High-efficiency design of a mixed-flow pump using a surrogate model

In the present work, the fluid flow characteristics of a mixed-flow pump have beenwere investigated numerically using three-dimensional Reynolds-averaged Navier-Stokes equations. The shear stress transport turbulence model and hexahedral grid system were used to analyze the flow in the mixed-flow pump. The efficiency of the mixed-flow pump was evaluated using the variation of two geometric variables related to the inlet angle of the diffuser vane. The design optimization of the mixed-flow pump was performed to maximize the its efficiency at the prescribed specific speed using a surrogate model. Latin hypercube sampling was used to determine the training points for the design of the experiment, and the surrogate model was constructed using the objective function values at the training points. The results show that the efficiency of the mixed-flow pump at the prescribed specific speed is improved considerably by the design optimization.     

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.     

Performance enhancement of axial fan blade through multi-objective optimization techniques

This paper presents an axial fan blade design optimization method incorporating a hybrid multi-objective evolutionary algorithm (hybrid MOEA). In flow analyses, Reynolds-averaged Navier-Stokes (RANS) equations were solved using the shear stress transport turbulence model. The numerical results for the axial and tangential velocities were validated by comparing them with experimental data. Six design variables relating to the blade lean angle and the blade profile were selected through Latin hypercube sampling of design of experiments (DOE) to generate design points within the selected design space. Two objective functions, namely, total efficiency and torque, were employed, and multi-objective optimization was carried out, to enhance the performance. A surrogate model, Response Surface Approximation (RSA), was constructed for each objective function based on the numerical solutions obtained at the specified design points. The Non-dominated Sorting of Genetic Algorithm (NSGA-II) with local search was used for multi-objective optimization. The Pareto-optimal solutions were obtained, and a trade-off analysis was performed between the two conflicting objectives in view of the design and flow constraints. It was observed that, by the process of multi-objective optimization, the total efficiency was enhanced and the torque reduced. The mechanisms of these performance improvements were elucidated by analysis of the Pareto-optimal solutions.     

大功率机车用轴流冷却风机叶轮气动性能优化

本文基于人工神经网络代理模型对某大功率机车用轴流冷却风机叶轮进行优化设计。采用S-A湍流模型和求解三维雷诺平均N-S方程分析叶轮内部流动,以叶片中弧线进口角、出口角和叶片的安装角为设计变量,优化目标函数选择效率和静压升。设计点采用随机离散层取样方式,在几何参数的设计范围内生成样本并进行三维流动分析,以得到目标函数的模拟值;取不同自由参数可变范围,多次优化。优化设计结果与原始模型相比提高效率1.5%,静压升提高87Pa,其非设计点性能也均有所提高,满足设计需要。     

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.     

Design optimization of mixed-flow pump impellers with various shaft diameters at the same specific speed

In this study, the hydraulic performance of a mixed-flow pump depending on the impeller hub ratio was analyzed using Computational- fluid-dynamics (CFD). The impeller inlet shape varies according to the hub ratio even at the same specific speed. It is important to ensure an optimum impeller design according to the hub ratio in order for the impeller shape to provide the desired performance at constant specific speed. The design variables of inlet part for meridional plane and vane plane development were defined for optimum impeller design. The objective functions were defined as the total head and total efficiency of the mixed-flow pump impellers. The optimum impeller design was carried out by controlling the design variables of impeller inlet parts by using the Response-surface-method (RSM). The tendency of impeller design variables depending on the hub ratio was identified by analyzing the optimum impeller design. Further, the impeller shape was designed on the basis of the tendency of the design variables depending on the hub ratio. Finally, the performance of an impeller with the designed shape was verified by numerical analysis.     

Multi-objective optimization for mixed-flow pump with blade angle of impeller exit and diffuser inlet

During design optimization, the impeller and diffuser of a mixed-flow pump are generally optimized separately. In such cases, the total head can be overdesigned. In this study, the designs of the impeller and diffuser were optimized simultaneously by using computational fluid dynamics and the Response surface method (RSM). Design variables were defined according to the vane plane development of the impeller and diffuser. Three-dimensional Reynolds-averaged Navier–Stokes equations for the shear stress transport turbulence model were discretized by finite volume approximations and solved on hexahedral grids to analyze the flow in the pump. The total head and total efficiency were selected as objective functions, with four design variables related to the impeller outlet angles and diffuser inlet angles used for optimization. The RSM was constructed based on the objective functions with design points generated from the central composite method. The hydraulic performance of the optimum model was analyzed.     

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.

     

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.     

基于CFX正交试验的深井离心泵导叶的优化设计

为提高深井离心泵的水力性能,针对100QJ16型深井泵,按照L9(34)正交表,选取空间导叶的进口冲角、包角、叶片出口安放角和叶片数等4个因素,每个因素取3个水平,设计出9个导叶模型,并分别与同一个叶轮装配。基于CFX软件,对两级模型泵进行了全流场数值模拟,获得9组方案在额定工况下的扬程和效率。采用极差分析法分析了各几何参数对扬程和效率的影响规律以及影响空间导叶性能的主要因素和次要因素。空间导叶进口冲角和叶片包角对两级泵的扬程和效率的影响较大。将优化方案进行了样机试验,其效率达到了设计要求。     

Design optimization of low-speed axial flow fan blade with three-dimensional RANS analysis

This work presents a numerical optimization procedure for a low-speed axial flow fan blade with polynomial response surface approximation model. Reynolds-averaged Navier-Stokes equations with SST turbulence model are discretized by finite volume approximations and solved on hexahedral grids for flow analyses. The blade profile as well as stacking line is modified to enhance blade total efficiency, i.e., the objective function. The design variables of blade lean, maximum thickness and location of maximum thickness are selected, and a design of experiments technique produces design points where flow analyses are performed to obtain values of the objective function. A gradient-based search algorithm is used to find the optimal design in the design space from the constructed response surface model for the objective function. As a main result, the efficiency is increased effectively by the present optimization procedure. And, it is also shown that the modification of blade lean is more effective to improve the efficiency rather than modifying blade profile. This paper was presented at the 9^th Asian International Conference on Fluid Machinery (AICFM9), Jeju, Korea, October 16–19, 2007.     

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.     

叶片型线对离心风机性能影响的研究

首先对某采用双圆弧叶片的高效离心风机进行实验和数值对比,并在叶轮前盘形状、轮盖和叶片进出口安装角都相同的情况下,分析了采用双圆弧叶片和等减速叶型的模型风机的性能变化。结果表明,使用双圆弧长短叶片风机模型的稳定工况范围更宽、全压更高,等减速模型则在设计流量和小流量下效率更高、流动损失更小。     

Multi-component optimization of a vertical inline pump based on multi-objective pso and artificial neural network

The vertical inline pump is a single-stage single-suction centrifugal pump with a curved inlet pipe before the impeller, which is widely used in where the constraint is installation space. In this paper, with the objective functions of efficiencies at 0.5Q_d, 1.0Q_d, and 1.5Q_d, a multi-objective optimization on inlet pipe and impeller was proposed to broaden the efficient operating period of a vertical inline pump. Two 5th order Bézier curves were adopted to fit the shape of the mid curve of the inlet pipe and the trend of the blade angle of the impeller. Fourteen design variables were selected after the data-mining process. 300 sample cases were generated using Latin hypercube sampling (LHS), and they were solved by 3D RANS code to obtain the objective functions. The feed-forward artificial neural network with a hidden layer and an output layer was adopted to fit the two objective functions and the 14 design variables. The Pareto frontiers were generated for the three objectives using multi-objective particle swarm optimization (MOPSO), and three different configurations on the Pareto front are selected for detailed study by computational fluid dynamics (CFD). The results showed that the profile of the inlet pipe and the blade have a dramatic impact on the performance of the vertical inline pump. The Pareto frontiers reported that the performance under the overload condition usually keeps stable when the nominal efficiency is lower than 82 %, or the part-load efficiency is lower than 62 %, and it will decrease rapidly after that. After optimization, the improvement of efficiencies at the part-load condition and nominal condition of the picked case were 9.65 % and 7.95 %, respectively.

     

后缘小翼智能旋翼有限偏角减振效果分析

建立了适合带后缘小翼的缩比模型智能旋翼减振优化分析方法。考虑小翼运动引起的气动力和惯性力对旋翼系统的影响,建立带后缘小翼的旋翼气动弹性分析模型,使用一种高效的代理模型方法计算带后缘小翼的翼型气动力。使用隐式梯形公式求解气弹耦合动力学方程得到桨叶的弹性响应,采用力积分法计算桨叶剖面振动载荷与桨毂载荷。以小翼操纵输入为设计变量,以桨毂载荷幅值为目标函数建立优化问题,使用最速下降法求解最佳减振效果对应的小翼偏转规律。结果表明本模型计算的结构与气动载荷可靠,对不同前进比状态,后缘小翼都能有效降低桨毂垂向振动载荷。使用直接约束法和目标权重法都能模拟小翼偏转能力不足的情况,小翼偏转能力对减振效果有明显影响,偏转能力不足时后缘小翼仍具有一定的减振效果。     

离心泵叶轮内部粘油流动激光测速计测量

利用二维激光测速计系统准确地测量了离心泵输送粘度为４８ｍｍ２／ｓ粘油时最优和小流量工况叶轮内部流动。试验表明,叶片吸力面有很宽的尾流,压力面不存在射流,叶轮内部流动属主流／尾流模型。尾流位于吸力面／前盖板、吸力面／后盖板拐角处,并覆盖整个吸力面。由最优工况变到小流量工况,尾流有扩大趋势。     

Evaluation of surrogate models for optimization of herringbone groove micromixer

Surrogate models have been applied to shape optimizations of a micromixer with the aim of assessing the performance of the models. The surrogate models considered include polynomial response surface approximation, Kriging, and radial basis neural network. In addition, a weighted average model based on global error measures is constructed. A mixing index at the exit of the micromixer is used as the objective function. The mixing index is calculated based on Navier-Stokes equations. Two cases of optimization, one with two design variables and the other with three design variables, have been tested. The design variables are selected among the ratio of the groove depth to channel height, the angle of groove, and the ratio of groove width to groove pitch. D-Optimal design generated sampling points are used for sampling. It is found that although the weighted average model does not predict the best optimal point, it does show consistent and reliable performance.     

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.     

基于正交设计法的中比转速泵无过载优化设计

以D82-19-2型中比转速离心泵为研究对象,选取导叶喉部面积、叶片数、叶片包角、叶轮出口直径、叶轮出口宽度、叶片出口角、叶轮进口直径7个参数为变量,运用正交设计法制定七因素三水平正交方案L18(37),借助数值模拟方法对泵的性能进行预测,通过分析得到了几何参数对中比转速离心泵性能影响的主次顺序:叶片数对扬程和效率的影响起主要作用,叶片包角对轴功率的影响起主要作用;正交优化方案的数值模拟结果表明,该方案既满足无过载性能的要求,又保持了较高的效率,可为中比转速离心泵无过载设计提供参考。