Investigation of an efficient shape optimization procedure for centrifugal pump impeller using eagle strategy algorithm and ANN (case study: slurry flow)

Investigation an efficient shape optimization method for centrifugal pump and other turbo-machine is significant to reduce time consumption of process and increase accuracy and modification. For analysis an efficient shape optimization procedure, slurry flow in centrifugal pump is investigated. Since a centrifugal water pump has been not designed to carry out slurry flows, its performance decreases and energy consumption of this kind of pump increases. Therefore, improvement of performance and reduction of energy consumed for these pumps are the major issues. Since the performance of a centrifugal pump strictly depends on its impeller shape, in this study, the shape of impeller was optimized in order to achieve a higher efficiency for slurry flow. To optimize the impeller geometry and to improve the performance of Berkeh 32–160 pump as for the case study, Artificial Neural Networks (ANN) and Eagle Strategy (ES) algorithms have been coupled with a validated 3D Navier–Stokes equations for two phase flow based on Eulerian-Eulerian model. In the next step, the pump experimentally tested in an established slurry flow test rig in laboratory. Measured data were used to verify the numerical results of initial pump with slurry flow. Finally, the complete numerical characteristic curves of the pump with the optimized impeller were compared to the validated numerical characteristic curves of that with the initial impeller to verify optimization. An efficiency improvement of 3.33% at only 9.9% increasing of head has been obtained for optimized geometry. The results indicated a reasonable improvement in the optimal design of pump impeller and a higher performance using the ES algorithm. Furthermore the ES and PSO algorithm was compared and results shows that ES is efficient than PSO algorithm in this application and this methodology is more efficient than other surrogate methods.     

Numerical flow-field analysis and design optimization of a high-energy first-stage centrifugal pump impeller

Described is the numerical flow-field analysis and design optimization of the first-stage impellers of a so-called high-energy centrifugal pump having two single-suction first-stage impellers and one double-suction second stage impeller. This study has been carried out with the aid of three-dimensional computational-fluid-dynamics calculations, employing the potential-flow approximation of the governing equations. The study was conducted because the first-stage impellers of the pump considered appeared to suffer from severe premature wear due to cavitation attack on the vane leading edges, which situation had to be improved. The analysis carried out for the existing design produced suggestions for improvement, and based on these suggestions a new first-stage impeller design was developed. Subsequently, this new design was numerically analyzed to substantiate its potentially better (cavitation) performance. It appeared that the blade inlet angle of the original impeller design was too excessive at mid span, causing best cavitation performance to occur at 160 percent of the rated flow. The new design has its best cavitation point at the rated flow, and will not suffer from premature wear due to cavitation attack like the existing design. Received: 1 March 1999 / Accepted: 21 September 1999     

The comparison of incomplete sensitivities and Genetic algorithms applications in 3D radial turbomachinery blade optimization

In the present work, a centrifugal pump impeller’s blades shape was redesigned to reach a higher efficiency in turbine mode using two different optimization algorithms: one is a local method as incomplete sensitivities–gradient based optimization algorithm coupled by 3D Navier–Stokes flow solver, and another is a global method as Genetic algorithms and artificial neural network coupled by 3D Navier–Stokes flow solver. New impeller was manufactured and tested in the test rig. Comparison of the local optimization method results with the global optimization method results showed that the gradient based method has detected the global optimum point. Experimental results confirmed the numerical efficiency improvement in all measured points. This study illustrated that the developed gradient based optimization method is efficient for 3D radial turbomachinery blade optimization.     

基于ANSYS的离心泵叶轮结构有限元分析

叶轮是泵的核心部分,泵的性能参数：流量、扬程、效率和特性曲线的形状等均与叶轮的设计有重要关系。本文对叶轮结构进行了有限元分析,准确且直观的得到了叶轮在载荷作用下的应力和应变,为叶轮的强度计算提供了可靠依据,验证了有限元建模方法和计算方法的正确性。     

Design optimization of a viscous micropump with two rotating cylinders for maximizing efficiency

This study presents design optimization of a viscous micropump with two rotating cylinders. The desired performance of the pump is to maximize the pumping efficiency while satisfying the constraints on flow rate and geometry. As a preliminary step, the effects of geometric configurations on the pumping performance are investigated by carrying out parametric studies using an unstructured grid Navier–Stokes method. Next, an optimization problem is formulated to determine the design variable values which maximize the pumping efficiency subject to the constraints. Then, a computational procedure, combining the analysis method with a sequential metamodel-based optimization method, is established to solve the optimization problem formulated. Finally, this procedure is applied to the optimization of ten design cases with varying flow rates specified. The optimization results demonstrate the effectiveness of the design optimization method presented in this study by showing that the efficiencies of the optimally designed micropumps are enhanced without any constraint violations.     

Adaptive finite element methods for shape optimization of linearly elastic structures

Grid adaptive methods combined with means for automatic remeshing are applied to problems in shape optimal design of linearly elastic structures. The quantitative effect of element distortion near the design boundaries is identified in terms of interpolation error associated with the finite element discretization. The grid adaptation is itself formulated as a structural optimization problem, with an objective function that reflects the discretization error. A ‘necessary condition’ from this formulation provides the basis for a computational procedure to predict the modified grid.To avoid the sometimes drastic distortion of the FEM grid that might otherwise occur in conjunction with design change, remeshing must be performed at intermediate stages of the overall solution process. In order to produce results for the optimal shape design without interruption in this process, the computer program combines numerical grid generation and automatic remeshing with the grid adaptation and design change. Results for several shape design problems obtained with the use of grid adaptation are compared to computational results predicted from a fixed grid. Both ‘r-’ and ‘h-adaptation’ are tested.     

Numerical analysis of the unsteady flow in the near-tongue region in a volute-type centrifugal pump for different operating points

An investigation is presented on the unsteady flow behaviour near the tongue region of a single-suction volute-type centrifugal pump with a specific speed of 0.47. For this study, the flow through the test pump, which was available at laboratory, was simulated by means of a commercial CFD software that solved the Navier-Stokes equations for three-dimensional unsteady flow (3D-URANS). A sensitivity analysis of the numerical model was performed in order to impose appropriate parameters regarding grid size, time step size and turbulence model. The predictions of the numerical model were contrasted with experimental results of both global (flow-head curve and static pressure distribution at volute front side) and unsteady variables (unsteady pressure distribution at the volute front side filtered at the blade-passing frequency). Once validated, the model was used to study the flow pulsations associated to the interaction between the impeller blades and the volute tongue as a function of the flow rate, for several flow rates ranging from 20% to 160% of the nominal flow rate. The study allowed relating the blade passage with the pulsations of pressure and tangential and radial velocity at a number of reference locations in the near-tongue region. The numerical model was also used to evaluate the evolution of the leakage flow between the impeller-tongue gap and of the flow exiting the impeller through some specific angular intervals, during one single-blade passage.     

离心叶轮内部流场计算机仿真及分析

大型电机的冷却通常采用直叶片的离心叶轮,其内部的流动结构及其随工况的变化对叶轮性能及电机冷却效果有重要影响.为减少对实验的依赖,提高改型设计的可靠性,采用全三维的Navier-Stokes方程,建立了离心叶轮的计算机仿真模型,结合湍流模型及相应的计算网络及边界条件,可以完成对叶轮性能及内部流场的计算.用仿真模型针对一实际应用的离心冷却风机叶轮进行了数值仿真计算.并对计算结果进行了详细的对比分析,得出了不同工况下详细的流场结构,包括相对速度在叶轮通道中的分布及相对速度流线图.揭示了小流量工况下流动分离及效率降低的机理,将冷却风扇叶轮的总体性能与内部的流场结构进行了关联.研究结果表明离心叶轮内部流动分离是导致其性能下降的主要原因.     

Double-disk rotating viscous micro-pump with slip flow

In this paper numerical solution was provided for the 2D, axisymmetric Navier-Stokes equations coupled with energy equation for gaseous slip flow between two micro rotating disks pump. A first-order slip boundary condition was applied to all internal solid walls. The objective is to study the effect of Knudsen number, rotational Reynolds number and gap height on pump head, flow rate, coefficient of moments and overall micro-pump efficiency. Pump head, flow rate, coefficient of moments and pump efficiency were calculated for various pump operating conditions when the mass flow rate is applied at the pump inlet port. Detailed investigations were performed for rotational Reynolds number equals to 10. Effect of gap height between the two disks was studied. Effect of rotational Reynolds number on maximum flow rate and maximum pressure rise was simulated. The present numerical results for no-slip were compared with previously published experimental and theoretical data and found to be in a very good agreement. Knudsen number Kn values were found to be major parameters that affect the performance of pump. Pump performance decreases with increasing Kn. Optimal pump performance occurs around middle point of pump operating range. Pump operating range decreases with increasing Kn numbers. Pump performance is found to experience a steep degradation for Kn approaching 0.1. Maximum flow rate increases with rotational speed almost linearly. Maximum pressure rise also increases with rotational speed. Reducing gap height results in increasing maximum pressure rise, while increasing gap height results in larger maximum flow rate.     

Computational fluid dynamic analysis and design optimization of jet pumps

Jet pumps have a wide variety of applications and are commonly used in thermal power plants and refrigeration systems. An initial jet-pump design was developed using an analytical approach and its efficiency was improved using an efficient and accurate computational fluid dynamics model of the compressible turbulent flow in the pump, whose predictions agreed well with corresponding experimental data. Parametric studies were performed to determine the influence of the pump’s geometry on its performance and the high fidelity CFD solutions were used to build surrogate models of the pump’s behavior using the moving least squares method. Global optimization was carried out using the surrogates. This approach resulted in pump efficiency increasing from 29% to 33% and enabled the energy requirements of the pump to be reduced by over 20%.     

On the optimal design of the form of hydroturbine impeller blades

When designing a hydraulic turbine, a machine of better performance characteristics and primarily of the highest possible efficiency should be created. In the process, a designer is given a numer of restrictions concerning dam height, impeller diameter, etc. The turbine efficiency can be increased by varying the impeller blade profile or the angular velocity of the impeller rotation and by some other design techniques.The problem of optimization of hydroturbine parameters has been investigated in a number of works (see e.g. Fedorov 1983, 1984; Klimovich and Fedorov 1984; Kazachkov and Provad 1989). This paper presents some optimum decisions obtained for one-and two-dimensional axisymmetrical flow models. The turbine efficiency and local cavitation coefficients are accepted as the goal functionals. Necessary optimizing conditions are described, and calculated optimum characteristics of blade systems are given.     

On the theoretical link between design parameters and performance in cross-flow fans: a numerical and experimental study

Cross-flow fan performance strictly depends on the complex configuration of the non-axisymmetrical flow field within the machine. The flow field, in turn, is deeply influenced by the design parameters of both casing and impeller geometry. In this paper, the relationship between the design parameters of the geometrical configuration and fan performance is discussed in a theoretical perspective, analyzing the features of the corresponding flow fields. These are reconstructed by a numerical study on cross-flow fan operation carried out for a representative set of configurations at different throttling conditions. Time-accurate solutions for a two-dimensional viscous and incompressible model of the fan using a sliding mesh technique are calculated with a commercial CFD code. The numerical results are validated with experimental data obtained from tests on performance and from local measurements of the flow field.     

Structural shape optimization using Cartesian grids and automatic <Emphasis Type="Italic">h</Emphasis>-adaptive mesh projection

We present a novel approach to 3D structural shape optimization that leans on an Immersed Boundary Method. A boundary tracking strategy based on evaluating the intersections between a fixed Cartesian grid and the evolving geometry sorts elements as internal, external and intersected. The integration procedure used by the NURBS-Enhanced Finite Element Method accurately accounts for the nonconformity between the fixed embedding discretization and the evolving structural shape, avoiding the creation of a boundary-fitted mesh for each design iteration, yielding in very efficient mesh generation process. A Cartesian hierarchical data structure improves the efficiency of the analyzes, allowing for trivial data sharing between similar entities or for an optimal reordering of the matrices for the solution of the system of equations, among other benefits. Shape optimization requires the sufficiently accurate structural analysis of a large number of different designs, presenting the computational cost for each design as a critical issue. The information required to create 3D Cartesian h-adapted mesh for new geometries is projected from previously analyzed geometries using shape sensitivity results. Then, the refinement criterion permits one to directly build h-adapted mesh on the new designs with a specified and controlled error level. Several examples are presented to show how the techniques here proposed considerably improve the computational efficiency of the optimization process.     

基于网格实现的汽轮机基础优化设计

工程优化设计往往需要进行大规模的数值计算,拥有大量闲置资源的网格环境为建立这种高性能计算平台提供了可能.但是网格资源的动态性、异构性和分布性的本质特征,阻碍了网格技术在工程应用上的普及.为了利用网格环境中大量的闲置资源来协同解决实际工程中复杂的优化设计问题,建立了一个4层结构的高性能网格计算平台,并利用Kriging近似模型,在该平台上开发了以减轻基础重量和降低基础振幅为目的的多目标汽轮机优化设计的网格算法.使用该算法,在网格平台上对两个汽轮机基础进行了优化设计,与序列线性规划方法的结果比较表明所开发的优化算法有较高的计算精度.还分析了当使用不同数量的计算节点时网格的加速情况,说明所发展的优化方法能够在网格环境中高效地运行,搭建的网格平台也适合于工程优化设计.     

Intelligent computer-aided design optimization of heat pumps

The Rankine vapor cycle plays a very important role in heat pump design and analysis. The vapor heat pump cycle design process can be long and tedious. The designer must obtain various cycle performance parameters, including compressor work, heat added, cooling load, and coefficient of performance (COP), both quickly and accurately. This paper describes the use of an intelligent computer-aided software program in design and possible refinements of vapor heat pump technology. Several different arrangements of Rankine heat pump cycles are demonstrated. Objectives for improvements, constraints, and design optimization, which cannot be easily accomplished using conventional hand calculations, are emphasized. Using the featured software increases the engineer's efficiency and abilities in analyzing vapor heat pump designs.     

Joint QoS optimization for layered computational grid

Many existing grid resource allocation and scheduling algorithms mainly focus on isolated layers of the grid architecture. The inflexibility of the strict layering structure results in an inefficient utilization of the grid resources. This paper takes a system view of the computational grid and aims to jointly optimize global QoS by adopting cross-layer design. Cross-layer design is based on information exchange and joint optimization among multiple grid layers. Parameters from different layers are provided to a cross-layer optimizer, which selects the values of the layer specific parameters maximizing joint global QoS. The objective of the paper is to jointly optimize the parameters of all layers in a decentralized optimization problem and decompose joint QoS optimization into three sub problems at fabric layer, collective layer and application layer. In simulation part, we compare the performance of the global joint QoS optimization approach with application layer local optimization and resource layer local optimization approach, respectively.     

Experimental evaluation of solution approaches for the K-route maximum flow problem

We describe the implementation and testing of approaches for the solution of the maximum K-route flow problem. More specifically, we focus on Kishimoto's algorithm, the binary search algorithm and the K-route flow algorithm. With the aim to compare the performances of the aforementioned methods, we report results of computational experiments carried out on a large set of randomly generated problems with varying topology and arc capacities. The numerical results show that Kishimoto's algorithm is generally the fastest for solving fully random networks and 3-D grid random networks. The binary search algorithm provides the best performance in solving grid random networks. The K-route flow algorithm is generally the fastest for solving fully random networks and 3-D grid random networks with capacity range of [1,1000] and certain values of K.     

High-fidelity aerostructural optimization with integrated geometry parameterization and mesh movement

This paper extends an integrated geometry parameterization and mesh movement strategy for aerodynamic shape optimization to high-fidelity aerostructural optimization based on steady analysis. This approach provides an analytical geometry representation while enabling efficient mesh movement even for very large shape changes, thus facilitating efficient and robust aerostructural optimization. The geometry parameterization methodology uses B-spline surface patches to describe the undeflected design and flying shapes with a compact yet flexible set of parameters. The geometries represented are therefore independent of the mesh used for the flow analysis, which is an important advantage to this approach. The geometry parameterization is integrated with an efficient and robust grid movement algorithm which operates on a set of B-spline volumes that parameterize and control the flow grid. A simple technique is introduced to translate the shape changes described by the geometry parameterization to the internal structure. A three-field formulation of the discrete aerostructural residual is adopted, coupling the mesh movement equations with the discretized three-dimensional inviscid flow equations, as well as a linear structural analysis. Gradients needed for optimization are computed with a three-field coupled adjoint approach. Capabilities of the framework are demonstrated via a number of applications involving substantial geometric changes.     

Computation of the Hessian matrix in aerodynamic inverse design using continuous adjoint formulations

Continuous adjoint formulations for the computation of (first and) second order derivatives of the objective function governing inverse design problems in 2D inviscid flows are presented. These are prerequisites for the use of the very efficient exact Newton method. Four new formulations based on all possible combinations of the direct differentiation method and the continuous adjoint approach to compute the sensitivity derivatives of objective functions, constrained by the flow equations, are presented. They are compared in terms of the expected CPU cost to compute the Hessian of the objective function used in single-objective optimization problems with N degrees of freedom. The less costly among them was selected for further study and tested in inverse design problems solved by means of the Newton method. The selected approach, which will be referred to as the direct-adjoint one, since it performs direct differentiation for the gradient and, then, uses the adjoint approach to compute the Hessian, requires as many as N+2 equivalent flow solutions for each Newton step. The major part of the CPU cost (N equivalent flow solutions) is for the computation of the gradient but, fortunately, this task is directly amenable to parallelization. The method is used to reconstruct ducts or cascade airfoils for a known pressure distribution along their solid boundaries, at inviscid flow conditions. The examined cases aim at demonstrating the accuracy of the proposed method in computing the exact Hessian matrix as well as the efficiency of the exact Newton method as an optimization tool in aerodynamic design.     

Valveless micropump with acoustically featured pumping chamber

This article presents a new design of a valveless micropump. The pump consists of a nozzle-shaped actuation chamber with acoustic resonator profile, which functions as both pumping chamber and flow rectification structure. The pump is fabricated by lamination of layers made of polymethyl-methacrylate (PMMA) and dry adhesives, and is driven by a piezoelectric disk. The performance of the pump has been studied by both experimental characterization and numerical simulations. Both the experimental and numerical results show that the pump works well at low frequencies of 20–100 Hz to produce relatively high backpressures and flowrates. Moreover, the numerical simulations show that in the pumping frequency range, the flow patterns inside the chamber are found to be asymmetric in one pumping cycle so as to create a net flowrate, while outside the pumping frequency range, the flow patterns become symmetric in the pumping cycle. The pumping frequency can be shifted by modifying the pump configuration and dimensions. The pump is suitable for microfluidic integrations.