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Aerodynamic shape optimization using control theory
Reuther, James
Aerodynamic shape design has long persisted as a difficult scientific challenge due its highly nonlinear flow physics and daunting geometric complexity. However, with the emergence of Computational Fluid Dynamics (CFD) it has become possible to make accurate predictions of flows which are not dominated by viscous effects. It is thus worthwhile to explore the extension of CFD methods for flow analysis to the treatment of aerodynamic shape design. Two new aerodynamic shape design methods are developed which combine existing CFD technology, optimal control theory, and numerical optimization techniques. Flow analysis methods for the potential flow equation and the Euler equations form the basis of the two respective design methods. In each case, optimal control theory is used to derive the adjoint differential equations, the solution of which provides the necessary gradient information to a numerical optimization method much more efficiently then by conventional finite differencing. Each technique uses a quasi-Newton numerical optimization algorithm to drive an aerodynamic objective function toward a minimum. An analytic grid perturbation method is developed to modify body fitted meshes to accommodate shape changes during the design process. Both Hicks-Henne perturbation functions and B-spline control points are explored as suitable design variables. The new methods prove to be computationally efficient and robust, and can be used for practical airfoil design including geometric and aerodynamic constraints. Objective functions are chosen to allow both inverse design to a target pressure distribution and wave drag minimization. Several design cases are presented for each method illustrating its practicality and efficiency. These include non-lifting and lifting airfoils operating at both subsonic and transonic conditions.
Aerodynamic Shape Optimization using an Evolutionary Algorithm
Holst, Terry L.; Pulliam, Thomas H.; Kwak, Dochan (Technical Monitor)
A method for aerodynamic shape optimization based on an evolutionary algorithm approach is presented and demonstrated. Results are presented for a number of model problems to access the effect of algorithm parameters on convergence efficiency and reliability. A transonic viscous airfoil optimization problem, both single and two-objective variations, is used as the basis for a preliminary comparison with an adjoint-gradient optimizer. The evolutionary algorithm is coupled with a transonic full potential flow solver and is used to optimize the inviscid flow about transonic wings including multi-objective and multi-discipline solutions that lead to the generation of pareto fronts. The results indicate that the evolutionary algorithm approach is easy to implement, flexible in application and extremely reliable.
Improving the efficiency of aerodynamic shape optimization on unstructured meshes
Carpentieri, G.; Tooren, M.J.L. van; Koren, B.
In this paper the exact discrete adjoint of a finite volume formulation on unstructured meshes for the Euler equations in two dimensions is derived and implemented to support aerodynamic shape optimization. The accuracy of the discrete exact adjoint is demonstrated and compared with that of the appr
Genetic Algorithms Applied to Multi-Objective Aerodynamic Shape Optimization
Holst, Terry L.
A genetic algorithm approach suitable for solving multi-objective problems is described and evaluated using a series of aerodynamic shape optimization problems. Several new features including two variations of a binning selection algorithm and a gene-space transformation procedure are included. The genetic algorithm is suitable for finding Pareto optimal solutions in search spaces that are defined by any number of genes and that contain any number of local extrema. A new masking array capability is included allowing any gene or gene subset to be eliminated as decision variables from the design space. This allows determination of the effect of a single gene or gene subset on the Pareto optimal solution. Results indicate that the genetic algorithm optimization approach is flexible in application and reliable. The binning selection algorithms generally provide Pareto front quality enhancements and moderate convergence efficiency improvements for most of the problems solved.
Multidisciplinary Aerodynamic-Structural Shape Optimization Using Deformation (MASSOUD)
Samareh, Jamshid A.
This paper presents a multidisciplinary shape parameterization approach. The approach consists of two basic concepts: (1) parameterizing the shape perturbations rather than the geometry itself and (2) performing the shape deformation by means of the soft object animation algorithms used in computer graphics. Because the formulation presented in this paper is independent of grid topology, we can treat computational fluid dynamics and finite element grids in the same manner. The proposed approach is simple, compact, and efficient. Also, the analytical sensitivity derivatives are easily computed for use in a gradient-based optimization. This algorithm is suitable for low-fidelity (e.g., linear aerodynamics and equivalent laminate plate structures) and high-fidelity (e.g., nonlinear computational fluid dynamics and detailed finite element modeling) analysis tools. This paper contains the implementation details of parameterizing for planform, twist, dihedral, thickness, camber, and free-form surface. Results are presented for a multidisciplinary application consisting of nonlinear computational fluid dynamics, detailed computational structural mechanics, and a simple performance module.
Multi-objective aerodynamic shape optimization of small livestock trailers
Gilkeson, C. A.; Toropov, V. V.; Thompson, H. M.; Wilson, M. C. T.; Foxley, N. A.; Gaskell, P. H.
This article presents a formal optimization study of the design of small livestock trailers, within which the majority of animals are transported to market in the UK. The benefits of employing a headboard fairing to reduce aerodynamic drag without compromising the ventilation of the animals' microclimate are investigated using a multi-stage process involving computational fluid dynamics (CFD), optimal Latin hypercube (OLH) design of experiments (DoE) and moving least squares (MLS) metamodels. Fairings are parameterized in terms of three design variables and CFD solutions are obtained at 50 permutations of design variables. Both global and local search methods are employed to locate the global minimum from metamodels of the objective functions and a Pareto front is generated. The importance of carefully selecting an objective function is demonstrated and optimal fairing designs, offering drag reductions in excess of 5% without compromising animal ventilation, are presented.
Torque-Matched Aerodynamic Shape Optimization of HAWT Rotor
Al-Abadi, Ali; Ertunç, Özgür; Beyer, Florian; Delgado, Antonio
Schmitz and Blade Element Momentum (BEM) theories are integrated to a gradient based optimization algorithm to optimize the blade shape of a horizontal axis wind turbine (HAWT). The Schmitz theory is used to generate an initial blade design. BEM theory is used to calculate the forces, torque and power extracted by the turbine. The airfoil shape (NREL S809) is kept the same, so that the shape optimization comprises only the chord and the pitch angle distribution. The gradient based optimization of the blade shape is constrained to the torque-rotational speed characteristic of the generator, which is going to be a part of the experimental set-up used to validate the results of the optimization study. Hence, the objective of the optimization is the maximization of the turbines power coefficient Cp while keeping the torque matched to that of the generator. The wind velocities and the rotational speeds are limited to those achievable in the wind tunnel and by the generator, respectively. After finding the optimum blade shape with the maximum Cp within the given range of parameters, the Cp of the turbine is evaluated at wind-speeds deviating from the optimum operating condition. For this purpose, a second optimization algorithm is used to find out the correct rotational speed for a given wind-speed, which is again constrained to the generator's torque rotational speed characteristic. The design and optimization procedures are later validated by high-fidelity numerical simulations. The agreement between the design and the numerical simulations is very satisfactory.
Torque-Matched Aerodynamic Shape Optimization of HAWT Rotor
Schmitz and Blade Element Momentum (BEM) theories are integrated to a gradient based optimization algorithm to optimize the blade shape of a horizontal axis wind turbine (HAWT). The Schmitz theory is used to generate an initial blade design. BEM theory is used to calculate the forces, torque and power extracted by the turbine. The airfoil shape (NREL S809) is kept the same, so that the shape optimization comprises only the chord and the pitch angle distribution. The gradient based optimization of the blade shape is constrained to the torque-rotational speed characteristic of the generator, which is going to be a part of the experimental set-up used to validate the results of the optimization study. Hence, the objective of the optimization is the maximization of the turbines power coefficient Cp while keeping the torque matched to that of the generator. The wind velocities and the rotational speeds are limited to those achievable in the wind tunnel and by the generator, respectively. After finding the optimum blade shape with the maximum Cp within the given range of parameters, the Cp of the turbine is evaluated at wind-speeds deviating from the optimum operating condition. For this purpose, a second optimization algorithm is used to find out the correct rotational speed for a given wind-speed, which is again constrained to the generator's torque rotational speed characteristic. The design and optimization procedures are later validated by high-fidelity numerical simulations. The agreement between the design and the numerical simulations is very satisfactory
Aerodynamic Optimization of the Nose Shape of a Train Using the Adjoint Method
Jorge Munoz-Paniagua
Full Text Available The adjoint method is used in this paper for the aerodynamic optimization of the nose shape of a train. This method has been extensively applied in aircraft or ground vehicle aerodynamic optimization, but is still in progress in train aerodynamics. Here we consider this innovative optimization method and present its application to reduce the aerodynamic drag when the train is subjected to front wind. The objective of this paper is to demonstrate the effectiveness of the method, highlighting the requirements, limitations and capabilities of it. Furthermore, a significant reduction of the aerodynamic drag in a short number of solver calls is aimed as well. The independence of the computational cost with respect to the number of design variables that define the optimal candidate is stressed as the most interesting characteristic of the adjoint method. This behavior permits a more complete modification of the shape of the train nose because the number of design variables is not a constraint anymore. The information obtained from the sensitivity field permits determining the regions of the geometry where a small modification of the nose shape might introduce a larger improvement of the train performance. A good agreement between this information and the successive geometry modifications is observed here.
Aerodynamic Shape Optimization Using A Real-Number-Encoded Genetic Algorithm
Holst, Terry L.; Pulliam, Thomas H.
A new method for aerodynamic shape optimization using a genetic algorithm with real number encoding is presented. The algorithm is used to optimize three different problems, a simple hill climbing problem, a quasi-one-dimensional nozzle problem using an Euler equation solver and a three-dimensional transonic wing problem using a nonlinear potential solver. Results indicate that the genetic algorithm is easy to implement and extremely reliable, being relatively insensitive to design space noise.
Shape optimization of turbine blades with the integration of aerodynamics and heat transfer
Rajadas J. N.
Full Text Available A multidisciplinary optimization procedure, with the integration of aerodynamic and heat transfer criteria, has been developed for the design of gas turbine blades. Two different optimization formulations have been used. In the first formulation, the maximum temperature in the blade section is chosen as the objective function to be minimized. An upper bound constraint is imposed on the blade average temperature and a lower bound constraint is imposed on the blade tangential force coefficient. In the second formulation, the blade average and maximum temperatures are chosen as objective functions. In both formulations, bounds are imposed on the velocity gradients at several points along the surface of the airfoil to eliminate leading edge velocity spikes which deteriorate aerodynamic performance. Shape optimization is performed using the blade external and coolant path geometric parameters as design variables. Aerodynamic analysis is performed using a panel code. Heat transfer analysis is performed using the finite element method. A gradient based procedure in conjunction with an approximate analysis technique is used for optimization. The results obtained using both optimization techniques are compared with a reference geometry. Both techniques yield significant improvements with the multiobjective formulation resulting in slightly superior design.
Application of shape-based similarity query for aerodynamic optimization of wind tunnel primary nozzle
Kolář Jan
Full Text Available The aerodynamic shape optimization of the supersonic flat nozzle is the aim of proposed paper. The nozzle discussed, is applied as a primary nozzle of the inlet part of supersonic wind tunnel. Supersonic nozzles of the measure area inlet parts need to guarantee several requirements of flow properties and quality. Mach number and minimal differences between real and required velocity and turbulence profiles at the nozzle exit are the most important parameters to meet. The aerodynamic shape optimization of the flat 2D nozzle in CFD is employed to reach as uniform exit velocity profile as possible, with the mean Mach number 1.4. Optimization process does not use any of standard routines of global or local optimum searching. Instead, newly formed routine, which exploits shape-based oriented sequence of nozzles, is used to research within whole discretized parametric space. The movement within optimization process is not driven by gradient or evolutionary too, instead, the Path of Minimal Shape Deformation is followed. Dynamic mesh approach is used to deform the shape and mesh from the actual nozzle to the subsequent one. Dynamic deformation of mesh allows to speed up whole converging process as an initialization of flow at the newly formed mesh is based on afore-computed shape. Shape-based similarity query in field of supersonic nozzles is discussed and applied. Evolutionary technique with genetic algorithm is used to search for minimal deformational path. As a result, the best variant from the set of solved shapes is analyzed at the base of momentum coefficient and desired Mach number at the nozzle exit.
Aerodynamic design optimization of helicopter rotor blades including airfoil shape for hover performance
Ngoc Anh Vu; Jae Woo Lee; Jung Il Shu
This study proposes a process to obtain an optimal helicopter rotor blade shape for aerodynamic performance in hover flight.A new geometry representation algorithm which uses the class function/shape function transformation (CST) is employed to generate airfoil coordinates.With this approach,airfoil shape is considered in terms of design variables.The optimization process is constructed by integrating several programs developed by author.The design variables include twist,taper ratio,point of taper initiation,blade root chord,and coefficients of the airfoil distribution function.Aerodynamic constraints consist of limits on power available in hover and forward flight.The trim condition must be attainable.This paper considers rotor blade configuration for the hover flight condition only,so that the required power in hover is chosen as the objective function of the optimization problem.Sensitivity analysis of each design variable shows that airfoil shape has an important role in rotor performance.The optimum rotor blade reduces the required hover power by 7.4% and increases the figure of merit by 6.5%,which is a good improvement for rotor blade design.
Aerodynamically shaped vortex generators
Hansen, Martin Otto Laver; Velte, Clara Marika; Øye, Stig;
An aerodynamically shaped vortex generator has been proposed, manufactured and tested in a wind tunnel. The effect on the overall performance when applied on a thick airfoil is an increased lift to drag ratio compared with standard vortex generators. Copyright © 2015 John Wiley & Sons, Ltd....
Aerodynamic Optimal Shape Design Based on Body-Fitted Grid Generation
Farzad Mohebbi
Full Text Available This paper is concerned with an optimal shape design problem in aerodynamics. The inverse problem in question consists in finding the optimal shape an airfoil placed in a potential flow at a given angle of attack should have such that the pressure distribution on its surface matches a desired one. The numerical method to achieve this aim is based on a body-fitted grid generation technique (elliptic, O-type to generate a mesh over the airfoil surface and solve for the flow equation. The O-type scheme is used due to its ability to generate a high quality (fine and orthogonal grid around the airfoil surface. This paper describes a novel and very efficient sensitivity analysis scheme to compute the sensitivity of the pressure distribution to variation of grid node positions and both the conjugate gradient method (CGM and a version of the quasi-Newton method (i.e., BFGS are used as optimization algorithms to minimize the difference between the computed pressure distribution on the airfoil surface and desired one. The elliptic grid generation technique allows us to map the physical domain (body onto a fixed computational domain and to discretize the flow equation using the finite difference method (FDM.
Synergetic Optimization of Missile Shapes for Aerodynamic and Radar Cross-Section Performance Based on Multi- objective Evolutionary Algorithm
A multiple-objective evolutionary algorithm (MOEA) with a new Decision Making (DM) scheme for MOD of conceptual missile shapes was presented, which is contrived to determine suitable tradeoffs from Pareto optimal set using interactive preference articulation. There are two objective functions, to maximize ratio of lift to drag and to minimize radar cross-section (RCS) value. 3D computational electromagnetic solver was used to evaluate RCS, electromagnetic performance. 3D Navier-Stokes flow solver was adopted to evaluate aerodynamic performance. A flight mechanics solver was used to analyze the stability of the missile. Based on the MOEA, a synergetic optimization of missile shapes for aerodynamic and radar cross-section performance is completed. The results show that the proposed approach can be used in more complex optimization case of flight vehicles.
Geometry Control System for Exploratory Shape Optimization Applied to High-Fidelity Aerodynamic Design of Unconventional Aircraft
Gagnon, Hugo
This thesis represents a step forward to bring geometry parameterization and control on par with the disciplinary analyses involved in shape optimization, particularly high-fidelity aerodynamic shape optimization. Central to the proposed methodology is the non-uniform rational B-spline, used here to develop a new geometry generator and geometry control system applicable to the aerodynamic design of both conventional and unconventional aircraft. The geometry generator adopts a component-based approach, where any number of predefined but modifiable (parametric) wing, fuselage, junction, etc., components can be arbitrarily assembled to generate the outer mold line of aircraft geometry. A unique Python-based user interface incorporating an interactive OpenGL windowing system is proposed. Together, these tools allow for the generation of high-quality, C2 continuous (or higher), and customized aircraft geometry with fast turnaround. The geometry control system tightly integrates shape parameterization with volume mesh movement using a two-level free-form deformation approach. The framework is augmented with axial curves, which are shown to be flexible and efficient at parameterizing wing systems of arbitrary topology. A key aspect of this methodology is that very large shape deformations can be achieved with only a few, intuitive control parameters. Shape deformation consumes a few tenths of a second on a single processor and surface sensitivities are machine accurate. The geometry control system is implemented within an existing aerodynamic optimizer comprising a flow solver for the Euler equations and a sequential quadratic programming optimizer. Gradients are evaluated exactly with discrete-adjoint variables. The algorithm is first validated by recovering an elliptical lift distribution on a rectangular wing, and then demonstrated through the exploratory shape optimization of a three-pronged feathered winglet leading to a span efficiency of 1.22 under a height
Aerodynamic shape optimization of wing and wing-body configurations using control theory
Reuther, James; Jameson, Antony
This paper describes the implementation of optimization techniques based on control theory for wing and wing-body design. In previous studies it was shown that control theory could be used to devise an effective optimization procedure for airfoils and wings in which the shape and the surrounding body-fitted mesh are both generated analytically, and the control is the mapping function. Recently, the method has been implemented for both potential flows and flows governed by the Euler equations using an alternative formulation which employs numerically generated grids, so that it can more easily be extended to treat general configurations. Here results are presented both for the optimization of a swept wing using an analytic mapping, and for the optimization of wing and wing-body configurations using a general mesh.
Aerodynamic shape optimization for alleviating dynamic stall characteristics of helicopter rotor airfoil
Wang Qing
Full Text Available In order to alleviate the dynamic stall effects in helicopter rotor, the sequential quadratic programming (SQP method is employed to optimize the characteristics of airfoil under dynamic stall conditions based on the SC1095 airfoil. The geometry of airfoil is parameterized by the class-shape-transformation (CST method, and the C-topology body-fitted mesh is then automatically generated around the airfoil by solving the Poisson equations. Based on the grid generation technology, the unsteady Reynolds-averaged Navier-Stokes (RANS equations are chosen as the governing equations for predicting airfoil flow field and the highly-efficient implicit scheme of lower–upper symmetric Gauss–Seidel (LU-SGS is adopted for temporal discretization. To capture the dynamic stall phenomenon of the rotor more accurately, the Spalart–Allmaras turbulence model is employed to close the RANS equations. The optimized airfoil with a larger leading edge radius and camber is obtained. The leading edge vortex and trailing edge separation of the optimized airfoil under unsteady conditions are obviously weakened, and the dynamic stall characteristics of optimized airfoil at different Mach numbers, reduced frequencies and angles of attack are also obviously improved compared with the baseline SC1095 airfoil. It is demonstrated that the optimized method is effective and the optimized airfoil is suitable as the helicopter rotor airfoil.
Leading Edge Device Aerodynamic Optimization
Marius Gabriel COJOCARU
Full Text Available Leading edge devices are conventionally used as aerodynamic devices that enhance performances during landing and in some cases during takeoff. The need to increase the efficiency of the aircrafts has brought the idea of maintaining as much as possible a laminar flow over the wings. This is possible only when the leading edge of the wings is free from contamination, therefore using the leading edge devices with the additional role of shielding during takeoff. Such a device based on the Krueger flap design is aerodynamically analyzed and optimized. The optimization comprises three steps: first, the positioning of the flap such that the shielding criterion is kept, second, the analysis of the flap size and third, the optimization of the flap shape. The first step is subject of a gradient based optimization process of the position described by two parameters, the position along the line and the deflection angle. For the third step the Adjoint method is used to gain insight on the shape of the Krueger flap that will extend the most the stall limit. All these steps have been numerically performed using Ansys Fluent and the results are presented for the optimized shape in comparison with the baseline configuration.
Aerodynamic optimization studies on advanced architecture computers
Chawla, Kalpana
The approach to carrying out multi-discipline aerospace design studies in the future, especially in massively parallel computing environments, comprises of choosing (1) suitable solvers to compute solutions to equations characterizing a discipline, and (2) efficient optimization methods. In addition, for aerodynamic optimization problems, (3) smart methodologies must be selected to modify the surface shape. In this research effort, a 'direct' optimization method is implemented on the Cray C-90 to improve aerodynamic design. It is coupled with an existing implicit Navier-Stokes solver, OVERFLOW, to compute flow solutions. The optimization method is chosen such that it can accomodate multi-discipline optimization in future computations. In the work , however, only single discipline aerodynamic optimization will be included.
Aerodynamic shape design optimization of fairing based on Kriging method%基于Kriging方法的整流罩气动外形设计优化
杨希祥; 周张; 彭科
The aerodynamic shape design optimization of fairing for launch vehicles based on Kriging approximate method was researched.In order to solve the computational complexity problem in aerodynamic shape design optimization of fairing,Kriging func-tion was introduced to establish the approximate model for predicting fairing aerodynamic parameter,the process for parameter esti-mation of Kriging function was deduced,and the specific implementation method was offered.The mathematic model for aerodynamic shape design optimization of fairing was established,and resolved with Kriging method.Simulation results show that convergence effi-ciency of proposed design method is more efficient,the average drag of optimal scheme is 22.2% less than the primary scheme,and all constraint conditions are well satisfied.All research finds can provide theoretical reference for aerodynamic shape design optimiza-tion of flight vehicles.%研究基于Kriging近似方法的运载火箭整流罩气动外形设计优化问题。提出采用Kriging函数建立整流罩气动参数计算近似模型,解决运载火箭整流罩气动外形设计优化计算复杂性问题,推导了Kriging函数参数估计流程,给出其具体仿真实现方法;建立整流罩气动外形设计优化问题数学模型,采用基于Kriging函数的近似方法求解。仿真结果表明,提出的设计优化方法收敛速度快,优化方案平均阻力比基线方案减小22.2%,各项约束均得到良好满足。为飞行器气动外形设计优化研究提供理论参考。
ZEUS-DO: A Design Oriented CFD-Based Unsteady Aerodynamic Capability for Flight Vehicle Multidisciplinary Configuration Shape Optimization Project
National Aeronautics and Space Administration — In practically all air-vehicle MDO studies to date involving configuration shape optimization, dynamic Aeroservoelastic constraints had to be left out. Flutter,...
外形参数化方法对气动优化过程的影响%Effect of Shape Parameterization on Aerodynamic Shape Optimization
尹强; 高正红
The effect of shape parameterization on automatic aerodynamic shape optimization based on discussion and comparison of various methods is studied, including PARSEC method, CST method, Hicks-Henne bump functions, tree-form deformation, etc. First, the complete formulation of the optimal design process using the Navi-er-Stokes equations is presented and the role parameterization played is pointed out Second, by comparing these techniques based on the accuracy they can construct several kinds of representative airfoils, advices concerning which parameterization method to be adopted and how to specify number and scope of variables are given. Improvement for the PARSEC method is also given. Finally, results are presented for drag minimization problems by using Hicks-Henne and PARSEC respectively, other conditions being equal, which illustrates the influence of parameterization on the efficiency and effect of airfoil optimization.%探讨了各类参数化方法(包括PARSEC,CST,HicksHenne,自由型变形等)的原理、优缺点及其对气动优化设计的影响.首先简述了基于NS方程进行气动优化设计的过程,指出参数化方法为优化问题提供了设计变量.然后研究了各类参数化方法的原理,给出了各类方法中参数的几何意义,并对PARSEC方法提出了改进.通过比较各类方法对代表性翼型的重构能力,给出了合理选择参数化方法,参数个数及其取值范围的建议.最后给出了在相同工况下分别使用Hicks-Herne和PAR-SEC两种参数化方法的气动减阻优化结果,研究了其对翼型气动优化效率和效果的影响.
Appliction of nontraditional optimization techniques for airfoil shape optimization
Mukesh, R.; Lingadurai, K; Selvakumar, U.
The method of optimization algorithms is one of the most important parameters which will strongly influence the fidelity of the solution during an aerodynamic shape optimization problem. Nowadays, various optimization methods, such as genetic algorithm (GA), simulated annealing (SA), and particle swarm optimization (PSO), are more widely employed to solve the aerodynamic shape optimization problems. In addition to the optimization method, the geometry parameterization becomes an important fac...
ZEUS-DO: A Design Oriented CFD-Based Unsteady Aerodynamic Capability for Flight Vehicle Multidisciplinary Configuration Shape Optimization Project
National Aeronautics and Space Administration — CFD-based design-oriented (DO) steady/unsteady aerodynamic analysis tools for Aeroelastic / Aeroservoelastic (AE/ASE) evaluation lag significantly behind other...
基于CST参数化的翼型优化遗传算法研究%Research on Genetic Algorithm for Aerodynamic Shape Optimization Based on CST
张磊; 陈红全
用外形建模的CST参数化方法,构建翼型几何可直接利用其后缘角、前缘半径等几何特征,其控制参数更能反映翼型特有的气动敏感性,有助于遗传算法搜索寻优.基于这一参数化方法,结合遗传算法,构造了用于翼型优化的设计方法.算法中,CST控制参数作为设计变量,采用二进制编码,并通过引入精英策略,提高了遗传算法的收敛性能.算法适应度评估涉及的流场求解则采用了基于Jameson有限体积法的Euler方程解算程序.先以NACA0012翼型为例,以其某一已知的表面压力分布为目标,进行了遗传算法的重构运算,给出了重构的翼型几何外形,验证了方法.在此基础上,进行了带约束的跨音速翼型优化设计,给出了升力系数极大化和阻力系数极小化等设计算例,展示出翼型优化设计的效果.%The CST parameterization method is applied to the aerodynamic shape optimization of airfoils. A binary coded Genetic Algorithm (GA) is used as the fundamental optimization method. Elilist strategy is introduced into GA to improve its performance of convergence. A finite volume Euler solver based on Jameson method is used for aerodynamic calculation. The presented results of airfoil reconstruction show thai the developed method is feasible. The method is then applied to the problems including lift coefficient maximization and drag coefficient minimization under prescribed constraints, to validate its performance when used in aerodynamic shape optimization of airfoils.
Aerodynamic shape optimization and design of airfoils with low Reynolds number%低雷诺数翼型的气动外形优化设计
陈学孔; 郭正; 易凡; 王瑞波; 刘光远; 李泓兴
对翼型参数化方法 Parsec 和 Hicks-Henne 型函数系列方法,进行了低雷诺数翼型的参数化描述研究。分析了低雷诺数翼型气动优化目标设置特点,确定改进的 Hicks-Henne 型函数作为翼型的参数化描述方法。从基于功率因子最大的角度出发,结合 Kriging 代理模型和遗传算法的运用,进行了低雷诺数翼型的气动外形正优化设计。引入传统高雷诺数翼型的多点优化方法,进行两组不同速度域、两种不同加权系数下的多点优化,优化速度域最大范围15m/s,并结合翼型的单点优化进行研究。结果表明:多点优化更适用于低雷诺数翼型的气动优化;如果某多点优化翼型功率因子均值提高29.54%、力矩系数方差降低27.79%,有利于飞行航时和稳定性提高;多点优化具有较好的工程应用价值。%Aerodynamic optimization and design of airfoils with low Reynolds number was introduced in this paper.Objective setting for the optimization and its feasibility were analyzed.Parameterizing quality of the series of Hicks-Henne shape functions and the parsec method were studied.Based on the consideration of power factor maximum,improved Hicks-Henne shape functions were selected as parametric method.Krig-ing surrogate model and genetic algorithm were adopted in the optimization and design system.Further-more,multi-point optimization method which is used to optimize conventional airfoils with high Reynolds number was extended to the case of airfoils with low Reynolds number.Four multi-point optimization cases set with different weighted coefficients in two different velocity design fields were calculated,with one veloci-ty field spanned as long as 15m/s.Combined with single-point optimization study,the final results verified that multi-point optimization was more suitable for aerodynamic shape optimization for low Reynolds number airfoils.One of the multi-point optimized airfoils
XIA Lu; GAO Zheng-hong
For aerodynamic shape optimization, the approximation management framework (AMF) method is used to organize and manage the variable-fidelity models. The method can take full advantage of the low-fidelity, cheaper models to concentrate the main workload on the low-fidelity models in optimization iterative procedure. Furthermore, it can take high-fidelity, more expensive models to monitor the procedure to make the method globally convergent to a solution of high-fidelity problem. Finally, zero order variable-fidelity aerodynamic optimization management framework and search algorithm are demonstrated on an airfoil optimization of UAV with a flying wing. Compared to the original shape, the aerodynamic performance of the optimal shape is improved. The results show the method has good feasibility and applicability.
Shape optimization of corrugated airfoils
Jain, Sambhav; Bhatt, Varun Dhananjay; Mittal, Sanjay
The effect of corrugations on the aerodynamic performance of a Mueller C4 airfoil, placed at a 5° angle of attack and Re=10{,}000, is investigated. A stabilized finite element method is employed to solve the incompressible flow equations in two dimensions. A novel parameterization scheme is proposed that enables representation of corrugations on the surface of the airfoil, and their spontaneous appearance in the shape optimization loop, if indeed they improve aerodynamic performance. Computations are carried out for different location and number of corrugations, while holding their height fixed. The first corrugation causes an increase in lift and drag. Each of the later corrugations leads to a reduction in drag. Shape optimization of the Mueller C4 airfoil is carried out using various objective functions and optimization strategies, based on controlling airfoil thickness and camber. One of the optimal shapes leads to 50 % increase in lift coefficient and 23 % increase in aerodynamic efficiency compared to the Mueller C4 airfoil.
Application of Nontraditional Optimization Techniques for Airfoil Shape Optimization
R. Mukesh
Full Text Available The method of optimization algorithms is one of the most important parameters which will strongly influence the fidelity of the solution during an aerodynamic shape optimization problem. Nowadays, various optimization methods, such as genetic algorithm (GA, simulated annealing (SA, and particle swarm optimization (PSO, are more widely employed to solve the aerodynamic shape optimization problems. In addition to the optimization method, the geometry parameterization becomes an important factor to be considered during the aerodynamic shape optimization process. The objective of this work is to introduce the knowledge of describing general airfoil geometry using twelve parameters by representing its shape as a polynomial function and coupling this approach with flow solution and optimization algorithms. An aerodynamic shape optimization problem is formulated for NACA 0012 airfoil and solved using the methods of simulated annealing and genetic algorithm for 5.0 deg angle of attack. The results show that the simulated annealing optimization scheme is more effective in finding the optimum solution among the various possible solutions. It is also found that the SA shows more exploitation characteristics as compared to the GA which is considered to be more effective explorer.
Nash equilibrium and multi criterion aerodynamic optimization
Tang, Zhili; Zhang, Lianhe
Game theory and its particular Nash Equilibrium (NE) are gaining importance in solving Multi Criterion Optimization (MCO) in engineering problems over the past decade. The solution of a MCO problem can be viewed as a NE under the concept of competitive games. This paper surveyed/proposed four efficient algorithms for calculating a NE of a MCO problem. Existence and equivalence of the solution are analyzed and proved in the paper based on fixed point theorem. Specific virtual symmetric Nash game is also presented to set up an optimization strategy for single objective optimization problems. Two numerical examples are presented to verify proposed algorithms. One is mathematical functions' optimization to illustrate detailed numerical procedures of algorithms, the other is aerodynamic drag reduction of civil transport wing fuselage configuration by using virtual game. The successful application validates efficiency of algorithms in solving complex aerodynamic optimization problem.
General shape optimization capability
Chargin, Mladen K.; Raasch, Ingo; Bruns, Rudolf; Deuermeyer, Dawson
A method is described for calculating shape sensitivities, within MSC/NASTRAN, in a simple manner without resort to external programs. The method uses natural design variables to define the shape changes in a given structure. Once the shape sensitivities are obtained, the shape optimization process is carried out in a manner similar to property optimization processes. The capability of this method is illustrated by two examples: the shape optimization of a cantilever beam with holes, loaded by a point load at the free end (with the shape of the holes and the thickness of the beam selected as the design variables), and the shape optimization of a connecting rod subjected to several different loading and boundary conditions.
Design Exploration of Aerodynamic Wing Shape for RLV Flyback Booster
Chiba, Kazuhisa; Obayashi, Shigeru; Nakahashi, Kazuhiro
The wing shape of flyback booster for a Two-Stage-To-Orbit reusable launch vehicle has been optimized considering four objectives. The objectives are to minimize the shift of aerodynamic center between supersonic and transonic conditions, transonic pitching moment and transonic drag coefficient, as well as to maximize subsonic lift coefficient. The three-dimensional Reynolds-averaged Navier-Stokes computation using the modified Spalart-Allmaras one-equation model is used in aerodynamic evaluation accounting for possible flow separations. Adaptive range multi-objective genetic algorithm is used for the present study because tradeoff can be obtained using a smaller number of individuals than conventional multi-objective genetic algorithms. Consequently, four-objective optimization has produced 102 non-dominated solutions, which represent tradeoff information among four objective functions. Moreover, Self-Organizing Maps have been used to analyze the present non-dominated solutions and to visualize tradeoffs and influence of design variables to the four objectives. Self-Organizing Maps contoured by the four objective functions and design variables are found to visualize tradeoffs and effects of each design variable.
A quantitative flow visualization technique for on-site sport aerodynamics optimization
Sciacchitano, A.; Caridi, G; Scarano, F.
Aerodynamics plays a crucial role in many speed sports, where races are often won by fractions of a second. A thorough understanding of the flow field around an athlete is of paramount importance to optimize the athletes' posture, garment roughness and equipment shape to achieve the minimum aerodynamic drag and maximum velocity. To date, aerodynamic measurements are typically conducted in wind tunnels, using balances or pressure sensors. As a consequence, no information on the flow field resp...
Integrated structural-aerodynamic design optimization
Haftka, R. T.; Kao, P. J.; Grossman, B.; Polen, D.; Sobieszczanski-Sobieski, J.
This paper focuses on the processes of simultaneous aerodynamic and structural wing design as a prototype for design integration, with emphasis on the major difficulty associated with multidisciplinary design optimization processes, their enormous computational costs. Methods are presented for reducing this computational burden through the development of efficient methods for cross-sensitivity calculations and the implementation of approximate optimization procedures. Utilizing a modular sensitivity analysis approach, it is shown that the sensitivities can be computed without the expensive calculation of the derivatives of the aerodynamic influence coefficient matrix, and the derivatives of the structural flexibility matrix. The same process is used to efficiently evaluate the sensitivities of the wing divergence constraint, which should be particularly useful, not only in problems of complete integrated aircraft design, but also in aeroelastic tailoring applications.
Parametric Deformation of Discrete Geometry for Aerodynamic Shape Design
Anderson, George R.; Aftosmis, Michael J.; Nemec, Marian
We present a versatile discrete geometry manipulation platform for aerospace vehicle shape optimization. The platform is based on the geometry kernel of an open-source modeling tool called Blender and offers access to four parametric deformation techniques: lattice, cage-based, skeletal, and direct manipulation. Custom deformation methods are implemented as plugins, and the kernel is controlled through a scripting interface. Surface sensitivities are provided to support gradient-based optimization. The platform architecture allows the use of geometry pipelines, where multiple modelers are used in sequence, enabling manipulation difficult or impossible to achieve with a constructive modeler or deformer alone. We implement an intuitive custom deformation method in which a set of surface points serve as the design variables and user-specified constraints are intrinsically satisfied. We test our geometry platform on several design examples using an aerodynamic design framework based on Cartesian grids. We examine inverse airfoil design and shape matching and perform lift-constrained drag minimization on an airfoil with thickness constraints. A transport wing-fuselage integration problem demonstrates the approach in 3D. In a final example, our platform is pipelined with a constructive modeler to parabolically sweep a wingtip while applying a 1-G loading deformation across the wingspan. This work is an important first step towards the larger goal of leveraging the investment of the graphics industry to improve the state-of-the-art in aerospace geometry tools.
高速列车受电弓绝缘子的气动噪声计算及外形优化%Aerodynamic noise calculation and shape optimization of high-speed train pantograph insulators
肖友刚; 时彧
By using large eddy simulation and FW - H equation, the aerodynamic noises radiated from pantograph insulators were calculated, including rectangular, circular, oval - shaped cross - section insulators, the optimized cross - section shape was confirmed. The results show that in the same model, the sound pressure level (SPL) distribution at each sound receiver point from different sound receivers is basically the same, but the amplitude is reduced with the increase of distance from insulators. In different models, the SPL distribution is different at each frequency point. From rectangular, circular to oval shaped cross -section model, the freguency of the maxmium SPL gradually reduces. For reducing aerodynamic noise, the oval section insulator is optimal, and the long oval axis should be consistent with the air flow. The pantograph with bigger parts size and less parts number is helpful to reduce the aerodynamic noise.%采用大涡模拟法和FW-H方程计算截面为矩形、圆形、椭圆形时受电弓绝缘子的气动噪声,确定了优化的受电弓绝缘子截面形状.研究结果表明:对同一个模型,噪声在各声接收点的分布规律基本相同,只是幅值不同;对不同模型,声压在各声接收点的分布规律不同;绝缘子截面从矩形→圆形→椭圆形,最大声压所在的频率区逐渐降低;从降低气动噪声的角度出发,优化的绝缘子截面形状应该是椭圆形,且椭圆的长轴应跟气流流向一致;加大受电弓零部件尺寸,减少受电弓零部件数量,有利于降低受电弓的气动噪声.
Shape Optimization of Wind Turbine Blades
Wang, Xudong; Shen, Wen Zhong; Zhu, Wei Jun; Sørensen, Jens Nørkær; Chen, Jin
This paper presents a design tool for optimizing wind turbine blades. The design model is based on an aerodynamic/aero-elastic code that includes the structural dynamics of the blades and the Blade Element Momentum (BEM) theory. To model the main aero-elastic behaviour of a real wind turbine, the...... rotor. The design variables used in the current study are the blade shape parameters, including chord, twist and relative thickness. To validate the implementation of the aerodynamic/aero-elastic model, the computed aerodynamic results are compared to experimental data for the experimental rotor used in...... the European Commision-sponsored project Model Experiments in Controlled Conditions, (MEXICO) and the computed aero-elastic results are examined against the FLEX code for flow post the Tjereborg 2 MW rotor. To illustrate the optimization technique, three wind turbine rotors of different sizes (the...
基于分层策略的翼型多参量气动优化设计研究%Research on Multi- parameters Aerodynamic Shape Optimization Design of Airfoil Based on Hierarchical Starategy
李鸿岩; 董军
与基于梯度的优化方法相比,遗传算法因其极强的鲁棒性、随机搜索及优化结果全局性等特点在工程优化中得到越来越广泛的应用.为提高优化设计的效率,改进了传统的遗传算法,采用并行分层策略基因遗传算法开展了翼型多参量气动优化设计研究,包括翼型和多段翼型的基因编码、外形参数化,以及动网格技术.结果表明,并行分层策略在得到较优气动优化结果的同时,极大地缩短了优化时间,提高了计算效率,具有广阔的工程应用前景.%Compared with the optimization method based on the gradient theory, genetic algorithm (GA) is more and more widely applied in the field of engineer optimization due to its robustness, randomicity and global optimal performance. In order to improve the efficiency of the optimization design,the traditional GA for multi- parameters aerodynamic shape optimum design of airfoil and multi- element airfoil is improved by using hierarchical parallelization strategy. Genetic coding and shape parameterization are investigated in this paper in combination with mesh moving technical. The results show that hierarchical starat-egy that can dramatically shorten the time for optimization and improve the computational efficiency is efficient and reasonable. So,this method has wide prospects for engineering applications.
Aerodynamic assessment of humpback whale ventral fin shapes
Rita Espasa, Damià
The ventral fins of the humpback whale (Megaptera novaeangliae) include a bulbous leading edge acting as a natural high-lift device. It has been suggested that application of this concept to wing design may yield advantages over traditional shapes (Miklosovic, et al., 2004). During the course of this project, the aerodynamic performance of whale fin models will be compared with conventional wing shapes. Based on the results of the study new wing design paradigms will be developed to improve t...
Duality based contact shape optimization
Vondrák, Vít; Dostal, Zdenek; Rasmussen, John
An implementation of semi-analytic method for the sensitivity analysis in contact shape optimization without friction is described. This method is then applied to the contact shape optimization.......An implementation of semi-analytic method for the sensitivity analysis in contact shape optimization without friction is described. This method is then applied to the contact shape optimization....
Aerodynamic Optimization of an Over-the-Wing-Nacelle-Mount Configuration
Daisuke Sasaki
Full Text Available An over-the-wing-nacelle-mount airplane configuration is known to prevent the noise propagation from jet engines toward ground. However, the configuration is assumed to have low aerodynamic efficiency due to the aerodynamic interference effect between a wing and a nacelle. In this paper, aerodynamic design optimization is conducted to improve aerodynamic efficiency to be equivalent to conventional under-the-wing-nacelle-mount configuration. The nacelle and wing geometry are modified to achieve high lift-to-drag ratio, and the optimal geometry is compared with a conventional configuration. Pylon shape is also modified to reduce aerodynamic interference effect. The final wing-fuselage-nacelle model is compared with the DLR F6 model to discuss the potential of Over-the-Wing-Nacelle-Mount geometry for an environmental-friendly future aircraft.
Comparison of two design methods of aerodynamic biobjectives for airfoil and wing shapes
ZHU; Ziqiang; FU; Hongyan; LIU; Hang; WANG; Xiaolu
A simplified adaptive wing, which deflects its leading edge and trailing edge flaps to vary its shape, is calculated to investigate the potential aerodynamic gains and compared with a biobjective optimization (BO) wing in the present paper. In subsonic-transonic flights the deflection angle of a flap is determined through optimization using a deterministic method. In supersonic flight the flaps are not deflected due to the requirement of having a minimum drag. For comparison the aerodynamic characteristics of a BO airfoil and wing is calculated. A parallel genetic algorithm is used in BO. Euler equations served as governing equations in flow field calculation. Numerical results in both 2D (airfoil) and 3D (wing) cases show that aerodynamic performances of the two design airfoils and wings are much better than those of the original ones, with the adaptive design one the best.
Adjoint gradient-based approach for aerodynamic optimization of transport aircraft
Ilic, Caslav
Aerodynamic design of transport aircraft has been steadily improved over past several decades, to the point where today highly-detailed shape control is needed to achieve further improvements. Aircraft manufacturers are therefore increasingly looking into formal optimization methods, driving high-fidelity CFD analysis of finely-parametrized candidate designs. We present an adjoint gradient-based approach for maximizing the aerodynamic performance index relevant to cruise-climb mission segment...
Aerodynamic Optimization of Micro Aerial Vehicle
Siew Ping Yeong
Full Text Available Computational fluid dynamics (CFD study was done on the propeller design of a micro aerial vehicle (quadrotor-typed to optimize its aerodynamic performance via Shear Stress Transport K-Omega (SST k-ω turbulence model. The quadrotor model used was WL-V303 Seeker. The design process started with airfoils selection and followed by the evaluation of drone model in hovering and cruising conditions. To sustain a 400g payload, by Momentum Theory an ideal thrust of 5.4 N should be generated by each rotor of the quadrotor and this resulted in an induced velocity of 7.4 m/s on the propeller during hovering phase, equivalent to Reynolds number of 10403 at 75% of the propeller blade radius. There were 6 propellers investigated at this Reynolds number. Sokolov airfoil which produced the largest lift-to-drag ratio was selected for full drone installation to be compared with the original model (benchmark. The CFD results showed that the Sokolov propeller generated 0.76 N of thrust more than the benchmark propeller at 7750 rpm. Despite generating higher thrust, higher drag was also experienced by the drone installed with Sokolov propellers. This resulted in lower lift-to-drag ratio than the benchmark propellers. It was also discovered that the aerodynamic performance of the drone could be further improved by changing the rotating direction of each rotor. Without making changes on the structural design, the drone performance increased by 39.58% in terms of lift-to-drag ratio by using this method.
Aerodynamic Optimization Design of Airfoil Based on AFSA and Hicks-Henne Shape Function%基于人工鱼群算法及Hicks-Henne型函数的翼型优化设计研究
王伟; 白俊强; 张扬; 朱军
As a new intelligent algorithm, AFSA is capable of overcoming local maxima and obtaining global minimum. And AFSA also have advantages in adaptive capacity of searching space, faster searching and without objective algorithm function gradient during implementation, which make AFSA applicable to a variety of airfoil design optimization. AFSA is combined with the numerical solution of N-S equations, relying on computational fluid dynamics(CFD) calculation technique to optimal design the airfoil shape in aerodynamic fields. Linear superposition of analytic functions based on Hicks-Henne shape function is used for airfoil shape description. Airfoil NA-CA0012 and RAE2822 are optimal designed using the algorithm mentioned above, the results reveal that the method developed is well applicable to the optimization of a variety of airfoil design.%人工鱼群算法作为一种新型智能算法,具有良好的克服局部极值、取得全局极值的能力,并且该算法具有对搜索空间具有一定自适应能力、寻优速度较快、算法的实现无需目标函数梯度值等特性,使得其能够适用于多种翼型的优化设计.将人工鱼群算法与N-S方程气动数值解法结合,依靠计算流体动力学(CFD)计算技术,对翼型进行气动外形优化设计.在基准翼型的基础上,对翼型的描述采用基于Hicks-Henne型函数的解析函数线性叠加法.利用上述开发的算法对NACA0012和RAE2822进行翼型优化设计,设计结果表明本文发展的优化方法能够很好地适用于进行多种翼型的优化设计.
Rasmussen, John
Structural optimization has attracted the attention since the days of Galileo. Olhoff and Taylor have produced an excellent overview of the classical research within this field. However, the interest in structural optimization has increased greatly during the last decade due to the advent of reliable general numerical analysis methods and the computer power necessary to use them efficiently. This has created the possibility of developing general numerical systems for shape optimization. Several authors, eg., Esping; Braibant & Fleury; Bennet & Botkin; Botkin, Yang, and Bennet; and Stanton have published practical and successful applications of general optimization systems. Ding and Homlein have produced extensive overviews of available systems. Furthermore, a number of commercial optimization systems based on well-established finite element codes have been introduced. Systems like ANSYS, IDEAS, OASIS, and NISAOPT are widely known examples. In parallel to this development, the technology of computer aided design (CAD) has gained a large influence on the design process of mechanical engineering. The CAD technology has already lived through a rapid development driven by the drastically growing capabilities of digital computers. However, the systems of today are still considered as being only the first generation of a long row of computer integrated manufacturing (CIM) systems. These systems to come will offer an integrated environment for design, analysis, and fabrication of products of almost any character. Thus, the CAD system could be regarded as simply a database for geometrical information equipped with a number of tools with the purpose of helping the user in the design process. Among these tools are facilities for structural analysis and optimization as well as present standard CAD features like drawing, modeling, and visualization tools. The state of the art of structural optimization is that a large amount of mathematical and mechanical techniques are
Three-dimensional inverse method for aerodynamic optimization in compressor
Design experience plays an important role in compressor design. Accumulated design experience is used to reduce the number of simulations and to make time for the whole optimization process to be compatible with industrial standards. However, the major drawbacks of this design strategy are that the design result depends on talented designers with rich design experience and this method does not easily produce better configurations than existing designs. These drawbacks are related to the parametric description of the blade, which is conventionally performed using only geometric parameters. A good solution to this problem is to use a blade parametrization based on an inverse design method. Inverse design methods have been widely used for the design of various kinds of turbomachines, proving that it is a valuable alternative to the iterative use of direct methods. One main design parameter in the inverse design approach is the blade loading on both the hub and the shroud along the meridional direction. The blade loading distributions have a more direct relationship to the aerodynamic performance because they influence the flow field in a more straight-forward way. Fewer design parameters are then required to describe the blade shape than a purely geometric expression of the blade. Therefore, an optimization design method using the inverse method to parameterize the blade geometry can reduce the overall optimization time. The optimization design process then gives the optimal blade loading distributions, instead of the optimal combination of the geometric parameters. This is a more general result which can be applied to similar design problems without repeating the optimization process
An approach for shape optimization of stratosphere airships based on multidisciplinary design optimization
Quan-bao WANG; Jian CHEN; Gong-yi FU; Deng-ping DUAN
Airship shape is crucial to the design of stratosphere airships. In this paper, multidisciplinary design optimization (MDO) technology is introduced into the design of airship shape. We devise a composite objective function, based on this technology, which takes account of various factors which influence airship performance, including aerodynamics, structures, energy and weight to determine the optimal airship shape. A shape generation algorithm is proposed and appropriate mathematical models are constructed. Simulation results show that the optimized shape gives an improvement in the value of the composite objective function compared with a reference shape.
Combined Shape and Topology Optimization
Christiansen, Asger Nyman
Shape and topology optimization seeks to compute the optimal shape and topology of a structure such that one or more properties, for example stiffness, balance or volume, are improved. The goal of the thesis is to develop a method for shape and topology optimization which uses the Deformable...... Simplicial Complex (DSC) method. Consequently, we present a novel method which combines current shape and topology optimization methods. This method represents the surface of the structure explicitly and discretizes the structure into non-overlapping elements, i.e. a simplicial complex. An explicit surface...... representation usually limits the optimization to minor shape changes. However, the DSC method uses a single explicit representation and still allows for large shape and topology changes. It does so by constantly applying a set of mesh operations during deformations of the structure. Using an explicit instead of...
Distributed optimization using virtual and real game strategies for multi-criterion aerodynamic design
TANG ZhiLi; BAI Wen; DONG Jun
This paper introduces the virtual and real game concepts to investigate multi-criterion optimization for optimum shape design in aerodynamics. The constrained acljoint meth-odology is used as the basic optimizer. Furthermore, the above is combined with the vir-tual and real game strategies to treat single-point/multi-point airfoil optimization. In a symmetric Nash Game, each optimizer attempts to optimize one's own target with ex-change of symmetric information with others. A Nash equilibrium is just the compromised solution among the multiple criteria. Several kinds of airfoil splitting and design cases are shown for the utility of virtual and real game strategies in aerodynamic design. Successful design results confirm the validity and efficiency of the present design method.
Distributed optimization using virtual and real game strategies for multi-criterion aerodynamic design
This paper introduces the virtual and real game concepts to investigate multi-criterion optimization for optimum shape design in aerodynamics. The constrained adjoint meth- odology is used as the basic optimizer. Furthermore, the above is combined with the vir- tual and real game strategies to treat single-point/multi-point airfoil optimization. In a symmetric Nash Game, each optimizer attempts to optimize one's own target with ex- change of symmetric information with others. A Nash equilibrium is just the compromised solution among the multiple criteria. Several kinds of airfoil splitting and design cases are shown for the utility of virtual and real game strategies in aerodynamic design. Successful design results confirm the validity and efficiency of the present design method.
A Hybrid Metaheuristic-Based Approach for the Aerodynamic Optimization of Small Hybrid Wind Turbine Rotors
Herbert-Acero, José F.; Martínez-Lauranchet, Jaime; Probst, Oliver;
the aerodynamic efficiency of small WT (SWT) rotors for a wide range of operational conditions. The design variables are (1) the airfoil shape at the different blade span positions and the radial variation of the geometrical variables of (2) chord length, (3) twist angle, and (4) thickness along the...... blade span. A wind tunnel validation study of optimized rotors based on the NACA 4-digit airfoil series is presented. Based on the experimental data, improvements in terms of the aerodynamic efficiency, the cut-in wind speed, and the amount of material used during themanufacturing process were achieved...
Aerodynamic Modelling and Optimization of Axial Fans
Sørensen, Dan Nørtoft
integrated propertiesshow that the computed results agree well with the measurements.Integrating a rotor-only version of the aerodynamic modelwith an algorithm for numerical designoptimization, enables the finding of an optimum fan rotor.The angular velocity of the rotor, the hub radius and the spanwise...... velocity, pressure andradial position are derived from the conservationlaws for mass, tangential momentum and energy.The resulting system of equations is non-linear and, dueto mass conservation and pressure equilibrium far downstream of the rotor,strongly coupled.The equations are solved using the Newton...
A Hybrid Metaheuristic-Based Approach for the Aerodynamic Optimization of Small Hybrid Wind Turbine Rotors
José F. Herbert-Acero
Full Text Available This work presents a novel framework for the aerodynamic design and optimization of blades for small horizontal axis wind turbines (WT. The framework is based on a state-of-the-art blade element momentum model, which is complemented with the XFOIL 6.96 software in order to provide an estimate of the sectional blade aerodynamics. The framework considers an innovative nested-hybrid solution procedure based on two metaheuristics, the virtual gene genetic algorithm and the simulated annealing algorithm, to provide a near-optimal solution to the problem. The objective of the study is to maximize the aerodynamic efficiency of small WT (SWT rotors for a wide range of operational conditions. The design variables are (1 the airfoil shape at the different blade span positions and the radial variation of the geometrical variables of (2 chord length, (3 twist angle, and (4 thickness along the blade span. A wind tunnel validation study of optimized rotors based on the NACA 4-digit airfoil series is presented. Based on the experimental data, improvements in terms of the aerodynamic efficiency, the cut-in wind speed, and the amount of material used during the manufacturing process were achieved. Recommendations for the aerodynamic design of SWT rotors are provided based on field experience.
Study on Aerodynamic Design Optimization of Turbomachinery Blades
Naixing CHEN; Hongwu ZHANG; Weiguang HUANG; Yanji XU
This paper describes the study on aerodynamics design optimization of turbomachinery blading developed by the authors at the Institute of Engineering Thermophysics, Chinese Academy of Sciences, during the recent few years. The present paper describes the aspects mainly on how to use a rapid approach of profiling a 3D blading and of grid generation for computation, a fast and accurate viscous computation method and an appropriate optimization methodology_ including a blade parameterization algorithm to optimize turbomachinery blading aerodynamically. Any blade configuration can be expressed by three curves, they are the camber lines, the thickness distributions and the radial stacking line, and then the blade geometry can be easily parameterized by a number of parameters with three polynomials. A gradient-based parameterization analytical method and a response surface method were applied herein for blade optimization. It was found that the optimization process provides reliable design for turbomachinery with reasonable computing time.
Robust, Optimal Subsonic Airfoil Shapes
Rai, Man Mohan
A method has been developed to create an airfoil robust enough to operate satisfactorily in different environments. This method determines a robust, optimal, subsonic airfoil shape, beginning with an arbitrary initial airfoil shape, and imposes the necessary constraints on the design. Also, this method is flexible and extendible to a larger class of requirements and changes in constraints imposed.
Computational methods for aerodynamic design using numerical optimization
Peeters, M. F.
Five methods to increase the computational efficiency of aerodynamic design using numerical optimization, by reducing the computer time required to perform gradient calculations, are examined. The most promising method consists of drastically reducing the size of the computational domain on which aerodynamic calculations are made during gradient calculations. Since a gradient calculation requires the solution of the flow about an airfoil whose geometry was slightly perturbed from a base airfoil, the flow about the base airfoil is used to determine boundary conditions on the reduced computational domain. This method worked well in subcritical flow.
Efficient optimization of integrated aerodynamic-structural design
Haftka, R. T.; Grossman, B.; Eppard, W. M.; Kao, P. J.; Polen, D. M.
Techniques for reducing the computational complexity of multidisciplinary design optimization (DO) of aerodynamic structures are described and demonstrated. The basic principles of aerodynamic and structural DO are reviewed; the formulation of the combined DO problem is outlined; and particular attention is given to (1) the application of perturbation methods to cross-sensitivity computations and (2) numerical approximation procedures. Trial DOs of a simple sailplane design are presented in tables and graphs and discussed in detail. The IBM 3090 CPU time for the entire integrated DO was reduced from an estimated 10 h to about 6 min.
Microgenetic optimization algorithm for optimal wavefront shaping
Anderson, Benjamin R; Gunawidjaja, Ray; Eilers, Hergen
One of the main limitations of utilizing optimal wavefront shaping in imaging and authentication applications is the slow speed of the optimization algorithms currently being used. To address this problem we develop a micro-genetic optimization algorithm ($\\mu$GA) for optimal wavefront shaping. We test the abilities of the $\\mu$GA and make comparisons to previous algorithms (iterative and simple-genetic) by using each algorithm to optimize transmission through an opaque medium. From our experiments we find that the $\\mu$GA is faster than both the iterative and simple-genetic algorithms and that both genetic algorithms are more resistant to noise and sample decoherence than the iterative algorithm.
Transonic Wing Shape Optimization Using a Genetic Algorithm
Holst, Terry L.; Pulliam, Thomas H.; Kwak, Dochan (Technical Monitor)
A method for aerodynamic shape optimization based on a genetic algorithm approach is demonstrated. The algorithm is coupled with a transonic full potential flow solver and is used to optimize the flow about transonic wings including multi-objective solutions that lead to the generation of pareto fronts. The results indicate that the genetic algorithm is easy to implement, flexible in application and extremely reliable.
Shape of optimal active flagella
Eloy, Christophe
Many eukaryotic cells use the active waving motion of flexible flagella to self-propel in viscous fluids. However, the criteria governing the selection of particular flagellar waveforms among all possible shapes has proved elusive so far. To address this question, we derive computationally the optimal shape of an internally-forced periodic planar flagellum deforming as a travelling wave. The optimum is here defined as the shape leading to a given swimming speed with minimum energetic cost. To calculate the energetic cost though, we consider the irreversible internal power expanded by the molecular motors forcing the flagellum, only a portion of which ending up dissipated in the fluid. This optimisation approach allows us to derive a family of shapes depending on a single dimensionless number quantifying the relative importance of elastic to viscous effects: the Sperm number. The computed optimal shapes are found to agree with the waveforms observed on spermatozoon of marine organisms, thus suggesting that the...
Topological Derivatives in Shape Optimization
Novotny, Antonio André
The topological derivative is defined as the first term (correction) of the asymptotic expansion of a given shape functional with respect to a small parameter that measures the size of singular domain perturbations, such as holes, inclusions, defects, source-terms and cracks. Over the last decade, topological asymptotic analysis has become a broad, rich and fascinating research area from both theoretical and numerical standpoints. It has applications in many different fields such as shape and topology optimization, inverse problems, imaging processing and mechanical modeling including synthesis and/or optimal design of microstructures, sensitivity analysis in fracture mechanics and damage evolution modeling. Since there is no monograph on the subject at present, the authors provide here the first account of the theory which combines classical sensitivity analysis in shape optimization with asymptotic analysis by means of compound asymptotic expansions for elliptic boundary value problems. This book is intende...
Optimization of aerodynamic efficiency for twist morphing MAV wing
N.I. Ismail
Full Text Available Twist morphing (TM is a practical control technique in micro air vehicle (MAV flight. However, TM wing has a lower aerodynamic efficiency (CL/CD compared to membrane and rigid wing. This is due to massive drag penalty created on TM wing, which had overwhelmed the successive increase in its lift generation. Therefore, further CL/CDmax optimization on TM wing is needed to obtain the optimal condition for the morphing wing configuration. In this paper, two-way fluid–structure interaction (FSI simulation and wind tunnel testing method are used to solve and study the basic wing aerodynamic performance over (non-optimal TM, membrane and rigid wings. Then, a multifidelity data metamodel based design optimization (MBDO process is adopted based on the Ansys-DesignXplorer frameworks. In the adaptive MBDO process, Kriging metamodel is used to construct the final multifidelity CL/CD responses by utilizing 23 multi-fidelity sample points from the FSI simulation and experimental data. The optimization results show that the optimal TM wing configuration is able to produce better CL/CDmax magnitude by at least 2% than the non-optimal TM wings. The flow structure formation reveals that low TV strength on the optimal TM wing induces low CD generation which in turn improves its overall CL/CDmax performance.
Quaternion Julia Set Shape Optimization
T. Kim
© 2015 The Eurographics Association and John Wiley & Sons Ltd. Published by John Wiley & Sons Ltd. We present the first 3D algorithm capable of answering the question: what would a Mandelbrot-like set in the shape of a bunny look like? More concretely, can we find an iterated quaternion rational map whose potential field contains an isocontour with a desired shape? We show that it is possible to answer this question by casting it as a shape optimization that discovers novel, highly complex sh...
Aerodynamic optimization by simultaneously updating flow variables and design parameters
Rizk, M. H.
The application of conventional optimization schemes to aerodynamic design problems leads to inner-outer iterative procedures that are very costly. An alternative approach is presented based on the idea of updating the flow variable iterative solutions and the design parameter iterative solutions simultaneously. Two schemes based on this idea are applied to problems of correcting wind tunnel wall interference and optimizing advanced propeller designs. The first of these schemes is applicable to a limited class of two-design-parameter problems with an equality constraint. It requires the computation of a single flow solution. The second scheme is suitable for application to general aerodynamic problems. It requires the computation of several flow solutions in parallel. In both schemes, the design parameters are updated as the iterative flow solutions evolve. Computations are performed to test the schemes' efficiency, accuracy, and sensitivity to variations in the computational parameters.
Variational Methods in Sensitivity Analysis and Optimization for Aerodynamic Applications
Ibrahim, A. H.; Hou, G. J.-W.; Tiwari, S. N. (Principal Investigator)
Variational methods (VM) sensitivity analysis, which is the continuous alternative to the discrete sensitivity analysis, is employed to derive the costate (adjoint) equations, the transversality conditions, and the functional sensitivity derivatives. In the derivation of the sensitivity equations, the variational methods use the generalized calculus of variations, in which the variable boundary is considered as the design function. The converged solution of the state equations together with the converged solution of the costate equations are integrated along the domain boundary to uniquely determine the functional sensitivity derivatives with respect to the design function. The determination of the sensitivity derivatives of the performance index or functional entails the coupled solutions of the state and costate equations. As the stable and converged numerical solution of the costate equations with their boundary conditions are a priori unknown, numerical stability analysis is performed on both the state and costate equations. Thereafter, based on the amplification factors obtained by solving the generalized eigenvalue equations, the stability behavior of the costate equations is discussed and compared with the state (Euler) equations. The stability analysis of the costate equations suggests that the converged and stable solution of the costate equation is possible only if the computational domain of the costate equations is transformed to take into account the reverse flow nature of the costate equations. The application of the variational methods to aerodynamic shape optimization problems is demonstrated for internal flow problems at supersonic Mach number range. The study shows, that while maintaining the accuracy of the functional sensitivity derivatives within the reasonable range for engineering prediction purposes, the variational methods show a substantial gain in computational efficiency, i.e., computer time and memory, when compared with the finite
Application of surrogate-based global optimization to aerodynamic design
Pérez, Esther
Aerodynamic design, like many other engineering applications, is increasingly relying on computational power. The growing need for multi-disciplinarity and high fidelity in design optimization for industrial applications requires a huge number of repeated simulations in order to find an optimal design candidate. The main drawback is that each simulation can be computationally expensive – this becomes an even bigger issue when used within parametric studies, automated search or optimization loops, which typically may require thousands of analysis evaluations. The core issue of a design-optimization problem is the search process involved. However, when facing complex problems, the high-dimensionality of the design space and the high-multi-modality of the target functions cannot be tackled with standard techniques. In recent years, global optimization using meta-models has been widely applied to design exploration in order to rapidly investigate the design space and find sub-optimal solutions. Indeed, surrogat...
Aerodynamic and Structural Integrated Optimization Design of Horizontal-Axis Wind Turbine Blades
Jie Zhu
Full Text Available A procedure based on MATLAB combined with ANSYS is presented and utilized for the aerodynamic and structural integrated optimization design of Horizontal-Axis Wind Turbine (HAWT blades. Three modules are used for this purpose: an aerodynamic analysis module using the Blade Element Momentum (BEM theory, a structural analysis module employing the Finite Element Method (FEM and a multi-objective optimization module utilizing the non-dominated sorting genetic algorithm. The former two provide a sufficiently accurate solution of the aerodynamic and structural performances of the blade; the latter handles the design variables of the optimization problem, namely, the main geometrical shape and structural parameters of the blade, and promotes function optimization. The scope of the procedure is to achieve the best trade-off performances between the maximum Annual Energy Production (AEP and the minimum blade mass under various design requirements. To prove the efficiency and reliability of the procedure, a commercial 1.5 megawatt (MW HAWT blade is used as a case study. Compared with the original scheme, the optimization results show great improvements for the overall performance of the blade.
CFD Research, Parallel Computation and Aerodynamic Optimization
Ryan, James S.
During the last five years, CFD has matured substantially. Pure CFD research remains to be done, but much of the focus has shifted to integration of CFD into the design process. The work under these cooperative agreements reflects this trend. The recent work, and work which is planned, is designed to enhance the competitiveness of the US aerospace industry. CFD and optimization approaches are being developed and tested, so that the industry can better choose which methods to adopt in their design processes. The range of computer architectures has been dramatically broadened, as the assumption that only huge vector supercomputers could be useful has faded. Today, researchers and industry can trade off time, cost, and availability, choosing vector supercomputers, scalable parallel architectures, networked workstations, or heterogenous combinations of these to complete required computations efficiently.
V. A. Sychevsky
Full Text Available Wood utilization is a critical direction of the industrial production advancement, where desiccation of wood holds a prominent place. Convective drying in chamber driers is the presentday dominant technique for wood desiccation. Nevertheless, available scientific literature on the subject does not place high emphasis on the issue of gas flow structure inside the drier installations and, in particular, in the clearance between horizontal rows of stacked saw timber. Whereas, the air flowing between horizontal rows facilitates wood heating and moisture removing from the boundary layer. The present article studies aerodynamics of the experimental timber drying test stand at the A. V. Luikov Heat and Mass Transfer Institute of NAS of Belarus. The timber drying test stand geometry structure is complicated, which is why aerodynamics valuation of the drier agent in the chamber involves the software system ANSYS Fluent 14.5. For that end, the researchers developed the convective drier installation geometrical model. A physico-mathematical simulation was developed for sawn timber convective drying aerodynamics in the timber drying test stand of the Heat and Mass Transfer Institute. Based on the computations made, the drier agent flow configuration was analyzed, stagnant pockets identified. It was found that the timber drying test stand was not operating within its optimal aerodynamic conditions. The drying chamber optimal aerodynamic conditions determination includes accounting for an additional canal between the chamber rear wall and the timber stack, absence of the screen above the stack, and presence of the screen between the floor and the stack. As well as variation of the drying agent speed, pressure differrential at the blower, the inter-row gobb amount variation. The paper offers recommendations on optimizing the drying installation aerodynamics based on the numerical simulation results. To this effect, speed of the drier agent in the chamber
Adjoint-based airfoil shape optimization in transonic flow
Gramanzini, Joe-Ray
The primary focus of this work is efficient aerodynamic shape optimization in transonic flow. Adjoint-based optimization techniques are employed on airfoil sections and evaluated in terms of computational accuracy as well as efficiency. This study examines two test cases proposed by the AIAA Aerodynamic Design Optimization Discussion Group. The first is a two-dimensional, transonic, inviscid, non-lifting optimization of a Modified-NACA 0012 airfoil. The second is a two-dimensional, transonic, viscous optimization problem using a RAE 2822 airfoil. The FUN3D CFD code of NASA Langley Research Center is used as the ow solver for the gradient-based optimization cases. Two shape parameterization techniques are employed to study their effect and the number of design variables on the final optimized shape: Multidisciplinary Aerodynamic-Structural Shape Optimization Using Deformation (MASSOUD) and the BandAids free-form deformation technique. For the two airfoil cases, angle of attack is treated as a global design variable. The thickness and camber distributions are the local design variables for MASSOUD, and selected airfoil surface grid points are the local design variables for BandAids. Using the MASSOUD technique, a drag reduction of 72.14% is achieved for the NACA 0012 case, reducing the total number of drag counts from 473.91 to 130.59. Employing the BandAids technique yields a 78.67% drag reduction, from 473.91 to 99.98. The RAE 2822 case exhibited a drag reduction from 217.79 to 132.79 counts, a 39.05% decrease using BandAids.
Optimization of aerodynamic efficiency for twist morphing MAV wing
N. I. Ismail; A.H. Zulkifli; M.Z. Abdullah; M. Hisyam Basri; Norazharuddin Shah Abdullah
Twist morphing (TM) is a practical control technique in micro air vehicle (MAV) flight. However, TM wing has a lower aerodynamic efficiency (CL/CD) compared to membrane and rigid wing. This is due to massive drag penalty created on TM wing, which had overwhelmed the successive increase in its lift generation. Therefore, further CL/CDmax optimization on TM wing is needed to obtain the optimal condition for the morphing wing configuration. In this paper, two-way fluid–structure interaction (FSI...
Fully integrated aerodynamic/dynamic optimization of helicopter rotor blades
Walsh, Joanne L.; Lamarsh, William J., II; Adelman, Howard M.
A fully integrated aerodynamic/dynamic optimization procedure is described for helicopter rotor blades. The procedure combines performance and dynamic analyses with a general purpose optimizer. The procedure minimizes a linear combination of power required (in hover, forward flight, and maneuver) and vibratory hub shear. The design variables include pretwist, taper initiation, taper ratio, root chord, blade stiffnesses, tuning masses, and tuning mass locations. Aerodynamic constraints consist of limits on power required in hover, forward flight and maneuvers; airfoil section stall; drag divergence Mach number; minimum tip chord; and trim. Dynamic constraints are on frequencies, minimum autorotational inertia, and maximum blade weight. The procedure is demonstrated for two cases. In the first case, the objective function involves power required (in hover, forward flight and maneuver) and dynamics. The second case involves only hover power and dynamics. The designs from the integrated procedure are compared with designs from a sequential optimization approach in which the blade is first optimized for performance and then for dynamics. In both cases, the integrated approach is superior.
Wing shape allometry and aerodynamics in calopterygid damselflies: a comparative approach
Outomuro, David; Adams, Dean C; Johansson, Frank
Background: Wing size and shape have important aerodynamic implications on flight performance. We explored how wing size was related to wing shape in territorial males of 37 taxa of the damselfly family Calopterygidae. Wing coloration was also included in the analyses because it is sexually and naturally selected and has been shown to be related to wing shape. We studied wing shape using both the non-dimensional radius of the second moment of wing area (RSM) and geometric morphometrics. Lower...
New trends in shape optimization
Leugering, Günter
This volume reflects "New Trends in Shape Optimization" and is based on a workshop of the same name organized at the Friedrich-Alexander University Erlangen-Nürnberg in September 2013. During the workshop senior mathematicians and young scientists alike presented their latest findings. The format of the meeting allowed fruitful discussions on challenging open problems, and triggered a number of new and spontaneous collaborations. As such, the idea was born to produce this book, each chapter of which was written by a workshop participant, often with a collaborator. The content of the individual chapters ranges from survey papers to original articles; some focus on the topics discussed at the Workshop, while others involve arguments outside its scope but which are no less relevant for the field today. As such, the book offers readers a balanced introduction to the emerging field of shape optimization.
Couplings in Multi-criterion Aerodynamic Optimization Problems Using Adjoint Methods and Game Strategies
Tang Zhili; Dong Jun
complete and complete decisions of the leader and followers respectively. Several design examples illustrate the efficiency of the coupling algorithms for multi-criterion aerodynamic design optimization problems.
Shape modification of bridge cables for aerodynamic vibration control
Kleissl, Kenneth; Georgakis, Christos
found to eliminate the risk of dry inclined galloping, with a reduction in lift fluctuations. Nevertheless, the particular cylinder is at risk of "drag crisis" instability. Finally, turbulent flow is shown to introduce a significant amount of aerodynamic damping by proving a more stable lift force over...... and faceted cylinders are found to suffer from either dry inclined galloping, "drag crisis" or Den Hartog galloping, the shrouded cylinder is found to be completely stable for all wind angles of attack, albeit with a slight increase in drag at traditional design wind velocities. The wavy cylinder is...
Aerodynamic effects of simulated ice shapes on two-dimensional airfoils and a swept finite tail
Alansatan, Sait
An experimental study was conducted to investigate the effect of simulated glaze ice shapes on the aerodynamic performance characteristics of two-dimensional airfoils and a swept finite tail. The two dimensional tests involved two NACA 0011 airfoils with chords of 24 and 12 inches. Glaze ice shapes computed with the LEWICE code that were representative of 22.5-min and 45-min ice accretions were simulated with spoilers, which were sized to approximate the horn heights of the LEWICE ice shapes. Lift, drag, pitching moment, and surface pressure coefficients were obtained for a range of test conditions. Test variables included Reynolds number, geometric scaling, control deflection and the key glaze ice features, which were horn height, horn angle, and horn location. For the three-dimensional tests, a 25%-scale business jet empennage (BJE) with a T-tail configuration was used to study the effect of ice shapes on the aerodynamic performance of a swept horizontal tail. Simulated glaze ice shapes included the LEWICE and spoiler ice shapes to represent 9-min and 22.5-min ice accretions. Additional test variables included Reynolds number and elevator deflection. Lift, drag, hinge moment coefficients as well as boundary layer velocity profiles were obtained. The experimental results showed substantial degradation in aerodynamic performance of the airfoils and the swept horizontal tail due to the simulated ice shapes. For the two-dimensional airfoils, the largest aerodynamic penalties were obtained when the 3-in spoiler-ice, which was representative of 45-min glaze ice accretions, was set normal to the chord. Scale and Reynolds effects were not significant for lift and drag. However, pitching moments and pressure distributions showed great sensitivity to Reynolds number and geometric scaling. For the threedimensional study with the swept finite tail, the 22.5-min ice shapes resulted in greater aerodynamic performance degradation than the 9-min ice shapes. The addition of 24
The external flow field around a certain mining dump truck was simulated. The airflow structure and the aerodynamic drag were discussed, and the relationship between airflow characteristics and aerodynamic drag were obtained. In order to solve the problem of head shape of the truck, three scenarios including edge rounding, installing splitter planes and their combination were put forward to improve the head shape through numerical simulation and analysis. The model and method were selected to be three dimensional and time-independent. The Reynolds-averaged Navier-Stokes equations were solved using the finite volume method. The RNG k-ε model was chosen for the closure of the turbulent quantities. The results show that the third scenario is the best one, because of its aerodynamic characteristics being better than those of unimproved model.
Variable Camber Continuous Aerodynamic Control Surfaces and Methods for Active Wing Shaping Control
Nguyen, Nhan T. (Inventor)
An aerodynamic control apparatus for an air vehicle improves various aerodynamic performance metrics by employing multiple spanwise flap segments that jointly form a continuous or a piecewise continuous trailing edge to minimize drag induced by lift or vortices. At least one of the multiple spanwise flap segments includes a variable camber flap subsystem having multiple chordwise flap segments that may be independently actuated. Some embodiments also employ a continuous leading edge slat system that includes multiple spanwise slat segments, each of which has one or more chordwise slat segment. A method and an apparatus for implementing active control of a wing shape are also described and include the determination of desired lift distribution to determine the improved aerodynamic deflection of the wings. Flap deflections are determined and control signals are generated to actively control the wing shape to approximate the desired deflection.
Optimization of wind turbine rotors - using advanced aerodynamic and aeroelastic models and numerical optimization
Døssing, Mads
of very large machines introduces new problems in the practical design, and optimization tools are necessary. These must combine the dynamic eects of both aerodynamics and structure in an integrated optimization environment. This is referred to as aeroelastic optimization. The Ris DTU optimization......During the last decades the annual energy produced by wind turbines has increased dramatically and wind turbines are now available in the 5MW range. Turbines in this range are constantly being developed and it is also being investigated whether turbines as large as 10-20MW are feasible. The design...
A new analytical approach, based on a lifting surface model and a full-span free wake analysis using the curved vortex element on the circular arc, is established for evaluating the aerodynamic characteristics of the helicopter rotor with an anhedral blade-tip and is emphasized to be applicable to various blade-tip configurations, such as the tapered, swept, anhedral and combined shapes. Sample calculations on the rotor aerodynamic characteristics for different anhedral tips in both hover and forward flight are performed. The results on the induced velocity, blade section lift distribution, tip vortex path and rotor performance are presented so that the effect of the anhedral tip on the rotor aerodynamic characteristics is fully analyzed.
Design optimization of shape memory alloy structures
Langelaar, M.
This thesis explores the possibilities of design optimization techniques for designing shape memory alloy structures. Shape memory alloys are materials which, after deformation, can recover their initial shape when heated. This effect can be used for actuation. Emerging applications for shape memory alloys are e.g. miniaturized medical instruments with embedded actuation, as well as microsystem components. However, designing effective shape memory alloy structures is a challenging task, due t...
The design of post-buckled spinal structures for airfoil shape control using optimization methods
Ursache, N.M.; Bressloff, N.W.; Keane, A.J.
In this paper we examine the use of optimization methods and a variety of shape definition schemes to design spinal structures for the control of deformable shape airfoils. The aim is to find structures that, when suitably loaded, can be used to alter the aerodynamic performance of a cladding that forms the airfoil. Further, by using structures that are acting in the post buckling regime it is possible to obtain significant changes in shape with only modest changes in applied load.
Divertor target shape optimization in realistic edge plasma geometry
Tokamak divertor design for next-step fusion reactors heavily relies on numerical simulations of the plasma edge. Currently, the design process is mainly done in a forward approach, where the designer is strongly guided by his experience and physical intuition in proposing divertor shapes, which are then thoroughly assessed by numerical computations. On the other hand, automated design methods based on optimization have proven very successful in the related field of aerodynamic design. By recasting design objectives and constraints into the framework of a mathematical optimization problem, efficient forward-adjoint based algorithms can be used to automatically compute the divertor shape which performs the best with respect to the selected edge plasma model and design criteria. In the past years, we have extended these methods to automated divertor target shape design, using somewhat simplified edge plasma models and geometries. In this paper, we build on and extend previous work to apply these shape optimization methods for the first time in more realistic, single null edge plasma and divertor geometry, as commonly used in current divertor design studies. In a case study with JET-like parameters, we show that the so-called one-shot method is very effective is solving divertor target design problems. Furthermore, by detailed shape sensitivity analysis we demonstrate that the development of the method already at the present state provides physically plausible trends, allowing to achieve a divertor design with an almost perfectly uniform power load for our particular choice of edge plasma model and design criteria. (paper)
Estimation of morphing airfoil shape and aerodynamic load using artificial hair sensors
Butler, Nathan S.; Su, Weihua; Thapa Magar, Kaman S.; Reich, Gregory W.
An active area of research in adaptive structures focuses on the use of continuous wing shape changing methods as a means of replacing conventional discrete control surfaces and increasing aerodynamic efficiency. Although many shape-changing methods have been used since the beginning of heavier-than-air flight, the concept of performing camber actuation on a fully-deformable airfoil has not been widely applied. A fundamental problem of applying this concept to real-world scenarios is the fact that camber actuation is a continuous, time-dependent process. Therefore, if camber actuation is to be used in a closed-loop feedback system, one must be able to determine the instantaneous airfoil shape as well as the aerodynamic loads at all times. One approach is to utilize a new type of artificial hair sensors developed at the Air Force Research Laboratory to determine the flow conditions surrounding deformable airfoils. In this work, the hair sensor measurement data will be simulated by using the flow solver XFoil, with the assumption that perfect data with no noise can be collected from the hair sensor measurements. Such measurements will then be used in an artificial neural network based process to approximate the instantaneous airfoil camber shape, lift coefficient, and moment coefficient at a given angle of attack. Various aerodynamic and geometrical properties approximated from the artificial hair sensor and artificial neural network system will be compared with the results of XFoil in order to validate the approximation approach.
Airfoil shape optimization using non-traditional optimization technique and its validation
R. Mukesh
Full Text Available Computational fluid dynamics (CFD is one of the computer-based solution methods which is more widely employed in aerospace engineering. The computational power and time required to carry out the analysis increase as the fidelity of the analysis increases. Aerodynamic shape optimization has become a vital part of aircraft design in the recent years. Generally if we want to optimize an airfoil we have to describe the airfoil and for that, we need to have at least hundred points of x and y co-ordinates. It is really difficult to optimize airfoils with this large number of co-ordinates. Nowadays many different schemes of parameter sets are used to describe general airfoil such as B-spline, and PARSEC. The main goal of these parameterization schemes is to reduce the number of needed parameters as few as possible while controlling the important aerodynamic features effectively. Here the work has been done on the PARSEC geometry representation method. The objective of this work is to introduce the knowledge of describing general airfoil using twelve parameters by representing its shape as a polynomial function. And also we have introduced the concept of Genetic Algorithm to optimize the aerodynamic characteristics of a general airfoil for specific conditions. A MATLAB program has been developed to implement PARSEC, Panel Technique, and Genetic Algorithm. This program has been tested for a standard NACA 2411 airfoil and optimized to improve its coefficient of lift. Pressure distribution and co-efficient of lift for airfoil geometries have been calculated using the Panel method. The optimized airfoil has improved co-efficient of lift compared to the original one. The optimized airfoil is validated using wind tunnel data.
Airfoil Shape Optimization in Transonic Flow
A computationally efficient and adaptable design tool is constructed by coupling a flow analysis code based on Euler equations, with the well established numerical optimization algorithms. Optimization technique involving two analysis methods of Simplex and Rosenbrock have been used. The optimization study involves the minimization of wave drag for two different airfoils with geometric constraints on the airfoil maximum thickness or the cross sectional area along with aerodynamic constraint on lift coefficient. The method is applied to these airfoils transonic flow design points, and the results are compared with the original values. This study shows that the conventional low speed airfoils can be optimized to become supercritical for transonic flight speeds, while existing supercritical airfoils can still be improved further at particular design condition. (author)
Development of a morphing flap using shape memory alloy actuators: the aerodynamic characteristics of a morphing flap
The discontinuous contour of a wing with conventional flaps diminishes the aerodynamic performance of an aircraft. A wing with a continuous contour does not experience extreme flow stream fluctuations during flight, and consequently has good aerodynamic characteristics. In this study, a morphing flap using shape memory alloy actuators is proposed, designed and fabricated, and its aerodynamic characteristics are investigated using aerodynamic analyses and wind tunnel tests. The ribs of the morphing flap are designed and fabricated with multiple elements joined together in a way that allows relative rotations of adjacent elements and forms a smooth contour of the morphing flap. The aerodynamic analyses of this multiple-element morphing-flap wing are performed using XFLR pro; its aerodynamic performance is compared with that of a mechanical-flap wing, and is measured through wind-tunnel tests. (papers)
User's manual for an aerodynamic optimization scheeme that updates flow variables and design parameters simultaneously
Rizk, Magdi H.
This user's manual is presented for an aerodynamic optimization program that updates flow variables and design parameters simultaneously. The program was developed for solving constrained optimization problems in which the objective function and the constraint function are dependent on the solution of the nonlinear flow equations. The program was tested by applying it to the problem of optimizing propeller designs. Some reference to this particular application is therefore made in the manual. However, the optimization scheme is suitable for application to general aerodynamic design problems. A description of the approach used in the optimization scheme is first presented, followed by a description of the use of the program.
Optimal shapes of compact strings
Maritan, Amos; Micheletti, Cristian; Trovato, Antonio; Banavar, Jayanth R.
Optimal geometrical arrangements, such as the stacking of atoms, are of relevance in diverse disciplines. A classic problem is the determination of the optimal arrangement of spheres in three dimensions in order to achieve the highest packing fraction; only recently has it been proved that the answer for infinite systems is a face-centred-cubic lattice. This simply stated problem has had a profound impact in many areas, ranging from the crystallization and melting of atomic systems, to optima...
Optimization of wind turbine rotors - using advanced aerodynamic and aeroelastic models and numerical optimization
Doessing, M.
During the last decades the annual energy produced by wind turbines has increased dramatically and wind turbines are now available in the 5MW range. Turbines in this range are constantly being developed and it is also being investigated whether turbines as large as 10-20MW are feasible. The design of very large machines introduces new problems in the practical design, and optimization tools are necessary. These must combine the dynamic effects of both aerodynamics and structure in an integrated optimization environment. This is referred to as aeroelastic optimization. The Risoe DTU optimization software HAWTOPT has been used in this project. The quasi-steady aerodynamic module have been improved with a corrected blade element momentum method. A structure module has also been developed which lays out the blade structural properties. This is done in a simplified way allowing fast conceptual design studies and with focus on the overall properties relevant for the aeroelastic properties. Aeroelastic simulations in the time domain were carried out using the aeroelastic code HAWC2. With these modules coupled to HAWTOPT, optimizations have been made. In parallel with the developments of the mentioned numerical modules, focus has been on analysis and a fundamental understanding of the key parameters in wind turbine design. This has resulted in insight and an effective design methodology is presented. Using the optimization environment a 5MW wind turbine rotor has been optimized for reduced fatigue loads due to apwise bending moments. Among other things this has indicated that airfoils for wind turbine blades should have a high lift coefficient. The design methodology proved to be stable and a help in the otherwise challenging task of numerical aeroelastic optimization. (Author)
The Effect of Aerodynamic Heating on Air Penetration by Shaped Charge Jets and Their Particles
Backofen, Joseph
The goal of this paper is to present recent work modeling thermal coupling between shaped charge jets and their particles with air while it is being penetrated to form a crater that subsequently collapses back onto the jet. This work complements research published at International Symposia on Ballistics: 1) 1987 - Shaped Charge Jet Aerodynamics, Particulation and Blast Field Modeling; and 2) 2007 - Air Cratering by Eroding Shaped Charge Jets. The current work shows how and when a shaped charge jet's tip and jet particles are softened enough that they can erode in a hydrodynamic manner as modeled in these papers. This paper and its presentation includes models for heat transfer from shocked air as a function of jet velocity as well as heat flow within the jet or particle. The work is supported by an extensive bibliographic search including publications on meteors and ballistic missile re-entry vehicles. The modeling shows that a jet loses its strength to the depth required to justify hydrodynamic erosion when its velocity is above a specific velocity related to the shock properties of air and the jet material's properties. As a result, the portion of a jet's kinetic energy converted at the aerodynamic shock into heating transferred back onto the jet affects the energy deposited into the air through drag and ablation which in turn affect air crater expansion and subsequent collapse back onto the jet and its particles as shown in high-speed photography.
Integrated optimization analyses of aerodynamic/stealth characteristics of helicopter rotor based on surrogate model
Jiang Xiangwen
Full Text Available Based on computational fluid dynamics (CFD method, electromagnetic high-frequency method and surrogate model optimization techniques, an integration design method about aerodynamic/stealth has been established for helicopter rotor. The developed integration design method is composed of three modules: integrated grids generation (the moving-embedded grids for CFD solver and the blade grids for radar cross section (RCS solver are generated by solving Poisson equations and folding approach, aerodynamic/stealth solver (the aerodynamic characteristics are simulated by CFD method based upon Navier–Stokes equations and Spalart–Allmaras (S–A turbulence model, and the stealth characteristics are calculated by using a panel edge method combining the method of physical optics (PO, equivalent currents (MEC and quasi-stationary (MQS, and integrated optimization analysis (based upon the surrogate model optimization technique with full factorial design (FFD and radial basis function (RBF, an integrated optimization analyses on aerodynamic/stealth characteristics of rotor are conducted. Firstly, the scattering characteristics of the rotor with different blade-tip swept and twist angles have been carried out, then time–frequency domain grayscale with strong scattering regions of rotor have been given. Meanwhile, the effects of swept-tip and twist angles on the aerodynamic characteristic of rotor have been performed. Furthermore, by choosing suitable object function and constraint condition, the compromised design about swept and twist combinations of rotor with high aerodynamic performances and low scattering characteristics has been given at last.
Shape optimization in biomimetics by homogenization modelling
Optimal shape design of microstructured materials has recently attracted a great deal of attention in material science. The shape and the topology of the microstructure have a significant impact on the macroscopic properties. The present work is devoted to the shape optimization of new biomorphic microcellular ceramics produced from natural wood by biotemplating. We are interested in finding the best material-and-shape combination in order to achieve the optimal prespecified performance of the composite material. The computation of the effective material properties is carried out using the homogenization method. Adaptive mesh-refinement technique based on the computation of recovered stresses is applied in the microstructure to find the homogenized elasticity coefficients. Numerical results show the reliability of the implemented a posteriori error estimator. (author)
Aerodynamic Optimization of Vertical Axis Wind Turbine with Trailing Edge Flaps
Ertem, Sercan; Ferreira, Carlos; Gaunaa, Mac;
Vertical Axis Wind Turbines (VAWT) are competitive concepts for very large scale (1020 MW) floating offshore applications. Rotor circulation control (loading control) opens a wide design space to enhance the aerodynamic and operational features of VAWT. The modified linear derivation of the...... Actuator Cylinder Model (Mod-Lin ACM) is used as the aerodynamic model to assess VAWT performance throughout the work. As the first step, optimum aerodynamic loadings of a VAWT with infinite number of blades are studied. Next, for the case of finite number of blades, direct and inverse optimization...... approaches are used. The direct method is coupled with a hybrid numerical optimizer to serve as a global method for designing flap sequences. The effectiveness of trailing edge flap on VAWT is investigated for three aerodynamic objectives which lead to improved power efficiency, rated power control and peak...
Aerodynamic Optimization of Vertical Axis Wind Turbine with Trailing Edge Flap
Ertem, Sercan; Ferreira, Carlos Simao; Gaunaa, Mac;
Vertical Axis Wind Turbines (VAWT) are competitive concepts for very large scale (10-20 MW)floating ofshore applications. Rotor circulation control (loading control) opens a wide design space to enhance the aerodynamic and operational features of VAWT. The modied linear derivation of the Actuator....... The direct method is coupled with a hybrid numerical optimizer to serve as a global method for designingap sequences. The efectiveness of trailing edgeap on VAWT is investigated for three aerodynamic objectives which lead to improved power effciency, rated power control and peak load control. The...... Cylinder Model (Mod-Lin ACM) is used as the aerodynamic model to assess VAWT performance throughout the work. As the rst step, optimum aerodynamic loadings of a VAWT with innite number of blades are studied. Next, for the case of nite number of blades, direct and inverse optimization approaches are used...
Mesh Regeneration Method for Jig-Shape Optimization Design of the High-Aspect-Ratio Wing
Huo, S. H.; Wang, F S; Z. Yuan; Yue, Z. F.
A mesh regeneration method was put forward, and its application on the jig-shape optimization design of a high-aspect-ratio wing was carried out in the present study. In the mesh regeneration method, some control lines were selected based on configuration characters of the wing structure firstly. And then a new aerodynamic model was built according to the new control lines distribution which always keeps the same outline. Finally, mesh generation and quality optimization were carried out. Thr...
Isogeometric analysis and shape optimization in electromagnetism
Nguyen, Dang Manh
In this thesis a recently proposed numerical method for solving partial differential equations, isogeometric analysis (IGA), is utilized for the purpose of shape optimization, with a particular emphasis on applications to two-dimensional design problems arising in electromagnetic applications. The...... parametrization are combined into an iterative algorithm for shape optimization of two dimensional electromagnetic problems. The algorithm may also be relevant for problems in other engineering disciplines. Using the methods developed in this thesis, remarkably we have obtained antennas that perform one million...... times better than an earlier topology optimization result. This shows a great potential of shape optimization using IGA in the area of electromagnetic antenna design in particular, and for electromagnetic...
Integrated aerodynamic/dynamic/structural optimization of helicopter rotor blades using multilevel decomposition
Walsh, Joanne L.; Young, Katherine C.; Pritchard, Jocelyn I.; Adelman, Howard M.; Mantay, Wayne R.
This paper describes an integrated aerodynamic/dynamic/structural (IADS) optimization procedure for helicopter rotor blades. The procedure combines performance, dynamics, and structural analyses with a general-purpose optimizer using multilevel decomposition techniques. At the upper level, the structure is defined in terms of global quantities (stiffness, mass, and average strains). At the lower level, the structure is defined in terms of local quantities (detailed dimensions of the blade structure and stresses). The IADS procedure provides an optimization technique that is compatible with industrial design practices in which the aerodynamic and dynamic designs are performed at a global level and the structural design is carried out at a detailed level with considerable dialog and compromise among the aerodynamic, dynamic, and structural groups. The IADS procedure is demonstrated for several examples.
Multilevel decomposition approach to integrated aerodynamic/dynamic/structural optimization of helicopter rotor blades
Walsh, Joanne L.; Young, Katherine C.; Pritchard, Jocelyn I.; Adelman, Howard M.; Mantay, Wayne R.
This paper describes an integrated aerodynamic, dynamic, and structural (IADS) optimization procedure for helicopter rotor blades. The procedure combines performance, dynamics, and structural analyses with a general purpose optimizer using multilevel decomposition techniques. At the upper level, the structure is defined in terms of local quantities (stiffnesses, mass, and average strains). At the lower level, the structure is defined in terms of local quantities (detailed dimensions of the blade structure and stresses). The IADS procedure provides an optimization technique that is compatible with industrial design practices in which the aerodynamic and dynamic design is performed at a global level and the structural design is carried out at a detailed level with considerable dialogue and compromise among the aerodynamic, dynamic, and structural groups. The IADS procedure is demonstrated for several cases.
Optimization of the head shape of the CRH3 high speed train
Aiming at optimizing the head shape of the CRH3 high speed train, an efficient optimization approach is proposed. The CFD analysis by solving Navier-Stokes equations is coupled with optimization calculation based on the multi-objective genetic algorithm, meanwhile the arbitrary shape deformation technique (ASD) is also introduced into the design flow, which greatly shortens the time consumption for geometry regeneration and flow field remeshing. As a result, the efficiency of the optimization calculation is highly improved. Statistical analysis is done to the designs in the design space, and the correlation between the design variables and the objective is studied to find out the key variables that most affect the objective. Response surface analysis is also performed to get the nonlinear relationship between the key design variables and the objective with the Kriging algorithm. Finally, after the optimization, an aerodynamic performance comparison between the optimal shape and the original shape reveals that the original shape of CRH3 high speed train owns a very stable aerodynamic performance and can be trustingly used in industry.
Optimal Nesting for Continuous Shape Stamping Processes
This paper discusses the optimal nesting problem for minimizing the scrap in continuous shape stamping processes. The shape sliding technique is used to propose a new approach, OVERLAP-and-ESCAPE, to solve the problem of continuously nesting shapes onto a metal coil of fixed or selectable width. The approach is used to construct the objective function of the mathematical model of the problem using the Simulated Annealing Algorithm to determine the globally minimal configurations for the nesting problems. Some representative cases are studied and the results are encouraging. An automatic nesting software package for manufacturing bicycle chain link blanks is also described.
Aerodynamic Drag Reduction for a Generic Truck Using Geometrically Optimized Rear Cabin Bumps
Abdellah Ait Moussa
Full Text Available The continuous surge in gas prices has raised major concerns about vehicle fuel efficiency, and drag reduction devices offer a promising strategy. In this paper, we investigate the mechanisms by which geometrically optimized bumps, placed on the rear end of the cabin roof of a generic truck, reduce aerodynamic drag. The incorporation of these devices requires proper choices of the size, location, and overall geometry. In the following analysis we identify these factors using a novel methodology. The numerical technique combines automatic modeling of the add-ons, computational fluid dynamics and optimization using orthogonal arrays, and probabilistic restarts. Numerical results showed reduction in aerodynamic drag between 6% and 10%.
Optimal convex shapes for concave functionals
Bucur, Dorin; Lamboley, Jimmy
Motivated by a long-standing conjecture of Polya and Szeg\\"o about the Newtonian capacity of convex bodies, we discuss the role of concavity inequalities in shape optimization, and we provide several counterexamples to the Blaschke-concavity of variational functionals, including capacity. We then introduce a new algebraic structure on convex bodies, which allows to obtain global concavity and indecomposability results, and we discuss their application to isoperimetriclike inequalities. As a byproduct of this approach we also obtain a quantitative version of the Kneser-S\\"uss inequality. Finally, for a large class of functionals involving Dirichlet energies and the surface measure, we perform a local analysis of strictly convex portions of the boundary via second order shape derivatives. This allows in particular to exclude the presence of smooth regions with positive Gauss curvature in an optimal shape for Polya-Szeg\\"o problem.
Adaptive finite element method for shape optimization
Morin, Pedro
We examine shape optimization problems in the context of inexact sequential quadratic programming. Inexactness is a consequence of using adaptive finite element methods (AFEM) to approximate the state and adjoint equations (via the dual weighted residual method), update the boundary, and compute the geometric functional. We present a novel algorithm that equidistributes the errors due to shape optimization and discretization, thereby leading to coarse resolution in the early stages and fine resolution upon convergence, and thus optimizing the computational effort. We discuss the ability of the algorithm to detect whether or not geometric singularities such as corners are genuine to the problem or simply due to lack of resolution - a new paradigm in adaptivity. © EDP Sciences, SMAI, 2012.
Modeling of aerodynamic Space-to-Surface flight with optimal trajectory for targeting
Gornev, Serge
Modeling has been created for a Space-to-Surface system defined for an optimal trajectory for targeting in terminal phase. The modeling includes models for simulation atmosphere, speed of sound, aerodynamic flight and navigation by an infrared system. The modeling simulation includes statistical analysis of the modeling results.
Design and performance of a shape memory alloy-reinforced composite aerodynamic profile
Based on a shape memory alloy (SMA)-reinforced composite developed separately, the applicability of the composite has been demonstrated through realization of a realistically scaled aerodynamic profile of around 0.5 m span by 0.5 m root chord whose skins had been made from this composite. The design, manufacturing and assembly of the profile are described. The curved skins were manufactured with two layers of SMA wires integrated into the layup of aramid fibre prepregs. All SMA wires were connected such that they can be operated as individual sets of wires and at low voltages, similar to the conditions for electrical energy generation in a real aircraft. The profile was then mounted on a vibration test rig and excited by a shaker at its tip which allowed the dynamic performance of the profile to be validated under internal actuation conditions generated through the SMA wires
Implant shape optimization using reverse FEA
Gladilin, Evgeny; Ivanov, A.; Roginsky, V.
This work presents a novel approach for the physically-based optimization of individual implants in cranio-maxillofacial surgery. The proposed method is based on solving an inverse boundary value problem of the cranio-maxillofacial surgery planning, i.e. finding an optimal implant shape for a desired correction of soft tissues. The paper describes the methodology for the generation of individual geometrical models of human head, the reverse finite element approach for solving biomechanical boundary value problems and two clinical studies dealing with the computer aided design of individual craniofacial implants.
Shape Optimization of Impeller Blades for 15,000 HP Centrifugal Compressor Using Fluid Structural Interaction Analysis
Kang, Hyun Su [Sungkyunkwan University, Suwon (Korea, Republic of); Oh, Jeongsu [Daejoo Machinery Co., Daegu (Korea, Republic of); Han, Jeong Sam [Andong National University, Andong (Korea, Republic of)
This paper discusses a one-way fluid structural interaction (FSI) analysis and shape optimization of the impeller blades for a 15,000 HP centrifugal compressor using the response surface method (RSM). Because both the aerodynamic performance and the structural safety of the impeller are affected by the shape of its blades, shape optimization is necessary using the FSI analysis, which includes a structural analysis for the induced fluid pressure and centrifugal force. The FSI analysis is performed in ANSYS Workbench: ANSYS CFX is used for the flow field and ANSYS Mechanical is used for the structural field. The response surfaces for the FSI results (efficiency, pressure ratio, maximum stress, etc.) generated based on the design of experiments (DOE) are used to find an optimal shape for the impeller blades, which provides the maximum aerodynamic performance subject to the structural safety constraints.
Shape Optimization of Impeller Blades for 15,000 HP Centrifugal Compressor Using Fluid Structural Interaction Analysis
This paper discusses a one-way fluid structural interaction (FSI) analysis and shape optimization of the impeller blades for a 15,000 HP centrifugal compressor using the response surface method (RSM). Because both the aerodynamic performance and the structural safety of the impeller are affected by the shape of its blades, shape optimization is necessary using the FSI analysis, which includes a structural analysis for the induced fluid pressure and centrifugal force. The FSI analysis is performed in ANSYS Workbench: ANSYS CFX is used for the flow field and ANSYS Mechanical is used for the structural field. The response surfaces for the FSI results (efficiency, pressure ratio, maximum stress, etc.) generated based on the design of experiments (DOE) are used to find an optimal shape for the impeller blades, which provides the maximum aerodynamic performance subject to the structural safety constraints
Full Text Available An investigation has been made to predict the effects of forebody and afterbody shapes on the aerodynamic characteristics of several projectile bodies at supersonic speeds using analytical methods combined with semi-empirical design curves. The considered projectile bodies had a length-to-diameter ratio of 6.67 and included three variations of forebody shape and three variations of afterbody shape. The results, which are verified by comparison with available experimental data, indicated that the lowest drag was achieved with a cone-cylinder at the considered Mach number range. It is also shown that the drag can be reduced by boattailing the afterbody. The centre-of-pressure assumed a slightly rearward location for the ogive-cylinder configuration when compared to the configuration with boattailed afterbody where it was the most forward. With the exception of the boattailed afterbody, all the bodies indicated inherent static stability above Mach number 2 for a centre-of-gravity location at about 40% from the body nose.
Aerodynamic reconfiguration and multicriterial optimization of centrifugal compressors – a case study
Valeriu DRAGAN
This paper continues the recent research of the author, with application to 3D computational fluid dynamics multicriterial optimization of turbomachinery parts. Computational Fluid Dynamics has been an ubicuous tool for compressor design for decades, helping the designers to test the aerodynamic parameters of their machines with great accuracy. Due to advances of multigrid methods and the improved robustness of structured solvers, CFD can nowadays be part of an optimization loop with artifici...
Elastically Shaped Wing Optimization and Aircraft Concept for Improved Cruise Efficiency
Nguyen, Nhan; Trinh, Khanh; Reynolds, Kevin; Kless, James; Aftosmis, Michael; Urnes, James, Sr.; Ippolito, Corey
This paper presents the findings of a study conducted tn 2010 by the NASA Innovation Fund Award project entitled "Elastically Shaped Future Air Vehicle Concept". The study presents three themes in support of meeting national and global aviation challenges of reducing fuel burn for present and future aviation systems. The first theme addresses the drag reduction goal through innovative vehicle configurations via non-planar wing optimization. Two wing candidate concepts have been identified from the wing optimization: a drooped wing shape and an inflected wing shape. The drooped wing shape is a truly biologically inspired wing concept that mimics a seagull wing and could achieve about 5% to 6% drag reduction, which is aerodynamically significant. From a practical perspective, this concept would require new radical changes to the current aircraft development capabilities for new vehicles with futuristic-looking wings such as this concept. The inflected wing concepts could achieve between 3% to 4% drag reduction. While the drag reduction benefit may be less, the inflected-wing concept could have a near-term impact since this concept could be developed within the current aircraft development capabilities. The second theme addresses the drag reduction goal through a new concept of elastic wing shaping control. By aeroelastically tailoring the wing shape with active control to maintain optimal aerodynamics, a significant drag reduction benefit could be realized. A significant reduction in fuel burn for long-range cruise from elastic wing shaping control could be realized. To realize the potential of the elastic wing shaping control concept, the third theme emerges that addresses the drag reduction goal through a new aerodynamic control effector called a variable camber continuous trailing edge flap. Conventional aerodynamic control surfaces are discrete independent surfaces that cause geometric discontinuities at the trailing edge region. These discontinuities promote
Multi-objective optimization strategies using adjoint method and game theory in aerodynamics
Zhili Tang
There are currently three different game strategies originated in economics:(1) Cooperative games (Pareto front),(2)Competitive games (Nash game) and (3)Hierarchical games (Stackelberg game).Each game achieves different equilibria with different performance,and their players play different roles in the games.Here,we introduced game concept into aerodynamic design, and combined it with adjoint method to solve multicriteria aerodynamic optimization problems.The performance distinction of the equilibria of these three game strategies was investigated by numerical experiments.We computed Pareto front, Nash and Stackelberg equilibria of the same optimization problem with two conflicting and hierarchical targets under different parameterizations by using the deterministic optimization method.The numerical results show clearly that all the equilibria solutions are inferior to the Pareto front.Non-dominated Pareto front solutions are obtained,however the CPU cost to capture a set of solutions makes the Pareto front an expensive tool to the designer.
On the Shape Optimization of Flapping Wings and their Performance Analysis
Ghommem, Mehdi; Niemi, Antti H; Calo, Victor M
The present work is concerned with the shape optimization of flapping wings in forward flight. The analysis is performed by combining a gradient-based optimizer with the unsteady vortex lattice method (UVLM). We describe the UVLM implementation and provide insights on how to select properly the mesh and time-step sizes to achieve invariant UVLM simulation results under further mesh refinement. Our objective is to identify a set of optimized shapes that maximize the propulsive efficiency, defined as the ratio of the propulsive power over the aerodynamic power, under lift, thrust, and area constraints. Several parameters affecting flight performance are investigated and their impact is described. These include the wing's aspect ratio, camber line, and curvature of the leading and trailing edges. This study provides guidance for shape design of engineered flying systems.
On the shape optimization of flapping wings and their performance analysis
Ghommem, Mehdi
The present work is concerned with the shape optimization of flapping wings in forward flight. The analysis is performed by combining a gradient-based optimizer with the unsteady vortex lattice method (UVLM). We describe the UVLM simulation procedure and provide the first methodology to select properly the mesh and time-step sizes to achieve invariant UVLM simulation results under mesh refinement. Our objective is to identify a set of optimized shapes that maximize the propulsive efficiency, defined as the ratio of the propulsive power over the aerodynamic power, under lift, thrust, and area constraints. Several parameters affecting flight performance are investigated and their impact is described. These include the wingÊ1/4s aspect ratio, camber line, and curvature of the leading and trailing edges. This study provides guidance for shape design of engineered flying systems. © 2013 Elsevier Masson SAS.
Shape and topology optimization of enzymatic microreactors
Pereira Rosinha, Ines
structure and results in the deformation of the configuration. Topologyoptimization contributes to the improvement of the layout of the material in a domain. Themechanical performance of a structure is evaluated by an objective function which can be for example maximizing its stiffness.The need for...... of extensive experimental work to find the best reactor configuration.Shape optimization has been applied to an YY-microreactor with a rectangular cross-section withthe intention to investigate the shape influence on the active mixing of substances and consequently in the reaction yield. The inlet...... such as height and width. This is achieved by a computational fluid dynamic (CFD) simulation study, which investigates a biocatalyticreaction for the production of optically pure chiral amines in the reactor system. The routine implements kinetic models into a CFD framework (ANSYS CFX®), which is...
Position control optimization of aerodynamic brake device for high-speed trains
Zuo, Jianyong; Luo, Zhuojun; Chen, Zhongkai
The aerodynamic braking is a clean and non-adhesion braking, and can be used to provide extra braking force during high-speed emergency braking. The research of aerodynamic braking has attracted more and more attentions in recent years. However, most researchers in this field focus on aerodynamic effects and seldom on issues of position control of the aerodynamic braking board. The purpose of this paper is to explore position control optimization of the braking board in an aerodynamic braking prototype. The mathematical models of the hydraulic drive unit in the aerodynamic braking system are analyzed in detail, and the simulation models are established. Three control functions—constant, linear, and quadratic—are explored. Two kinds of criteria, including the position steady-state error and the acceleration of the piston rod, are used to evaluate system performance. Simulation results show that the position steady state-error is reduced from around 12-2 mm by applying a linear instead of a constant function, while the acceleration is reduced from 25.71-3.70 m/s2 with a quadratic control function. Use of the quadratic control function is shown to improve system performance. Experimental results obtained by measuring the position response of the piston rod on a test-bench also suggest a reduced position error and smooth movement of the piston rod. This implies that the acceleration is smaller when using the quadratic function, thus verifying the effectiveness of control schemes to improve to system performance. This paper proposes an effective and easily implemented control scheme that improves the position response of hydraulic cylinders during position control.
Aerodynamic optimization of supersonic compressor cascade using differential evolution on GPU
Aissa, Mohamed Hasanine; Verstraete, Tom; Vuik, Cornelis
Differential Evolution (DE) is a powerful stochastic optimization method. Compared to gradient-based algorithms, DE is able to avoid local minima but requires at the same time more function evaluations. In turbomachinery applications, function evaluations are performed with time-consuming CFD simulation, which results in a long, non affordable, design cycle. Modern High Performance Computing systems, especially Graphic Processing Units (GPUs), are able to alleviate this inconvenience by accelerating the design evaluation itself. In this work we present a validated CFD Solver running on GPUs, able to accelerate the design evaluation and thus the entire design process. An achieved speedup of 20x to 30x enabled the DE algorithm to run on a high-end computer instead of a costly large cluster. The GPU-enhanced DE was used to optimize the aerodynamics of a supersonic compressor cascade, achieving an aerodynamic loss minimization of 20%.
Optimization of rotor blades for combined structural, dynamic, and aerodynamic properties
He, Cheng-Jian; Peters, David A.
Optimal helicopter blade design with computer-based mathematical programming has received more and more attention in recent years. Most of the research has focused on optimum dynamic characteristics of rotor blades to reduce vehicle vibration. There is also work on optimization of aerodynamic performance and on composite structural design. This research has greatly increased our understanding of helicopter optimum design in each of these aspects. Helicopter design is an inherently multidisciplinary process involving strong interactions among various disciplines which can appropriately include aerodynamics; dynamics, both flight dynamics and structural dynamics; aeroelasticity: vibrations and stability; and even acoustics. Therefore, the helicopter design process must satisfy manifold requirements related to the aforementioned diverse disciplines. In our present work, we attempt to combine several of these important effects in a unified manner. First, we design a blade with optimum aerodynamic performance by proper layout of blade planform and spanwise twist. Second, the blade is designed to have natural frequencies that are placed away from integer multiples of the rotor speed for a good dynamic characteristics. Third, the structure is made as light as possible with sufficient rotational inertia to allow for autorotational landing, with safe stress margins and flight fatigue life at each cross-section, and with aeroelastical stability and low vibrations. Finally, a unified optimization refines the solution.
Multi-objective optimization for the optimum shape design is introduced in aerodynamics using the Game theory. Based on the control theory, the employed optimizer and the negative feedback are used to implement the constraints. All the constraints are satisfied implicitly and automatically in the design. Furthermore,the above methodology is combined with a formulation derived from the Game theory to treat multi-point airfoil optimization. Airfoil shapes are optimized according to various aerodynamics criteria. In the symmetric Nash game, each "player" is responsible for one criterion, and the Nash equilibrium provides a solution to the multipoint optimization. Design results confirm the efficiency of the method.%将经济学中的Nash均衡理论引入到气动优化设计中,探索一种新颖的处理互为冲突的多目标气动外形优化设计方法.基本的优化器为基于伴随方法的确定性优化算法,文中通过引入负反馈技术发展了约束最优控制理论,所有的约束条件都被自动的和隐含的满足.在对称Nash策略中,每一个优化器都力图优化自己的目标,而Nash平衡则提供了多个目标之间的一种妥协解.设计算例表明,文中的Nash竞争策略在多目标气动优化设计中是有效的.
Aerodynamic Design Optimization on Unstructured Meshes Using the Navier-Stokes Equations
Nielsen, Eric J.; Anderson, W. Kyle
A discrete adjoint method is developed and demonstrated for aerodynamic design optimization on unstructured grids. The governing equations are the three-dimensional Reynolds-averaged Navier-Stokes equations coupled with a one-equation turbulence model. A discussion of the numerical implementation of the flow and adjoint equations is presented. Both compressible and incompressible solvers are differentiated and the accuracy of the sensitivity derivatives is verified by comparing with gradients obtained using finite differences. Several simplifying approximations to the complete linearization of the residual are also presented, and the resulting accuracy of the derivatives is examined. Demonstration optimizations for both compressible and incompressible flows are given.
Development and application of an optimization procedure for flutter suppression using the aerodynamic energy concept
Nissim, E.; Abel, I.
An optimization procedure is developed based on the responses of a system to continuous gust inputs. The procedure uses control law transfer functions which have been partially determined by using the relaxed aerodynamic energy approach. The optimization procedure yields a flutter suppression system which minimizes control surface activity in a gust environment. The procedure is applied to wing flutter of a drone aircraft to demonstrate a 44 percent increase in the basic wing flutter dynamic pressure. It is shown that a trailing edge control system suppresses the flutter instability over a wide range of subsonic mach numbers and flight altitudes. Results of this study confirm the effectiveness of the relaxed energy approach.
Parallel Computation of Sensitivity Derivatives with Application to Aerodynamic Optimization of a Wing
Biedron, Robert T.; Samareh, Jamshid A.; Green, Lawrence T.
This paper focuses on the parallel computation of aerodynamic derivatives via automatic differentiation of the Euler/Navier-Stokes solver CFL3D. The comparison with derivatives obtained by finite differences is presented and the scaling of the time required to obtain the derivatives relative to the number of processors employed for the computation is shown. Finally, the derivative computations are coupled with an optimizer and surface/volume grid deformation tools to perform an optimization to reduce the drag of a three-dimensional wing.
Aerodynamic reconfiguration and multicriterial optimization of centrifugal compressors – a case study
Valeriu DRAGAN
Full Text Available This paper continues the recent research of the author, with application to 3D computational fluid dynamics multicriterial optimization of turbomachinery parts. Computational Fluid Dynamics has been an ubicuous tool for compressor design for decades, helping the designers to test the aerodynamic parameters of their machines with great accuracy. Due to advances of multigrid methods and the improved robustness of structured solvers, CFD can nowadays be part of an optimization loop with artificial neural networks or evolutive algorithms. This paper presents a case study of an air centrifugal compressor rotor optimized using Numeca's Design 3D CFD suite. The turbulence model used for the database generation and the optimization stage is Spalart Allmaras. Results indicate a fairly quick convergence time per individual as well as a good convergence of the artificial neural network optimizer.
Shape Optimization of Revolute-Jointed Rigid-Flexible Manipulator
Mahto, S.; Dixit, U. S.
This work illustrates the shape optimization of flexible link of revolute-jointed rigid-flexible manipulator. Flexible link is considered as Euler-Bernoulli beam and dynamic analysis is carried out by finite element based on Langrange approach. Nonlinear classical search technique (Sequential Quadratic Programming method) is applied to extremize the four different objectives. Different optimized shapes are obtained for different optimization problems. Optimized shapes improve the static and dynamic response of the system viz. fundamental frequency, hub angles, flexural vibration, etc.
Shape optimization of self-avoiding curves
Walker, Shawn W.
This paper presents a softened notion of proximity (or self-avoidance) for curves. We then derive a sensitivity result, based on shape differential calculus, for the proximity. This is combined with a gradient-based optimization approach to compute three-dimensional, parameterized curves that minimize the sum of an elastic (bending) energy and a proximity energy that maintains self-avoidance by a penalization technique. Minimizers are computed by a sequential-quadratic-programming (SQP) method where the bending energy and proximity energy are approximated by a finite element method. We then apply this method to two problems. First, we simulate adsorbed polymer strands that are constrained to be bound to a surface and be (locally) inextensible. This is a basic model of semi-flexible polymers adsorbed onto a surface (a current topic in material science). Several examples of minimizing curve shapes on a variety of surfaces are shown. An advantage of the method is that it can be much faster than using molecular dynamics for simulating polymer strands on surfaces. Second, we apply our proximity penalization to the computation of ideal knots. We present a heuristic scheme, utilizing the SQP method above, for minimizing rope-length and apply it in the case of the trefoil knot. Applications of this method could be for generating good initial guesses to a more accurate (but expensive) knot-tightening algorithm.
Aerodynamic Optimization of Rocket Control Surface Geometry Using Cartesian Methods and CAD Geometry
Nelson, Andrea; Aftosmis, Michael J.; Nemec, Marian; Pulliam, Thomas H.
Aerodynamic design is an iterative process involving geometry manipulation and complex computational analysis subject to physical constraints and aerodynamic objectives. A design cycle consists of first establishing the performance of a baseline design, which is usually created with low-fidelity engineering tools, and then progressively optimizing the design to maximize its performance. Optimization techniques have evolved from relying exclusively on designer intuition and insight in traditional trial and error methods, to sophisticated local and global search methods. Recent attempts at automating the search through a large design space with formal optimization methods include both database driven and direct evaluation schemes. Databases are being used in conjunction with surrogate and neural network models as a basis on which to run optimization algorithms. Optimization algorithms are also being driven by the direct evaluation of objectives and constraints using high-fidelity simulations. Surrogate methods use data points obtained from simulations, and possibly gradients evaluated at the data points, to create mathematical approximations of a database. Neural network models work in a similar fashion, using a number of high-fidelity database calculations as training iterations to create a database model. Optimal designs are obtained by coupling an optimization algorithm to the database model. Evaluation of the current best design then gives either a new local optima and/or increases the fidelity of the approximation model for the next iteration. Surrogate methods have also been developed that iterate on the selection of data points to decrease the uncertainty of the approximation model prior to searching for an optimal design. The database approximation models for each of these cases, however, become computationally expensive with increase in dimensionality. Thus the method of using optimization algorithms to search a database model becomes problematic as the
A global optimization approach to turbine blade design based on hierarchical fair competition genetic algorithms with dynamic niche (HFCDN-GAs) coupled with Reynolds-averaged Navier-Stokes (RANS) equation is presented. In order to meet the search theory of GAs and the aerodynamic performances of turbine, Bezier curve is adopted to parameterize the turbine blade profile, and a fitness function pertaining to optimization is designed. The design variables are the control points' ordinates of characteristic polygon of Bezier curve representing the turbine blade profile. The object function is the maximum lift-drag ratio of the turbine blade. The constraint conditions take into account the leading and trailing edge metal angle, and the strength and aerodynamic performances of turbine blade. And the treatment method of the constraint conditions is the flexible penalty function. The convergence history of test function indicates that HFCDN-GAs can locate the global optimum within a few search steps and have high robustness. The lift-drag ratio of the optimized blade is 8.3% higher than that of the original one. The results show that the proposed global optimization approach is effective for turbine blade.
Optimization design of blade shapes for wind turbines
Chen, Jin; Wang, Xudong; Shen, Wen Zhong;
For the optimization design of wind turbines, the new normal and tangential induced factors of wind turbines are given considering the tip loss of the normal and tangential forces based on the blade element momentum theory and traditional aerodynamic model. The cost model of the wind turbines and...... the optimization design model are developed. In the optimization model, the objective is the minimum cost of energy and the design variables are the chord length, twist angle and the relative thickness. Finally, the optimization is carried out for a 2 MW blade by using this optimization design model....... The performance of blades is validated through the comparison and analysis of the results. The reduced cost shows that the optimization model is good enough for the design of wind turbines. The results give a proof for the design and research on the blades of large scale wind turbines and also...
Aerodynamic design applying automatic differentiation and using robust variable fidelity optimization
Takemiya, Tetsushi
, and that (2) the AMF terminates optimization erroneously when the optimization problems have constraints. The first problem is due to inaccuracy in computing derivatives in the AMF, and the second problem is due to erroneous treatment of the trust region ratio, which sets the size of the domain for an optimization in the AMF. In order to solve the first problem of the AMF, automatic differentiation (AD) technique, which reads the codes of analysis models and automatically generates new derivative codes based on some mathematical rules, is applied. If derivatives are computed with the generated derivative code, they are analytical, and the required computational time is independent of the number of design variables, which is very advantageous for realistic aerospace engineering problems. However, if analysis models implement iterative computations such as computational fluid dynamics (CFD), which solves system partial differential equations iteratively, computing derivatives through the AD requires a massive memory size. The author solved this deficiency by modifying the AD approach and developing a more efficient implementation with CFD, and successfully applied the AD to general CFD software. In order to solve the second problem of the AMF, the governing equation of the trust region ratio, which is very strict against the violation of constraints, is modified so that it can accept the violation of constraints within some tolerance. By accepting violations of constraints during the optimization process, the AMF can continue optimization without terminating immaturely and eventually find the true optimum design point. With these modifications, the AMF is referred to as "Robust AMF," and it is applied to airfoil and wing aerodynamic design problems using Euler CFD software. The former problem has 21 design variables, and the latter 64. In both problems, derivatives computed with the proposed AD method are first compared with those computed with the finite
Dose-shaping using targeted sparse optimization
particular, Etotsparse-optimized plans for the pancreas case and head-and-neck case exhibited substantially improved sparing of the spinal cord and parotid glands, respectively, while maintaining or improving sparing for other OARs and markedly improving PTV homogeneity. Plan deliverability for Etotsparse-optimized plans was shown to be better than their associated clinical plans, according to the two-dimensional modulation index.Conclusions: These results suggest that our formulation may be used to improve dose-shaping and OAR-sparing for complicated disease sites, such as the pancreas or head and neck. Furthermore, our objective function and constraints are linear and constitute a linear program, which converges to the global minimum quickly, and can be easily implemented in treatment planning software. Thus, the authors expect fast translation of our method to the clinic where it may have a positive impact on plan quality for challenging disease sites
Theoretical studies on particle shape classification based on simultaneous small forward angle light scattering and aerodynamic sizing
Jin-Bi, Zhang; Lei, Ding; Ying-Ping, Wang; Li, Zhang; Jin-Lei, Wu; Hai-Yang, Zheng; Li, Fang
Particle shape contributes to understanding the physical and chemical processes of the atmosphere and better ascertaining the origins and chemical compositions of the particles. The particle shape can be classified by the aspect ratio, which can be estimated through the asymmetry factor measured with angularly resolved light scattering. An experimental method of obtaining the asymmetry factor based on simultaneous small forward angle light scattering and aerodynamic size measurements is described briefly. The near forward scattering intensity signals of three detectors in the azimuthal angles at 120° offset are calculated using the methods of T-matrix and discrete dipole approximation. Prolate spheroid particles with different aspect ratios are used as the shape models with the assumption that the symmetry axis is parallel to the flow axis and perpendicular to the incident light. The relations between the asymmetry factor and the optical size and aerodynamic size at various equivalent sizes, refractive indices, and mass densities are discussed in this paper. The numerically calculated results indicate that an elongated particle may be classified at diameter larger than 1.0 μm, and may not be distinguished from a sphere at diameter less than 0.5 μm. It is estimated that the lowest detected aspect ratio is around 1.5:1 in consideration of the experimental errors. Project supported by the National Natural Science Foundation of China (Grant No. 41275132).
Isogeometric Analysis and Shape Optimization in Fluid Mechanics
Nielsen, Peter Nørtoft
This thesis brings together the fields of fluid mechanics, as the study of fluids and flows, isogeometric analysis, as a numerical method to solve engineering problems using computers, and shape optimization, as the art of finding "best" shapes of objects based on some notion of goodness. The flow...... approximations, and for shape optimization purposes also due to its tight connection between the analysis and geometry models. The thesis is initiated by short introductions to fluid mechanics, and to the building blocks of isogeometric analysis. As the first contribution of the thesis, a detailed description is...... isogeometric analysis may serve as a natural framework for shape optimization within fluid mechanics. We construct an efficient regularization measure for avoiding inappropriate parametrizations during optimization, and various numerical examples of shape optimization for fluids are considered, serving to...
Research on the Aerodynamic Noise Optimization of Wind Turbine Airfoil%风力机翼型气动噪声优化设计研究
刘雄; 罗文博; 陈严; 叶枝全; 周鹏展
In order to obtain wind turbine airfoils with high lift-to-drag ratio and low noise level, the aerodynamic noise is introduced into the wind turbine airfoil design process. To evaluate the airfoil aerodynamic noise level, the airfoil self-noise model is studied and the NASA self-noise model based on extensive experiments is applied to modeling the airfoil aerodynamic noise. With the airfoil profile described by using shape function perturbation method, taking the aerodynamic performance as a constraint, a noise optimization method is set up with the objective to satisfy the lowest self-noise level. In the design process, XFOIL is used to get the boundary layer parameters and evaluate the airfoil aerodynamic performance. By combining the flow field solver and the direct optimization method, and using the complex method to carry out the search iterations, a Matlab based optimization program is developed. By taking NACA 4415 as the original airfoil and applying the developed program, an airfoil with high aerodynamic performance and low noise level is obtained.%为获得高升阻比、低噪声水平的风力机翼型,将气动噪声引入到风力机专用翼型的设计中.为评价翼型气动噪声水平,对翼型自身噪声进行讨论和研究,应用NASA基于大量试验而得到的翼型自身噪声模型进行建模.采用型函数扰动法对翼型廓线进行表示,以翼型自身噪声水平作为优化目标,将气动特性作为性能约束,建立翼型的优化设计模型.设计过程中,采用XFOIL获取翼型边界层参数,及对翼型的气动性能进行评价.将流场求解程序和直接优化方法相结合,采用复合形法进行搜索寻优,用Matlab编制优化程序.以NACA4415作为原始翼型进行优化设计,得到一种具有高气动性能、低噪声水平的风力机专用翼型.
A Shape Optimization Study for Tool Design in Resistance Welding
Bogomolny, Michael; Bendsøe, Martin P.; Hattel, Jesper Henri
The purpose of this study is to apply shape optimization tools for design of resistance welding electrodes. The numerical simulation of the welding process has been performed by a simplified FEM model implemented in COMSOL. The design process is formulated as an optimization problem where...... to simplify the calculation of shape sensitivities and to generate a generic tool that can be interfaced with other simulation tools. An example numerical study shows the potential of applying optimal design techniques in this area....
Optimal Aerodynamic Design of Conventional and Coaxial Helicopter Rotors in Hover and Forward Flight
Giovanetti, Eli B.
This dissertation investigates the optimal aerodynamic performance and design of conventional and coaxial helicopters in hover and forward flight using conventional and higher harmonic blade pitch control. First, we describe a method for determining the blade geometry, azimuthal blade pitch inputs, optimal shaft angle (rotor angle of attack), and division of propulsive and lifting forces among the components that minimize the total power for a given forward flight condition. The optimal design problem is cast as a variational statement that is discretized using a vortex lattice wake to model inviscid forces, combined with two-dimensional drag polars to model profile losses. The resulting nonlinear constrained optimization problem is solved via Newton iteration. We investigate the optimal design of a compound vehicle in forward flight comprised of a coaxial rotor system, a propeller, and optionally, a fixed wing. We show that higher harmonic control substantially reduces required power, and that both rotor and propeller efficiencies play an important role in determining the optimal shaft angle, which in turn affects the optimal design of each component. Second, we present a variational approach for determining the optimal (minimum power) torque-balanced coaxial hovering rotor using Blade Element Momentum Theory including swirl. We show that the optimal hovering coaxial rotor generates only a small percentage of its total thrust on the portion of the lower rotor operating in the upper rotor's contracted wake, resulting in an optimal design with very different upper and lower rotor twist and chord distributions. We also show that the swirl component of induced velocity has a relatively small effect on rotor performance at the disk loadings typical of helicopter rotors. Third, we describe a more refined model of the wake of a hovering conventional or coaxial rotor. We approximate the rotor or coaxial rotors as actuator disks (though not necessarily uniformly loaded
Shape and topology optimization of enzymatic microreactors
Pereira Rosinha, Ines; Woodley, John; Gernaey, Krist; Krühne, Ulrich
Metoder til optimering af strukturer er et hyppigt brugt værktøj af bygningsingeniører og maskiningeniører til finde optimale strukturer. Optimeringen er baseret på brugen af en række beregningsteknikker der beregner optimal form og topologi af et givent objekt. Form optimering anvendes direkte på begrænsende overflader af en struktur og resulterer i deformation af objektet.Topologioptimering anvendes til at forbedre strukturen af objektet. Den mekaniske ydeevne af strukturen evalueres basere...
Discrete Geometry Toolkit for Shape Optimization Project
National Aeronautics and Space Administration — Simulation-based design optimization has been steadily maturing over the past two decades, but not without its own unique and persistent challenges. The proposed...
aerodynamics and heat transfer
J. N. Rajadas
Full Text Available A multidisciplinary optimization procedure, with the integration of aerodynamic and heat transfer criteria, has been developed for the design of gas turbine blades. Two different optimization formulations have been used. In the first formulation, the maximum temperature in the blade section is chosen as the objective function to be minimized. An upper bound constraint is imposed on the blade average temperature and a lower bound constraint is imposed on the blade tangential force coefficient. In the second formulation, the blade average and maximum temperatures are chosen as objective functions. In both formulations, bounds are imposed on the velocity gradients at several points along the surface of the airfoil to eliminate leading edge velocity spikes which deteriorate aerodynamic performance. Shape optimization is performed using the blade external and coolant path geometric parameters as design variables. Aerodynamic analysis is performed using a panel code. Heat transfer analysis is performed using the finite element method. A gradient based procedure in conjunction with an approximate analysis technique is used for optimization. The results obtained using both optimization techniques are compared with a reference geometry. Both techniques yield significant improvements with the multiobjective formulation resulting in slightly superior design.
Nguyen, D. M.; Evgrafov, Anton; Gravesen, Jens
We consider the benchmark problem of magnetic energy density enhancement in a small spatial region by varying the shape of two symmetric conducting scatterers. We view this problem as a prototype for a wide variety of geometric design problems in electromagnetic applications. Our approach for...
Aerodynamic control of bridge cables through shape modification: A preliminary study
Kleissl, Kenneth; Georgakis, Christos
This paper examines the viability of modifying bridge cable shape and surface for the purpose of controlling wind-induced vibrations. To this end, an extensive wind-tunnel test campaign was carried out on various cable shapes about the critical Reynolds number region. Cable shapes were chosen to...
Isogeometric shape optimization of magnetic density separators
Dang Manh, N.; Evgrafov, A.; Gravesen, J; Lahaye, D
Purpose: The waste recycling industry increasingly relies on magnetic density separators. These devices generate an upward magnetic force in ferro-fluids allowing to separate the immersed particles according to their mass density. Recently a new separator design that significantly reduces the required amount of permanent magnet material has been proposed. The purpose of this paper is to alleviate the undesired end-effects in this design by altering the shape of the ferromagnetic covers of the...
On the Use of CAD and Cartesian Methods for Aerodynamic Optimization
Nemec, M.; Aftosmis, M. J.; Pulliam, T. H.
The objective for this paper is to present the development of an optimization capability for Curt3D, a Cartesian inviscid-flow analysis package. We present the construction of a new optimization framework and we focus on the following issues: 1) Component-based geometry parameterization approach using parametric-CAD models and CAPRI. A novel geometry server is introduced that addresses the issue of parallel efficiency while only sparingly consuming CAD resources; 2) The use of genetic and gradient-based algorithms for three-dimensional aerodynamic design problems. The influence of noise on the optimization methods is studied. Our goal is to create a responsive and automated framework that efficiently identifies design modifications that result in substantial performance improvements. In addition, we examine the architectural issues associated with the deployment of a CAD-based approach in a heterogeneous parallel computing environment that contains both CAD workstations and dedicated compute engines. We demonstrate the effectiveness of the framework for a design problem that features topology changes and complex geometry.
Optimal shape and motion of undulatory swimming organisms
Tokić, Grgur; Yue, Dick K.P.
Undulatory swimming animals exhibit diverse ranges of body shapes and motion patterns and are often considered as having superior locomotory performance. The extent to which morphological traits of swimming animals have evolved owing to primarily locomotion considerations is, however, not clear. To shed some light on that question, we present here the optimal shape and motion of undulatory swimming organisms obtained by optimizing locomotive performance measures within the framework of a comb...
Isogeometric shape optimization in fluid mechanics
Nørtoft, Peter; Gravesen, Jens
steady-state, incompressible Navier-Stokes equations, governing a laminar flow in the domain, must be solved. Based on isogeometric analysis, we use B-splines as the basis for both the design optimization and the flow analysis, thereby unifying the models for geometry and analysis, and, at the same time...
Laboratory Transferability of Optimally Shaped Laser Pulses for Quantum Control
Tibbetts, Katharine Moore; Rabitz, Herschel
Optimal control experiments can readily identify effective shaped laser pulses, or "photonic reagents", that achieve a wide variety of objectives. For many practical applications, an important criterion is that a particular photonic reagent prescription still produce a good, if not optimal, target objective yield when transferred to a different system or laboratory, {even if the same shaped pulse profile cannot be reproduced exactly. As a specific example, we assess the potential for transferring optimal photonic reagents for the objective of optimizing a ratio of photoproduct ions from a family of halomethanes through three related experiments.} First, applying the same set of photonic reagents with systematically varying second- and third-order chirp on both laser systems generated similar shapes of the associated control landscape (i.e., relation between the objective yield and the variables describing the photonic reagents). Second, optimal photonic reagents obtained from the first laser system were found...
Design of pressure vessels using shape optimization: An integrated approach
Previous papers related to the optimization of pressure vessels have considered the optimization of the nozzle independently from the dished end. This approach generates problems such as thickness variation from nozzle to dished end (coupling cylindrical region) and, as a consequence, it reduces the optimality of the final result which may also be influenced by the boundary conditions. Thus, this work discusses shape optimization of axisymmetric pressure vessels considering an integrated approach in which the entire pressure vessel model is used in conjunction with a multi-objective function that aims to minimize the von-Mises mechanical stress from nozzle to head. Representative examples are examined and solutions obtained for the entire vessel considering temperature and pressure loading. It is noteworthy that different shapes from the usual ones are obtained. Even though such different shapes may not be profitable considering present manufacturing processes, they may be competitive for future manufacturing technologies, and contribute to a better understanding of the actual influence of shape in the behavior of pressure vessels. - Highlights: → Shape optimization of entire pressure vessel considering an integrated approach. → By increasing the number of spline knots, the convergence stability is improved. → The null angle condition gives lower stress values resulting in a better design. → The cylinder stresses are very sensitive to the cylinder length. → The shape optimization of the entire vessel must be considered for cylinder length.
Design of pressure vessels using shape optimization: An integrated approach
Carbonari, R.C., E-mail: firstname.lastname@example.com [Department of Mechatronic Engineering, Escola Politecnica da Universidade de Sao Paulo, Av. Prof. Mello Moraes, 2231 Sao Paulo, SP 05508-900 (Brazil); Munoz-Rojas, P.A., E-mail: firstname.lastname@example.com [Department of Mechanical Engineering, Universidade do Estado de Santa Catarina, Bom Retiro, Joinville, SC 89223-100 (Brazil); Andrade, E.Q., E-mail: firstname.lastname@example.com [CENPES, PDP/Metodos Cientificos, Petrobras (Brazil); Paulino, G.H., E-mail: firstname.lastname@example.com [Newmark Laboratory, Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, 205 North Mathews Av., Urbana, IL 61801 (United States); Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, 158 Mechanical Engineering Building, 1206 West Green Street, Urbana, IL 61801-2906 (United States); Nishimoto, K., E-mail: email@example.com [Department of Naval Architecture and Ocean Engineering, Escola Politecnica da Universidade de Sao Paulo, Av. Prof. Mello Moraes, 2231 Sao Paulo, SP 05508-900 (Brazil); Silva, E.C.N., E-mail: email@example.com [Department of Mechatronic Engineering, Escola Politecnica da Universidade de Sao Paulo, Av. Prof. Mello Moraes, 2231 Sao Paulo, SP 05508-900 (Brazil)
Previous papers related to the optimization of pressure vessels have considered the optimization of the nozzle independently from the dished end. This approach generates problems such as thickness variation from nozzle to dished end (coupling cylindrical region) and, as a consequence, it reduces the optimality of the final result which may also be influenced by the boundary conditions. Thus, this work discusses shape optimization of axisymmetric pressure vessels considering an integrated approach in which the entire pressure vessel model is used in conjunction with a multi-objective function that aims to minimize the von-Mises mechanical stress from nozzle to head. Representative examples are examined and solutions obtained for the entire vessel considering temperature and pressure loading. It is noteworthy that different shapes from the usual ones are obtained. Even though such different shapes may not be profitable considering present manufacturing processes, they may be competitive for future manufacturing technologies, and contribute to a better understanding of the actual influence of shape in the behavior of pressure vessels. - Highlights: > Shape optimization of entire pressure vessel considering an integrated approach. > By increasing the number of spline knots, the convergence stability is improved. > The null angle condition gives lower stress values resulting in a better design. > The cylinder stresses are very sensitive to the cylinder length. > The shape optimization of the entire vessel must be considered for cylinder length.
The Multipoint Global Shape Optimization of Flying Configuration with Movable Leading Edges Flaps
Adriana NASTASE
Full Text Available The aerodynamical global optimized (GO shape of flying configuration (FC, at two cruising Mach numbers, can be realized by morphing. Movable leading edge flaps are used for this purpose. The equations of the surfaces of the wing, of the fuselage and of the flaps in stretched position are approximated in form of superpositions of homogeneous polynomes in two variables with free coefficients. These coefficients together with the similarity parameters of the planform of the FC are the free parameters of the global optimization. Two enlarged variational problems with free boundaries occur. The first one consists in the determination of the GO shape of the wing-fuselageFC, with the flaps in retracted position, which must be of minimum drag, at higher cruising Mach number. The second enlarged variational problem consists in the determination of the GO shape of the flaps in stretched position in such a manner that the entire FC shall be of minimum drag at the second lower Mach number. The iterative optimum-optimorum (OO theory of the author is used for the solving of these both enlarged variational problems. The inviscid GO shape of the FC is used only in the first step of iteration and the own developed hybrid solutions for the compressible Navier-Stokes partial-differential equations (PDEs are used for the determination of the friction drag coefficient and up the second step of iteration of OO theory.
The Optimal Shape of a Javelin
Farjoun, Yossi
The problem of finding the optimal tapering of a free (non-supported) javelin is described and solved. For the optimal javelin, the lowest mode of vibration has the highest possible frequency. With this tapering inner damping will lead to the cessation of the vibration at the fastest possible rate. The javelin is modeled as a beam of uniform material. The differential equations governing the vibration and the tapering of the beam are derived. These equations have a difficult singularity at the tips of the beam. A procedure using a similarity solution is used to solve this singular system, and the solution is found. The maximal frequency is found to be almost 5 times larger than the frequency of a cylindrical rod.
Reentry-Vehicle Shape Optimization Using a Cartesian Adjoint Method and CAD Geometry
Nemec, Marian; Aftosmis, Michael J.
A DJOINT solutions of the governing flow equations are becoming increasingly important for the development of efficient analysis and optimization algorithms. A well-known use of the adjoint method is gradient-based shape. Given an objective function that defines some measure of performance, such as the lift and drag functionals, its gradient is computed at a cost that is essentially independent of the number of design variables (e.g., geometric parameters that control the shape). Classic aerodynamic applications of gradient-based optimization include the design of cruise configurations for transonic and supersonic flow, as well as the design of high-lift systems. are perhaps the most promising approach for addressing the issues of flow solution automation for aerodynamic design problems. In these methods, the discretization of the wetted surface is decoupled from that of the volume mesh. This not only enables fast and robust mesh generation for geometry of arbitrary complexity, but also facilitates access to geometry modeling and manipulation using parametric computer-aided design (CAD). In previous work on Cartesian adjoint solvers, Melvin et al. developed an adjoint formulation for the TRANAIR code, which is based on the full-potential equation with viscous corrections. More recently, Dadone and Grossman presented an adjoint formulation for the two-dimensional Euler equations using a ghost-cell method to enforce the wall boundary conditions. In Refs. 18 and 19, we presented an accurate and efficient algorithm for the solution of the adjoint Euler equations discretized on Cartesian meshes with embedded, cut-cell boundaries. Novel aspects of the algorithm were the computation of surface shape sensitivities for triangulations based on parametric-CAD models and the linearization of the coupling between the surface triangulation and the cut-cells. The accuracy of the gradient computation was verified using several three-dimensional test cases, which included design
Numerical simulation of ridge ice shapes on airfoil aerodynamics%冰脊对翼型气动特性影响的数值模拟研究
周莉; 徐浩军; 杨哲; 蔡军
Ridge ice can severely deteriorate the airfoil' s aerodynamic performance. Numerical simulation was conducted to determine the effect of simulated upper-surface spanwise ice shapes such as ice-shape location, ice-shape size and Reynolds number on airfoil aerodynamics. The simulation results show that decreases of lift coefficient and stall angle of attack as well as increases of drag coefficient can be caused by ridge ice. Besides, the effect of ice-shape windward on aerodynamic coefficients is greater than downstream ice-shape. In particular, the upper surface critical ice-shape location tended to be in between the location of minimum pressure and the location of the most adverse pressure gradient. With the increment of ice-shape size, effect on airfoil aerodynamics also increases. However, change of airfoil aerodynamics under different Reynolds number is slight.%冰脊会造成翼型气动性能严重损失.在不同的冰脊形状、弦向位置、冰脊高度和雷诺数条件下,对翼型气动特性进行r数值模拟研究.仿真结果表明:出现冰脊后,翼型的升力系数下降、失速迎角减小且阻力系数增大;冰脊迎风面形状对气动系数的影响比冰脊下游形状的影响更大;冰脊最危险的弦向位置在最小压力区与最大逆压梯度区之间;冰脊越高对翼型气动特性的影响越大,而不同雷诺数下翼型气动特性变化并不明显.
Three-dimensional shape optimization using boundary element method
Yamazaki, Koetsu; Sakamoto, Jiro; Kitano, Masami
A practical design sensitivity calculation technique of displacements and stresses for three-dimensional bodies based on the direct differentiation method of discrete boundary integral equations is formulated in detail. Then, the sensitivity calculation technique is applied to determine optimum shapes of minimum weight subjected to stress constraints, where an approximated subproblem is constructed repeatedly and solved sequentially by the mathematical programming method. The shape optimization technique suggested here is applied to determine optimum shapes of a cavity shape in a cube and a connecting rod.
ROBUST (Rotorcraft Blade Universal Shape Transformation) System for Controlled Aerodynamic Warping Project
National Aeronautics and Space Administration — In rotorcraft flight dynamics, optimized warping camber/twist change is a potentially enabling technology for improved overall rotorcraft performance. Recent...
Shape optimization of a sodium cooled fast reactor
Schmitt, Damien; Allaire, Grégoire; Pantz, Olivier; Pozin, Nicolas
Traditional designs of sodium cooled fast reactors have a positive sodium expansion feedback. During a loss of flow transient without scram, sodium heating and boiling thus insert a positive reactivity and prevents the power from decreasing. Recent studies led at CEA, AREVA and EDF show that cores with complex geometries can feature a very low or even a negative sodium void worth.(1, 2) Usual optimization methods for core conception are based on a parametric description of a given core design(3).(4) New core concepts and shapes can then only be found by hand. Shape optimization methods have proven very efficient in the conception of optimal structures under thermal or mechanical constraints.(5, 6) First studies show that these methods could be applied to sodium cooled core conception.(7) In this paper, a shape optimization method is applied to the conception of a sodium cooled fast reactor core with low sodium void worth. An objective function to be minimized is defined. It includes the reactivity change induced by a 1% sodium density decrease. The optimization variable is a displacement field changing the core geometry from one shape to another. Additionally, a parametric optimization of the plutonium content distribution of the core is made, so as to ensure that the core is kept critical, and that the power shape is flat enough. The final shape obtained must then be adjusted to a get realistic core layout. Its caracteristics can be checked with reference neutronic codes such as ERANOS. Thanks to this method, new shapes of reactor cores could be inferred, and lead to new design ideas.
An improved adaptive sampling and experiment design method for aerodynamic optimization
Huang Jiangtao
Full Text Available Experiment design method is a key to construct a highly reliable surrogate model for numerical optimization in large-scale project. Within the method, the experimental design criterion directly affects the accuracy of the surrogate model and the optimization efficient. According to the shortcomings of the traditional experimental design, an improved adaptive sampling method is proposed in this paper. The surrogate model is firstly constructed by basic sparse samples. Then the supplementary sampling position is detected according to the specified criteria, which introduces the energy function and curvature sampling criteria based on radial basis function (RBF network. Sampling detection criteria considers both the uniformity of sample distribution and the description of hypersurface curvature so as to significantly improve the prediction accuracy of the surrogate model with much less samples. For the surrogate model constructed with sparse samples, the sample uniformity is an important factor to the interpolation accuracy in the initial stage of adaptive sampling and surrogate model training. Along with the improvement of uniformity, the curvature description of objective function surface gradually becomes more important. In consideration of these issues, crowdness enhance function and root mean square error (RMSE feedback function are introduced in C criterion expression. Thus, a new sampling method called RMSE and crowdness enhance (RCE adaptive sampling is established. The validity of RCE adaptive sampling method is studied through typical test function firstly and then the airfoil/wing aerodynamic optimization design problem, which has high-dimensional design space. The results show that RCE adaptive sampling method not only reduces the requirement for the number of samples, but also effectively improves the prediction accuracy of the surrogate model, which has a broad prospects for applications.
Shape Optimization of Vehicle Radiator Using Computational Fluid Dynamics (cfd)
Maddipatla, Sridhar; Guessous, Laila
Automotive manufacturers need to improve the efficiency and lifetime of all engine components. In the case of radiators, performance depends significantly on coolant flow homogeneity across the tubes and overall pressure drop between the inlet and outlet. Design improvements are especially needed in tube-flow uniformity to prevent premature fouling and failure of heat exchangers. Rather than relying on ad-hoc geometry changes, the current study combines Computational Fluid Dynamics with shape optimization methods to improve radiator performance. The goal is to develop an automated suite of virtual tools to assist in radiator design. Two objective functions are considered: a flow non-uniformity coefficient,Cf, and the overall pressure drop, dP*. The methodology used to automate the CFD and shape optimization procedures is discussed. In the first phase, single and multi-variable optimization methods, coupled with CFD, are applied to simplified 2-D radiator models to investigate effects of inlet and outlet positions on the above functions. The second phase concentrates on CFD simulations of a simplified 3-D radiator model. The results, which show possible improvements in both pressure and flow uniformity, validate the optimization criteria that were developed, as well as the potential of shape optimization methods with CFD to improve heat exchanger design. * Improving Radiator Design Through Shape Optimization, L. Guessous and S. Maddipatla, Paper # IMECE2002-33888, Proceedings of the 2002 ASME International Mechanical Engineering Congress and Exposition, November 2002
Computational Aerodynamic Analysis of Three-Dimensional Ice Shapes on a NACA 23012 Airfoil
Jun, GaRam; Oliden, Daniel; Potapczuk, Mark G.; Tsao, Jen-Ching
The present study identifies a process for performing computational fluid dynamic calculations of the flow over full three-dimensional (3D) representations of complex ice shapes deposited on aircraft surfaces. Rime and glaze icing geometries formed on a NACA23012 airfoil were obtained during testing in the NASA Glenn Research Centers Icing Research Tunnel (IRT). The ice shape geometries were scanned as a cloud of data points using a 3D laser scanner. The data point clouds were meshed using Geomagic software to create highly accurate models of the ice surface. The surface data was imported into Pointwise grid generation software to create the CFD surface and volume grids. It was determined that generating grids in Pointwise for complex 3D icing geometries was possible using various techniques that depended on the ice shape. Computations of the flow fields over these ice shapes were performed using the NASA National Combustion Code (NCC). Results for a rime ice shape for angle of attack conditions ranging from 0 to 10 degrees and for freestream Mach numbers of 0.10 and 0.18 are presented. For validation of the computational results, comparisons were made to test results from rapid-prototype models of the selected ice accretion shapes, obtained from a separate study in a subsonic wind tunnel at the University of Illinois at Urbana-Champaign. The computational and experimental results were compared for values of pressure coefficient and lift. Initial results show fairly good agreement for rime ice accretion simulations across the range of conditions examined. The glaze ice results are promising but require some further examination.
Shape optimization of rigid inclusions for elastic plates with cracks
Shcherbakov, Viktor
In the paper, we consider an optimal control problem of finding the most safe rigid inclusion shapes in elastic plates with cracks from the viewpoint of the Griffith rupture criterion. We make use of a general Kirchhoff-Love plate model with both vertical and horizontal displacements, and nonpenetration conditions are fulfilled on the crack faces. The dependence of the first derivative of the energy functional with respect to the crack length on regular shape perturbations of the rigid inclusion is analyzed. It is shown that there exists a solution of the optimal control problem.
Three-dimensional shape optimization using the boundary element method
Yamazaki, Koetsu; Sakamoto, Jiro; Kitano, Masami
A practical design sensitivity calculation technique of displacements and stresses for three-dimensional bodies based on the direct differentiation method of discrete boundary integral equations is formulated in detail. Then the sensitivity calculation technique is applied to determine optimum shapes of minimum weight subjected to stress constraints, where an approximated subproblem is constructed repeatedly and solved sequentially by the mathematical programming method. The shape optimization technique suggested here is applied to determine optimum shapes of a cavity in a cube and a connecting rod.
Adjoint Algorithm for CAD-Based Shape Optimization Using a Cartesian Method
Nemec, Marian; Aftosmis, Michael J.
Adjoint solutions of the governing flow equations are becoming increasingly important for the development of efficient analysis and optimization algorithms. A well-known use of the adjoint method is gradient-based shape optimization. Given an objective function that defines some measure of performance, such as the lift and drag functionals, its gradient is computed at a cost that is essentially independent of the number of design variables (geometric parameters that control the shape). More recently, emerging adjoint applications focus on the analysis problem, where the adjoint solution is used to drive mesh adaptation, as well as to provide estimates of functional error bounds and corrections. The attractive feature of this approach is that the mesh-adaptation procedure targets a specific functional, thereby localizing the mesh refinement and reducing computational cost. Our focus is on the development of adjoint-based optimization techniques for a Cartesian method with embedded boundaries.12 In contrast t o implementations on structured and unstructured grids, Cartesian methods decouple the surface discretization from the volume mesh. This feature makes Cartesian methods well suited for the automated analysis of complex geometry problems, and consequently a promising approach to aerodynamic optimization. Melvin et developed an adjoint formulation for the TRANAIR code, which is based on the full-potential equation with viscous corrections. More recently, Dadone and Grossman presented an adjoint formulation for the Euler equations. In both approaches, a boundary condition is introduced to approximate the effects of the evolving surface shape that results in accurate gradient computation. Central to automated shape optimization algorithms is the issue of geometry modeling and control. The need to optimize complex, "real-life" geometry provides a strong incentive for the use of parametric-CAD systems within the optimization procedure. In previous work, we presented
Isogeometric shape optimization of photonic crystals via Coons patches
Qian, Xiaoping; Sigmund, Ole
In this paper, we present an approach that extends isogeometric shape optimization from optimization of rectangular-like NURBS patches to the optimization of topologically complex geometries. We have successfully applied this approach in designing photonic crystals where complex geometries have...... of multiple patches is motivated by the need for representing topologically complex geometries. The Coons patches are used as a design representation so that designers do not need to specify interior control points and they provide a mechanism to compute analytical sensitivities for internal nodes in...
Combined shape and topology optimization of 3D structures
Christiansen, Asger Nyman; Bærentzen, Jakob Andreas; Nobel-Jørgensen, Morten;
We present a method for automatic generation of 3D models based on shape and topology optimization. The optimization procedure, or model generation process, is initialized by a set of boundary conditions, an objective function, constraints and an initial structure. Using this input, the method will...... automatically deform and change the topology of the initial structure such that the objective function is optimized subject to the specified constraints and boundary conditions. For example, this tool can be used to improve the stiffness of a structure before printing, reduce the amount of material needed to...
基于改进粒子群算法的参数化机翼气动优化%Aerodynamic Optimization for Parameterized Wing Based on Improved Particle-Swarm-Optimization Algorithm
金鑫; 孙刚
Aerodynamic drag reduction design is the key to the design of civil aircraft. To solve the drag reduction problem of wing a new method was proposed based on non-uniform B-spline modeling technology and an improved particle swarm optimization(PSO) algorithm. The former was used to describe the wing shapes with small amount of calculation: it not only had good local control of shape, but also ensured the overall appearance of smoothness; the latter, as a new intelligent optimization method, had fast convergence ability and global search ability for multi-objective optimization problems. The results showed that cubic non-uniform B-spline curves and bi-cubic non-uniform B-spline surface could describe the airfoil and wing shapes more accurately with fewer control points, and the efficiency of multi-objective aerodynamic optimization had been improved. Even for the airfoil and wing with high efficiency factor, aerodynamic performance also made a further increase.%机翼减阻设计是民用客机气动设计的关键,本文提出了一种基于非均匀B样条曲线曲面造型技术和改进的粒子群算法的新型优化方法.前者用来描述机翼的外形,具有计算量小的优点,在优化过程中不仅具有良好的局部操控性,又能保证整体外形的光顺性;后者作为一种新兴的智能化优化方法,具有简单易行、收敛速度快、全局搜索能力强等优点,同时又适用于多目标优化问题.研究结果表明:三次非均匀B样条曲线曲面能够方便地使用较少的控制顶点较为精确地描述翼型及机翼的外形,在此基础上利用改进的粒子群算法进行的多目标气动优化设计,优化效率得到了提升.在效率因子本身较高的初始外形基础上,最终外形的气动性能也取得了较大幅度的提高.
Laboratory transferability of optimally shaped laser pulses for quantum control
Optimal control experiments can readily identify effective shaped laser pulses, or "photonic reagents," that achieve a wide variety of objectives. An important additional practical desire is for photonic reagent prescriptions to produce good, if not optimal, objective yields when transferred to a different system or laboratory. Building on general experience in chemistry, the hope is that transferred photonic reagent prescriptions may remain functional even though all features of a shaped pulse profile at the sample typically cannot be reproduced exactly. As a specific example, we assess the potential for transferring optimal photonic reagents for the objective of optimizing a ratio of photoproduct ions from a family of halomethanes through three related experiments. First, applying the same set of photonic reagents with systematically varying second- and third-order chirp on both laser systems generated similar shapes of the associated control landscape (i.e., relation between the objective yield and the variables describing the photonic reagents). Second, optimal photonic reagents obtained from the first laser system were found to still produce near optimal yields on the second laser system. Third, transferring a collection of photonic reagents optimized on the first laser system to the second laser system reproduced systematic trends in photoproduct yields upon interaction with the homologous chemical family. These three transfers of photonic reagents are demonstrated to be successful upon paying reasonable attention to overall laser system characteristics. The ability to transfer photonic reagents from one laser system to another is analogous to well-established utilitarian operating procedures with traditional chemical reagents. The practical implications of the present results for experimental quantum control are discussed
Shape Optimization Of Front Axle Support Of Tractor
Shree Dewangan
Full Text Available The front axle support of tractor is the part of tractor which holds the engine of tractor and also gives support to it and lies between engine and front axle of tractor. According to the present market demand of off highway vehicle the low cost and light weight vehicle is in demand to fulfill the requirement of cost efficient vehicle. In this paper analysis of front axle support is done for study of stress generated in the component and then after optimization of its shape and according to the shape its weight will also reduced. Considering the effect of forces acted on such a heavy parts in tractor designed by casting having dynamic loads of less frequency with greater amplitude may cause great damage to the component. According to the production techniques of components in tractor front axle requires a properly designed support with high stiffness. The design of component was modeled in Creo parametric 2.0 and the analysis was performed in solid works. Shape optimization technique is used for performing optimization cause miserable reduction in weight of connecting rod. The optimized component is 10.35% lighter compare to initial design.
Optimization of endwall contouring in axial compressor S-shaped ducts
Jin Donghai
Full Text Available This paper presents a numerical investigation of the potential aerodynamic benefits of using endwall contouring in a fairly aggressive duct with six struts based on the platform for endwall design optimization. The platform is constructed by integrating adaptive genetic algorithm (AGA, design of experiments (DOE, response surface methodology (RSM based on the artificial neural network (ANN, and a 3D Navier–Stokes solver. The visual analysis method based on DOE is used to define the design space and analyze the impact of the design parameters on the target function (response. Optimization of the axisymmetric and the non-axisymmetric endwall contouring in an S-shaped duct is performed and evaluated to minimize the total pressure loss. The optimal ducts are found to reduce the hub corner separation and suppress the migration of the low momentum fluid. The non-axisymmetric endwall contouring is shown to remove the separation completely and reduce the net duct loss by 32.7%.
Fin shape thermal optimization using Bejan's constuctal theory
Lorenzini, Giulio
The book contains research results obtained by applying Bejan's Constructal Theory to the study and therefore the optimization of fins, focusing on T-shaped and Y-shaped ones. Heat transfer from finned surfaces is an example of combined heat transfer natural or forced convection on the external parts of the fin, and conducting along the fin. Fin's heat exchange is rather complex, because of variation of both temperature along the fin and convective heat transfer coefficient. Furthermore possible presence of more fins invested by the same fluid flow has to be considered.Classical fin theory tri
Optimization on shape curves with application to specular stereo
Balzer, Jonathan
We state that a one-dimensional manifold of shapes in 3-space can be modeled by a level set function. Finding a minimizer of an independent functional among all points on such a shape curve has interesting applications in computer vision. It is shown how to replace the commonly encountered practice of gradient projection by a projection onto the curve itself. The outcome is an algorithm for constrained optimization, which, as we demonstrate theoretically and numerically, provides some important benefits in stereo reconstruction of specular surfaces. © 2010 Springer-Verlag.
Rotor Cascade Shape Optimization with Unsteady Passing Wakes Using Implicit Dual-Time Stepping and a Genetic Algorithm
Eun Seok Lee
Full Text Available An axial turbine rotor cascade-shape optimization with unsteady passing wakes was performed to obtain an improved aerodynamic performance using an unsteady flow, Reynolds-averaged Navier-Stokes equations solver that was based on explicit, finite difference; Runge-Kutta multistage time marching; and the diagonalized alternating direction implicit scheme. The code utilized Baldwin-Lomax algebraic and k-ε turbulence modeling. The full approximation storage multigrid method and preconditioning were implemented as iterative convergence-acceleration techniques. An implicit dual-time stepping method was incorporated in order to simulate the unsteady flow fields. The objective function was defined as minimization of total pressure loss and maximization of lift, while the mass flow rate was fixed during the optimization. The design variables were several geometric parameters characterizing airfoil leading edge, camber, stagger angle, and inter-row spacing. The genetic algorithm was used as an optimizer, and the penalty method was introduced for combining the constraints with the objective function. Each individual's objective function was computed simultaneously by using a 32-processor distributedmemory computer. The optimization results indicated that only minor improvements are possible in unsteady rotor/stator aerodynamics by varying these geometric parameters.
Novel Strategies for Aerodynamic Performance Improvement of Wind Turbines in Turbulent Flow
Al-Abadi, Ali
In this thesis, the influence of the turbulence on the performance of the Horizontal Axis Wind Turbine (HAWT) has been investigated. For that numerical optimizations for aerodynamic shape design, pitch-control, analysis and semi-empirical performance predictions are developed. These methods are numerically and experimentally validated. First, a turbine Torque-Matched Aerodynamic Shape Optimization method (TMASO) which maximizes the power while matching the drive unit torque has been develo...
Optimal boundary conditions at the staircase-shaped coastlines
Kazantsev, Eugene
A 4D-Var data assimilation technique is applied to the rectangular-box configuration of the NEMO in order to identify the optimal parametrization of boundary conditions at lateral boundaries. The case of the staircase-shaped coastlines is studied by rotating the model grid around the center of the box. It is shown that, in some cases, the formulation of the boundary conditions at the exact boundary leads to appearance of exponentially growing modes while optimal boundary conditions allow to correct the errors induced by the staircase-like appriximation of the coastline.
Shape optimization for Stokes problem with threshold slip
Haslinger, J.; Stebel, Jan; Taoufik, S.
Roč. 59, č. 6 (2014), s. 631-652. ISSN 0862-7940 R&D Projects: GA ČR GA201/09/0917; GA ČR(CZ) GAP201/12/0671 Institutional support: RVO:67985840 Keywords : Stokes problem * friction boundary condition * shape optimization Subject RIV: BA - General Mathematics Impact factor: 0.400, year: 2014 http://link.springer.com/article/10.1007%2Fs10492-014-0077-z
Irregular Shaped Building Design Optimization with Building Information Modelling
Lee Xia Sheng
Full Text Available This research is to recognise the function of Building Information Modelling (BIM in design optimization for irregular shaped buildings. The study focuses on a conceptual irregular shaped "twisted" building design similar to some existing sculpture-like architectures. Form and function are the two most important aspects of new buildings, which are becoming more sophisticated as parts of equally sophisticated "systems" that we are living in. Nowadays, it is common to have irregular shaped or sculpture-like buildings which are very different when compared to regular buildings. Construction industry stakeholders are facing stiff challenges in many aspects such as buildability, cost effectiveness, delivery time and facility management when dealing with irregular shaped building projects. Building Information Modelling (BIM is being utilized to enable architects, engineers and constructors to gain improved visualization for irregular shaped buildings; this has a purpose of identifying critical issues before initiating physical construction work. In this study, three variations of design options differing in rotating angle: 30 degrees, 60 degrees and 90 degrees are created to conduct quantifiable comparisons. Discussions are focused on three major aspects including structural planning, usable building space, and structural constructability. This research concludes that Building Information Modelling is instrumental in facilitating design optimization for irregular shaped building. In the process of comparing different design variations, instead of just giving "yes or no" type of response, stakeholders can now easily visualize, evaluate and decide to achieve the right balance based on their own criteria. Therefore, construction project stakeholders are empowered with superior evaluation and decision making capability.
Preliminary Assessment of Optimal Longitudinal-Mode Control for Drag Reduction through Distributed Aeroelastic Shaping
Ippolito, Corey; Nguyen, Nhan; Lohn, Jason; Dolan, John
The emergence of advanced lightweight materials is resulting in a new generation of lighter, flexible, more-efficient airframes that are enabling concepts for active aeroelastic wing-shape control to achieve greater flight efficiency and increased safety margins. These elastically shaped aircraft concepts require non-traditional methods for large-scale multi-objective flight control that simultaneously seek to gain aerodynamic efficiency in terms of drag reduction while performing traditional command-tracking tasks as part of a complete guidance and navigation solution. This paper presents results from a preliminary study of a notional multi-objective control law for an aeroelastic flexible-wing aircraft controlled through distributed continuous leading and trailing edge control surface actuators. This preliminary study develops and analyzes a multi-objective control law derived from optimal linear quadratic methods on a longitudinal vehicle dynamics model with coupled aeroelastic dynamics. The controller tracks commanded attack-angle while minimizing drag and controlling wing twist and bend. This paper presents an overview of the elastic aircraft concept, outlines the coupled vehicle model, presents the preliminary control law formulation and implementation, presents results from simulation, provides analysis, and concludes by identifying possible future areas for research
Shape Memory as a Process: Optimizing Polymer Design for Shape Recovery
Vaia, Richard; Koerner, Hilmar; Lee, Kyungmin; Strong, Robert; Smith, Mattew; Wang, Huabin; White, Tim; Tan, Loon-Seng
Shape memory is a process that enables the reversible storage and recovery of mechanical energy through a change in shape. Polymers provide a unique alternative to kinematic designs and other materials (e.g. metallic alloys) for applications requiring large deformation and novel control options. The effect control of storage and relaxation of strain energy associated with chain deformation depends on the nonlinear visco-elasitc behavior and glassy dynamics of the polymer network. Considering the molecular understanding of rubbery elasticity, chain entanglements in concentrated polymer liquids, affine deformation of networks, and glass fragility, heuristic guidelines can be formulated to optimize the molecular design of a polymer for shape memory. These are applied to the development of a polymer system for shape memory processes at high-temperature (200^oC). The low-crosslink density polyimide exhibits very rapid shape recovery, excellent fixity, high creep resistance, and good cyclability. Furthermore, the molecular design affords a very narrow temperature range for programming and triggering shape change that can also be accessed by photo-isomerization of the cross-link nodes.
Shape optimization of draft tubes for Agnew microhydro turbines
Highlights: • The draft tube of Agnew microhydro turbine was optimized. • Pareto optimal solutions were determined by neural networks and NSGA-II algorithm. • The pressure recovery factor increases with height and angle over design ranges. • The loss coefficient reaches the minimum values at angles about 2o. • Swirl of the incoming flow has great influence on the optimization results. - Abstract: In this study, the shape optimization of draft tubes utilized in Agnew type microhydro turbines has been discussed. The design parameters of the draft tube such as the cone angle and the height above the tailrace are considered in defining an optimization problem whose goal is to maximize the pressure recovery factor and minimize the energy loss coefficient of flow. The design space is determined by considering the experimental constraints and parameterized by the method of face-centered uniform ascertain distribution. The numerical simulations are performed using the boundary conditions found from laboratory tests and the obtained results are analyzed to create and validate a feed-forward neural network model, which is implemented as a surrogate model. The optimal Pareto solutions are finally determined using the NSGA-II evolutionary algorithm and compared for different inlet conditions. The results predict that the high swirl of the incoming flow drastically reduces the performance of the draft tube
Simultaneous beam sampling and aperture shape optimization for SPORT
Purpose: Station parameter optimized radiation therapy (SPORT) was recently proposed to fully utilize the technical capability of emerging digital linear accelerators, in which the station parameters of a delivery system, such as aperture shape and weight, couch position/angle, gantry/collimator angle, can be optimized simultaneously. SPORT promises to deliver remarkable radiation dose distributions in an efficient manner, yet there exists no optimization algorithm for its implementation. The purpose of this work is to develop an algorithm to simultaneously optimize the beam sampling and aperture shapes. Methods: The authors build a mathematical model with the fundamental station point parameters as the decision variables. To solve the resulting large-scale optimization problem, the authors devise an effective algorithm by integrating three advanced optimization techniques: column generation, subgradient method, and pattern search. Column generation adds the most beneficial stations sequentially until the plan quality improvement saturates and provides a good starting point for the subsequent optimization. It also adds the new stations during the algorithm if beneficial. For each update resulted from column generation, the subgradient method improves the selected stations locally by reshaping the apertures and updating the beam angles toward a descent subgradient direction. The algorithm continues to improve the selected stations locally and globally by a pattern search algorithm to explore the part of search space not reachable by the subgradient method. By combining these three techniques together, all plausible combinations of station parameters are searched efficiently to yield the optimal solution. Results: A SPORT optimization framework with seamlessly integration of three complementary algorithms, column generation, subgradient method, and pattern search, was established. The proposed technique was applied to two previously treated clinical cases: a head and
Simultaneous beam sampling and aperture shape optimization for SPORT
Zarepisheh, Masoud; Li, Ruijiang; Xing, Lei, E-mail: email@example.com [Department of Radiation Oncology, Stanford University, Stanford, California 94305 (United States); Ye, Yinyu [Department of Management Science and Engineering, Stanford University, Stanford, California 94305 (United States)
Purpose: Station parameter optimized radiation therapy (SPORT) was recently proposed to fully utilize the technical capability of emerging digital linear accelerators, in which the station parameters of a delivery system, such as aperture shape and weight, couch position/angle, gantry/collimator angle, can be optimized simultaneously. SPORT promises to deliver remarkable radiation dose distributions in an efficient manner, yet there exists no optimization algorithm for its implementation. The purpose of this work is to develop an algorithm to simultaneously optimize the beam sampling and aperture shapes. Methods: The authors build a mathematical model with the fundamental station point parameters as the decision variables. To solve the resulting large-scale optimization problem, the authors devise an effective algorithm by integrating three advanced optimization techniques: column generation, subgradient method, and pattern search. Column generation adds the most beneficial stations sequentially until the plan quality improvement saturates and provides a good starting point for the subsequent optimization. It also adds the new stations during the algorithm if beneficial. For each update resulted from column generation, the subgradient method improves the selected stations locally by reshaping the apertures and updating the beam angles toward a descent subgradient direction. The algorithm continues to improve the selected stations locally and globally by a pattern search algorithm to explore the part of search space not reachable by the subgradient method. By combining these three techniques together, all plausible combinations of station parameters are searched efficiently to yield the optimal solution. Results: A SPORT optimization framework with seamlessly integration of three complementary algorithms, column generation, subgradient method, and pattern search, was established. The proposed technique was applied to two previously treated clinical cases: a head and
In-Space Radiator Shape Optimization using Genetic Algorithms
Hull, Patrick V.; Kittredge, Ken; Tinker, Michael; SanSoucie, Michael
Future space exploration missions will require the development of more advanced in-space radiators. These radiators should be highly efficient and lightweight, deployable heat rejection systems. Typical radiators for in-space heat mitigation commonly comprise a substantial portion of the total vehicle mass. A small mass savings of even 5-10% can greatly improve vehicle performance. The objective of this paper is to present the development of detailed tools for the analysis and design of in-space radiators using evolutionary computation techniques. The optimality criterion is defined as a two-dimensional radiator with a shape demonstrating the smallest mass for the greatest overall heat transfer, thus the end result is a set of highly functional radiator designs. This cross-disciplinary work combines topology optimization and thermal analysis design by means of a genetic algorithm The proposed design tool consists of the following steps; design parameterization based on the exterior boundary of the radiator, objective function definition (mass minimization and heat loss maximization), objective function evaluation via finite element analysis (thermal radiation analysis) and optimization based on evolutionary algorithms. The radiator design problem is defined as follows: the input force is a driving temperature and the output reaction is heat loss. Appropriate modeling of the space environment is added to capture its effect on the radiator. The design parameters chosen for this radiator shape optimization problem fall into two classes, variable height along the width of the radiator and a spline curve defining the -material boundary of the radiator. The implementation of multiple design parameter schemes allows the user to have more confidence in the radiator optimization tool upon demonstration of convergence between the two design parameter schemes. This tool easily allows the user to manipulate the driving temperature regions thus permitting detailed design of in
Methods for the design and optimization of shaped tokamaks
Two major questions associated with the design and optimization of shaped tokamaks are considered. How do physics and engineering constraints affect the design of shaped tokamaks? How can the process of designing shaped tokamaks be improved? The first question is addressed with the aid of a completely analytical procedure for optimizing the design of a resistive-magnet tokamak reactor. It is shown that physics constraints---particularly the MHD beta limits and the Murakami density limit---have an enormous, and sometimes, unexpected effect on the final design. The second question is addressed through the development of a series of computer models for calculating plasma equilibria, estimating poloidal field coil currents, and analyzing axisymmetric MHD stability in the presence of resistive conductors and feedback. The models offer potential advantages over conventional methods since they are characterized by extremely fast computer execution times, simplicity, and robustness. Furthermore, evidence is presented that suggests that very little loss of accuracy is required to achieve these desirable features. 94 refs., 66 figs., 14 tabs
Optimizing water permeability through the hourglass shape of aquaporins.
Gravelle, Simon; Joly, Laurent; Detcheverry, François; Ybert, Christophe; Cottin-Bizonne, Cécile; Bocquet, Lydéric
The ubiquitous aquaporin channels are able to conduct water across cell membranes, combining the seemingly antagonist functions of a very high selectivity with a remarkable permeability. Whereas molecular details are obvious keys to perform these tasks, the overall efficiency of transport in such nanopores is also strongly limited by viscous dissipation arising at the connection between the nanoconstriction and the nearby bulk reservoirs. In this contribution, we focus on these so-called entrance effects and specifically examine whether the characteristic hourglass shape of aquaporins may arise from a geometrical optimum for such hydrodynamic dissipation. Using a combination of finite-element calculations and analytical modeling, we show that conical entrances with suitable opening angle can indeed provide a large increase of the overall channel permeability. Moreover, the optimal opening angles that maximize the permeability are found to compare well with the angles measured in a large variety of aquaporins. This suggests that the hourglass shape of aquaporins could be the result of a natural selection process toward optimal hydrodynamic transport. Finally, in a biomimetic perspective, these results provide guidelines to design artificial nanopores with optimal performances. PMID:24067650
Blade Shape Optimization of Liquid Turbine Flow Sensor
郭素娜; 张涛; 孙立军; 杨振; 杨文量
Based on the characteristic curve analysis, the method using 2D(K ) square difference of meter factor at different flow rates was developed to evaluate the performance of turbine flow sensor in this study. Then according to the distribution of entrance velocity, it was supposed that reducing the blade area near the tip could decrease the linearity error of a sensor. Therefore, the influence of different blade shape parameters on the performance of the sensor was investigated by combining computational fluid dynamics(CFD)simulation with experimental test. The experimental results showed that, for the liquid turbine flow sensor with a diameter of 10 mm, the linearity error was smallest, and the performance of sensor was optimal when blade shape parameter equaled 0.25.
Shape insensitive optimal adhesion of nanoscale fibrillar structures
Gao, Huajian; Yao, Haimin
Gecko and many insects have adopted nanoscale fibrillar structures on their feet as adhesion devices. Here, we consider adhesion between a single fiber and a substrate by van der Waals or electrostatic interactions. For a given contact area A, the theoretical pull-off force of the fiber is σthA where σth is the theoretical strength of adhesion. We show that it is possible to design an optimal shape of the tip of the fiber to achieve the theoretical pull-off force. However, such design tends t...
Riblets in the viscous sublayer : Optimal Shape Design of Microstructures
Friedmann, Elfriede
Previous research has established that a smooth surface has not necessarily minimal drag: Many experiments by different laboratories, e.g. NASA and DLR Berlin, indicate that an extra surface layer with tiny grooves aligned in the stream-wise direction can be used to reduce the drag. The aim of this project is to find the optimal shape of such microstructures on surfaces of submerged bodies. We assume that these microstructures remain in the viscous sublayer where the flow equations are the 3D...
Reliability-Based Shape Optimization using Stochastic Finite Element Methods
Enevoldsen, Ib; Sørensen, John Dalsgaard; Sigurdsson, G.
stochastic fields (e.g. loads and material parameters such as Young's modulus and the Poisson ratio). In this case stochastic finite element techniques combined with FORM analysis can be used to obtain measures of the reliability of the structural systems, see Der Kiureghian & Ke (6) and Liu & Der Kiureghian......Application of first-order reliability methods FORM (see Madsen, Krenk & Lind [8)) in structural design problems has attracted growing interest in recent years, see e.g. Frangopol [4), Murotsu, Kishi, Okada, Yonezawa & Taguchi [9) and Sørensen [14). In probabilistically based optimal design of...... (7). In this paper a reliability-based shape optimization problem is formulated with the total expected cost as objective function and some requirements for the reliability measures (element or systems reliability measures) as constraints, see section 2. As design variables sizing variables...
Optimization of tokamak plasma equilibrium shape using parallel genetic algorithms
In the device of non-circular cross sectional tokamaks, the plasma equilibrium shape has a strong influence on the confinement and MHD stability. The plasma equilibrium shape is determined by the configuration of the poloidal field (PF) system. Usually there are many PF systems that could support the specified plasma equilibrium, the differences are the number of coils used, their positions, sizes and currents. It is necessary to find the optimal choice that meets the engineering constrains, which is often done by a constrained optimization. The Genetic Algorithms (GAs) based method has been used to solve the problem of the optimization, but the time complexity limits the algorithms to become widely used. Due to the large search space that the optimization has, it takes several hours to get a nice result. The inherent parallelism in GAs can be exploited to enhance their search efficiency. In this paper, we introduce a parallel genetic algorithms (PGAs) based approach which can reduce the computational time. The algorithm has a master-slave structure, the slave explore the search space separately and return the results to the master. A program is also developed, and it can be running on any computers which support massage passing interface. Both the algorithm and the program are detailed discussed in the paper. We also include an application that uses the program to determine the positions and currents of PF coils in EAST. The program reach the target value within half an hour and yield a speedup rate of 5.21 on 8 CPUs. (author)
Theory and numerics for shape optimization in superconductivity
Heese, H.
We consider a mathematical model for a thin superconducting film which is magnetically shielded by permanent magnets in order to improve the current carrying capability of the film. In a first part we study the behaviour of the magnetic field of the combined system, which is characterized via a boundary value problem for Laplace's equation for the quasi-scalar magnetic potential. In a second part we formulate and analyze a related geometric optimization problem that can be interpreted as a homogenization of the current distribution in the superconducting film by means of shape optimization for the magnet boundaries. We present a uniqueness and existence analysis for the boundary value problem based on boundary integral equations. The theoretical studies are complemented by a numerical approximation scheme for the potential, for which we prove exponential convergence rates under appropriate smoothness assumptions on the geometry. As central result for the geometric optimization problem we prove the differentiable dependence of the current distribution on the geometry, which also leads to an abstract existence result. Based on the differentiability result we derive two numerical schemes to realize the geometric optimization problem iteratively. The first approach relies on explicit parametrizations for the boundaries leading to a steepest descent scheme. The second approach uses level set methods which are based on an implicit boundary representation. The feasibility of both approaches is shown in a variety of examples. (orig.)
Theory and numerics for shape optimization in superconductivity
We consider a mathematical model for a thin superconducting film which is magnetically shielded by permanent magnets in order to improve the current carrying capability of the film. In a first part we study the behaviour of the magnetic field of the combined system, which is characterized via a boundary value problem for Laplace's equation for the quasi-scalar magnetic potential. In a second part we formulate and analyze a related geometric optimization problem that can be interpreted as a homogenization of the current distribution in the superconducting film by means of shape optimization for the magnet boundaries. We present a uniqueness and existence analysis for the boundary value problem based on boundary integral equations. The theoretical studies are complemented by a numerical approximation scheme for the potential, for which we prove exponential convergence rates under appropriate smoothness assumptions on the geometry. As central result for the geometric optimization problem we prove the differentiable dependence of the current distribution on the geometry, which also leads to an abstract existence result. Based on the differentiability result we derive two numerical schemes to realize the geometric optimization problem iteratively. The first approach relies on explicit parametrizations for the boundaries leading to a steepest descent scheme. The second approach uses level set methods which are based on an implicit boundary representation. The feasibility of both approaches is shown in a variety of examples. (orig.)
Robust buckling optimization of laminated composite structures using discrete material optimization considering "worst" shape imperfections
Henrichsen, Søren Randrup; Lindgaard, Esben; Lund, Erik
Robust buckling optimal design of laminated composite structures is conducted in this work. Optimal designs are obtained by considering geometric imperfections in the optimization procedure. Discrete Material Optimization is applied to obtain optimal laminate designs. The optimal geometric...... imperfection is represented by the "worst" shape imperfection. The two optimization problems are combined through the recurrence optimization. Hereby the imperfection sensitivity of the considered structures can be studied. The recurrence optimization is demonstrated through a U-profile and a cylindrical panel...... example. The imperfection sensitivity of the optimized structure decreases during the recurrence optimization for both examples, hence robust buckling optimal structures are designed....
Blunt-body drag reduction through base cavity shape optimization
Lorite-Díez, Manuel; Jiménez-González, José Ignacio; Gutiérrez-Montes, Cándido; Martínez-Bazán, Carlos
We present a numerical study on the drag reduction of a turbulent incompressible flow around two different blunt bodies, of height H and length L, at a Reynolds number Re = ρU∞ H / μ = 2000 , where U∞ is the turbulent incompressible free-stream velocity, ρ is their density and μ their viscosity. The study is based on the optimization of the geometry of a cavity placed at the rear part of the body with the aim of increasing the base pressure. Thus, we have used an optimization algorithm, which implements the adjoint method, to compute the two-dimensional incompressible turbulent steady flow sensitivity field of axial forces on both bodies, and consequently modify the shape of the cavity to reduce the induced drag force. In addition, we have performed three dimensional numerical simulations using an IDDES model in order to analyze the drag reduction effect of the optimized cavities at higher Reynolds numbers.The results show average drag reductions of 17 and 25 % for Re=2000, as well as more regularized and less chaotic wake flows in both bodies. Supported by the Spanish MINECO, Junta de Andalucía and EU Funds under projects DPI2014-59292-C3-3-P and P11-TEP7495.
The design of missile's dome that fits both optical and aerodynamic needs
Wei, Qun; Zhang, Xin; Jia, Hongguang
Optical guidance missiles requires a dome which fits both optical and aerodynamic needs when they attack at 3 Ma. In this study, ellipse is the figure chosen to be the dome's shape. The ellipticity ɛ is the main variable should to be decided. The optimized function was built by optical and aerodynamic performance function multiply by their weights. The optical and aerodynamic functions were all obtained by computational fluid dynamic (CFD) simulation's results after normalization. In this study, the optical and aerodynamic performances have equal weights, after optimzing the ellipticity ɛis 2 for the missile.
Shaping Diffraction-Grating Grooves to Optimize Efficiency
Backlund, John; Wilson, Daniel; Mouroulis, Pantazis; Maker, Paul; Muller, Richard
A method of shaping diffraction-grating grooves to optimize the spectral efficiency, spectral range, and image quality of a spectral imaging instrument is under development. The method is based on the use of an advanced design algorithm to determine the possibly complex shape of grooves needed to obtain a desired efficiency-versus-wavelength response (see figure). Then electron- beam fabrication techniques are used to realize the required groove shape. The method could be used, for example, to make the spectral efficiency of the grating in a given wavelength range proportional to the inverse of the spectral efficiency of a photodetector array so that the overall spectral efficiency of the combination of the grating and the photodetector array would be flat. The method has thus far been applied to one-dimensional gratings only, but in principle, it is also applicable to two-dimensional gratings. The algorithm involves calculations in the spatial-frequency domain. The spatial-frequency spectrum of a grating is represented as a diffraction-order spectral-peak-width function multiplied by an efficiency function for a single grating groove. This representation affords computational efficiency and accuracy by making it possible to consider only the response from one grating groove (one period of the grating), instead of from the whole grating area, in determining the response from the entire grating. This combination of efficiency and accuracy is crucial for future extensions of the algorithm to two-dimensional designs and to designs in which polarization must also be taken into account. The algorithm begins with the definition of target values of relative efficiency that represent the desired spectral response of the grating in certain spectral frequencies calculated from the diffraction order and wavelength. The grating period is divided into a number of cells - typically, 100. The phase contribution from each cell is determined from the phase of the incident
分级型进化算法及其在翼型跨声速气动优化中的应用%Hierarchial Evolutionary Algorithms and Its Application in Transonic Airfoil Optimization in Aerodynamics
王江峰; 伍贻兆
提出了变精度模型的分级型进化算法并对初始翼型为NACA0012的二维翼型进行了跨声速流动下的形状增升优化.借鉴自然进化中不同进化阶段个体适应度评估环境不同的机理,构造了分级精度模型以加速优化过程.对翼型进行了给定气动条件下的形状增升优化,给出了优化结果,并与传统基因算法及单精度模型算法结果进行了对比.%Hierarchical evolutionary algorithms based on genetic algorithms (GAs) and Nash strategy of game theory are proposed to accelerate the optimization process and implemented in transonic aerodynamic shape optimization problems. Inspired from the natural evolution history that different periods with certain environments have different criteria for the evaluations of individuals' fitness, a hierarchical fidelity model is introduced to reach high optimization efficiency. The shape of an NACA0012 based airfoil is optimized in maximizing the lift coefficient under a given transonic flow condition. Optimized results are presented and compared with the single model results and traditional GA.
Optimization methods applied to the aerodynamic design of helicopter rotor blades
Walsh, Joanne L.; Bingham, Gene J.; Riley, Michael F.
Described is a formal optimization procedure for helicopter rotor blade design which minimizes hover horsepower while assuring satisfactory forward flight performance. The approach is to couple hover and forward flight analysis programs with a general-purpose optimization procedure. The resulting optimization system provides a systematic evaluation of the rotor blade design variables and their interaction, thus reducing the time and cost of designing advanced rotor blades. The paper discusses the basis for and details of the overall procedure, describes the generation of advanced blade designs for representative Army helicopters, and compares design and design effort with those from the conventional approach which is based on parametric studies and extensive cross-plots.
Shape Optimization of 'S' Type Load Cell Using Finite Element Method
Mr. S. M. Ghanvat; Prof. H. G. Patil
In this work 'S' type load cell is considered for shape optimization by using finite element method. The shape optimization is carried out to minimize the weight of 'S' type load cell without exceeding allowable strain. The intention of the work is to create the geometry of 'S' type load cell to find out the optimum solution. FEM software ANSYS is used for shape optimization of 'S' type load cell. If the stress
Structural and Aerodynamic Optimization of UltraLightweight Technology for Research in Astronomy (ULTRA)
Etzel, P. B.; Martin, R.; Romeo, R.; Fesen, R.; Hale, R.; Taghavi, R.; Anthony-Twarog, B. J.; Shawl, S. J.; Twarog, B. A.
The focus of ULTRA (see poster by Twarog et al.) is a three-year plan to develop and test ultralightweight technology for research applications in astronomy. The goal is to demonstrate that a viable alternative exists to traditional glass-mirror technology by designing, fabricating, and testing a research telescope prototype comprising fiber reinforced plastic (CFRP) materials. To date, several mirror designs have been tested. The main goal in the first year has been to develop a 0.4m diameter mirror and OTA that serve as prototypes for the 1m telescope design. Mirrors of 0.4m diameter have been successfully fabricated which yield diffraction limited images. This poster will include a display of the complete OTA (including optics), optics test results, and astronomical images taken with prototype mirrors. Finite element analysis has been used to evaluate the OTA and mirror designs. Preliminary design details were incorporated in a knowledge-based system. Adaptive Modeling Language (AML), an object oriented programming language developed by Technosoft, Inc., was used to develop a parameterized geometric model of the preliminary design. The system can generate mirrors with radials/circumferentials, tube core substructures, as well as modeling the support structure. Computational fluid dynamics analyses were performed for sweep, inclination and ambient wind speed. Finite element analyses were performed for core density and arrangement, skin thickness, back-surface curvature, spider configuration and arrangement of the OTA, while the loading conditions considered thus far are thermal, inertial, and aerodynamic pressure loads. Experimental tests, including ultrasonic nondestructive evaluations, infrared imaging, modal testing, and wind tunnel tests, have been performed on the first prototype mirror, with the primary goal of validating analytical models and identifying potential manufacturing induced variations to be expected among "like" mirrors. Support of this work by
Pulse shape analysis optimization with segmented HPGe-detectors
Lewandowski, Lars; Birkenbach, Benedikt; Reiter, Peter [Institute for Nuclear Physics, University of Cologne (Germany); Bruyneel, Bart [CEA, Saclay (France); Collaboration: AGATA-Collaboration
Measurements with the position sensitive, highly segmented AGATA HPGe detectors rely on the gamma-ray-tracking GRT technique which allows to determine the interaction point of the individual gamma-rays hitting the detector. GRT is based on a pulse shape analysis PSA of the preamplifier signals from the 36 segments and the central electrode of the detector. The achieved performance and position resolution of the AGATA detector is well within the specifications. However, an unexpected inhomogeneous distribution of interaction points inside the detector volume is observed as a result of the PSA even when the measurement is performed with an isotropically radiating gamma ray source. The clustering of interaction points motivated a study in order to optimize the PSA algorithm or its ingredients. Position resolution results were investigated by including contributions from differential crosstalk of the detector electronics, an improved preamplifier response function and a new time alignment. Moreover the spatial distribution is quantified by employing different χ{sup 2}-minimization procedures.
Aerodynamic Losses in Turbines with and without Film Cooling, as Influenced by Mainstream Turbulence, Surface Roughness, Airfoil Shape, and Mach Number
Phil Ligrani
Full Text Available The influences of a variety of different physical phenomena are described as they affect the aerodynamic performance of turbine airfoils in compressible, high-speed flows with either subsonic or transonic Mach number distributions. The presented experimental and numerically predicted results are from a series of investigations which have taken place over the past 32 years. Considered are (i symmetric airfoils with no film cooling, (ii symmetric airfoils with film cooling, (iii cambered vanes with no film cooling, and (iv cambered vanes with film cooling. When no film cooling is employed on the symmetric airfoils and cambered vanes, experimentally measured and numerically predicted variations of freestream turbulence intensity, surface roughness, exit Mach number, and airfoil camber are considered as they influence local and integrated total pressure losses, deficits of local kinetic energy, Mach number deficits, area-averaged loss coefficients, mass-averaged total pressure loss coefficients, omega loss coefficients, second law loss parameters, and distributions of integrated aerodynamic loss. Similar quantities are measured, and similar parameters are considered when film-cooling is employed on airfoil suction surfaces, along with film cooling density ratio, blowing ratio, Mach number ratio, hole orientation, hole shape, and number of rows of holes.
Validation of a pair of computer codes for estimation and optimization of subsonic aerodynamic performance of simple hinged-flap systems for thin swept wings
Carlson, Harry W.; Darden, Christine M.
Extensive correlations of computer code results with experimental data are employed to illustrate the use of linearized theory attached flow methods for the estimation and optimization of the aerodynamic performance of simple hinged flap systems. Use of attached flow methods is based on the premise that high levels of aerodynamic efficiency require a flow that is as nearly attached as circumstances permit. A variety of swept wing configurations are considered ranging from fighters to supersonic transports, all with leading- and trailing-edge flaps for enhancement of subsonic aerodynamic efficiency. The results indicate that linearized theory attached flow computer code methods provide a rational basis for the estimation and optimization of flap system aerodynamic performance at subsonic speeds. The analysis also indicates that vortex flap design is not an opposing approach but is closely related to attached flow design concepts. The successful vortex flap design actually suppresses the formation of detached vortices to produce a small vortex which is restricted almost entirely to the leading edge flap itself.
Aerodynamic performance of transonic and subsonic airfoils: Effects of surface roughness, turbulence intensity, Mach number, and streamline curvature-airfoil shape
Zhang, Qiang
The effects of surface roughness, turbulence intensity, Mach number, and streamline curvature-airfoil shape on the aerodynamic performance of turbine airfoils are investigated in compressible, high speed flows. The University of Utah Transonic Wind Tunnel is employed for the experimental part of the study. Two different test sections are designed to produce Mach numbers, Reynolds numbers, passage mass flow rates, and physical dimensions, which match values along turbine blades in operating engines: (i) a nonturning test section with a symmetric airfoil, and (ii) a cascade test section with a cambered turbine vane. The nonuniform, irregular, three-dimensional surface roughness is characterized using the equivalent sand grain roughness size. Changing the airfoil surface roughness condition has a substantial effect on wake profiles of total pressure loss coefficients, normalized Mach number, normalized kinetic energy, and on the normalized and dimensional magnitudes of Integrated Aerodynamic Losses produced by the airfoils. Comparisons with results for a symmetric airfoil and a cambered vane show that roughness has more substantial effects on losses produced by the symmetric airfoil than the cambered vane. Data are also provided that illustrate the larger loss magnitudes are generally present with flow turning and cambered airfoils, than with symmetric airfoils. Wake turbulence structure of symmetric airfoils and cambered vanes are also studied experimentally. The effects of surface roughness and freestream turbulence levels on wake distributions of mean velocity, turbulence intensity, and power spectral density profiles and vortex shedding frequencies are quantified one axial chord length downstream of the test airfoils. As the level of surface roughness increases, all wake profile quantities broaden significantly and nondimensional vortex shedding frequencies decrease. Wake profiles produced by the symmetric airfoil are more sensitive to variations of surface
An Optimization Approach to Improving Collections of Shape Maps
Nguyen, Andy; Ben‐Chen, Mirela; Welnicka, Katarzyna;
Finding an informative, structure‐preserving map between two shapes has been a long‐standing problem in geometry processing, involving a variety of solution approaches and applications. However, in many cases, we are given not only two related shapes, but a collection of them, and considering eac......‐of‐the‐art mapping methods on various shape databases....
Integration of Rotor Aerodynamic Optimization with the Conceptual Design of a Large Civil Tiltrotor
Acree, C. W., Jr.
Coupling of aeromechanics analysis with vehicle sizing is demonstrated with the CAMRAD II aeromechanics code and NDARC sizing code. The example is optimization of cruise tip speed with rotor/wing interference for the Large Civil Tiltrotor (LCTR2) concept design. Free-wake models were used for both rotors and the wing. This report is part of a NASA effort to develop an integrated analytical capability combining rotorcraft aeromechanics, structures, propulsion, mission analysis, and vehicle sizing. The present paper extends previous efforts by including rotor/wing interference explicitly in the rotor performance optimization and implicitly in the sizing.
Sensitivity Analysis Based Multiple Objective Preform Die Shape Optimal Design in Metal Forging
The multiple objective preform design optimization was put forward. The final forging's shape and deformation uniformity were considered in the multiple objective. The objective is to optimize the shape and the deformation uniformity of the final forging at the same time so that a more high integrate quality of the final forging can be obtained. The total objective was assembled by the shape and uniformity objective using the weight adding method. The preform die shape is presented by cubic B-spline curves. The control points of B-spline curves are used as the design variables. The forms of the total objective function, shape and uniformity sub-objective function are given. The sensitivities of the total objective function and the sub-objective functions with respect to the design variables are developed. Using this method, the preform die shape of an H-shaped forging process is optimally designed. The optimization results are very satisfactory.
Burger, Martin
In this paper, we construct a level set method for an elliptic obstacle problem, which can be reformulated as a shape optimization problem. We provide a detailed shape sensitivity analysis for this reformulation and a stability result for the shape Hessian at the optimal shape. Using the shape sensitivities, we construct a geometric gradient flow, which can be realized in the context of level set methods. We prove the convergence of the gradient flow to an optimal shape and provide a complete analysis of the level set method in terms of viscosity solutions. To our knowledge this is the first complete analysis of a level set method for a nonlocal shape optimization problem. Finally, we discuss the implementation of the methods and illustrate its behavior through several computational experiments. © 2011 World Scientific Publishing Company.
Generalized Shape and Gauge Decoupling Load Distribution Optimization Based on IGA for Tandem Cold Mill
PENG Peng; YANG Quan
Load distribution is the foundation of shape control and gauge control, in which it is necessary to take into account the shape control ability of TCM (tandem cold mill) for strip shape and gauge quality. First, the objective function of generalized shape and gauge decoupling load distribution optimization was established, which considered the rolling force characteristics of the first and last stands in TCM, the relative power, and the TCM shape control ability. Then, IGA (immune genetic algorithm) was used to accomplish this multi-objective load distribution optimization for TCM. After simulation and comparison with the practical load distribution strategy in one tandem cold mill, general-ized shape and gauge decoupling load distribution optimization on the basis of IGA approved good ability of optimizing shape control and gauge control simultaneously.
Optimization of geometrical parameters aerodynamic design aircraft articulated tandem with wings
О.В. Кузьменко
Full Text Available The features of a task of optimization of the plane with unmanned completely wing are considered the existing approaches the block diagram of mathematical model of the plane with unmanned completely wing is given in the decision of similar tasks.
Aerodynamic optimization by simultaneously updating flow variables and design parameters with application to advanced propeller designs
Rizk, Magdi H.
A scheme is developed for solving constrained optimization problems in which the objective function and the constraint function are dependent on the solution of the nonlinear flow equations. The scheme updates the design parameter iterative solutions and the flow variable iterative solutions simultaneously. It is applied to an advanced propeller design problem with the Euler equations used as the flow governing equations. The scheme's accuracy, efficiency and sensitivity to the computational parameters are tested.
Optimal choice of trapezoidal shaping parameters in digital nuclear spectrometer system
Trapezoidal shaping method is widely applied to pulse amplitude extraction in digital nuclear spectrometer system, the optimal selection of the shaping parameters can improve the energy resolution and pulse counting rate. From the view of noise characteristics, ballistic deficit compensation characteristics and pulse pile-up characteristics, in this paper the optimal selection of the trapezoidal shaping parameters is studied on. According to the theoretical analysis and experimental verification, the optimal choice of trapezoidal shaping parameters is similar to the triangle, the rise time is longer and the flat-top width is shorter. (authors)
Shape Optimization for Navier-Stokes Equations with Algebraic Turbulence Model: Existence Analysis
We study a shape optimization problem for the paper machine headbox which distributes a mixture of water and wood fibers in the paper making process. The aim is to find a shape which a priori ensures the given velocity profile on the outlet part. The mathematical formulation leads to an optimal control problem in which the control variable is the shape of the domain representing the header, the state problem is represented by a generalized stationary Navier-Stokes system with nontrivial mixed boundary conditions. In this paper we prove the existence of solutions both to the generalized Navier-Stokes system and to the shape optimization problem
Optimizing coherent anti-Stokes Raman scattering by genetic algorithm controlled pulse shaping
Yang, Wenlong; Sokolov, Alexei
The hybrid coherent anti-Stokes Raman scattering (CARS) has been successful applied to fast chemical sensitive detections. As the development of femto-second pulse shaping techniques, it is of great interest to find the optimum pulse shapes for CARS. The optimum pulse shapes should minimize the non-resonant four wave mixing (NRFWM) background and maximize the CARS signal. A genetic algorithm (GA) is developed to make a heuristic searching for optimized pulse shapes, which give the best signal the background ratio. The GA is shown to be able to rediscover the hybrid CARS scheme and find optimized pulse shapes for customized applications by itself.
Shape optimization for Navier-Stokes equations with algebraic turbulence model : numerical analysis and computation
Haslinger, J.; Stebel, J. (Jan)
We study the shape optimization problem for the paper machine headbox which distributes a mixture of water and wood fibers in the paper making process. The aim is to find a shape which a priori ensures the given velocity profile on the outlet part. The mathematical formulation leads to the optimal control problem in which the control variable is the shape of the domain representing the header, the state problem is represented by the generalized Navier-Stokes system with nontrivial boundary co...
Shape optimization of truss-stiffened shell structures with variable thickness
Kegl, Marko; Brank, Boštjan
This paper presents an effective approach to shape optimal design of statically loaded elastic shell-like structures. The shape parametrization is based on a design element technique. The chosen design element is a rational Bézier body, enhanced with a smoothly varying scalar field. A body-like designelement makes possible to unify the shape optimization of both pure shells and truss-stiffened shell structures. The scalar field of the design element is obtained by attaching to each control po...
变体平尾翼型气动外形设计方法%Airfoil Aerodynamic Optimization Method of Morphing Horizontal Stabilizer
杜厦; 昂海松
A morphing airfoil instead of traditional horizontal stabilizer and control elements is proposed in order to make the aircraft keep the optimal lift/drag ratio during flight attitude controlling. Bornstein polynomial with order "n" is used to describe the airfoil configuration. A set of airfoil that can provide a minimum drag coefficient at different lift coefficient in a confirmed flight environment is obtained by aerodynamic optimization simulation using the genetic algorithm. It is proved that the morphing airfoil can provide a smaller drag coefficient than the traditional control element do when the same lift coefficient is provided. The relationship between shape control parameters and lift is fitted according to the optimized airfoil. A set of example is used to verify the morphing regularity.%为了使飞机在控制飞行姿态时仍然能保持最优升阻比,提出了一种通过改变翼型形状来代替传统控制舵面采控制飞机俯仰的方法.采用伯恩斯坦多项式对机翼的翼型进行数学建模,并采用遗传算法通过空气动力学仿真对翼型进行优化得到一组在一定飞行环境下、产生附加阻力最小且随升力系数变化的翼型形状.通过对比证明在提供相同升力的情况下,变体翼比传统的控制舵面产生更小的附加阻力.根据翼型形状和升力系数的变化采用数据拟合的方法得到翼型形状控制参数随升力变化的规律.通过算例对变化规律的验证表明其可以用来作为飞行姿态控制的翼型形状变化依据.
Shape design by optimal flow control and reduced basis techniques: applications to bypass configurations in haemodynamics
Rozza, Gianluigi; Quarteroni, Alfio
The purpose of this thesis is to develop numerical methods for optimization, control and shape design in computational fluid dynamics, more precisely in haemodynamics. The application studied is related with the shape optimization of an aorto-coronaric bypass. The optimization process has to keep into account aspects which are very different and sometimes conflicting, for this reason the process has been organized in more levels dealing with a geometrical scale. Moreover we have chosen to use...
Iron Pole Shape Optimization of IPM Motors Using an Integrated Method
Full Text Available An iron pole shape optimization method to reduce cogging torque in Interior Permanent Magnet (IPM motors is developed by using the reduced basis technique coupled by finite element and design of experiments methods. Objective function is defined as the minimum cogging torque. The experimental design of Taguchi method is used to build the approximation model and to perform optimization. This method is demonstrated on the rotor pole shape optimization of a 4-poles/24-slots IPM motor.
Practical Aerodynamic Design Optimization Based on the Navier-Stokes Equations and a Discrete Adjoint Method
Grossman, Bernard
on a free-form deformation technique has been utilized and the resulting codes have been integrated with an optimization package. Lastly, sample optimizations have been shown for inviscid and turbulent flow over an ONERA M6 wing. Drag reductions have been demonstrated by reducing shock strengths across the span of the wing.
Shark skin inspired riblet structures as aerodynamically optimized high temperature coatings for blades of aeroengines
This paper deals with different structuring methods for high temperature resistant nickel alloys. The ideal structured surface for a possible application on the blades of aeroengines combines high oxidation resistance with low drag in a hot gas flow. The effect of drag reduction due to riblet structured surfaces was originally inspired by shark scales, which have a drag reducing riblet structure. The necessary riblet sizes for effective drag reduction depend on the temperature, pressure and velocity of the flowing medium (gas or liquid). These riblet sizes were calculated for the different sections in an aeroengine. The riblets were successfully produced on a NiCoCrAlY coating by picosecond laser treatment. This method is suitable for larger structures within the range of some tens of micrometers. Furthermore, experiments were performed by depositing different materials through polymer and metal masks via electrodeposition and physical vapor deposition. All fabricated structures were oxidized at 900–1000 °C for up to 100 h to simulate the temperature conditions in an aeroengine. The resulting shape of the riblets was characterized using scanning electron microscopy. The most accurate structures were obtained by using photolithography with a subsequent electrodeposition of nickel. This method is suited for single digit micrometer structures. The reduction of the wall shear stress was measured in an oil channel. The riblet structures prior to oxidation showed a reduction of the wall shear stress of up to 4.9% compared to a normal smooth surface. This proves that the fabricated riblet design can be used as a drag reducing surface
Shape optimization of small span textile reinforced cementitious composite shells
TYSMANS, Tine; ADRIAENSSENS, Sigrid; Wastiels, Jan
p. 1755-1766 The property of concrete to be poured into any shape and harden at ambient temperatures makes it the most widely-used material for shells. Using this traditionally brittle material in shells restricts their forms to mostly compression shapes. Often steel reinforcement is still necessary to carry tensile forces occurring under different load combinations and to limit crack formation. A new composite material, textile reinforced cementitious composite (TRC), eliminates this rest...
Shape optimization of a Sodium Fast Reactor core
Dombre Emmanuel
Full Text Available We apply in this paper a geometrical shape optimization method for the design of the core of a SFR (Sodium-cooled Fast Reactor in order to minimize a thermal counter-reaction known as the sodium void effect. In this kind of reactors, by increasing the temperature, the core may become liable to a strong increase of reactivity, a key-parameter governing the chain-reaction at quasi-static states. We first use the one group energy diffusion model and give the generalization to the two groups energy equation. We then give some numerical results in the case of the one group energy equation. Note that the application of our method leads to some designs whose interfaces can be parametrized by very smooth curves which can stand very far from realistic designs. We don't explain here the method that it would be possible to use for recovering an operational design but there exists several penalization methods (see [2] that could be employed to this end. On applique dans cet article une méthode d'optimisation géométrique dans le cadre de la conception d'un cœur de réacteur SFR (Sodium-cooled Fast Reactor, i.e. réacteur à neutron rapide refroidi au sodium dans le but de minimiser une contre réaction thermique connue sous le nom d'effet de vidange sodium. Lorsqu'une augmentation de température survient, ce type de réacteur peut être sujet à une forte augmentation de réactivité, un paramètre clé dans le contrôle de la réaction en chaîne en régime quasi-statique. On a recours à l'équation de diffusion à un groupe puis on donne la généralisation du modèle d'optimisation pour l'équation de la diffusion à deux groupes d'énergie. On présente ensuite quelques résultats numériques obtenus dans le cas de l'équation à un groupe d'énergie. On note que l'application de cette méthode conduit à des designs de cœur présentant des interfaces très régulières qui sont loin d'un design de cœur faisable sur le
Optimal shape and location of sensors for parabolic equations with random initial data
Privat, Yannick; Trélat, Emmanuel; Zuazua, Enrique
In this article, we consider parabolic equations on a bounded open connected subset Rn. We model and investigate the problem of optimal shape and location of the observation domain having a prescribed measure. This problem is motivated by the question of knowing how to shape and place sensors in some domain in order to maximize the quality of the observation: for instance, what is the optimal location and shape of a thermometer? We show that it is relevant to consider a spectral optimal desig...
Optimized shapes of magnetic arrays for drug targeting applications
Barnsley, Lester C.; Carugo, Dario; Stride, Eleanor
Arrays of permanent magnet elements have been utilized as light-weight, inexpensive sources for applying external magnetic fields in magnetic drug targeting applications, but they are extremely limited in the range of depths over which they can apply useful magnetic forces. In this paper, designs for optimized magnet arrays are presented, which were generated using an optimization routine to maximize the magnetic force available from an arbitrary arrangement of magnetized elements, depending ...
Geometric optimal design of a magneto-rheological brake considering different shapes for the brake envelope
When designing a magneto-rheological brake (MRB), it is well known that the shape of the brake envelope significantly affects the performance characteristics of the brake. In this study, different shapes for the MR brake envelope, such as rectangular, polygonal or spline shape, are considered and the most suitable shape identified. MRBs with different envelope shapes are introduced followed by the derivation of the braking torque based on Bingham-plastic behavior of the magneto-rheological fluid (MRF). Optimization of the design of the MRB with different envelope shapes is then done. The optimization problem is to find the optimal value for the significant geometric dimensions of the MRB that can produce a certain required braking torque while the brake mass is minimized. A finite element analysis integrated with an optimization tool is employed to obtain optimal solutions for the MRBs. From the results, the most suitable shape for the brake envelope is identified and discussed with the reduction of mass. In addition, the results of the analysis are compared with the experimental results to verify the proposed optimal design characteristics. (paper)
Novel free-form hohlraum shape design and optimization for laser-driven inertial confinement fusion
The hohlraum shape attracts considerable attention because there is no successful ignition method for laser-driven inertial confinement fusion at the National Ignition Facility. The available hohlraums are typically designed with simple conic curves, including ellipses, parabolas, arcs, or Lame curves, which allow only a few design parameters for the shape optimization, making it difficult to improve the performance, e.g., the energy coupling efficiency or radiation drive symmetry. A novel free-form hohlraum design and optimization approach based on the non-uniform rational basis spline (NURBS) model is proposed. In the present study, (1) all kinds of hohlraum shapes can be uniformly represented using NURBS, which is greatly beneficial for obtaining the optimal available hohlraum shapes, and (2) such free-form uniform representation enables us to obtain an optimal shape over a large design domain for the hohlraum with a more uniform radiation and higher drive temperature of the fuel capsule. Finally, a hohlraum is optimized and evaluated with respect to the drive temperature and symmetry at the Shenguang III laser facility in China. The drive temperature and symmetry results indicate that such a free-form representation is advantageous over available hohlraum shapes because it can substantially expand the shape design domain so as to obtain an optimal hohlraum with high performance
Novel free-form hohlraum shape design and optimization for laser-driven inertial confinement fusion
Jiang, Shaoen; Jing, Longfei, E-mail: firstname.lastname@example.com; Ding, Yongkun [Laser Fusion Research Center, China Academy Engineering Physics, Mianyang 621900 (China); Huang, Yunbao, E-mail: email@example.com [Mechatronics School of Guangdong University of Technology, Guangzhou 510006 (China)
The hohlraum shape attracts considerable attention because there is no successful ignition method for laser-driven inertial confinement fusion at the National Ignition Facility. The available hohlraums are typically designed with simple conic curves, including ellipses, parabolas, arcs, or Lame curves, which allow only a few design parameters for the shape optimization, making it difficult to improve the performance, e.g., the energy coupling efficiency or radiation drive symmetry. A novel free-form hohlraum design and optimization approach based on the non-uniform rational basis spline (NURBS) model is proposed. In the present study, (1) all kinds of hohlraum shapes can be uniformly represented using NURBS, which is greatly beneficial for obtaining the optimal available hohlraum shapes, and (2) such free-form uniform representation enables us to obtain an optimal shape over a large design domain for the hohlraum with a more uniform radiation and higher drive temperature of the fuel capsule. Finally, a hohlraum is optimized and evaluated with respect to the drive temperature and symmetry at the Shenguang III laser facility in China. The drive temperature and symmetry results indicate that such a free-form representation is advantageous over available hohlraum shapes because it can substantially expand the shape design domain so as to obtain an optimal hohlraum with high performance.
Automated Finite Element Modeling of Wing Structures for Shape Optimization
Harvey, Michael Stephen
The displacement formulation of the finite element method is the most general and most widely used technique for structural analysis of airplane configurations. Modem structural synthesis techniques based on the finite element method have reached a certain maturity in recent years, and large airplane structures can now be optimized with respect to sizing type design variables for many load cases subject to a rich variety of constraints including stress, buckling, frequency, stiffness and aeroelastic constraints (Refs. 1-3). These structural synthesis capabilities use gradient based nonlinear programming techniques to search for improved designs. For these techniques to be practical a major improvement was required in computational cost of finite element analyses (needed repeatedly in the optimization process). Thus, associated with the progress in structural optimization, a new perspective of structural analysis has emerged, namely, structural analysis specialized for design optimization application, or.what is known as "design oriented structural analysis" (Ref. 4). This discipline includes approximation concepts and methods for obtaining behavior sensitivity information (Ref. 1), all needed to make the optimization of large structural systems (modeled by thousands of degrees of freedom and thousands of design variables) practical and cost effective.
SU-E-T-295: Simultaneous Beam Sampling and Aperture Shape Optimization for Station Parameter Optimized Radiation Therapy (SPORT)
Purpose: Station Parameter Optimized Radiation Therapy (SPORT) was recently proposed to fully utilize the technical capability of emerging digital LINACs, in which the station parameters of a delivery system, (such as aperture shape and weight, couch position/angle, gantry/collimator angle) are optimized altogether. SPORT promises to deliver unprecedented radiation dose distributions efficiently, yet there does not exist any optimization algorithm to implement it. The purpose of this work is to propose an optimization algorithm to simultaneously optimize the beam sampling and aperture shapes. Methods: We build a mathematical model whose variables are beam angles (including non-coplanar and/or even nonisocentric beams) and aperture shapes. To solve the resulting large scale optimization problem, we devise an exact, convergent and fast optimization algorithm by integrating three advanced optimization techniques named column generation, gradient method, and pattern search. Column generation is used to find a good set of aperture shapes as an initial solution by adding apertures sequentially. Then we apply the gradient method to iteratively improve the current solution by reshaping the aperture shapes and updating the beam angles toward the gradient. Algorithm continues by pattern search method to explore the part of the search space that cannot be reached by the gradient method. Results: The proposed technique is applied to a series of patient cases and significantly improves the plan quality. In a head-and-neck case, for example, the left parotid gland mean-dose, brainstem max-dose, spinal cord max-dose, and mandible mean-dose are reduced by 10%, 7%, 24% and 12% respectively, compared to the conventional VMAT plan while maintaining the same PTV coverage. Conclusion: Combined use of column generation, gradient search and pattern search algorithms provide an effective way to optimize simultaneously the large collection of station parameters and significantly improves
SU-E-T-295: Simultaneous Beam Sampling and Aperture Shape Optimization for Station Parameter Optimized Radiation Therapy (SPORT)
Zarepisheh, M; Li, R; Xing, L [Stanford UniversitySchool of Medicine, Stanford, CA (United States); Ye, Y [Stanford Univ, Management Science and Engineering, Stanford, Ca (United States); Boyd, S [Stanford University, Electrical Engineering, Stanford, CA (United States)
Purpose: Station Parameter Optimized Radiation Therapy (SPORT) was recently proposed to fully utilize the technical capability of emerging digital LINACs, in which the station parameters of a delivery system, (such as aperture shape and weight, couch position/angle, gantry/collimator angle) are optimized altogether. SPORT promises to deliver unprecedented radiation dose distributions efficiently, yet there does not exist any optimization algorithm to implement it. The purpose of this work is to propose an optimization algorithm to simultaneously optimize the beam sampling and aperture shapes. Methods: We build a mathematical model whose variables are beam angles (including non-coplanar and/or even nonisocentric beams) and aperture shapes. To solve the resulting large scale optimization problem, we devise an exact, convergent and fast optimization algorithm by integrating three advanced optimization techniques named column generation, gradient method, and pattern search. Column generation is used to find a good set of aperture shapes as an initial solution by adding apertures sequentially. Then we apply the gradient method to iteratively improve the current solution by reshaping the aperture shapes and updating the beam angles toward the gradient. Algorithm continues by pattern search method to explore the part of the search space that cannot be reached by the gradient method. Results: The proposed technique is applied to a series of patient cases and significantly improves the plan quality. In a head-and-neck case, for example, the left parotid gland mean-dose, brainstem max-dose, spinal cord max-dose, and mandible mean-dose are reduced by 10%, 7%, 24% and 12% respectively, compared to the conventional VMAT plan while maintaining the same PTV coverage. Conclusion: Combined use of column generation, gradient search and pattern search algorithms provide an effective way to optimize simultaneously the large collection of station parameters and significantly improves
On second order shape optimization methods for electrical impedance tomography
Afraites, Lekbir; Kateb, Djalil
This paper is devoted to the analysis of a second order method for recovering the \\emph{a priori} unknown shape of an inclusion $\\omega$ inside a body $\\Omega$ from boundary measurement. This inverse problem - known as electrical impedance tomography - has many important practical applications and hence has focussed much attention during the last years. However, to our best knowledge, no work has yet considered a second order approach for this problem. This paper aims to fill that void: we investigate the existence of second order derivative of the state $u$ with respect to perturbations of the shape of the interface $\\partial\\omega$, then we choose a cost function in order to recover the geometry of $\\partial \\omega$ and derive the expression of the derivatives needed to implement the corresponding Newton method. We then investigate the stability of the process and explain why this inverse problem is severely ill-posed by proving the compactness of the Hessian at the global minimizer.
Co-Optimization of Blunt Body Shapes for Moving Vehicles
Brown, James L. (Inventor); Garcia, Joseph A (Inventor); Kinney, David J. (Inventor); Bowles, Jeffrey V (Inventor); Mansour, Nagi N (Inventor)
A method and associated system for multi-disciplinary optimization of various parameters associated with a space vehicle that experiences aerocapture and atmospheric entry in a specified atmosphere. In one embodiment, simultaneous maximization of a ratio of landed payload to vehicle atmospheric entry mass, maximization of fluid flow distance before flow separation from vehicle, and minimization of heat transfer to the vehicle are performed with respect to vehicle surface geometric parameters, and aerostructure and aerothermal vehicle response for the vehicle moving along a specified trajectory. A Pareto Optimal set of superior performance parameters is identified.
On second order shape optimization methods for electrical impedance tomography
Afraites, Lekbir; Dambrine, Marc; Kateb, Djalil
This paper is devoted to the analysis of a second order method for recovering the \\emph{a priori} unknown shape of an inclusion $\\omega$ inside a body $\\Omega$ from boundary measurement. This inverse problem - known as electrical impedance tomography - has many important practical applications and hence has focussed much attention during the last years. However, to our best knowledge, no work has yet considered a second order approach for this problem. This paper aims to fill that void: we in...
Optimization of ultrasonic array inspections using an efficient hybrid model and real crack shapes
Models which simulate the interaction of ultrasound with cracks can be used to optimize ultrasonic array inspections, but this approach can be time-consuming. To overcome this issue an efficient hybrid model is implemented which includes a finite element method that requires only a single layer of elements around the crack shape. Scattering Matrices are used to capture the scattering behavior of the individual cracks and a discussion on the angular degrees of freedom of elastodynamic scatterers is included. Real crack shapes are obtained from X-ray Computed Tomography images of cracked parts and these shapes are inputted into the hybrid model. The effect of using real crack shapes instead of straight notch shapes is demonstrated. An array optimization methodology which incorporates the hybrid model, an approximate single-scattering relative noise model and the real crack shapes is then described
Optimization of ultrasonic array inspections using an efficient hybrid model and real crack shapes
Felice, Maria V.; Velichko, Alexander; Wilcox, Paul D.; Barden, Tim; Dunhill, Tony
Models which simulate the interaction of ultrasound with cracks can be used to optimize ultrasonic array inspections, but this approach can be time-consuming. To overcome this issue an efficient hybrid model is implemented which includes a finite element method that requires only a single layer of elements around the crack shape. Scattering Matrices are used to capture the scattering behavior of the individual cracks and a discussion on the angular degrees of freedom of elastodynamic scatterers is included. Real crack shapes are obtained from X-ray Computed Tomography images of cracked parts and these shapes are inputted into the hybrid model. The effect of using real crack shapes instead of straight notch shapes is demonstrated. An array optimization methodology which incorporates the hybrid model, an approximate single-scattering relative noise model and the real crack shapes is then described.
Optimization of ultrasonic array inspections using an efficient hybrid model and real crack shapes
Felice, Maria V., E-mail: email@example.com [Department of Mechanical Engineering, University of Bristol, Bristol, U.K. and NDE Laboratory, Rolls-Royce plc., Bristol (United Kingdom); Velichko, Alexander, E-mail: firstname.lastname@example.com; Wilcox, Paul D., E-mail: email@example.com [Department of Mechanical Engineering, University of Bristol, Bristol (United Kingdom); Barden, Tim; Dunhill, Tony [NDE Laboratory, Rolls-Royce plc., Bristol (United Kingdom)
Models which simulate the interaction of ultrasound with cracks can be used to optimize ultrasonic array inspections, but this approach can be time-consuming. To overcome this issue an efficient hybrid model is implemented which includes a finite element method that requires only a single layer of elements around the crack shape. Scattering Matrices are used to capture the scattering behavior of the individual cracks and a discussion on the angular degrees of freedom of elastodynamic scatterers is included. Real crack shapes are obtained from X-ray Computed Tomography images of cracked parts and these shapes are inputted into the hybrid model. The effect of using real crack shapes instead of straight notch shapes is demonstrated. An array optimization methodology which incorporates the hybrid model, an approximate single-scattering relative noise model and the real crack shapes is then described.
Genetic Algorithms for Multicriteria Shape Optimization of Induction Furnace
Kůs, Pavel; Mach, F.; Karban, P.; Doležel, Ivo
Melville: AMER INST PHYSICS, 2012, s. 2344-2347. (1479). ISBN 978-0-7354-1091-6. ISSN 0094-243X. [International Conference of Numerical Analysis and Applied Mathematics (ICNAAM). Kos (GR), 19.09.2012-25.09.2012] Institutional support: RVO:61388998 Keywords : optimization * coupled problems * hp-FEM Subject RIV: BA - General Mathematics
Shape interior modeling and mass property optimization using ray-reps
Wu, Jun; Kramer, Lou; Westermann, Rüdiger
We present a novel method for the modeling and optimization of the material distribution inside 3D shapes, such that their 3D printed replicas satisfy prescribed constraints regarding mass properties. In particular, we introduce an extension of ray-representation to shape interior modeling, and...
Shape Optimization for Navier–Stokes Equations with Algebraic Turbulence Model: Numerical Analysis and Computation
We study the shape optimization problem for the paper machine headbox which distributes a mixture of water and wood fibers in the paper making process. The aim is to find a shape which a priori ensures the given velocity profile on the outlet part. The mathematical formulation leads to the optimal control problem in which the control variable is the shape of the domain representing the header, the state problem is represented by the generalized Navier-Stokes system with nontrivial boundary conditions. This paper deals with numerical aspects of the problem.
Optimality of VWAP Execution Strategies under General Shaped Market Impact Functions
Kato, Takashi
In this short note, we study an optimization problem of expected implementation shortfall (IS) cost under general shaped market impact functions. In particular, we find that an optimal strategy is a VWAP (volume weighted average price) execution strategy when the market model is a Black-Scholes type with stochastic clock and market trading volume is large.
An optimization approach for extracting and encoding consistent maps in a shape collection
Huang, Qi-Xing
We introduce a novel approach for computing high quality point-topoint maps among a collection of related shapes. The proposed approach takes as input a sparse set of imperfect initial maps between pairs of shapes and builds a compact data structure which implicitly encodes an improved set of maps between all pairs of shapes. These maps align well with point correspondences selected from initial maps; they map neighboring points to neighboring points; and they provide cycle-consistency, so that map compositions along cycles approximate the identity map. The proposed approach is motivated by the fact that a complete set of maps between all pairs of shapes that admits nearly perfect cycleconsistency are highly redundant and can be represented by compositions of maps through a single base shape. In general, multiple base shapes are needed to adequately cover a diverse collection. Our algorithm sequentially extracts such a small collection of base shapes and creates correspondences from each of these base shapes to all other shapes. These correspondences are found by global optimization on candidate correspondences obtained by diffusing initial maps. These are then used to create a compact graphical data structure from which globally optimal cycle-consistent maps can be extracted using simple graph algorithms. Experimental results on benchmark datasets show that the proposed approach yields significantly better results than state-of-theart data-driven shape matching methods. © 2012 ACM.
Analytical optimal pulse shapes obtained with the aid of genetic algorithms
Guerrero, Rubén D., E-mail: firstname.lastname@example.com [Department of Physics, Universidad Nacional de Colombia, Bogota (Colombia); Arango, Carlos A. [Department of Chemical Sciences, Universidad Icesi, Cali (Colombia); Reyes, Andrés [Department of Chemistry, Universidad Nacional de Colombia, Bogota (Colombia)
We propose a methodology to design optimal pulses for achieving quantum optimal control on molecular systems. Our approach constrains pulse shapes to linear combinations of a fixed number of experimentally relevant pulse functions. Quantum optimal control is obtained by maximizing a multi-target fitness function using genetic algorithms. As a first application of the methodology, we generated an optimal pulse that successfully maximized the yield on a selected dissociation channel of a diatomic molecule. Our pulse is obtained as a linear combination of linearly chirped pulse functions. Data recorded along the evolution of the genetic algorithm contained important information regarding the interplay between radiative and diabatic processes. We performed a principal component analysis on these data to retrieve the most relevant processes along the optimal path. Our proposed methodology could be useful for performing quantum optimal control on more complex systems by employing a wider variety of pulse shape functions.
Analytical optimal pulse shapes obtained with the aid of genetic algorithms
We propose a methodology to design optimal pulses for achieving quantum optimal control on molecular systems. Our approach constrains pulse shapes to linear combinations of a fixed number of experimentally relevant pulse functions. Quantum optimal control is obtained by maximizing a multi-target fitness function using genetic algorithms. As a first application of the methodology, we generated an optimal pulse that successfully maximized the yield on a selected dissociation channel of a diatomic molecule. Our pulse is obtained as a linear combination of linearly chirped pulse functions. Data recorded along the evolution of the genetic algorithm contained important information regarding the interplay between radiative and diabatic processes. We performed a principal component analysis on these data to retrieve the most relevant processes along the optimal path. Our proposed methodology could be useful for performing quantum optimal control on more complex systems by employing a wider variety of pulse shape functions
Effect of Local Junction Losses in the Optimization of T-shaped Flow Channels
Kosaraju, Srinivas
T-shaped channels are extensively used in flow distribution applications such as irrigation, chemical dispersion, gas pipelines and space heating and cooling. The geometry of T-shaped channels can be optimized to reduce the overall pressure drop in stem and branch sections. Results of such optimizations are in the form of geometric parameters such as the length and diameter ratios of the stem and branch sections. The traditional approach of this optimization accounts for the pressure drop across the stem and branch sections, however, ignores the pressure drop in the T-junction. In this paper, we conduct geometry optimization while including the effect of local junction losses in laminar flows. From the results, we are able to identify a non-dimensional parameter that can be used to predict the optimal geometric configurations. This parameter can also be used to identify the conditions in which the local junction losses can be ignored during the optimization.
Rotor Pole Shape Optimization of Permanent Magnet Brushless DC Motors Using the Reduced Basis Technique
Full Text Available In this paper, a magnet shape optimization method for reduction of cogging torque and torque ripple in Permanent Magnet (PM brushless DC motors is presented by using the reduced basis technique coupled by finite element and design of experiments methods. The primary objective of the method is to reduce the enormous number of design variables required to define the magnet shape. The reduced basis technique is a weighted combination of several basis shapes. The aim of the method is to find the best combination using the weights for each shape as the design variables. A multi-level design process is developed to find suitable basis shapes or trial shapes at each level that can be used in the reduced basis technique. Each level is treated as a separated optimization problem until the required objective is achieved. The experimental design of Taguchi method is used to build the approximation model and to perform optimization. This method is demonstrated on the magnet shape optimization of a 6-poles/18-slots PM BLDC motor.
Numerical Modeling of Surface and Volumetric Cooling using Optimal T- and Y-shaped Flow Channels
Kosaraju, Srinivas
The T- and Y-shaped flow channels can be optimized for reduced pressure drop and pumping power. The results of the optimization are in the form of geometric parameters such as length and diameter ratios of the stem and branch sections. While these flow channels are optimized for minimum pressure drop, they can also be used for surface and volumetric cooling applications such as heat exchangers, air conditioning and electronics cooling. In this paper, we studied the heat transfer characteristics of multiple T- and Y-shaped flow channel configurations using numerical simulations. All configurations are subjected to same pumping power and heat generation constraints and their heat transfer performance is studied.
Optimal wavy surface to suppress vortex shedding using second-order sensitivity to shape changes
Tammisola, Outi
A method to find optimal 2nd-order perturbations is presented, and applied to find the optimal spanwise-wavy surface for suppression of cylinder wake instability. Second-order perturbations are required to capture the stabilizing effect of spanwise waviness, which is ignored by standard adjoint-based sensitivity analyses. Here, previous methods are extended so that (i) 2nd-order sensitivity is formulated for base flow changes satisfying linearised Navier-Stokes, and (ii) the resulting method is applicable to a 2D global instability problem. This makes it possible to formulate 2nd-order sensitivity to shape modifications. Using this formulation, we find the optimal shape to suppress the a cylinder wake instability. The optimal shape is then perturbed by random distributions in full 3D stability analysis to confirm that it is a local optimal at the given amplitude and wavelength. Furthermore, it is shown that none of the 10 random wavy shapes alone stabilize the wake flow at Re=50, while the optimal shape does....
Improvement of light coupling in BGO detector module by optimization of the crystal shape
Detector shape optimization study was carried out for the high resolution 4x4 array BGO-PMT coupling scheme to be employed in the spherical positron emission tomograph. To improve the light collection efficiency in the BGO detector array, the authors have employed bullet nose shape BGO crystal in the front side as well as in the back side of detector the latter to be coupled to PMT's photocathode. First, it is believed that the smooth and round front side bullet nose shape could eliminate the sharp corners of the crystal thereby improves the light collection efficiency. Secondly, the bullet nose shape at the back side of crystal which to be coupled to PMT will provide optimal coupling between the crystal and PMT by the focusing property of the bullet nose shape of the crystal. Computer simulations and experimental study were carried out and results are reported