Representing the Change - Free Form Deformation for Evolutionary Design Optimization

2008 ◽  
pp. 63-86 ◽  
Author(s):  
Stefan Menzel ◽  
Bernhard Sendhoff
Keyword(s):  
Design Optimization ◽  
Free Form ◽  
Evolutionary Design ◽  
Free Form Deformation

Multidisciplinary Design Optimization Based on Parameterized Free-Form Deformation for Single Turbine

AIAA Journal ◽  
2019 ◽  
Vol 57 (5) ◽  
pp. 2075-2087
Author(s):  
Lei Li ◽  
Tianyu Yuan ◽  
Yuan Li ◽  
Weizhu Yang ◽  
Jialei Kang
Keyword(s):  
Design Optimization ◽  
Multidisciplinary Design Optimization ◽  
Multidisciplinary Design ◽  
Free Form ◽  
Free Form Deformation

Aerodynamic design optimization of a hypersonic rocket sled deflector using the free-form deformation technique

2021 ◽  
pp. 095441002199498
Author(s):  
Tianjiao Dang ◽  
Bingfei Li ◽  
Dike Hu ◽  
Yachuan Sun ◽  
Zhen Liu
Keyword(s):  
Design Optimization ◽  
Optimization Method ◽  
Free Form ◽  
Aerodynamic Design ◽  
Aerodynamic Shape ◽  
Aerodynamic Design Optimization ◽  
Continuous Adjoint Method ◽  
Free Form Deformation ◽  
Shape Parameterization ◽  
Continuous Adjoint

An aerodynamic design optimization of a hypersonic rocket sled deflector is presented using the free-form deformation (FFD) technique. The objective is to optimize the aerodynamic shape of the hypersonic rocket sled deflector to increase its negative lift and enhance the motion stability of the rocket sled. The FFD technique is selected as the aerodynamic shape parameterization method, and the continuous adjoint method based on the gradient method is used to search the optimization in the geometric shape parameter space; the computational fluid dynamics method for a hypersonic rocket sled is employed. An automatic design optimization method for the deflector is carried out based on the aerodynamic requirements of the rocket sled. The optimization results show that the optimized deflector meets the design requirement of increasing the negative lift under the constraint of drag. By improving the pressure distribution on the surface of the deflector, the negative lift is increased by 7.39%, which confirms the effectiveness of the proposed method.

Aerodynamic Design Optimization of an Axial Flow Compressor Stator Using Parameterized Free-Form Deformation

2019 ◽  
Vol 141 (10) ◽  
Author(s):  
Richard Amankwa Adjei ◽  
WeiZhe Wang ◽  
YingZheng Liu
Keyword(s):  
Genetic Algorithm ◽  
Flow Field ◽  
Design Optimization ◽  
Operating Conditions ◽  
Free Form ◽  
Aerodynamic Design ◽  
Objective Functions ◽  
Aerodynamic Design Optimization ◽  
Design Variables ◽  
Free Form Deformation

AbstractThis paper describes an aerodynamic design optimization of a highly loaded compressor stator blade using parameterized free-form deformation (FFD). The optimization methodology presented utilizes a B-spline-based FFD control volume to map the blade from the object space to the parametric space via transformation operations in order to perturb the blade surface. Coupled with a multi-objective genetic algorithm (MOGA) and a Gaussian process-based response surface method (RSM), a fully automated iterative loop was used to run the optimization on a fitted correlation function. A weighted average reduction of 6.1% and 36.9% in total pressure loss and exit whirl angle was achieved, showing a better compromise of objective functions with smoother blade shape than other results obtained in the open literature. Data mining of the Pareto set of optimums revealed four groups of data interactions of which some design variables were found to have skewed scatter relationship with objective functions and can be redefined for further improvement of performance. Analysis of the flow field showed that the thinning of the blade at midspan and reduction in camber distribution were responsible for the elimination of the focal-type separation vortex by redirecting the secondary flow in an axially forward direction toward the midspan and near the hub endwall downstream. Furthermore, the reduction in exit whirl angle especially at the shroud was due to the mild bow shape which generated radial forces on the flow field thereby reducing the flow diffusion rate at the suction surface corner. This effect substantially delayed or eliminated the formation of corner separation at design and off-design operating conditions. Parameterized FFD was found to have superior benefits of smooth surface generation with low number of design variables while maintaining a good compromise between objective functions when coupled with a genetic algorithm.

Multidisciplinary Design Optimization for Performance Improvement of an Axial Flow Fan Using Free-Form Deformation

2020 ◽  
Vol 143 (1) ◽  
Author(s):  
Richard Amankwa Adjei ◽  
Chengwei Fan ◽  
WeiZhe Wang ◽  
YingZheng Liu
Keyword(s):  
Data Mining ◽  
Design Optimization ◽  
Performance Improvement ◽  
Multidisciplinary Design Optimization ◽  
Static Stress ◽  
Chord Length ◽  
Multidisciplinary Design ◽  
Free Form ◽  
Free Form Deformation ◽  
Operating Points

Abstract This paper describes a multidisciplinary design optimization for performance improvement of an electric-ducted fan rotor using free-form deformation (FFD) and data mining techniques. A practical partitioning approach for FFD parameterization was applied in combination with engineering design parameters to optimize the fan rotor. Regression analysis was used to initially determine an approximation function for the blade static stress and subsequently integrated into a fully coupled iterative loop to optimize the blade considering two operating points. Two optimization solutions for 10 and 12 blades were performed. Percentage improvements in the efficiency of 1.05% and 1.32% were realized for 10 and 12 blades, respectively, at near peak efficiency flowrate. Also, blade static stress was reduced by percentages of 5.49% and 12.37% for 10 and 12 blades compared with the baseline. Data mining results revealed key design variable sensitivities where blade twist, sweep, chord, and hub thickness distribution were found to be the most influential for 12 blades while for 10 blades, blade lean, sweep and chord at the midspan and tip. The optimized blades were found to have a significant increase in chord from midspan to tip mimicking a wide chord fan blade particularly for 10 blades. Analysis of the flow field revealed that the axial velocity from 0.4 to 0.8 spanwise length increased significantly for the optimum blades due to the increase in blade twist and chord length at all stable operating points. However, the leakage trajectory relative to the blade chord was observed to be larger and interacted with the trailing edge wake flow downstream for the optimum blades at near-stall conditions. Furthermore, the increase in chord length and the thinning of the blade close to the trailing edge from 0.4 to 0.8 span reduced the suction-side blade loading and static stress.

Airfoil Optimization Using Area-Preserving Free-Form Deformation

2015 ◽  
Author(s):  
Stavros N. Leloudas ◽  
Giorgos A. Strofylas ◽  
Ioannis K. Nikolos
Keyword(s):  
Cross Sectional Area ◽  
Equality Constraint ◽  
Optimization Process ◽  
Free Form ◽  
Sectional Area ◽  
Cross Sectional ◽  
Airfoil Optimization ◽  
Free Form Deformation ◽  
Correction Problem ◽  
Area Preserving

Given the importance of structural integrity of aerodynamic shapes, the necessity of including a cross-sectional area equality constraint among other geometrical and aerodynamic ones arises during the optimization process of an airfoil. In this work an airfoil optimization scheme is presented, based on Area-Preserving Free-Form Deformation (AP FFD), which serves as an alternative technique for the fulfillment of a cross-sectional area equality constraint. The AP FFD is based on the idea of solving an area correction problem, where a minimum possible offset is applied on all free-to-move control points of the FFD lattice, subject to the area preservation constraint. Due to the linearity of the area constraint in each axis, the extraction of an inexpensive closed-form solution to the area preservation problem is possible by using Lagrange Multipliers. A parallel Differential Evolution (DE) algorithm serves as the optimizer, assisted by two Artificial Neural Networks as surrogates. The use of multiple surrogate models, in conjunction with the inexpensive solution to the area correction problem, render the optimization process time efficient. The application of the proposed methodology for wind turbine airfoil optimization demonstrates its applicability and effectiveness.

Shape Optimization by Free-Form Deformation: Existence Results and Numerical Solution for Stokes Flows

2013 ◽  
Vol 60 (3) ◽  
pp. 537-563 ◽  
Author(s):  
Francesco Ballarin ◽  
Andrea Manzoni ◽  
Gianluigi Rozza ◽  
Sandro Salsa
Keyword(s):  
Shape Optimization ◽  
Numerical Solution ◽  
Existence Results ◽  
Free Form ◽  
Stokes Flows ◽  
Free Form Deformation

Fully Free-Form Deformation Features (δ-F4) Incorporating Discontinuities

2004 ◽  
Author(s):  
Vincent Cheutet ◽  
Jean-Philippe Pernot ◽  
Jean-Claude Leon ◽  
Bianca Falcidieno ◽  
Franca Giannini
Keyword(s):  
Surface Deformation ◽  
Geometric Constraints ◽  
Free Form ◽  
Initial Surface ◽  
Cad Systems ◽  
Free Form Deformation ◽  
Deformation Features ◽  
Generate Surface ◽  
Prototype Software ◽  
Free Form Surfaces

To limit low-level manipulations of free-form surfaces, the concept of Fully Free Form Deformation Features (δ-F4) have been introduced. They correspond to shapes obtained by deformation of a surface area according to specified geometric constraints. In our work, we mainly focused on those features aimed at enforcing the visual effect of the so-called character lines, extensively used by designers to specify the shape of an object. Therefore, in the proposed approach, 3D lines are used to drive surface deformation over specified areas. Depending on the wished shape and reflection light effects, the insertion of character lines may generate surface tangency discontinuities. In CAD systems, such kind of discontinuities is generally created by a decomposition of the initial surface into several patches. This process can be tedious and very complex, depending on the shape of the deformation area and the desired surface continuity. Here, a method is proposed to create discontinuities on a surface, using the trimming properties of surfaces. The corresponding deformation features produce the resulting surface in a single modification step and handle simultaneously more constraints than current CAD systems. The principle of the proposed approach is based on arbitrary shaped discontinuities in the parameter domain of the surface to allow the surface exhibiting geometric discontinuities at user-prescribed points or along lines. The proposed approach is illustrated with examples obtained using our prototype software.

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