Fast Prediction of Multiple Parameters Related to Iced Airfoil Based on POD and Kriging Methods

Document Type : Regular Article


1 College of Aeronautics, Northwestern Polytechnical University, Xi'an, Shaanxi,710072, China

2 Key Laboratory of Icing and Anti/De-icing, China Aerodynamics Research and Development Center, Mianyang, Sichuan, 621000, China

3 School of Aeronautical Engineering, Civil Aviation Flight University of China, Guanghan, Sichuan, 618300, China



Ice accretion threatens aircraft safety. With the wide application of unmanned aerial vehicles (UAVs), the design of ice-tolerant UAVs has become a problem that must be solved. Forty conditions for the continuous/intermittent maximum icing conditions were sampled in Appendix C of Federal Aviation Regulations Part 25. Herein, numerical simulations of icing were performed on an NACA 0009 airfoil for 5, 15, and 30 min, and the ice mass and ice shapes were obtained at different times. Numerical simulations of the aerodynamic characteristics of the iced configuration at 5, 15, and 30 min were conducted, and the coefficients of lift, drag, and pitch moment were obtained. Surrogate models of the ice shape, mass of the ice accretion, lift coefficient, drag coefficient, and pitch moment coefficient at different moments were built based on proper orthogonal decomposition and kriging interpolation. The results demonstrate that the surrogate models accurately predicted the ice shape, ice mass, lift coefficient, drag coefficient, and pitch moment coefficient at different moments. Compared with the numerical simulation results, the maximum relative errors of the ice mass, lift coefficient, drag, and pitch moment predicted by the surrogate models were 7.8%, 3.4%, 3.9%, and 7.6%, respectively. This method can help in designing the ice-tolerant UAVs and envelope determination under icing conditions.


Berkooz, G., P. Holmes and J. L. Lumley (1993). The Proper Orthogonal Decomposition in the Analysis of Turbulent Flows. Annual Review of Fluid Mechanics 25(1), 539–575.##
Bhola, R., N. H. Krishna, K. N. Ramesh, J. Senthilnath and G. Anand (2018). Detection of the power lines in UAV remote sensed images using spectral-spatial methods. Journal of Environmental Management 206(15), 1233-1242.##
Bourgault, Y, H. Beaugendre and W. G. Habashi (2000). Development of a shallow-water icing model in FENSAP-ICE. Journal of Aircraft 37(4), 640-646.##
Bragg, M. B., T. Basar T, W. R. Perkins, M. S. Selig, P. G. Voulgaris and J. W. Melody (2002). Smart icing systems for aircraft icing safety. 40th AIAA Aerospace Sciences Meeting & Exhibit AIAA-2002-0813.##
Bragg, M. B. and W. J. Coirier (1986). Aerodynamic measurements of an airfoil with simulated glaze ice. 24th AIAA Aerospace Sciences Meeting AIAA-86-0484.##
Cebeci, T. and F. Kafyeke (2003). Aircraft icing. Annual Review of Fluid Mechanics 35(1), 11-21.##
Gui, Y. W., Z. H. Zhou, Y. H. Li and H. J. Xu (2017). Multiple safety boundaries protection on aircraft icing. Acta Aeronautica et Astronautica Sinica 38(2), 520723.##
Han, Z. H. (2016). Kriging surrogate model and its application to design optimization: A review of recent progress. Acta Aeronautica et Astronautica Sinica 37(11), 3197-3225.##
He, H, G. R. Zhu, C. He and G. P. Chen (2014). Crashworthiness optimization based on Kriging metamodeling. Journal of Nanjing University of Aeronautics & Astronautics 46(2), 297-303.##
Hossain, K. N., V. Sharma, M. B. Bragg and P. G. Voulgaris (2003). Envelope protection and control adaptation in icing encounters. Proceedings of the Aiaa Aerospace Sciences Meeting & Exhibit AIAA-2003-25.##
Idris, M. K., J. Qiu, G. W. Melenka and G. Grau (2020). Printing electronics directly onto carbon fiber composites: unmanned aerial vehicle (UAV) wings with integrated heater for de-icing. Engineering Research Express 2(2), 025022.##
Jaiswal, P., Y. Pasco, G. Yakhina and S. Moreau (2022). Experimental investigation of aerofoil tonal noise at low Mach number. Journal of Fluid Mechanics 932, A31.##
Jia, Y. Z. (2018). Investigation of ice ridge forming process and protecting method. Ms. D. thesis, the Northwestern Polytechnical University, Xi’an, China.##
Kim, M., E. E. Essel and P. E. Sullivan (2022). Effect of varying frequency of a synthetic jet on flow separation over an airfoil. Physics of Fluids 34(1), 015122.##
Krige, D. G. (1951). A statistical approach to some basic mine valuation problems on the Witwatersrand. Journal of the Southern African Institute of Mining and Metallurgy 52(6), 119139.##
Liu, T., D. Li, R. R. Huang and Z. H. Zhang (2019). Ice shape prediction method of aero-icing based on reduced order model. Journal of Beijing University of Aeronautics and Astronautics 45(5), 1033- 1041.##
Makkonen, L. (1981). Estimating intensity of atmospheric ice accretion on stationary structures. Journal of Applied Meteorology and Climatology 20(5), 595-600.##
Pei, B., H. Xu, Y. Xue, W. Chen and A. Shen (2018). In-flight icing risk prediction and management in consideration of wing stall. Aircraft Engineering & Aerospace Technology 90(1), 24-32.##
Pellissier, M. C., W. G. Habashi and A. Pueyo (2012). Optimization via FENSAP-ICE of aircraft hot-air anti-icing systems. Journal of Aircraft 48(1), 265-276.##
Potapczuk, M. G. (2013). Aircraft icing research at NASA Glenn research center. Journal of Aerospace Engineering 26(2), 260-276.##
Radmanesh, M., B. Sharma, M. Kumar and D. French (2021). PDE solution to UAV/UGV trajectory planning problem by spatio-temporal estimation during wildfires. Chinese Journal of Aeronautics 34(5), 601-616.##
Scherer, J., S. Yahyanejad, S. Hayat, E. Yanmaz, T. Andre, A. Khan, V. Vukadinovic, H. Hellwagber and B. Rinner (2015). An autonomous multi-UAV system for search and rescue. Proceedings of the First Workshop on Micro Aerial Vehicle Networks, Systems, and Applications for Civilian Use. 33-38.##
Sharma, V., P. G. Voulgaris and E. Frazzoli (2004). Aircraft autopilot analysis and envelope protection for operation under icing conditions. Journal of Guidance Control & Dynamics 27(3), 454-465.##
Shin, J. and T. Bond (1992). Results of an icing test on a NACA 0012 airfoil in the NASA Lewis icing research tunnel. 30th Aerospace Sciences Meeting and Exhibit. AIAA-1992-647.##
Sirovich, L. (1987). Turbulence and the dynamics of coherent structures Ⅰ-Coherent structures, Ⅱ-Symmetries and transformations, Ⅲ-Dynamics and scaling. Quarterly of Applied Mathematics 45(3), 561-571.##
Smith, W. L. (1929). Weather problems peculiar to the New York-Chicago airway. Monthly Weather Review 57(12), 503-506.##
Thompson, G. (2019). High Resolution Numerical Weather model forecasts of icing at the ground and in the air. Proceeding. Int. Workshop on Atmospheric Icing of Structures, Reykjavík, Iceland, IWAIS.##
Vukits, T. J. (2002). Overview and risk assessment of icing for transport category aircraft and components. 40th AIAA Aerospace Sciences Meeting and Exhibit, AIAA-2002-0811.##
Wang, M., J. Su, T. Li, X. Wang, Q. Ji, Y. Cao, L. Lin and Y. Liu (2018). Determination of Arctic melt pond fraction and sea ice roughness from Unmanned Aerial Vehicle (UAV) imagery. Advances in Polar Sciences 29(3), 181-189.##
Yao, S. B., D. L. Guo, Z. X. Sun, G. W. Yang and D. W. Chen (2013). Multi-objective optimization of the streamlined head of high-speed trains based on the kriging model. Science China 43(2), 186-200.##
Zeppetelli, D. and W. G. Habashi (2012). In-flight icing risk management through computational fluid dynamics-icing analysis. Journal of Aircraft 49(2), 611-621.##