Integral Airfoil Generation of Multi-rotor Aircraft Based on Optimization of Upper Wing Contour and CFD Simulation

Wang, Z.; Zhu, Y.; Yuan, Q.; Gu, W. B.; Xie, X. B.

doi:10.47176/jafm.17.05.2169

Integral Airfoil Generation of Multi-rotor Aircraft Based on Optimization of Upper Wing Contour and CFD Simulation

Document Type : Regular Article

Authors

¹ Army Command Academy of PLA, Jiangsu Nanjing 210045, China

² Army Engineering University of PLA, Nanjing, Jiangsu, 210007, China

³ Southwest University of Science and Technology, Mianyang, Sichuan, 621010, China

10.47176/jafm.17.05.2169

Abstract

Regarding the airfoil optimization design of multi-rotor unmanned aerial vehicles, this paper proposes an integral airfoil design method based on upper airfoil contour optimization. Firstly, by designing concave descent input curves with 0-1 distribution, the upper arc of different optimized airfoils is obtained using the Tangent circles method. Secondly, an integral airfoil generation method is developed after establishing the middle arc. As the upper and lower arcs of different shapes are randomly combined, various airfoil profiles are obtained by random assortment. Finally, the effectiveness and accuracy of the designed airfoil are validated through Python programming. The airfoil is generated by the XFOIL program, and the optimal airfoil is output with a lift-to-drag ratio as the target. Meanwhile, an accurate Fluent analysis model is established, and a comparison verification is conducted on the data with the attack angle falling within [-8.02, 12.04] and lift-to-drag ratio falling within [-50, 100]. After Fluent modeling of the designed airfoil, the Euclidean distance between the calculated angle-lift-drag ratio data curve and the data curve tested by the wind tunnel is 0.0331, while the Euclidean distance between the simulated data in the literature and the wind tunnel data is 0.0408. It indicates that our precise model achieves 18.9% higher accuracy than the literature model. Testing and verification results indicate that our designed airfoil based on upper arc optimization and its corresponding airfoil library can meet the design requirements for the aerodynamic performance of airfoils in practical applications. It provides a valuable reference for the development of airfoil design, optimization, and generation methods.

Keywords

Main Subjects

Computational Fluid Dynamics

References

Aghabeigi, M., Khodaygan, S., & Movahhedy, M. R. (2022). Tolerance analysis of a compliant assembly using random Non-Uniform Rational B-Spline curves and isogeometric method. Journal of Computational Design and Engineering, 9(6), 2170-2195. https://doi.org/10.1093/jcde/qwac093.

Akram, M. T., & Kim, M. H. (2021). Aerodynamic shape optimization of NREL S809 airfoil for wind turbine blades using Reynolds-averaged Navier stokes model—Part II. Applied Sciences, 11(5), 2211. https://doi.org/10.3390/app11052211.

Bharadwaj, P., Mulder, W., & Drijkoningen, G. (2016). Full waveform inversion with an auxiliary bump functional. Geophysical Journal International, 206(2), 1076-1092. https://doi.org/10.1093/gji/ggw129.

Buckley, H. P., & Zingg, D. W. (2013). Approach to aerodynamic design through numerical optimization. AIAA Journal, 51(8), 1972-1981. https://doi.org/10.2514/1.J052268.

Chen, X., & Agarwal, R. K. (2014). Shape optimization of airfoils in transonic flow using a multi-objective genetic algorithm. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 228(9), 1654-1667. https://doi.org/10.1177/0954410013500613.

Fujii, K., & Dulikravich, G. (Eds.). (2013). Recent Development of Aerodynamic Design Methodologies: Inverse Design and Optimization (Vol. 65). Springer Science & Business Media.

Gardner, B., & Selig, M. (2003, January). Airfoil design using a genetic algorithm and an inverse method. 41st Aerospace Sciences Meeting and Exhibit (p. 43). https://doi.org/10.2514/6.2003-43.

Guibault, F., Bentamy, A., & Trépanier, J. Y. (2002). Constraints specifications on NURBS Surfaces for Wing Geometric Representation. 9th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization (p. 5400). https://doi.org/10.2514/6.2003-43.

Hicks, R. M., & Henne, P. A. (1978). Wing design by numerical optimization. Journal of Aircraft, 15(7), 407-412. https://doi.org/10.2514/3.58379.

Huang, D., Allen, T. T., Notz, W. I., & Zeng, N. (2006). Global optimization of stochastic black-box systems via sequential kriging meta-models. Journal of Global Optimization, 34, 441-466. https://doi.org/10.1007/s10898-005-2454-3.

Khurana, M., Winarto, H., & Sinha, A. (2008, October). Application of swarm approach and artificial neural networks for airfoil shape optimization. 12th AIAA/ISSMO Multidisciplinary Analysis And Optimization Conference (p. 5954). https://doi.org/10.2514/6.2008-5954.

Kou, J., Botero-Bolívar, L., Ballano, R., Marino, O., de Santana, L., Valero, E., & Ferrer, E. (2023). Aeroacoustic airfoil shape optimization enhanced by autoencoders. Expert Systems with Applications, 217, 119513. https://doi.org/10.48550/arXiv.2210.00101.

Kulfan, B. M. (2008). Universal parametric geometry representation method. Journal of Aircraft, 45(1), 142-158. https://doi.org/10.2514/1.29958.

Lee, K. D., & Eyi, S. (1992). Aerodynamic design via optimization. Journal of Aircraft, 29(6), 1012-1019. https://doi.org/10.2514/3.46278.

Lepine, J., Guibault, F., Trepanier, J. Y., & Pepin, F. (2001). Optimized nonuniform rational B-spline geometrical representation for aerodynamic design of wings. AIAA Journal, 39(11), 2033-2041. https://doi.org/10.2514/2.1206.

Leung, T., & Zingg, D. (2009). Single-and multi-point aerodynamic shape optimization using a parallel Newton-Krylov approach. 19th AIAA Computational Fluid Dynamics (p. 3803). https://doi.org/10.2514/6.2009-3803.

Li, J., Zhang, M., Tay, C. M. J., Liu, N., Cui, Y., Chew, S. C., & Khoo, B. C. (2022). Low-Reynolds-number airfoil design optimization using deep-learning-based tailored airfoil modes. Aerospace Science and Technology, 121, 107309. https://doi.org/10.1016/j.ast.2021.107309.

Li, M., Liu, X., Jia, D., & Liang, Q. (2015). Interpolation using non-uniform rational B-spline for the smooth milling of ruled-surface impeller blades. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 229(7), 1118-1130. https://doi.org/10.1177/0954405415586966.

McGhee, R. J. (1980). Low-speed aerodynamic characteristics of a 17-percent-thick medium speed airfoil designed for general aviation applications. National Aeronautics and Space Administration, Scientific and Technical Information Branch.

Mengistu, T., & Ghaly, W. (2002). A geometrical representation of turbomachinery cascades using NURBS. 40th AIAA Aerospace Sciences Meeting & Exhibit (p. 318). https://doi.org/10.2514/6.2002-318.

Nemec, M., Zingg, D. W., & Pulliam, T. H. (2004). Multipoint and multi-objective aerodynamic shape optimization. AIAA Journal, 42(6), 1057-1065. https://doi.org/10.2514/1.10415.

Painchaud-Ouellet, S., Tribes, C., Trépanier, J. Y., & Pelletier, D. (2006). Airfoil shape optimization using a nonuniform rational b-splines parametrization under thickness constraint. AIAA Journal, 44(10), 2170-2178. https://doi.org/10.2514/1.15117.

Prautzsch, H., Boehm, W., & Paluszny, M. (2002). Bézier and B-spline techniques (Vol. 6). Berlin: Springer.

Ramamoorthy, P., & Padmavathi, K. (1977). Airfoil design by optimization. Journal of Aircraft, 14(2), 219-221. https://doi.org/10.2514/3.44587.

Ribeiro, A. F. P., Awruch, A. M., & Gomes, H. M. (2012). An airfoil optimization technique for wind turbines. Applied Mathematical Modelling, 36(10), 4898-4907. https://doi.org/10.1016/j.apm.2011.12.026.

Sekar, V., Zhang, M., Shu, C., & Khoo, B. C. (2019). Inverse design of airfoil using a deep convolutional neural network. AIAA Journal, 57(3), 993-1003. https://doi.org/10.2514/1.J057894.

Sevilla, R., Fernández-Méndez, S., & Huerta, A. (2011). NURBS-enhanced finite element method (NEFEM) a seamless bridge between CAD and FEM. Archives of Computational Methods in Engineering, 18, 441-484. https://doi.org/10.1007/s11831-011-9066-5.

Sun, G., Sun, Y., & Wang, S. (2015). Artificial neural network based inverse design: Airfoils and wings. Aerospace Science and Technology, 42, 415-428. https://doi.org/10.1016/j.ast.2015.01.030.

Vicini, A., & Quagliarella, D. (1997). Inverse and direct airfoil design using a multiobjective genetic algorithm. AIAA Journal, 35(9), 1499-1505. https://doi.org/10.2514/2.274.

Wang, G., Chen, Q., & Zhou, M. (2004). NUAT B-spline curves. Computer Aided Geometric Design, 21(2), 193-205. https://doi.org/10.1016/j.cagd.2003.10.002.

Zakaria, R., Wahab, A. F., Ismail, I., & Zulkifly, M. I. E. (2021). Complex uncertainty of surface data modeling via the type-2 fuzzy B-spline model. Mathematics, 9(9), 1054. https://doi.org/10.3390/math9091054.

Zhang, T. T., Wang, Z. G., Huang, W., & Yan, L. (2018). A review of parametric approaches specific to aerodynamic design process. Acta Astronautica, 145, 319-331. https://doi.org/10.1016/j.actaastro.2018.02.011.

Zhou, H., Zhou, S., Gao, Z., Dong, H., & Yang, K. (2021). Blades optimal design of squirrel cage fan based on Hicks-Henne function. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 235(19), 3844-3858. https://doi.org/10.1177/0954406220969728.