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Article

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

1
Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal
2
IDMEC, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal
3
DAEP, ISAE-SUPAERO, Université de Toulouse, 10 av. Edouard Belin, BP 54032, 31055 Toulouse, France
*
Author to whom correspondence should be addressed.
This paper is an extended version of our paper published in 5th International Conference on Numerical and Symbolic Computation Developments and Applications (SYMCOMP 2021).
Academic Editor: Maria Amélia Ramos Loja
Math. Comput. Appl. 2021, 26(2), 34; https://doi.org/10.3390/mca26020034
Received: 11 March 2021 / Revised: 16 April 2021 / Accepted: 17 April 2021 / Published: 20 April 2021
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. View Full-Text
Keywords: aerodynamic shape optimization; computational fluid dynamics; topology optimization; airfoil aerodynamic shape optimization; computational fluid dynamics; topology optimization; airfoil
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MDPI and ACS Style

Gibert Martínez, I.; Afonso, F.; Rodrigues, S.; Lau, F. A Sequential Approach for Aerodynamic Shape Optimization with Topology Optimization of Airfoils. Math. Comput. Appl. 2021, 26, 34. https://doi.org/10.3390/mca26020034

AMA Style

Gibert Martínez I, Afonso F, Rodrigues S, Lau F. A Sequential Approach for Aerodynamic Shape Optimization with Topology Optimization of Airfoils. Mathematical and Computational Applications. 2021; 26(2):34. https://doi.org/10.3390/mca26020034

Chicago/Turabian Style

Gibert Martínez, Isaac; Afonso, Frederico; Rodrigues, Simão; Lau, Fernando. 2021. "A Sequential Approach for Aerodynamic Shape Optimization with Topology Optimization of Airfoils" Math. Comput. Appl. 26, no. 2: 34. https://doi.org/10.3390/mca26020034

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