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Application of Mathematical Optimization Methodsfor Designing Airfoil Considering Viscosity

  • AERO- AND GAS-DYNAMICS OF FLIGHT VEHICLES AND THEIR ENGINES
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Abstract

The paper describes the process of optimization of the airfoil parametrized by the Bezier curve with the use of multicriteria methods of stochastic optimization, namely, the genetic algorithm and the particle swarm method. Various methods of multiparametric optimization are compared in conditions of a significantly viscous environment. The influence of the first approximation on the final geometry of the airfoil is revealed.

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REFERENCES

  1. Zhihui Li and Xinqian Zheng, Review of Design Optimization Methods for Turbomachinery Aerodynamics, Progress in Aerospace Sciences, 2017, vol. 93, pp. 1–23.

    Article  Google Scholar 

  2. Rybakov, V.N., Kuz’michev, V.S., Tkachenko, A.Yu., and Krupenich, I.N., A Method of Working Process Parameter Optimization of a Unified Engine Core and a Gas Turbine Engine Family Being Created on Its Basis, Izv. Vuz. Av. Tekhnika, 2018, vol. 61, no. 1, pp. 78–82 [Russian Aeronautics (Engl. Transl.), 2018, vol. 61, no. 1, pp. 78–83].

    Google Scholar 

  3. Il’inskii, N.B., Matematicheskie problemy proektirovaniya krylovykh profilei: uslozhnennye skhemy techeniya; postroenie i optimizatsiya formy krylovykh profilei (Mathematical Problems of Designing Wing Airfoils: Complicated Flow Schemes; Construction and Optimization of the Shape of Wing Airfoils), Kazan: Kazan. univ., 2011.

    Google Scholar 

  4. Abzalilov, D.F. and Mardanov, R.F., Calculation and Optimization of Aerodynamic Characteristics of Airfoils with Jet Blowing in the Presence of Vortex in the Flow, Izv. Vuz. Av. Tekhnika, 2016, vol. 59, no. 3, pp. 58–63 [Russian Aeronautics (Engl. Transl.), 2016, vol. 59, no. 3, pp. 358–363].

    Google Scholar 

  5. Xinshuai Zhang, Fangfang Xie, Tingwei Ji, Zaoxu Zhu, and Yao Zheng, Multi-Fidelity Deep Neural Network Surrogate Model for Aerodynamic Shape Optimization, Computer Methods in Applied Mechanics and Engineering, 2021, vol. 373, article no. 113485.

    Article  MathSciNet  Google Scholar 

  6. Kharal, A. and Saleem, A., Neural Networks Based Airfoil Generation for a Given Cp Using Bezier–PARSEC Parameterization, Aerospace Science and Technology, 2012, vol. 23, issue 1, pp. 330–344.

    Article  Google Scholar 

  7. Xinyu Hui, Junqiang Bai, Hui Wang, and Yang Zhang, Fast Pressure Distribution Prediction of Airfoils Using Deep Learning, Aerospace Science and Technology, 2020, vol. 105, article no. 105949.

    Article  Google Scholar 

  8. Haizhou Wu, Xuejun Liu, Wei An, Songcan Chen, and Hongqiang Lyu, A Deep Learning Approach for Efficiently and Accurately Evaluating the Flow Field of Supercritical Airfoils, Computers and Fluids, 2020, vol. 198, article no. 104393.

    Article  MathSciNet  Google Scholar 

  9. Viquerat, J., Rabault, J., Kuhnle, A., Ghraieb, H., Larcher, A., and Hachem, E., Direct Shape Optimization through Deep Reinforcement Learning, Journal of Computational Physics, 2021, vol. 428, article no. 110080.

    Article  MathSciNet  Google Scholar 

  10. Anitha, D., Shamili, G.K., Ravi Kumar, P., and Sabari Vihar, R., Air Foil Shape Optimization Using CFD and Parametrization Methods, Materials Today: Proceedings, 2018, vol. 5, issue 2, part 1, pp. 5364–5373.

    Google Scholar 

  11. Sobieczky, H., Geometry Generator for CFD and Applied Aerodynamics, in New Design Concepts for High Speed Air Transport, Vienna: Springer, 1997, pp. 137–157.

    Chapter  Google Scholar 

  12. Sobieczky, H., Parametric Airfoils and Wings, Recent Development of Aerodynamic Design Methodologies. Inverse Design and Optimization, Springer Vieweg, 1999, pp. 71–87.

    Chapter  Google Scholar 

  13. Hyeon Wook Lim and Hyoungjin Kim, Multi-Objective Airfoil Shape Optimization Using an Adaptive Hybrid Evolutionary Algorithm, Aerospace Science and Technology, 2019, vol. 87, pp. 141–153.

    Article  Google Scholar 

  14. Xuesong Wei, Xiaoyang Wang, and Songying Chen, Research on Parameterization and Optimization Procedure of Low-Reynolds-Number Airfoils Based on Genetic Algorithm and Bezier Curve, Advances in Engineering Software, 2020, vol. 149, article no. 102864.

    Article  Google Scholar 

  15. Zou, P., Bricker, J., and Uijttewaal, W., Optimization of Submerged Floating Tunnel Cross Section Based on Parametric Bézier Curves and Hybrid Backpropagation—Genetic Algorithm, Marine Structures, 2020, vol. 74, article no. 102807.

    Article  Google Scholar 

  16. He, W. and Liu, X., Improved Aerofoil Parameterisation Based on Class/Shape Function Transformation, The Aeronautical Journal, 2019, vol. 123, issue 1261, pp. 632–640.

    Article  Google Scholar 

  17. Xiaojing Wu, Weiwei Zhang, Xuhao Peng, and Ziyi Wang, Benchmark Aerodynamic Shape Optimization with the POD-Based CST Airfoil Parametric Method, Aerospace Science and Technology, 2019, vol. 84, pp. 632–640.

    Article  Google Scholar 

  18. Kulfan, B.M., Universal Parametric Geometry Representation Method, Journal of Aerocraft, 2008, vol. 45, issue 1, pp. 142–158.

    Article  Google Scholar 

  19. Masdari, M., Tahani, M., Naderi, M.H., and Babayan, N., Optimization of Airfoil Based Savonius Wind Turbine Using Coupled Discrete Vortex Method and Salp Swarm Algorithm, Journal of Cleaner Production, 2019, vol. 222, pp. 47–56.

    Article  Google Scholar 

  20. Drela, M. and Giles, M.B., Viscous-Inviscid Analysis of Transonic and Low Reynolds Number Airfoils, AIAA Journal, 1987, vol. 25, issue 10, pp. 1347–1355.

    Article  Google Scholar 

  21. Drela, M., XFOIL: an Analysis and Design System for Low Reynolds Number Airfoils, in Low Reynolds Number Aerodynamics, Mueller, T.J. Ed., Berlin: Springer-Verlag, 1989, pp. 1–12.

    Google Scholar 

  22. Khramov, A.A. and Ishkov, S.A., Optimization of Project-Ballistic Parameters for Low Earth Orbit Spacecraft with Propulsion Systems with Energy Storage, Izv. Vuz. Av. Tekhnika, 2016, vol. 59, no. 3, pp. 52–57 [Russian Aeronautics (Engl. Transl.), 2016, vol. 59, no. 3, pp. 351–357].

    Google Scholar 

  23. Onushkin, Yu.P., Sizov, D.A., and Poluyakhtov, V.A., Comprehensive Approach to Mathematical Modeling and Helicopter Flight Task Optimization, Izv. Vuz. Av. Tekhnika, 2017, vol. 60, no. 2, pp. 22–27 [Russian Aeronautics (Engl. Transl.), 2017, vol. 60, no. 2, pp. 184–189].

    Google Scholar 

  24. Wang, X., Jin, Y., Schmitt, S., and Olhofer, M., An Adaptive Bayesian Approach to Surrogate-Assisted Evolutionary Multi-Objective Optimization, Information Sciences, 2020, vol. 519, pp. 317–331.

    Article  MathSciNet  Google Scholar 

  25. Pehlivanoglu, Y.V., Efficient Accelerators for PSO in an Inverse Design of Multi-Element Airfoils, Aerospace Science and Technology, 2019, vol. 91, pp. 110–121.

    Article  Google Scholar 

  26. Jun Tao, Gang Sun, Xinyu Wang, and Liqiang Guo, Robust Optimization for a Wing at Drag Divergence Mach Number Based on an Improved PSO Algorithm, Aerospace Science and Technology, 2019, vol. 92, pp. 653–667.

    Article  Google Scholar 

  27. Chegini, S.N., Bagheri, A., and Najafi, F., PSOSCALF: A New Hybrid PSO Based on Sine Cosine Algorithm and Levy Flight for Solving Optimization Problems, Applied Soft Computing, 2018, vol. 73, pp. 697–726.

    Article  Google Scholar 

  28. Saleem, A. and Kim, M.-H., Aerodynamic Performance Optimization of an Airfoil-Based Airborne Wind Turbine Using Genetic Algorithm, Energy, 2020, vol. 203, article no. 117841.

    Article  Google Scholar 

  29. Fusi, F., Congedo, P.M., Guardone, A., and Quaranta, G., Assessment of Robust Optimization for Design of Rotorcraft Airfoils in Forward Flight, Aerospace Science and Technology, 2020, vol. 107, article no. 106355.

    Article  Google Scholar 

  30. ZhaoCheng Sun, YuFeng Mao, and MengHao Fan, Performance Optimization and Investigation of Flow Phenomena on Tidal Turbine Blade Airfoil Considering Cavitation and Roughness, Applied Ocean Research, 2020, vol. 106, article no. 102463.

    Google Scholar 

  31. Kennedy, J. and Eberhart, R.C., Swarm Intelligence, USA: Morgan Kaufmann, 2001.

    Google Scholar 

  32. Clerc, M. and Kennedy, J., The Particle Swarm—Explosion, Stability, and Convergence in a Multidimensional Complex Space, IEEE Transactions on Evolutionary Computation, 2002, vol. 6, no. 1, pp. 58–73.

    Article  Google Scholar 

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ACKNOWLEDGEMENTS

The work was financially supported by the Ministry of Science and Higher Education of the Russian Federation during the implementation of the project “Fundamentals of Mechanics, Monitoring and Control Systems of Unmanned Aircraft Systems with Shape-Forming Structures Deeply Integrated with Power Plants and Having Unique Properties Not Applied Today in Manned Aviation”, no. FEFM-2020-0001.

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Authors and Affiliations

  1. Ustinov Baltic State Technical University “VOENMEH”, ul. 1ya Krasnoarmeiskaya 1, 190005, St. Petersburg, Russia

    N. V. Prodan & A. A. Kurnukhin

  2. Sevastopol State University, ul. Universitetskaya 33, 299053, Sevastopol, Russia

    N. V. Prodan & A. A. Kurnukhin

Authors
  1. N. V. Prodan
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  2. A. A. Kurnukhin
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Correspondence to A. A. Kurnukhin.

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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Aviatsionnaya Tekhnika, 2021, No. 4, pp. 74 - 80.

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Prodan, N.V., Kurnukhin, A.A. Application of Mathematical Optimization Methodsfor Designing Airfoil Considering Viscosity. Russ. Aeronaut. 64, 670–677 (2021). https://doi.org/10.3103/S1068799821040115

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  • DOI: https://doi.org/10.3103/S1068799821040115

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