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

Farzad Mohebbi,Mathieu Sellier,Ben Evans

doi:10.3390/fluids6030106

Farzad Mohebbi, Mathieu Sellier + Show 1 more

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https://doi.org/10.3390/fluids6030106

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Abstract

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.

Highlights

The advent of computers of ever-increasing power, speed, and memory capacity over the past decades has enabled the development of various aerodynamic shape optimization algorithms which rely on combining computational fluid dynamics with numerical optimization methods
The comparisons between the results obtained from the numerical solution (ANSYS Fluent, S-A turbulence model) and the experimental data [12] are shown in Figure 8a and Figure 8b
The expression for the exact step length which was previously by the authors for inviscid transonic flows, was extended to viscous transonic flows over developed by the authors inviscid flows,the was extended to viscous transonic airfoils

Summary

Introduction

The advent of computers of ever-increasing power, speed, and memory capacity over the past decades has enabled the development of various aerodynamic shape optimization algorithms which rely on combining computational fluid dynamics with numerical optimization methods. Among the optimization methods commonly used in aerodynamic shape optimization problems are gradient-based methods such as the steepest descent, conjugate gradient, and quasi-Newton methods. In these methods, the calculation of two variables (1) direction of descent and (2) step length are needed during the iterative process to update the current solution. The effectiveness of a gradient-based aerodynamic shape optimization problem relies very much on the accuracy of the calculation of these two variables. In aerodynamic shape optimization problems, the finite-difference method and the adjoint method are two methods to calculate the gradient of the objective function with respect to design variables.

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