Three-dimensional Inverse Design Research Articles

A Robust Mixing Plane and Its Application in Three-Dimensional Inverse Design of Transonic Turbine Stages

A robust mixing plane method satisfying interface flux conservation, nonreflectivity and retaining interface flow variation; valid at all Mach numbers and applicable for any machine configuration is formulated and implemented in a vertex based finite volume solver for flow analysis and inverse design. The formulation is based on superposing perturbed flow variables derived from the three-dimensional (3D) characteristics obtained along the flow direction on the exchanged mixed out averaged quantities. The method is extended for low speed applications using low Mach number preconditioning. Subsequently, inverse design runs over a single stage transonic low pressure (LP) turbine configuration conducted at a fixed mass flow boundary condition and spanwise loading condition similar to the baseline generates optimized configurations providing performance improvement while achieving prespecified target meridional load distribution.

Full 3-D viscous optimization design of a reversible pump turbine runner

The bi-directional operation of reversible pump turbines presents a great challenge in terms of runner design. In the present paper, an optimal design system for the pump turbine runner is presented by coupling three-dimensional (3-D) inverse design with the Computational Fluid Dynamics (CFD), Design of Experiment (DoE), Response Surface Methodology (RSM) and Multi Objective Genetic Algorithm (MOGA). A pump-turbine runner was designed using the system, with selecting blade loading distributions and blade lean as the input parameters, and the runner efficiency for both pump and turbine mode as optimization objectives. The CFD results show that a high efficiency runner can be designed using the present system.

An impingement heat sink module design problem in determining optimal non-uniform fin widths

A three-dimensional inverse design problem is examined in this study for estimating the optimal non-uniform fin widths of an impingement heat sink module using a general purpose commercial code (CFD-ACE+) and the Levenberg–Marquardt Method (LMM). The optimal heat sink was designed based on the original 10 by 10 squared fin array with a fixed fin volume and height. The objective of this study is to minimize the thermal resistance (Rth) of the fin array and to obtain the optimal dimensions of non-uniform fin widths. The results obtained using the LMM to solve this three-dimensional fin design problem were initially justified numerically. Under the design operating condition Re=5000, Rth can be decreased by 12.98% and 4.81% compared to the original and to Yang and Peng’s optimal heat sinks, respectively. At the same time, the thermal performances of the optimal heat sink can be improved significantly. For instance, the Nusselt number (Nu) and the Coefficient of Enhancement (COE) can be increased by 14.92% and 15%, respectively, compared to the original heat sink, and these parameters can be increased by 5.06% and 3%, respectively, when compared to the optimal heat sink proposed by Yang and Peng. Finally, prototypes of the original and optimized heat sinks were fabricated and used to experimentally verify the validity of this work. The experimental results demonstrated that by utilizing the fabricated heat sinks and operating under the design condition Re=5000, Rth can be decreased by 12.49% and Nu and COE can be increased by 14.21% and 14%, respectively, compared to the original fin array. Consequently, the thermal performances of optimal impingement heat sinks can be greatly improved.

An inverse design method for optimizing design parameters of heat sink modules with encapsulated chip

A three-dimensional inverse design problem in estimating the design variables for heat sink modules with an encapsulated chip is solved in the present study by using the Levenberg–Marquardt Method (LMM) and the general purpose commercial code CFD-ACE+ in an irregular domain. Three different types of heat sinks are examined at a fixed fin array volume to determine the most efficient type of heat sink. Moreover, Aluminum and Copper heat sinks are compared to find the optimum design of the module. Results obtained by using the LMM to solve this 3-D inverse design problem are justified based on the numerical experiments and it is concluded that the double row plate fin type heat sink performs best since it can obtain the lowest temperature distribution on the bottom surface of heat sink module. Moreover, larger heat transfer area of heat sink does not guarantee better thermal performance. Due to higher thermal conductivity of Copper heat sink, it also has better thermal performance than the Aluminum heat sink.

Parametric design of a Francis turbine runner by means of a three-dimensional inverse design method

The present paper describes the parametric design of a Francis turbine runner. The runner geometry is parameterized by means of a 3D inverse design method, while CFD analyses were performed to assess the hydrodymanic and suction performance of different design configurations that were investigated. An initial runner design was first generated and used as baseline for parametric study. The effects of several design parameter, namely stacking condition and blade loading was then investigated in order to determine their effect on the suction performance. The use of blade parameterization using the inverse method lead to a major advantage for design of Francis turbine runners, as the three-dimensional blade shape is describe by parameters that closely related to the flow field namely blade loading and stacking condition that have a direct impact on the hydrodynamics of the flow field. On the basis of this study, an optimum configuration was designed which results in a cavitation free flow in the runner, while maintaining a high level of hydraulic efficiency. The paper highlights design guidelines for application of inverse design method to Francis turbine runners. The design guidelines have a general validity and can be used for similar design applications since they are based on flow field analyses and on hydrodynamic design parameters.

On the Coupling of Inverse Design and Optimization Techniques for the Multiobjective, Multipoint Design of Turbomachinery Blades

Automatic optimization techniques have been used in recent years for the aerodynamic and mechanical design of turbomachine components. Despite the many advantages, their use is usually limited to simple applications in industrial practice, because of their high computational cost. In this paper, an optimization strategy is presented, which enables the three-dimensional multipoint, multiobjective aerodynamic optimization of turbomachinery blades in a time frame compatible with industrial standards. The design strategy is based on the coupling of three-dimensional inverse design, response surface method, multiobjective evolutionary algorithms, and computational fluid dynamics analyses. The blade parametrization is performed by means of a three-dimensional inverse design method, where aerodynamic parameters, such as the blade loading, are used to describe the blade shape. Such a parametrization allows for a direct control of the aerodynamic flow field and performance, leading to a major advantage in the optimization process. The design method was applied to the redesign of a centrifugal and of an axial compressor stage. The two examples confirmed the validity of the design strategy to perform the three-dimensional optimization of turbomachine components, accounting for both design and off-design performance, in a time-efficient manner. The coupling of response functions and inverse design parametrization also allowed for an easy sensitivity analysis of the impact of the design parameters on the performance ones, contributing to the development of design guidelines that can be exploited for similar design applications.

1706 半開放形プロペラファンの三次元空力設計(S19-1 流体機械に関連した流動現象とその解析・計測(1)ファン内流れの計測と解析,21世紀地球環境革命の機械工学:人・マイクロナノ・エネルギー・環境)

A three-dimensional aerodynamic design method for half-ducted propeller fan has been presented. The half-ducted propeller fan has internal and external flow feature. It is important to take into account non-uniform meridional flow distributions around it. The present design method consists of two parts: a three-dimensional inverse design of fan rotor blade and an axisymmetric viscous flow calculation on the meridional plane. Continuing the process between the blade design using the three-dimensional inverse design method and the evaluation of the viscous flow fields around the rotor using the axisymmetric viscous flow calculation, the blade shape matching the flow fields around the rotor is converged. It is found that the present design method is useful to the half-ducted propeller fan design tool.

1635 斜流ポンプの多目的最適化設計 : 第1報 設計パラメータの感度解析(J12-2 流体機械に関連した流体解析と数値最適化技術(2),J12 流体機械に関連した流体解析と数値最適化技術)

A sensitivity analysis of mixed-flow impeller's design parameters was performed in the first stage of optimization design of mixed-flow pumps that have a performance trade-off. High efficiency, non-stall, and low shut-off power were set as objective functions. This study was done by combining the three-dimensional inverse design method and CFD, some design parameters of impeller were founded to have trade-off problem for performance.

Investigation of an Inversely Designed Centrifugal Compressor Stage—Part I: Design and Numerical Verification

In this paper the three-dimensional inverse design code TURBOdesign-1 is applied to the design of the blade geometry of a centrifugal compressor impeller with splitter blades. In the design of conventional impellers the splitter blades normally have the same geometry as the full blades and are placed at mid-pitch location between the two full blades, which can usually result in a mismatch between the flow angle and blade angles at the splitter leading edge. In the inverse design method the splitter and full blade geometry is computed independently for a specified distribution of blade loading on the splitter and full blades. In this paper the basic design methodology is outlined and then the flow in the conventional and inverse designed impeller is compared in detail by using computational fluid dynamics (CFD) code TASCflow. The CFD results confirm that the inverse design impeller has a more uniform exit flow, better control of tip leakage flow and higher efficiency than the conventional impeller. The results also show that the shape of the trailing edge geometry has a very appreciable effect on the impeller Euler head and this must be accurately modeled in all CFD computations to ensure closer match between CFD and experimental results. Detailed measurements are presented in part II of the paper.

Three-dimensional inverse design of axial compressor stator blade using neural-networks and direct Navier–Stokes solver

In this article we describe a new method for the aerodynamic optimisation and inverse design problem resolution. This method is based on the coupling of a classical optimiser with a neural-network. A Navier–Stokes flow solver is used for an accurate computation of the objective function. At first the neural-network, which has been trained by an initial small database, is used to obtain, by the interpolation of the design sensitivities, a new design point, which is then computed by the Navier–Stokes solver in order to update the neural-network training database for further iterative step. Since the neural-network provides the optimiser with the derivatives, the objective function has to be evaluated only once at every step. By this method, the computational effort is significantly reduced with respect to the classical optimisation methods based on the design sensitivities, that are computed directly by the flow solver. The method proposed has been positively tested on the inverse design of a three-dimensional axial compressor blade, and a summary of the results is provided.

Hydrodynamic Design of Pump Diffuser Using Inverse Design Method and CFD

A new approach to optimizing a pump diffuser is presented, based on a three-dimensional inverse design method and a Computational Fluid Dynamics (CFD) technique. The blade shape of the diffuser was designed for a specified distribution of circulation and a given meridional geometry at a low specific speed of 0.109 (non-dimensional) or 280 (m3/min, m, rpm). To optimize the three-dimensional pressure fields and the secondary flow behavior inside the flow passage, the diffuser blade was more fore-loaded at the hub side as compared with the casing side. Numerical calculations, using a stage version of Dawes three-dimensional Navier-Stokes code, showed that such a loading distribution can suppress flow separation at the corner region between the hub and the blade suction surface, which was commonly observed with conventional designs having a compact bowl size (small outer diameter). The improvements in stage efficiency were confirmed experimentally over the corresponding conventional pump stage. The application of multi-color oil-film flow visualization confirmed that the large area of the corner separation was completely eliminated in the inverse design diffuser.

A three-dimensional inverse method using navier—stokes equations for turbomachinery blading

A new numerical method for solving fully three-dimensional inverse shape design problem of turbomachinery blading has been developed. The general inverse problem refers to the problem in which the pressure distributions on suction and pressure surfaces of blade are given, but the corresponding blade profile is unknown. In this paper, the calculations are based on the 3D Navier-Stokes equations expressed in terms of nonorthogonal curvilinear coordinates and corresponding nonorthogonal velocity components, and the explicit time marching algorithm and Baldwin-Lomax turbulence model are adopted. A special treatment for boundary conditions on blade surfaces is employed to satisfy the given pressure distribution. In computational process, an initial blade profile is supposed at starting, and then the blade surfaces will move regularly with time steps in the time marching process until the convergence is reached. The movement velocities at every point of blade surfaces are obtained from the solution of the Navier-Stokes equations. After each revision of the blade profile, the grid is reconstructed, and the aerodynamic parameters need to be transferred between the old and new grid points by an accurate interpolation method. Thus the viscous inverse problem is solved in a new process. The computational results for two test cases indicate that the method presented in this paper is very effective.

Three-Dimensional Automatic Optimization Method for Turbomachinery Blade Design

In deriving automatic numerical optimization algorithms for aerodynamic applications, it is quite important to choose a suitable cost function and a suitable set of design parameters. The unknown airfoil/blade profiles are usually chosen to be the design parameters. However, there are certain advantages in using the pressure/velocity distribution as the design variable in some applications; the optimized distribution can be used in a three-dimensional inverse design method to generate the actual profile shape. In this paper this approach will be addressed. Two methods are used to parameterize the circulation distribution for compressor blades. The Dawes code is used to calculate the viscous effect. An automatic optimization algorithm is developed, and two objective functions defined by the entropy loss or the aerodynamic blockage are examined.

An object-oriented framework for the implementation of adjoint techniques in the design and control of complex continuum systems

Specific object-oriented software design concepts are elaborated for a novel implementation of a class of adjoint optimization problems typical of the infinite-dimensional design and control of continuum systems. For clarity, the design steps and ideas are elucidated using an inverse natural convection design problem. Effective application of software design concepts such as inheritance, data encapsulation, information hiding, etc., is demonstrated through instances from the example considered. Two test numerical examples are considered and the CPU statistics for one of these problems are compared with those corresponding to a procedural implementation of the same problem. The numerical examples include a three-dimensional inverse design problem that demonstrates the effectiveness of the present object-oriented approach in developing dimension-independent robust design codes. Copyright © 2000 John Wiley & Sons, Ltd.

Inverse Design and CFD Investigation of Blood Pump Impeller

In this paper, a three-dimensional inverse design method using mean swirl specification is applied to the design of centrifugal blood pump impeller blades. CFD investigation of the passage flows is carried out to analyze the flow field and pressure generated across the blade. The results show that the possibility of blood cells' damage may not be increased when the pressure developed is increased. This technique can provide designers valuable insight on the development of efficient blood pump with reduced risk of blood traumatization.

On the role of three-dimensional inverse design methods in turbomachinery shape optimization

The application of a three-dimensional (3D) inverse design method in which the blade geometry is computed for a specified distribution of circulation to the design of turbomachinery blades is explored by using two examples. In the first instance the method is applied to the design of radial and mixed flow impellers to suppress secondary flows. Based on our understanding of the fluid dynamics of the flow in the impeller, simple guidelines are developed for input specification of the inverse method in order to systematically design impellers with suppressed secondary flows and a more uniform exit flow field. In the second example the method is applied to the design of a vaned diffuser. Again based on the understanding of the detailed flow field in the diffuser obtained by using 3D viscous calculations and oil flow visualizations, simple design guidelines are developed for input specification to the inverse method in order to suppress corner separation. In both cases the guidelines are verified numerically and in the case of the diffuser further experimental validation is presented.

On the Simultaneous Design of Blade and Duct Geometry of Marine Ducted Propulsors

In ducted propulsor design for marine vessels, due to the strong interaction between the duct and the propeller blades, it is very important to design the duct and the blade geometry simultaneously. Here, a three-dimensional inverse design method is presented to take this into consideration. The method is based on three-dimensional potential flow; however, the effect of the inlet shear flow and the resulting rotational flow is also modeled via the Clebsch formulation. The duct profile is designed to achieve a target velocity distribution while the blade geometry is computed to attain a desired mass-flow rate and a certain circulation distribution. The method is applied to the design of three generic ducted propulsors with a 7-bladed contrarotating configuration.

On the Design Criteria for Suppression of Secondary Flows in Centrifugal and Mixed Flow Impellers

In this paper, for the first time, a set of guidelines is presented for the systematic design of mixed flow and centrifugal compressors and pumps with suppressed secondary flows and a uniform exit flow field. The paper describes the shape of the optimum pressure distribution for the suppression of secondary flows in the impeller with reference to classical secondary flow theory. The feasibility of achieving this pressure distribution is then demonstrated by deriving guidelines for the design specifications of a three-dimensional inverse design method, in which the blades are designed subject to a specified circulation distribution or 2πrVθ. The guidelines will define the optimum choice of the blade loading or ∂rVθ/∂m and the stacking condition for the blades. These guidelines are then used in the design of three different low specific speed centrifugal pump impellers and a high specific speed industrial centrifugal compressor impellers. The flows through all the designed impellers are computed numerically by a three-dimensional viscous code and the resulting flow field is compared to that obtained in the corresponding conventional impeller. The results show consistent suppression of secondary flows in all cases. The design guidelines are validated experimentally by comparing the performance of the inverse designed centrifugal compressor impeller with the corresponding conventional impeller. The overall performance of the stage with the inverse designed impeller with suppressed secondary flows was found to be 5 percent higher than the conventional impeller at the peak efficiency point. Exit flow traverse results at the impeller exit indicate a more uniform exit flow than that measured at the exit from the conventional impeller.

Suppression of Secondary Flows in a Mixed-Flow Pump Impeller by Application of Three-Dimensional Inverse Design Method: Part 1—Design and Numerical Validation

This paper describes the design of the blade geometry of a medium specific speed mixed flow pump impeller by using a three-dimensional inverse design method in which the blade circulation (or rVθ) is specified. The design objective is the reduction of impeller exit flow nonuniformity by reducing the secondary flows on the blade suction surface. The paper describes in detail the aerodynamic criteria used for the suppression of secondary flows with reference to the loading distribution and blade stacking condition used in the design. The flow through the designed impeller is computed by Dawes’ viscous code, which indicates that the secondary flows are well suppressed on the suction surface. Comparison between the predicted exit flow field of the inverse designed impeller and a corresponding conventional impeller indicates that the suppression of secondary flows has resulted in substantial improvement in the exit flow field. Experimental comparison of the flow fields inside and at exit from the conventional and the inverse designed impeller is made in Part 2 of the paper.

Suppression of Secondary Flows in a Mixed-Flow Pump Impeller by Application of Three-Dimensional Inverse Design Method: Part 2—Experimental Validation

In Part 1 of this paper, a mixed-flow pump impeller was designed by a fully three-dimensional inverse design method, aimed at suppressing the secondary flows on the blade suction surface. In this part, the internal flow fields of the impeller are investigated experimentally, using flow visualization and phase-locked measurements of the impeller exit flow, in order to validate the effects of secondary flow suppression. The flow fields are compared with those of a conventional impeller, and it is confirmed that the secondary flows on the blade suction surface are well suppressed and the uniformity of the exit flow fields is improved substantially, in both circumferential and spanwise directions. The effects of tip clearance and the number of blades for the inverse designed impeller are also investigated experimentally and numerically.