Document Type : Research Article


Department of Mechanical Engineering, Technical and Engineering Faculty, Ferdowsi University of Mashhad, Mashhad, Iran


In this study, the variation of amplitude and wavelength of the sinusoidal wing in the post-stall condition have been studied to evaluate the effect of each of these parameters on the control of the stall phenomenon and the stall’s sensitivity to Each of these two parameters is measured. For this purpose, an EPPLER considered as a wavy leading-edge wing’s cross-section and a numerical simulation is performed for Reynolds 140,000 at 22 AOA, which is exactly at post stall condition. The results show that the height of the flow separation area is more sensitive to the amplitude in tubercled wings, while the width of the flow separation area is strongly dependent on the wavelength of the sinusoidal function. The lift coefficient to drag coefficient ratio (L/D) is also more sensitive to increasing the amplitude and has decreased by 7.5%.


Main Subjects

[1] P. Watts and F. E. Fish, "The influence of passive, leading edge tubercles on wing performance," in Proc. Twelfth Intl. Symp. Unmanned Untethered Submers. Technol, 2001: Auton. Undersea Syst. Inst. Durham New Hampshire.
[2] D. Miklosovic, M. Murray, L. Howle, and F. Fish, "Leading-edge tubercles delay stall on humpback whale (Megaptera novaeangliae) flippers," Physics of fluids, vol. 16, no. 5, pp. L39-L42, 2004.
[3] D. S. Miklosovic, M. M. Murray, and L. E. Howle, "Experimental evaluation of sinusoidal leading edges," Journal of aircraft, vol. 44, no. 4, pp. 1404-1408, 2007.
[4] P. W. Weber, L. E. Howle, M. M. Murray, and D. S. Miklosovic, "Computational evaluation of the performance of lifting surfaces with leading-edge protuberances," Journal of Aircraft, vol. 48, no. 2, pp. 591-600, 2011.
[5] E. A. Van Nierop, S. Alben, and M. P. Brenner, "How bumps on whale flippers delay stall: an aerodynamic model," Physical review letters, vol. 100, no. 5, p. 054502, 2008.
[6] A. Esmaeili, H. Delgado, and J. Sousa, "Numerical simulations of Low-Reynolds-number flow past finite wings with leading-edge protuberances," Journal of Aircraft, vol. 55, no. 1, pp. 226-238, 2018.
[7] H. Delgado, A. Esmaeili, and J. M. Melo De Sousa, "Stereo PIV measurements of low-aspect-ratio Low-Reynolds-number wings with sinusoidal leading edges for improved computational modeling," in 52nd Aerospace Sciences Meeting, 2014, p. 1280.
[8] H. Jabbari, M. H. Djavareshkian, and A. Esmaeili, "Static roughness element effects on protuberance full-span wing at micro aerial vehicle application," Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, vol. 236, no. 10, pp. 2074-2091, 2022.
[9] H. Jabbari, E. Ali, and M. H. Djavareshkian, "Acoustic and phase portrait analysis of leading-edge roughness element on laminar separation bubbles at low Reynolds number flow," Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, vol. 236, no. 9, pp. 1782-1798, 2022.
[10] K. L. Hansen, R. M. Kelso, and B. B. Dally, "Performance variations of leading-edge tubercles for distinct airfoil profiles," AIAA journal, vol. 49, no. 1, pp. 185-194, 2011.
[11] R. Kelso, N. Rostamzadeh, and K. Hansen, "Tubercle geometric configurations: optimization and alternatives," Flow Control Through Bio-inspired Leading-Edge Tubercles: Morphology, Aerodynamics, Hydrodynamics and Applications, pp. 69-84, 2020.
[12] P. Chaitanya et al., "Performance and mechanism of sinusoidal leading edge serrations for the reduction of turbulence–aerofoil interaction noise," Journal of Fluid Mechanics, vol. 818, pp. 435-464, 2017.
[13] A. Esmaeili and A. Nikkhoo, "Investigation of Thickness, Camber and Maximum Proximity Effect on Infinite Wavy Wing," Journal of Aeronautical Engineering, vol. 23, no. 1, pp. 73-85, 2021.
[14] W. G. Szymczak, J. C. Rogers, J. M. Solomon, and A. E. Bergert, "A numerical algorithm for hydrodynamic free boundary problems," Journal of Computational Physics, vol. 106, no. 2, pp. 319-336, 1993.
[15] M. Kobayashi, J. Pereira, and J. Sousa, "Comparison of several open boundary numerical treatments for laminar recirculating flows," International Journal for Numerical Methods in Fluids, vol. 16, no. 5, pp. 403-419, 1993.
[16] R. B. Langtry, F. Menter, S. Likki, Y. Suzen, P. Huang, and S. Völker, "A correlation-based transition model using local variables—part II: test cases and industrial applications," Journal of turbomachinery, pp. 423-434, 2006.
[17] J. Guerreiro and J. Sousa, "Low-Reynolds-number effects in passive stall control using sinusoidal leading edges," AIAA journal, vol. 50, no. 2, pp. 461-469, 2012.
[18] A. Esmaeili, "Experimental and computational investigation of hybrid passive-active stall control for micro aerial vehicles," Universidade De Lisboa Instituto Superior TécnicO, 2018.
[19] C. Cai et al., "Periodic and aperiodic flow patterns around an airfoil with leading-edge protuberances," Physics of fluids, vol. 29, no. 11, p. 115110, 2017.