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Airfoil response to periodic vertical and longitudinal gusts

Published online by Cambridge University Press:  17 January 2024

Tong Wang ,
Li-Hao Feng Open the ORCID record for Li-Hao Feng [Opens in a new window] ,
Yu-Tian Cao  and
Jin-Jun Wang Open the ORCID record for Jin-Jun Wang [Opens in a new window]
Tong Wang
Affiliation:
Fluid Mechanics Key Laboratory of Education Ministry, Beijing University of Aeronautics and Astronautics, Beijing 100191, PR China
Li-Hao Feng*
Affiliation:
Fluid Mechanics Key Laboratory of Education Ministry, Beijing University of Aeronautics and Astronautics, Beijing 100191, PR China
Yu-Tian Cao
Affiliation:
Fluid Mechanics Key Laboratory of Education Ministry, Beijing University of Aeronautics and Astronautics, Beijing 100191, PR China
Jin-Jun Wang
Affiliation:
Fluid Mechanics Key Laboratory of Education Ministry, Beijing University of Aeronautics and Astronautics, Beijing 100191, PR China
*
† Email address for correspondence: lhfeng@buaa.edu.cn
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Abstract

Gust response has consistently been a concern in engineering. Critical theories have been proposed in the past to predict the unsteady lift response of an airfoil experiencing vertical gusts by Atassi, and longitudinal gusts by Greenberg. However, their applicability for an airfoil with non-zero angles of attack still needs clarification. Thus, force measurements are conducted to examine these theories’ validity and quasi-steady corrections are applied to compensate potential disparities between the idealised and real flow conditions. Velocity measurements are performed to scrutinise the effect of gusts on the flow around the airfoil, and subsequently to reveal the underlying mechanism governing the airfoil's response to gust-induced perturbations. In the study, two pitching vanes are arranged upstream to generate periodic vertical and longitudinal gusts, whereas a downstream airfoil with angles of attack of 0–12° is subjected to two gust types. It is found that Greenberg's theory demonstrates superior predictive capability in pre-stall regimes, with the potential for its effectiveness to be expanded to post-stall regimes through theoretical refinements. In contrast, Atassi's theory exhibits significant deviations from experimental outcomes across the measured angles of attack. Nevertheless, a modified version of the theory aligns better with experimental results at small angles of attack, whereas substantial discrepancies persist as the angle of attack increases. In the pre-stall regime, the aerodynamic response of the airfoil to vertical gusts displays a linear correlation with the flow angle near the leading edge. In the post-stall regime, the vertical gust induces dynamic stall of the airfoil. The flow angle has an essential effect on the lift coefficient but it alone is inadequate to dictate the trend of the lift coefficient. The vorticity statistics show that negative vortex circulation strongly correlates with the lift coefficient. Thus, further correction of the theory or a new vortex model can be expected to predict the lift variation.

JFM classification

Aerodynamics: Aerodynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 979 , 25 January 2024 , A35
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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References

Andreu-Angulo, I. & Babinsky, H. 2022 Mitigation of airfoil gust loads through pitch. AIAA J. 60 (9), 5273–5285.CrossRefGoogle Scholar
Andreu-Angulo, I., Babinsky, H., Biler, H., Sedky, G. & Jones, A.R. 2020 Effect of transverse gust velocity profiles. AIAA J. 58 (12), 5123–5133.CrossRefGoogle Scholar
Atassi, H.M. 1984 The Sears problem for a lifting airfoil revisited - new results. J. Fluid Mech. 141, 109–122.CrossRefGoogle Scholar
Billah, K.Y. & Scanlan, R.H. 1991 Resonance, Tacoma Narrows bridge failure, and undergraduate physics textbooks. Am. J. Phys. 59 (2), 118–124.CrossRefGoogle Scholar
Carr, L.W. 1988 Progress in analysis and prediction of dynamic stall. J. Aircraft 25 (1), 6–17.CrossRefGoogle Scholar
Champagnat, F., Plyer, A., Le Besnerais, G., Leclaire, B., Davoust, S. & Le Sant, Y. 2011 Fast and accurate PIV computation using highly parallel iterative correlation maximization. Exp. Fluids 50 (4), 1169–1182.CrossRefGoogle Scholar
Choi, J., Colonius, T. & Williams, D.R. 2015 Surging and plunging oscillations of an airfoil at low Reynolds number. J. Fluid Mech. 763, 237–253.CrossRefGoogle Scholar
Commerford, G.L. & Carta, F.O. 1974 Unsteady aerodynamic response of a two-dimensional airfoil at high reduced frequency. AIAA J. 12 (1), 43–48.CrossRefGoogle Scholar
Cordes, U., Kampers, G., Meissner, T., Tropea, C., Peinke, J. & Hölling, M. 2017 Note on the limitations of the Theodorsen and Sears functions. J. Fluid Mech. 811, R1.CrossRefGoogle Scholar
Ellington, C.P., van den Berg, C., Willmott, A.P. & Thomas, A.L.R. 1996 Leading-edge vortices in insect flight. Nature 384 (6610), 626–630.CrossRefGoogle Scholar
Feng, L.H., Choi, K.S. & Wang, J.J. 2015 Flow control over an airfoil using virtual Gurney flaps. J. Fluid Mech. 767, 595–626.CrossRefGoogle Scholar
Feng, L.H., Li, Z.Y. & Chen, Y.L. 2020 Lift enhancement strategy and mechanism for a plunging airfoil based on vortex control. Phys. Fluids 32 (8), 087116.CrossRefGoogle Scholar
Fernandez, F., Cleaver, D. & Gursul, I. 2021 Unsteady aerodynamics of a wing in a novel small-amplitude transverse gust generator. Exp. Fluids 62 (1), 9.CrossRefGoogle Scholar
Fidkowski, K.J. 2022 A coupled inviscid–viscous airfoil analysis solver, revisited. AIAA J. 60 (5), 2961–2971.CrossRefGoogle Scholar
Goldstein, M.E. & Atassi, H. 1976 A complete second-order theory for the unsteady flow about an airfoil due to a periodic gust. J. Fluid Mech. 74 (4), 741–765.CrossRefGoogle Scholar
Granlund, K., Monnier, B., Ol, M. & Williams, D. 2014 Airfoil longitudinal gust response in separated vs. attached flows. Phys. Fluids 26 (2), 027103.CrossRefGoogle Scholar
Greenberg, J.M. 1947 Airfoil in sinusoidal motion in a pulsating stream. NACA Tech. Note.Google Scholar
Hakkinen, R.J. & Richardson, A.S. 1957 Theoretical and experimental investigation of random gust loads part I: aerodynamic transfer function of a simple wing configuration in incompressible flow. NACA Tech. Note.Google Scholar
He, X., Guo, Q., Xu, Y., Feng, L. & Wang, J. 2023 Aerodynamics and fluid–structure interaction of an airfoil with actively controlled flexible leeward surface. J. Fluid Mech. 954, A34.CrossRefGoogle Scholar
He, P. & Xia, J. 2023 Aeroelastic model of flexible blades of wind turbines under complex wind speed profiles. Acta Mechanica Sin. 39 (9), 322477.CrossRefGoogle Scholar
Isaacs, R. 1945 Airfoil theory for flows of variable velocity. J. Aeronaut. Sci. 12 (1), 113–117.CrossRefGoogle Scholar
Jancauskas, E.D. & Melbourne, W.H. 1986 The aerodynamic admittance of two-dimensional rectangular section cylinders in smooth flow. J. Wind Eng. Ind. Aerodyn. 23, 395–408.CrossRefGoogle Scholar
Kim, D.H., Chang, J.W. & Chung, J. 2011 Low-Reynolds-number effect on aerodynamic characteristics of a NACA 0012 airfoil. J. Aircraft 48 (4), 1212–1215.CrossRefGoogle Scholar
Leishman, G.J. 2006 Principles of Helicopter Aerodynamics, 2nd edn. Cambridge University Press.Google Scholar
Leung, J.M., Wong, J.G., Weymouth, G.D. & Rival, D.E. 2018 Modeling transverse gusts using pitching, plunging, and surging airfoil motions. AIAA J. 56 (8), 3271–3278.CrossRefGoogle Scholar
Li, Z.Y., Feng, L.H., Kissing, J., Tropea, C. & Wang, J.J. 2020 Experimental investigation on the leading-edge vortex formation and detachment mechanism of a pitching and plunging plate. J. Fluid Mech. 901, A17.CrossRefGoogle Scholar
Li, M., Li, Q. & Shi, H. 2021 Effect of sinusoidal vertical gust on the pressure distributions on and flow structures around a rectangular cylinder. Exp. Fluids 62 (7), 148.CrossRefGoogle Scholar
Ma, L., Feng, L., Pan, C., Gao, Q. & Wang, J. 2015 Fourier mode decomposition of PIV data. Sci. China Technol. Sci. 58 (11), 1935–1948.CrossRefGoogle Scholar
Ma, R., Yang, Y., Li, M. & Li, Q. 2021 The unsteady lift of an oscillating airfoil encountering a sinusoidal streamwise gust. J. Fluid Mech. 908, A22.CrossRefGoogle Scholar
Mark Rennie, R., Catron, B., Zubair Feroz, M., Williams, D. & He, X. 2019 Dynamic behavior and gust simulation in an unsteady flow wind tunnel. AIAA J. 57 (4), 1423–1433.CrossRefGoogle Scholar
Pan, C., Xue, D., Xu, Y., Wang, J.J. & Wei, R.J. 2015 Evaluating the accuracy performance of Lucas-Kanade algorithm in the circumstance of PIV application. Sci. China Phys. Mech. Astron. 58 (10), 104704.CrossRefGoogle Scholar
Sears, W.R. 1941 Some aspects of non-stationary airfoil theory and its practical application. J. Aeronaut. Sci. 8 (3), 104–108.CrossRefGoogle Scholar
Sedky, G., Gementzopoulos, A., Andreu-Angulo, I., Lagor, F.D. & Jones, A.R. 2022 Physics of gust response mitigation in open-loop pitching manoeuvres. J. Fluid Mech. 944, A38.CrossRefGoogle Scholar
Shyy, W. & Liu, H. 2007 Flapping wings and aerodynamic lift: the role of leading-edge vortices. AIAA J. 45 (12), 2817–2819.CrossRefGoogle Scholar
Spinato, F., Tavner, P.J., van Bussel, G.J.W. & Koutoulakos, E. 2009 Reliability of wind turbine subassemblies. IET Renew. Power Gener. 3 (4), 387–401.CrossRefGoogle Scholar
Strangfeld, C., Müller-Vahl, H., Nayeri, C.N., Paschereit, C.O. & Greenblatt, D. 2016 Airfoil in a high amplitude oscillating stream. J. Fluid Mech. 793, 79–108.CrossRefGoogle Scholar
Theodorsen, T. 1935 General theory of aerodynamic instability and the mechanism of flutter. NACA Tech. Rep.Google Scholar
van der Wall, B.G. & Leishman, J.G. 1994 On the influence of time-varying flow velocity on unsteady aerodynamics. J. Am. Helicopter Soc. 39 (4), 25–36.CrossRefGoogle Scholar
Wang, T. & Feng, L.H. 2022 Characterization of vertical and longitudinal gusts generated by twin pitching airfoils. Phys. Fluids 34 (9), 097116.CrossRefGoogle Scholar
Wang, T., Feng, L.H. & Li, Z.Y. 2021 a Effect of leading-edge protuberances on unsteady airfoil performance at low Reynolds number. Exp. Fluids 62 (10), 217.CrossRefGoogle Scholar
Wang, M.Y., Hashmi, S.A., Sun, Z.X., Guo, D.L., Vita, G., Yang, G.W. & Hemida, H. 2021 b Effect of surface roughness on the aerodynamics of a high-speed train subjected to crosswinds. Acta Mechanica Sin. 37 (7), 1090–1103.CrossRefGoogle Scholar
Wang, S., Zhou, Y., Alam, M.M. & Yang, H. 2014 Turbulent intensity and Reynolds number effects on an airfoil at low Reynolds numbers. Phys. Fluids 26 (11), 115107.CrossRefGoogle Scholar
Wei, N.J., Kissing, J., Wester, T.T.B., Wegt, S., Schiffmann, K., Jakirlic, S., Hölling, M., Peinke, J. & Tropea, C. 2019 Insights into the periodic gust response of airfoils. J. Fluid Mech. 876, 237–263.CrossRefGoogle Scholar
Williams, D.R. & King, R. 2018 Alleviating unsteady aerodynamic loads with closed-loop flow control. AIAA J. 56 (6), 2194–2207.CrossRefGoogle Scholar
Winslow, J., Otsuka, H., Govindarajan, B. & Chopra, I. 2018 Basic understanding of airfoil characteristics at low Reynolds numbers (104–105). J. Aircraft 55 (3), 1050–1061.CrossRefGoogle Scholar
Yang, Y., Li, M., Ma, C. & Li, S. 2017 Experimental investigation on the unsteady lift of an airfoil in a sinusoidal streamwise gust. Phys. Fluids 29 (5), 051703.CrossRefGoogle Scholar
Young, A.M. & Smyth, A.S.M. 2021 Gust–airfoil coupling with a loaded airfoil. AIAA J. 59 (3), 773–785.CrossRefGoogle Scholar
Zhou, J., Adrian, R.J., Balachandar, S. & Kendall, T.M. 1999 Mechanisms for generating coherent packets of hairpin vortices in channel flow. J. Fluid Mech. 387, 353–396.CrossRefGoogle Scholar
Zhu, W., Mccrink, M.H., Bons, J.P. & Gregory, J.W. 2020 The unsteady Kutta condition on an airfoil in a surging flow. J. Fluid Mech. 893, R2.CrossRefGoogle Scholar