Reduction of the Adjoint Gradient Formula for Aerodynamic Shape Optimization Problems

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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Approximate Hessian for Accelerated Convergence of Aerodynamic Shape Optimization Problems

8th AIAA Theoretical Fluid Mechanics Conference ◽

10.2514/6.2017-4338 ◽

2017 ◽

Cited By ~ 1

Author(s):

Doug Shi-Dong ◽

Sivakumaran Nadarajah

Keyword(s):

Shape Optimization ◽

Optimization Problems ◽

Aerodynamic Shape Optimization ◽

Aerodynamic Shape ◽

Accelerated Convergence ◽

Approximate Hessian

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Multiobjective aerodynamic shape optimization of NACA0012 airfoil based mesh morphing

International Journal for Simulation and Multidisciplinary Design Optimization ◽

10.1051/smdo/2020006 ◽

2020 ◽

Vol 11 ◽

pp. 11

Author(s):

Rabii El Maani ◽

Soufiane Elouardi ◽

Bouchaib Radi ◽

Abdelkhalak El Hami

Keyword(s):

Experimental Data ◽

Shape Optimization ◽

Optimization Problems ◽

Search Algorithm ◽

Setup Time ◽

Aerodynamic Shape Optimization ◽

Aerodynamic Coefficients ◽

Aerodynamic Shape ◽

Drag Forces ◽

Naca0012 Airfoil

The actual use of computational fluid dynamics (CFD) by aerospace companies is the trade-off result between the perceived costs and benefits. Computational costs are restricted to swamp the design process even if the benefits are widely recognized. The need for fast turnaround, counting the setup time, is also crucial. CFD integrates mathematical relations and algorithms to analyze and solve fluid flow problems. CFD analysis of an airfoil produces results such as the lift and drag forces that determine the performance of an airfoil. Thus, optimizing these aerodynamic performances has proved extremely valuable in practice. The aim of this paper is to model a transonic, compressible and turbulent flow over a NACA 0012 airfoil, using a density based implicit solver, for which a comparison and a validation will be made throught the published experimental data. The numerical results show that the predicted aerodynamic coefficients are in a satisfying agreement with experimental data. Then an aerodynamic shape optimization algorithm, based on a multiobjective algorithm that is an extension of the Backtracking Search Algorithm which was initially developed for single-objective optimization problems only, was used in order to obtain an improved performance control of the aerodynamic coefficients of the optimized airfoil.

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