scholarly journals A Sequential Approach for Aerodynamic Shape Optimization with Topology Optimization of Airfoils

2021 ◽  
Vol 26 (2) ◽  
pp. 34
Author(s):  
Isaac Gibert Martínez ◽  
Frederico Afonso ◽  
Simão Rodrigues ◽  
Fernando Lau
Keyword(s):  
Topology Optimization ◽  
Shape Optimization ◽  
Volume Fraction ◽  
Optimization Techniques ◽  
Free Form ◽  
Aerodynamic Shape Optimization ◽  
Sequential Approach ◽  
Airfoil Surface ◽  
Aerodynamic Shape ◽  
Design Variables

The objective of this work is to study the coupling of two efficient optimization techniques, Aerodynamic Shape Optimization (ASO) and Topology Optimization (TO), in 2D airfoils. To achieve such goal two open-source codes, SU2 and Calculix, are employed for ASO and TO, respectively, using the Sequential Least SQuares Programming (SLSQP) and the Bi-directional Evolutionary Structural Optimization (BESO) algorithms; the latter is well-known for allowing the addition of material in the TO which constitutes, as far as our knowledge, a novelty for this kind of application. These codes are linked by means of a script capable of reading the geometry and pressure distribution obtained from the ASO and defining the boundary conditions to be applied in the TO. The Free-Form Deformation technique is chosen for the definition of the design variables to be used in the ASO, while the densities of the inner elements are defined as design variables of the TO. As a test case, a widely used benchmark transonic airfoil, the RAE2822, is chosen here with an internal geometric constraint to simulate the wing-box of a transonic wing. First, the two optimization procedures are tested separately to gain insight and then are run in a sequential way for two test cases with available experimental data: (i) Mach 0.729 at α=2.31°; and (ii) Mach 0.730 at α=2.79°. In the ASO problem, the lift is fixed and the drag is minimized; while in the TO problem, compliance minimization is set as the objective for a prescribed volume fraction. Improvements in both aerodynamic and structural performance are found, as expected: the ASO reduced the total pressure on the airfoil surface in order to minimize drag, which resulted in lower stress values experienced by the structure.

Parameter assessment for virtual Stackelberg game in aerodynamic shape optimization

2018 ◽  
Vol 32 (12n13) ◽  
pp. 1840044
Author(s):  
Jing Wang ◽  
Fangfang Xie ◽  
Yao Zheng ◽  
Jifa Zhang
Keyword(s):  
Shape Optimization ◽  
Stackelberg Game ◽  
Critical Parameters ◽  
Aerodynamic Shape Optimization ◽  
Aerodynamic Optimization ◽  
Aerodynamic Shape ◽  
Design Variables ◽  
Design Cycle ◽  
Parametric Studies ◽  
The Impact

In this paper, parametric studies of virtual Stackelberg game (VSG) are conducted to assess the impact of critical parameters on aerodynamic shape optimization, including design cycle, split of design variables and role assignment. Typical numerical cases, including the inverse design and drag reduction design of airfoil, have been carried out. The numerical results confirm the effectiveness and efficiency of VSG. Furthermore, the most significant parameters are identified, e.g. the increase of design cycle can improve the optimization results but it will also add computational burden. These studies will maximize the productivity of the effort in aerodynamic optimization for more complicated engineering problems, such as the multi-element airfoil and wing-body configurations.

Aerodynamic Optimization Design of Airfoil Based on Directly Manipulated FFD Technique

2013 ◽  
Vol 390 ◽  
pp. 121-128 ◽  
Author(s):  
Jun Qiang Bai ◽  
Song Chen
Keyword(s):  
Shape Optimization ◽  
Drag Reduction ◽  
Optimization Design ◽  
High Order ◽  
Control Points ◽  
Aerodynamic Shape Optimization ◽  
Aerodynamic Optimization ◽  
Aerodynamic Shape ◽  
Design Variables ◽  
Geometrical Constraints

The method of applying direct manipulated FFD (DFFD) technique into aerodynamic shape optimization has been proposed and researched. Due to the disadvantage of the original FFD method within which the geometrical manipulation is not direct and intuitive, the DFFD approach has been developed by solving each displacement of the FFD control points with some specified geometry points movements, so that the deformation of the target geometry could be directly manipulated. Besides, it has been illustrated that by DFFD method a relatively small number of design variables together with high order FFD control frame could be accomplished. The study cases has shown that applying this method in aerodynamic shape optimization of airfoil for drag reduction is of good feasibility and result, and could be coupled with effective geometrical constraints like airfoil thickness.

Aerodynamic Shape Optimization of Diffuser Augmented Wind Turbine Shrouds Using Asynchronous Differential Evolution

2018 ◽  
Author(s):  
Stavros N. Leloudas ◽  
Georgios N. Lygidakis ◽  
Giorgos A. Strofylas ◽  
Ioannis K. Nikolos
Keyword(s):  
Shape Optimization ◽  
Differential Evolution ◽  
Wind Turbine ◽  
Stokes Equations ◽  
Free Form ◽  
Finite Volume Scheme ◽  
Computational Domain ◽  
Aerodynamic Shape Optimization ◽  
Aerodynamic Shape ◽  
De Algorithm

An adaptable numerical scheme for the aerodynamic shape optimization of axisymmetric diffuser-augmented wind turbine shrouds is demonstrated in this work, using an asynchronous and parallel version of a Differential Evolution (DE) algorithm. The simulation of the incompressible flow field about each candidate geometry is succeeded by means of an in-house Computational Fluid Dynamics (CFD) solver, that has been developed based on the specially modified, by the artificial compressibility approach, Navier-Stokes equations, expressed in non-dimensional form, for 2D-axisymmetric frames of reference. The discretization of the computational domain is made with 2D hybrid unstructured meshes, composed by both triangular and quadrilateral elements, combined with a node-centered finite-volume scheme, while the Free-Form Deformation (FFD) technique is applied, for both the parameterization of the design geometry and the morphing of the computational mesh. The required data transfer between the DE algorithm and the CFD solver is accomplished with appropriate text files, while the parallel implementation is achieved utilizing the Message Passing Interface (MPI) library functions. Further acceleration of the optimization procedure is succeeded by the combination of the DE with surrogate models, in order to replace the costly CFD-based evaluations of the candidate solutions with fast, but approximate estimations of their cost function.

scholarly journals On an Exact Step Length in Gradient-Based Aerodynamic Shape Optimization—Part II: Viscous Flows

Fluids ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 106
Author(s):  
Farzad Mohebbi ◽  
Ben Evans ◽  
Mathieu Sellier
Keyword(s):  
Shape Optimization ◽  
Viscous Flows ◽  
Optimization Method ◽  
Step Length ◽  
Aerodynamic Shape Optimization ◽  
Ansys Fluent ◽  
Transonic Flows ◽  
Aerodynamic Shape ◽  
Design Variables ◽  
Gradient Based

This study presents an extension of a previous study (On an Exact Step Length in Gradient-Based Aerodynamic Shape Optimization) to viscous transonic flows. In this work, we showed that the same procedure to derive an explicit expression for an exact step length βexact in a gradient-based optimization method for inviscid transonic flows can be employed for viscous transonic flows. The extended numerical method was evaluated for the viscous flows over the transonic RAE 2822 airfoil at two common flow conditions in the transonic regime. To do so, the RAE 2822 airfoil was reconstructed by a Bezier curve of degree 16. The numerical solution of the transonic turbulent flow over the airfoil was performed using the solver ANSYS Fluent (using the Spalart–Allmaras turbulence model). Using the proposed step length, a gradient-based optimization method was employed to minimize the drag-to-lift ratio of the airfoil. The gradient of the objective function with respect to design variables was calculated by the finite-difference method. Efficiency and accuracy of the proposed method were investigated through two test cases.

scholarly journals Application of Nontraditional Optimization Techniques for Airfoil Shape Optimization

2012 ◽  
Vol 2012 ◽  
pp. 1-6 ◽  
Author(s):  
R. Mukesh ◽  
K. Lingadurai ◽  
U. Selvakumar
Keyword(s):  
Genetic Algorithm ◽  
Simulated Annealing ◽  
Shape Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Optimization Algorithms ◽  
Optimization Techniques ◽  
Aerodynamic Shape Optimization ◽  
Shape Optimization Problem ◽  
Aerodynamic Shape

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.

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