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Solving the Two Objective Evolutionary Shape Optimization of a Natural Laminar Airfoil and Shock Control Bump with Game Strategies

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Abstract

In order to improve the performances of a civil aircraft at transonic regimes, it is critical to develop new computational optimization methods reducing friction drag. Natural laminar flow (NLF) airfoil/wing design remain efficient methods to reduce the turbulence skin friction. However, the existence of wide range of favorable pressure gradient on a laminar flow airfoil/wing surface leads to strong shock waves occurring at the neighborhood of the trailing edge of the airfoil/wing. Consequently, the reduction of the friction drag due to the extension of the laminar flow surface of the airfoil is compensated with an increase of the shock wave induced drag. In this paper, an evolutionary algorithm (EAs) hybridized with different games (cooperative Pareto game, competitive Nash game and hierarchical Stackelberg game) for comparison is implemented to optimize the airfoil shape with a larger laminar flow range and a weaker shock wave drag simultaneously due to a shock control bump (SCB) active device. Numerical experiments demonstrate that each game coupled to the EAs optimizer can easily capture either a Pareto front, a Nash equilibrium or a Stackelberg equilibrium of this two-objective shape optimization problem. From the analysis/synthesis of 2D results it is concluded that a variety of laminar flow airfoils with greener aerodynamic performances can be significantly improved due to optimal SCB shape and position when compared to the baseline airfoil geometry. This methodology illustrate the potentiality of such an approach to solve the challenging shape optimization of the NLF wings in industrial design environments.

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Acknowledgements

This work has also benefited partially from the support of EU-China international cooperation projects from EC and MIIT. Acknowledgements also dedicate to NUAA and CIMNE colleagues for fruitful discussions on game theory and for institutions’ partial support provided during crossed visits of the authors to CIMNE and NUAA.

Funding

This study was funded by National natural Science Foundation of China (NSFC) under Grant Number 11272149.

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Authors and Affiliations

  1. College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics (NUAA), Nanjing, 210016, China

    Z. Tang & Y. Chen

  2. AVIC Aerodynamics Research Institute, Haerbin, 15001, China

    L. Zhang

  3. International Center for Numerical Methods in Engineering (CIMNE), Universitat Politècnica de Catalunya, Barcelona, Spain

    J. Périaux

  4. Faculty of Information Technology, University of Jyväskylä, Jyväskylä, Finland

    J. Périaux

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  1. Z. Tang
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  2. Y. Chen
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  4. J. Périaux
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Correspondence to Z. Tang.

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Tang, Z., Chen, Y., Zhang, L. et al. Solving the Two Objective Evolutionary Shape Optimization of a Natural Laminar Airfoil and Shock Control Bump with Game Strategies. Arch Computat Methods Eng 26, 119–141 (2019). https://doi.org/10.1007/s11831-017-9231-6

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  • DOI: https://doi.org/10.1007/s11831-017-9231-6

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