas-liquid flow in impeller flow passage were also pointed out by unsteady simulations. Experimental results of the pump differential pressure were compared with the numerical simulation results, to validate the accuracy of numerical simulation method. The flow characteristics in pump with modified impeller and its performance at different inlet GVFs were both compared with that of the normal impeller. The steady simulation results of normal impeller in different inlet GVFs show that gas concentrating area in the flow passage increases as inlet GVF grows. The unsteady simulation results indicate that gas pocket firstly occurs on the pressure side of impeller, then moves to the suction side in the middle area of blade and finally transfers to outlet of impeller and disappears. The errors between numerical simulation results and experiment data are below 10 %, which validated the feasibility of the numerical simulation method. Simulation results on the split vane impeller demonstrate that the gas accumulation area in flow passage of the modified impeller is dramatically decreased compared to that of the normal impeller. The performance of the modified impeller is generally better than the normal impeller especially in high inlet GVF conditions.

     

High performance hydraulic design techniques of mixed-flow pump impeller and diffuser

In this paper, we describe a numerical study about the performance improvement of a mixed-flow pump by optimizing the design of the impeller and diffuser using a commercial computational fluid dynamics (CFD) code and design-of-experiments (DOE). The design variables of impeller and diffuser in the vane plane development were defined with a fixed meridional plane. The design variables were defined by the vane plane development, which indicates the blade-angle distributions and length of the impeller and diffuser. The vane plane development was controlled using the blade-angle in a fixed meridional plane. The blade shape of the impeller and diffuser were designed using a traditional method in which the inlet and exit angles are connected smoothly. First, the impeller optimum design was performed with impeller design variables. The diffuser optimum design was performed with diffuser design variables while the optimally designed impeller shape was fixed. The importance of the impeller and diffuser design variables was analyzed using 2^k factorial designs, and the design optimization of the impeller and diffuser design variables was determined using the response surface method (RSM). The objective functions were defined as the total head (Ht) and the total efficiency (?t) at the design flow rate. The optimally designed model was verified using numerical analysis, and the numerical analysis results for both the optimum model and the reference model were compared to determine the reasons for the improved pump performance. A pump performance test was carried out for the optimum model, and its reliability was proved by a comparative analysis of the results of the numerical analysis and an experiment using the optimum model.     

Effect of the blade loading distribution on hydrodynamic performance of a centrifugal pump with cylindrical blades

The effect of the blade loading distribution on head, radial force and pressure pulsation of a low specific-speed centrifugal pump with cylindrical impeller blades were investigated in the present study. Blade shapes were obtained by adopting the 1D inverse design method, impellers with different blade loading curves were obtained while the distribution of the blade loading was carefully tailored. Threedimensional URANS simulation method based on the Shear stress transport (SST) k-ω turbulence model was employed for the analyzation of flow patterns. Numerical results including the pressure distribution and velocity profile were validated by comparing with the available experimental data, and an acceptable agreement was obtained. Three typical parameters of the blade loading curve, including the location of the fore-loading point (m_pre), location of the aft-loading point (m_post) and slope of the rectilinear segment (K), were analyzed. Results showed that the well-designed blade loading curve, such as the fore-loading impeller, can effectively reduce the pressure pulsation amplitude and the radial force. The significant effect of the variation of the aft-loading point on pump hydrodynamic performance was also investigated. Meanwhile, pressure and velocity distributions at different slopes of the blade loading curves show that the fore-loading impeller produces more uniform flow issuing from the impeller than that of the pump with aft-loading impeller, thus reduces the radial force and pressure pulsation of the pump.     

叶片进口边位置对双吸离心泵性能的影响分析

针对一种国内生产的双吸泵,利用CFD软件对其内部流场进行数值模拟,依据一元理论对叶轮的水力设计进行检查。在不改变原叶轮设计的基础上分别将叶片进口边三次后移构造出三种叶型A1、A2、A3。数值计算结果表明:在任意工况下叶轮A2的效率比A1、A3的效率都高,且在最优工况下叶轮A2的最高效率比原叶轮的效率高5.8%,高效区也明显变宽。研究表明,在推荐值1～1.3以外时,叶片间有效进出口面积的比值并非越小,泵的性能越好;叶片进口边的位置对泵的性能有很大的影响,适当改变进口边位置可以有效地改善叶轮进口的流动状态。     

MULTIOBJECT OPTIMIZATION OF A CENTRIFUGAL IMPELLER USING EVOLUTIONARY ALGORITHMS

Application of the multiobjective evolutionary algorithms to the aerodynamic optimization design of a centrifugal impeller is presented. The aerodynamic performance of a centrifugal impeller is evaluated by using the three-dimensional Navier-Stokes solutions. The typical centrifugal impeller is redesigned for maximization of the pressure rise and blade load and minimization of the rotational total pressure loss at the given flow conditions. The Bezier curves are used to parameterize the three-dimensional impeller blade shape. The present method obtains many reasonable Pareto optimal designs that outperform the original centrifugal impeller. Detailed observation of the certain Pareto optimal design demonstrates the feasibility of the present multiobjective optimization method tool for turbomachinery design.     

Multiparameter optimization for the nonlinear performance improvement of centrifugal pumps using a multilayer neural network

To increase efficiency at the design point of a centrifugal pump, this study adopted an artificial neural network in the construction of an accurate nonlinear function between the optimization objective and the design variables of impellers. Modified particle swarm optimization was further applied to refine the mathematical model globally. The database, which consisted of 200 sets of impellers, were generated from the Latin hypercube sampling method, and their corresponding efficiencies were obtained automatically from numerical simulation. Design variables were the distributions of blade angles, and results established that the difference between the numerical performance curve and the experimental results was acceptable. Optimization with a two-layer feedforward network improved the pump efficiency at the design point by 0.454 %. Flow complexity improved as the blade curvature increased. The application of the multilayer neural network could provide a meaningful reference to single- and multi-objective optimization of complex and nonlinear pump performance.

     

基于流场计算的螺旋离心泵叶轮静力学分析

为研究螺旋离心泵叶轮结构的振动特性,首先建立螺旋离心泵内部流场三维模型,对设计工况下的螺旋离心泵内流场进行了定常数值模拟,得到了叶片表面的压力载荷分布;建立叶轮有限元模型,以螺旋离心泵全流道三维定常数值模拟计算结果为基础,利用顺序耦合技术进行了有预应力的叶轮静应力分析和模态分析,结果表明:叶轮的最大应力出现在叶片进口的轮毂处,叶轮强度满足设计要求;叶轮最大的形变区域出现在叶片进口的轮缘处;叶轮的变形域随着频率的增加而增大;叶轮的各阶固有频率远大于泵的运行频率,因此在运行过程中不易发生共振现象。     

双向轴流泵装置性能预测与内部流动分析

对一采用S形叶片的双向轴流泵装置进行数值研究,在不同流量工况条件下分析泵的正、反向运转性能,对该泵的瞬时启动过程进行了监测并对泵内的非定常空化现象进行了分析。研究表明,正、反向运转时,泵的性能存在明显的差异,反向的扬程和效率均高于正向;在泵正向启动过程中,叶轮背面进口边产生空化区,反向运转时未发生明显的空化现象;两种运转模式下,叶轮进出口断面上压力脉动特征频率分布相似,但叶轮进口的压力脉动幅值较高。     

3D Particle image velocimetry test of inner flow in a double blade pump impeller

The double blade pump is widely used in sewage treatment industry,however,the research on the internal flow characteristics of the double blade pump with particle image velocimetry(PIV) technology is very little at present.To reveal inner flow characteristics in double blade pump impeller under off-design and design conditions,inner flows in a double blade pump impeller,whose specific speed is 111,are measured under the five off-design conditions and design condition by using 3D PIV test technology.In order to ensure the accuracy of the 3D PIV test,the external trigger synchronization system which makes use of fiber optic and equivalent calibration method are applied.The 3D PIV relative velocity synthesis procedure is compiled by using Visual C++ 2005.Then absolute velocity distribution and relative velocity distribution in the double blade pump impeller are obtained.Test results show that vortex exists in each condition,but the location,size and velocity of vortex core are different.Average absolute velocity value of impeller outlet increases at first,then decreases,and then increases again with increase of flow rate.Again average relative velocity values under 0.4,0.8,and 1.2 design condition are higher than that under 1.0 design condition,while under 0.6 and 1.4 design condition it is lower.Under low flow rate conditions,radial vectors of absolute velocities at impeller outlet and blade inlet near the pump shaft decrease with increase of flow rate,while that of relative velocities at the suction side near the pump shaft decreases.Radial vectors of absolute velocities and relative velocities change slightly under the two large flow rate conditions.The research results can be applied to instruct the hydraulic optimization design of double blade pumps.     

离心泵叶轮主要几何参数与反作用度之间的关系研究

反作用度对离心泵叶片的形状有很大的影响,在离心泵叶轮的水力设计中应该予以考虑。基于反作用度的定义,建立了反作用度与离心泵叶片几何参数的关系;同时用数学方法论证了离心泵反作用度与叶片出口角之间的关系;在此基础上,探讨了比转速与反作用度的关系。分析表明:反作用度随比转速的增大而增大。考虑反作用度对叶轮流道的影响作用,将推导出的公式应用于离心泵的水力设计中,预估叶片进口角,以减小了冲角选取的盲目性。