Gradient based aerodynamic shape optimization using the FIVER embedded boundary method

2016 ◽  
Author(s):  
Dante De Santis ◽  
Matthew J. Zahr ◽  
Charbel Farhat
Keyword(s):  
Shape Optimization ◽  
Aerodynamic Shape Optimization ◽  
Aerodynamic Shape ◽  
Boundary Method ◽  
Embedded Boundary ◽  
Gradient Based ◽  
Embedded Boundary Method

scholarly journals Discrete adjoint aerodynamic shape optimization using symbolic analysis with OpenFEMflow

2021 ◽  
Author(s):  
Ali Elham ◽  
Michel J. L. van Tooren
Keyword(s):  
Shape Optimization ◽  
Open Source ◽  
Symbolic Analysis ◽  
State Variables ◽  
Aerodynamic Shape Optimization ◽  
Computationally Efficient ◽  
Exact Integration ◽  
Aerodynamic Shape ◽  
Discrete Adjoint ◽  
Gradient Based

AbstractThe combination of gradient-based optimization with the adjoint method for sensitivity analysis is a very powerful and popular approach for aerodynamic shape optimization. However, differentiating CFD codes is a time consuming and sometimes a challenging task. Although there are a few open-source adjoint CFD codes available, due to the complexity of the code, they might not be very suitable to be used for educational purposes. An adjoint CFD code is developed to support students for learning adjoint aerodynamic shape optimization as well as developing differentiated CFD codes. To achieve this goal, we used symbolic analysis to develop a discrete adjoint CFD code. The least-squares finite element method is used to solve the compressible Euler equations around airfoils in the transonic regime. The symbolic analysis method is used for exact integration to generate the element stiffness and force matrices. The symbolic analysis is also used to compute the exact derivatives of the residuals with respect to both design variables (e.g., the airfoil geometry) and the state variables (e.g., the flow velocity). Besides, the symbolic analysis allows us to compute the exact Jacobian of the governing equations in a computationally efficient way, which is used for Newton iteration. The code includes a build-in gradient-based optimization algorithm and is released as open-source to be available freely for educational purposes.

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 Optimal Aerodynamic Shape Optimization of a Paraglider Airfoil Based on the Sharknose Concept

2018 ◽  
Vol 221 ◽  
pp. 05002
Author(s):  
Amir A. Abdelqodus ◽  
Innokentiy A. Kursakov
Keyword(s):  
Shape Optimization ◽  
Stokes Equations ◽  
Pressure Coefficient ◽  
Aerodynamic Performance ◽  
Navier Stokes ◽  
Aerodynamic Shape Optimization ◽  
Aerodynamic Shape ◽  
Air Inlet ◽  
Gradient Based ◽  
Lift And Drag

The effects of classical air inlet configurations on the aerodynamic performance of a paraglider airfoil are firstly presented. Followed by conducting gradient-based aerodynamic shape optimization of the baseline airfoil used in the investigation of the classical air inlets. Different air inlet configurations are introduced to the optimized profile, and there effects on the aerodynamic performance are then compared to the initial and optimized airfoils. The Reynolds averaged Navier-Stokes equations (RANS) are solved for the flow field around the closed and open airfoils. The canopy is assumed to be smooth, rigid and impermeable. Results are focused on both of lift and drag coefficients for performance analysis and on the internal pressure coefficient which can be critical for a real flexible wing regarding the risk of collapse.

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.

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