Inverse Method of Centrifugal Pump Impeller Based on Proper Orthogonal Decomposition (POD) Method

To improve the accuracy and reduce the calculation cost for the inverse problem of centrifugal pump impeller, the new inverse method based on proper orthogonal decomposition(POD) is proposed. The pump blade shape is parameterized by quartic Bezier curve, and the initial snapshots is generated by introducing the perturbation of the blade shape control parameters. The internal flow field and its hydraulic performance is predicted by CFD method.The snapshots vector includes the blade shape parameter and the distribution of blade load. The POD basis for the snapshots set are deduced by proper orthogonal decomposition.The sample vector set is expressed in terms of the linear combination of the orthogonal basis. The objective blade shape corresponding to the objective distribution of blade load is obtained by least square fit. The Iterative correction algorithm for the centrifugal pump blade inverse method based on POD is proposed. The objective blade load distributions are corrected according to the difference of the CFD result and the POD result. The two dimensional and three dimensional blade calculation cases show that the proposed centrifugal pump blade inverse method based on POD have good convergence and high accuracy, and thecalculation cost is greatly reduced. After two iterations, the deviation of the blade load and the pump hydraulic performance are limited within 4.0% and 6.0% individually for most of the flow rate range. This paper provides a promising inverse method for centrifugal pump impeller, which will benefit the hydraulic optimization of centrifugal pump.     

OPTIMIZATION METHOD ON IMPELLER MERIDIONAL CONTOUR AND 3D BLADE

An optimization method for 3D blade and meridional contour of centrifugal or mixed-flow impeller based on the 3D viscous computational fluid dynamics (CFD) analysis is proposed. The blade is indirectly parameterized using the angular momentum and calculated by inverse design method. The design variables are separated into two categories: the meridional contour design variables and the blade design variables. Firstly, only the blade is optimized using genetic algorithm with the meridional contour remained constant. The artificial neural network (ANN) techniques with the training sample data schemed according to design of experiment theory are adopted to construct the response relation between the blade design variables and the impeller performance. Then, based on the ANN approximated relation between the meridional contour design variables and impeller performance, the meridional contour is optimized. Fewer design variables and less calculation effort is required in this method that may be widely used in the optimization of three-dimension impellers. An optimized impeller in a mixed-flow pump, where the head and the efficiency are enhanced by 12.9% and 4.5% respectively, confirms the validity of this newly proposed method.     

基于iSIGHT平台的轴流泵叶片水力性能优化研究

将数值优化技术与CFD流场计算相结合,由数学过程代替设计人员的经验,控制叶片设计修改方向,构建轴流泵叶片自动优化设计平台。以多学科优化软件iSIGHT为基础,以现有优秀的轴流泵叶片模型为研究对象,建立了参数化建模、网格划分、流场计算和数值优化相结合的轴流泵叶片自动优化设计平台。以叶轮效率最高为目标函数,以扬程和汽蚀余量为约束条件,用该平台对设计工况下的初始叶片进行自动优化设计。对比分析优化前后叶片的水力性能,优化后叶片的水力性能有所提高,表明本文采用的自动优化设计方法是有效和可行的。     

一种新的制造技术──无夹具制造

提出了无夹具制造的概念和“固定一寻位一加工”的制造模式。给出了实现无夹具制造的信息流模式。控制方法以及系统实现中关键问题的方案。介绍了试验系统及试验结果。理论分析与试验结果表明，所提出的无夹具制造技术是可行的。     

基于轴流泵间隙流动的新水力设计方法

轴流泵叶轮轮毂与轮缘处间隙流动及边界层对轴流泵性能的影响很大,应用Numeca及Flu-ent等软件对轴流泵叶轮轮缘间隙中的流动进行数值模拟,根据流动模拟结果对叶轮叶片型线及轮毂、轮缘处的叶型设计进行修正,使其速度-压力分布比较理想,并提出了基于间隙流动的轴流泵水力设计方法,这种新的水力设计方法有利于改进轮缘和轮毂处边界层以及轮缘间隙中的流动,达到提高轴流泵效率的目的。     

Influence of blade wrap angle on centrifugal pump performance by numerical and experimental study

The existing research on improving the hydraulic performance of centrifugal pumps mainly focuses on the design method and the parameter optimization. The traditional design method for centrifugal impellers relies more on experience of engineers that typically only satisfies the continuity equation of the fluid. In this study, on the basis of the direct and inverse iteration design method which simultaneously solves the continuity and motion equations of the fluid and shapes the blade geometry by controlling the wrap angle, three centrifugal pump impellers are designed by altering blade wrap angles while keeping other parameters constant. The three-dimensional flow fields in three centrifugal pumps are numerically simulated, and the simulation results illustrate that the blade with larger wrap angle has more powerful control ability on the flow pattern in impeller. The three pumps have nearly the same pressure distributions at the small flow rate, but the pressure gradient increase in the pump with the largest wrap angle is smoother than the other two pumps at the design and large flow rates. The pump head and efficiency are also influenced by the blade wrap angle. The highest head and efficiency are also observed for the largest angle. An experiment rig is designed and built to test the performance of the pump with the largest wrap angle. The test results show that the wide space of its efficiency area and the stability of its operation ensure the excellent performance of the design method and verify the numerical analysis. The analysis on influence of the blade wrap angle for centrifugal pump performance in this paper can be beneficial to the optimization design of the centrifugal pump.     

大型风力机叶片的耦合优化方法

为了降低兆瓦级风力机叶片的制造成本,通过耦合叶素动量理论与复合材料欧拉伯努利梁强度设计理论,综合考虑风能效率和成本,以叶片的风能效率成本最小化为优化目标,提出了大型风力发电机叶片的多学科优化设计方法。并基于该方法,对某50 m风力机叶片进行了优化设计。研究结果表明,该方法能够找到风能效率与成本的平衡设计点,叶片风能效率成本比传统设计方法设计的叶片减少了8.84%。     

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.     

变壁厚涡轮冷却叶片参数化造型设计

提出了一种基于函数解析的变壁厚涡轮冷却叶片参数化设计方法。根据叶片外型线上定义的若干参数点,采用三次样条插值方法得到叶片壁面厚度分布函数,再通过计算得到冷却通道型线上离散数据点,在CAD平台下建立了变壁厚涡轮冷却叶片参数化模型。为实现涡轮冷却叶片的自动设计优化和多学科设计优化,获得更佳的叶片设计方案奠定了基础。     

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。     

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.     

The effect of runner blade loading on the performance and internal flow of a Francis hydro turbine model

As a core component of a hydropower station, hydro turbines play a vital role in the integration of a power station. Research on the technology of hydro turbine is continuously increasing with the development of water electricity. It is effective and successful to design a Francis turbine runner blade with good performance by one-dimensional hydraulic design method. For the one-dimensional hydraulic design, the runner blade angle at leading and trailing edges can be defined by calculation of Euler’s head. Design of the runner blade profile at several cross sections is needed to design a runner shape. In this study, there are three different blade loadings conducted to compare the internal flow characteristics and performance. The result shows that the front loading achieves the best efficiency in comparison to other loadings, which is good at suppressing the loss at draft tube.     

空冷汽轮机低压级组叶片模化设计与开发

针对空冷汽轮机低压级组叶片设计困难的问题,基于叶片模化设计技术,结合先进的计算流体动力学(CFD)技术,提出了空冷汽轮机低压级组叶片模化和改型优化设计方法.该方法主要是用于将母型低压级组叶片通过模化设计改进为与设计目标总体性能参数相近的低压级组,在此基础上,应用三维气动分析设计优化方法对低压级组进行了改型优化设计,得到了满足设计要求的空冷低压级组叶片;同时,对低压级组进行变工况分析,以保证低压级组在许用范围内具有较好的变工况性能.该方法将多种先进技术相结合,缩短了开发周期,降低了开发成本.研究结果表明,采用该方法开发的低压级组能够很好地继承母型低压级组的优良特性,保证了叶片的安全性和可靠性,具有良好的气动性能和适用范围.     

Optimization of a seven-stage centrifugal compressor by using a quasi-3D inverse design method

This paper focuses on performance improvement of a centrifugal compressor. An inverse design method for 3D design approaches is formulated to address this concern. The design procedure encompasses two major steps. First, with the use of ball spine algorithm, which is an inverse design algorithm, on the meridional plane of impeller, the hub and shroud of impeller are computed based on a modified pressure distribution along them. Second, an original and progressive algorithm is developed for design of blade camber line profile on the blade-to-blade planes of impeller based on blade loading improvement. Full 3D analysis of the current and designed compressor is accomplished by using a Reynolds-averaged Navier-Stokes equations solver. A comparison between the analysis results of the current and designed compressor shows that the total-to-total isentropic efficiency and pressure ratio of the designed compressor under the same operating conditions are enhanced by more than 4.5% and 5%, respectively.     

基于最速下降法的风扇叶片三维优化设计

以某航空发动机三级风扇为研究对象,选择叶片厚度为优化变量,叶片绝热效率为优化目标,采用全三维叶型优化方法对某三级风扇中的第二级转子进行了优化设计。在设计转速下,对优化前后的单转子及其所在的三级风扇进行了全三维数值模拟,并对计算结果进行了对比分析。结果表明,在设计转速工作点,优化后叶型波前马赫数降低,激波强度减弱,叶片槽道内激波损失、径向掺混损失均有所减小,激波与附面层相互作用减弱：优化后单转子效率提高了1．6％,采用优化后转子叶型的三级风扇总效率提高了0．5％。     

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.

     

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.     

不确定性参数识别的模态区间逆响应面法

结合模态区间分析及响应面的相关理论,提出一种新的不确定性参数识别方法,即模态区间逆响应面法。首先,以有界区间数来量化结构参数的不确定性,通过合理的实验设计确定样本数据;然后,以响应为输入,设计参数为输出,采用逐步回归分析构造设计参数与结构响应的模态区间逆响应面模型,进而直接在模态区间逆响应面模型上进行模态区间运算,即可识别材料参数的变异性区间;最后,采用一组钢板模态实验来验证所提方法的可行性及可靠性。结果表明:所提方法可准确识别钢板材料参数的取值区间,有效地解决多重变量区间运算存在的区间过估计问题,识别过程避免区间迭代优化,具有较高的计算效率。     

液力变矩器叶栅系统三维优化设计方法研究

为实现液力变矩器叶栅系统的完全三维设计及其优化,开发了一套包含束流初值搜索、循环圆与叶形的参数化设计、网格划分、流场分析、试验设计和优化算法在内的三维优化设计系统,并且为各环节开发了相应设计工具。快速的束流初值遗传算法搜索为三维多目标优化提供合理初值;循环圆设计工具可以快速灵活地给出平面分布和几何约束,而后叶形设计分别为泵轮、涡轮和导轮叶片指定叶片角度和加厚形式,空间三维叶片设计整合前面设计结果生成叶片空间姿态,同时在整个叶片成型过程中完全采用参数驱动的形式;为对各个参数对传动性能的影响有准确反映,对设计结果进行了自动的网格划分和数值分析,并将分析结果反馈给优化设计环节以及后续相关部件的有限元分析环节;优化设计采用试验设计与全局优化算法相结合以提高设计的稳健性,加速收敛。通过对D400型液力变矩器的三维优化,得到了一组新的优化叶片,传动特性得到提高、同时减少了设计用时和优化迭代次数,表明叶栅的三维优化设计系统是开发新型性能优良液力变矩器的更为有效和准确的工具。