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 On an Exact Step Length in Gradient-Based Aerodynamic Shape Optimization

Fluids ◽  
2020 ◽  
Vol 5 (2) ◽  
pp. 70
Author(s):  
Farzad Mohebbi ◽  
Ben Evans
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Shape Optimization ◽  
Difference Method ◽  
Optimization Problems ◽  
Step Length ◽  
Aerodynamic Shape Optimization ◽  
Aerodynamic Shape ◽  
Design Variables ◽  
Gradient Based

This study proposeda novel exact expression for step length (size) in gradient-based aerodynamic shape optimization for an airfoil in steady inviscid transonic flows. The airfoil surfaces were parameterized using Bezier curves. The Bezier curve control points were considered as design variables and the finite-difference method was used to compute the gradient of the objective function (drag-to-lift ratio) with respect to the design variables. An exact explicit expression was derived for the step length in gradient-based shape optimization problems. It was shown that the derived step length was independent of the method used for calculating the gradient (adjoint method, finite-difference method, etc.). The obtained results reveal the accuracy of the derived step length.

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.

Constrained Adjoint-Based Aerodynamic Shape Optimization of a Single-Stage Transonic Compressor

2012 ◽  
Author(s):  
Benjamin Walther ◽  
Siva Nadarajah
Keyword(s):  
Shape Optimization ◽  
Pressure Ratio ◽  
Internal Flow ◽  
Optimization Method ◽  
Single Stage ◽  
Programming Algorithm ◽  
Aerodynamic Shape Optimization ◽  
Aerodynamic Shape ◽  
Transonic Compressor ◽  
Adjoint Approach

This paper develops a discrete adjoint formulation for the constrained aerodynamic shape optimization in a multistage turbomachinery environment. The adjoint approach for viscous, internal flow problems and the corresponding adjoint boundary conditions are discussed. To allow for a concurrent rotor/stator optimization a non-reflective adjoint mixing-plane formulation is proposed. A sequential-quadratic programming algorithm is utilized to determine an improved airfoil shape based on the objective function gradient provided by the adjoint solution. The functionality of the proposed optimization method is demonstrated by the redesign of a midspan section of a single-stage transonic compressor. The objective is to maximize the isentropic efficiency while constraining the mass flow rate and the total pressure ratio.

An Introduction of Aerodynamic Shape Optimization Platform for Compressor Blade

2016 ◽  
Author(s):  
Duan Yanhui ◽  
Wu Wenhua ◽  
Fan Zhaolin ◽  
Chen Ti
Keyword(s):  
Flow Field ◽  
Shape Optimization ◽  
High Efficiency ◽  
Optimization Method ◽  
Compressor Blade ◽  
Field Calculation ◽  
Aerodynamic Shape Optimization ◽  
Aerodynamic Shape ◽  
Grid Deformation ◽  
First Case

In this paper, an aerodynamic shape optimization platform for compressor blade is introduced. The platform divided into modules on flow field calculation, optimization method, parameterization and grid deformation. Flow field calculation of compressor blade is based on computational fluid dynamics (CFD), which is used for multi-block structure grid. Particle swarm optimization (PSO) is built as optimization method module, in which cost functions are calculated parallel. In parametric module, 3D blade is decomposed in a series of characteristic sections and the section is parameterized by Hicks-Henne function. Algebraic interpolation method is used for grid deformation, which is a high efficiency and robust method. Two cases of rotor 37 are presented. The result of the first case shows that, the CFD code of the optimal platform is reliable and robust. For the second case, the optimal platform is verified by designing rotor 37. The result shows that, the optimal platform is effective for design of compressor blade.

Sign in / Sign up

Export Citation Format

Share Document