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Three-dimensional transition and force characteristics of low-Reynolds-number flows past a plunging airfoil

Published online by Cambridge University Press:  23 October 2023

An-Kang Gao Open the ORCID record for An-Kang Gao [Opens in a new window] ,
Chris D. Cantwell Open the ORCID record for Chris D. Cantwell [Opens in a new window] ,
Onur Son Open the ORCID record for Onur Son [Opens in a new window]  and
Spencer J. Sherwin Open the ORCID record for Spencer J. Sherwin [Opens in a new window]
An-Kang Gao
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, PR China Department of Aeronautics, Imperial College London, London SW7 2AZ, UK
Chris D. Cantwell
Affiliation:
Department of Aeronautics, Imperial College London, London SW7 2AZ, UK
Onur Son
Affiliation:
Department of Mechanical Engineering, University of Bath, Bath BA2 7AY, UK Department of Aeronautical Engineering, Gebze Technical University, Kocaeli 41400, Turkey
Spencer J. Sherwin*
Affiliation:
Department of Aeronautics, Imperial College London, London SW7 2AZ, UK
*
†Email address for correspondence: jfluidmech@imperial.ac.uk
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Abstract

The three-dimensional (3-D) transition of the leading-edge vortex (LEV) and the force characteristics of the plunging airfoil are investigated in the chord-based Strouhal number $St_c$ range of 0.10 to 1.0 by means of experimental measurements, numerical simulations and linear stability analysis in order to understand the spanwise instabilities and the effects on the force. We find that the interaction pattern of the LEV, the LEV from a previous cycle (pLEV) and the trailing-edge vortex (TEV) is the primary mechanism that affects the 3-D transition and associated force characteristics. For $St_c \leq 0.16$, the 3-D transition is dominated by the LEV–TEV interaction. For $0.16 < St_c \leq 0.44$, the TEV lies in the middle of the LEV and the pLEV and therefore vortex interaction between them is relatively weak; as a result, the LEV remains two-dimensional up to a relatively high Reynolds number of $Re = 4000$ at $St_c = 0.32$. For $0.44 < St_{c} \leq 0.54$, and at relatively low Reynolds numbers, the pLEV and the TEV tend to form a clockwise vortex pair, which is beneficial for the high lift and stability of the LEV. For $0.49 \leq St_c$, the pLEV and TEV tend to form an anticlockwise vortex pair, which is detrimental to the lift and flow stability. In the last $St_c$ range, vortex interaction involving the LEV, the TEV and the pLEV results in an unstable period-doubling mode which has a wavelength of about two chord-lengths and the 3-D transition enhances the lift.

JFM classification

Vortex Flows: Vortex instability Vortex Flows: Vortex interactions

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JFM Papers
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Journal of Fluid Mechanics , Volume 973 , 25 October 2023 , A43
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© The Author(s), 2023. Published by Cambridge University Press

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References

Andersen, A., Bohr, T., Schnipper, T. & Walther, J.H. 2017 Wake structure and thrust generation of a flapping foil in two-dimensional flow. J. Fluid Mech. 812, R4.CrossRefGoogle Scholar
Andro, J.-Y. & Jacquin, L. 2009 Frequency effects on the aerodynamic mechanisms of a heaving airfoil in a forward flight configuration. Aerosp. Sci. Technol. 13 (1), 71–80.CrossRefGoogle Scholar
Barkley, D., Blackburn, H.M. & Sherwin, S.J. 2008 Direct optimal growth analysis for timesteppers. Intl J. Numer. Meth. Fluids 57 (9), 1435–1458.CrossRefGoogle Scholar
Cantwell, C.D., et al. 2015 Nektar++: an open-source spectral/HP element framework. Comput. Phys. Commun. 192, 205–219.CrossRefGoogle Scholar
Chang, C.-C. 1992 Potential flow and forces for incompressible viscous flow. Proc. R. Soc. Lond. A 437 (1901), 517–525.Google 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
Cleaver, D.J., Wang, Z. & Gursul, I. 2012 Bifurcating flows of plunging aerofoils at high Strouhal numbers. J. Fluid Mech. 708, 349–376.CrossRefGoogle Scholar
Cleaver, D.J., Wang, Z., Gursul, I. & Visbal, M.R. 2011 Lift enhancement by means of small-amplitude airfoil oscillations at low Reynolds numbers. AIAA J. 49 (9), 2018–2033.CrossRefGoogle Scholar
Deng, J., Sun, L. & Shao, X. 2015 Dynamical features of the wake behind a pitching foil. Phys. Rev. E 92 (6), 063013.CrossRefGoogle ScholarPubMed
Deng, J., Sun, L. & Shao, X. 2017 Floquet stability analysis in the wake of a NACA0015 airfoil at post-stall angles of attack. Phys. Fluids 29 (9), 094104.CrossRefGoogle Scholar
Deng, J., Sun, L., Teng, L., Pan, D. & Shao, X. 2016 The correlation between wake transition and propulsive efficiency of a flapping foil: a numerical study. Phys. Fluids 28 (9), 094101.CrossRefGoogle Scholar
Dong, S., Karniadakis, G.E. & Chryssostomidis, C. 2014 A robust and accurate outflow boundary condition for incompressible flow simulations on severely-truncated unbounded domains. J. Comput. Phys. 261, 83–105.CrossRefGoogle Scholar
Eldredge, J.D. & Jones, A.R. 2019 Leading-edge vortices: mechanics and modeling. Annu. Rev. Fluid Mech. 51 (1), 75–104.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
Floryan, D., Van Buren, T. & Smits, A.J. 2020 Swimmers’ wake structures are not reliable indicators of swimming performance. Bioinspir. Biomim. 15 (2), 024001.CrossRefGoogle Scholar
Gao, A.-K., Sherwin, S.J. & Cantwell, C.D. 2020 Three-dimensional instabilities of vortices shed from a plunging wing: computations. In 73rd Annual Meeting of the APS Division of Fluid Dynamics (APSDFD 2020), Bulletin of the American Physical Society. American Physical Society.Google Scholar
Gao, A.-K., Sherwin, S.J. & Cantwell, C.D. 2022 Three-dimensional transition of a low Reynolds number flow past a plunging NACA 0012 airfoil at post-stall angle of attack. In 12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12), Osaka, Japan..CrossRefGoogle Scholar
Gao, A.-K. & Wu, J. 2019 A note on the Galilean invariance of aerodynamic force theories in unsteady incompressible flows. Acta Mechanica Sin. 35 (6), 1150–1154.CrossRefGoogle Scholar
Gao, A.-K., Zou, S.-F., Shi, Y. & Wu, J.Z. 2019 Passing-over leading-edge vortex: the thrust booster in heaving airfoil. AIP Adv. 9 (3), 035314.CrossRefGoogle Scholar
Godoy-Diana, R., Aider, J.-L. & Wesfreid, J.E. 2008 Transitions in the wake of a flapping foil. Phys. Rev. E 77 (1), 016308.CrossRefGoogle ScholarPubMed
Greenblatt, D. & Williams, D.R. 2022 Flow control for unmanned air vehicles. Annu. Rev. Fluid Mech. 54, 383–412.CrossRefGoogle Scholar
Gursul, I., Cleaver, D.J. & Wang, Z. 2014 Control of low Reynolds number flows by means of fluid–structure interactions. Prog. Aerosp. Sci. 64, 17–55.CrossRefGoogle Scholar
Gursul, I. & Ho, C.-M. 1992 High aerodynamic loads on an airfoil submerged in an unsteady stream. AIAA J. 30 (4), 1117–1119.CrossRefGoogle Scholar
He, W., Gioria, R.S., Pérez, J.M. & Theofilis, V. 2017 Linear instability of low Reynolds number massively separated flow around three NACA airfoils. J. Fluid Mech. 811, 701–741.CrossRefGoogle Scholar
Jones, A.R., Cetiner, O. & Smith, M.J. 2022 Physics and modeling of large flow disturbances: discrete gust encounters for modern air vehicles. Annu. Rev. Fluid Mech. 54, 469–493.CrossRefGoogle Scholar
Karniadakis, G.E., Israeli, M. & Orszag, S.A. 1991 High-order splitting methods for the incompressible Navier–Stokes equations. J. Comput. Phys. 97 (2), 414–443.CrossRefGoogle Scholar
Lee, J.-J., Hsieh, C.-T., Chang, C.C. & Chu, C.-C. 2012 Vorticity forces on an impulsively started finite plate. J. Fluid Mech. 694, 464–492.CrossRefGoogle Scholar
Lewin, G.C. & Haj-Hariri, H. 2003 Modelling thrust generation of a two-dimensional heaving airfoil in a viscous flow. J. Fluid Mech. 492, 339–362.CrossRefGoogle Scholar
Li, G.-J. & Lu, X.-Y. 2012 Force and power of flapping plates in a fluid. J. Fluid Mech. 712, 598–613.CrossRefGoogle Scholar
Martín-Alcántara, A. & Fernandez-Feria, R. 2019 Assessment of two vortex formulations for computing forces of a flapping foil at high Reynolds numbers. Phys. Rev. Fluids 4, 024702.CrossRefGoogle Scholar
Martín-Alcántara, A., Fernandez-Feria, R. & Sanmiguel-Rojas, E. 2015 Vortex flow structures and interactions for the optimum thrust efficiency of a heaving airfoil at different mean angles of attack. Phys. Fluids 27 (7), 073602.CrossRefGoogle Scholar
McCroskey, W.J. 1982 Unsteady airfoils. Annu. Rev. Fluid Mech. 14 (1), 285–311.CrossRefGoogle Scholar
Meneghini, J.R., Carmo, B.S., Tsiloufas, S.P., Gioria, R.S. & Aranha, J.A.P. 2011 Wake instability issues: from circular cylinders to stalled airfoils. J. Fluids Struct. 27 (5–6), 694–701.CrossRefGoogle Scholar
Menon, K. & Mittal, R. 2021 a Quantitative analysis of the kinematics and induced aerodynamic loading of individual vortices in vortex-dominated flows: a computation and data-driven approach. J. Comput. Phys. 443, 110515.CrossRefGoogle Scholar
Menon, K. & Mittal, R. 2021 b Significance of the strain-dominated region around a vortex on induced aerodynamic loads. J. Fluid Mech. 918, R3.CrossRefGoogle Scholar
Moriche, M., Flores, O. & García-Villalba, M. 2016 Three-dimensional instabilities in the wake of a flapping wing at low Reynolds number. Intl J. Heat Fluid Flow 62, 44–55.CrossRefGoogle Scholar
Moriche, M., Gonzalo, A., Flores, O. & García-Villalba, M. 2021 a Three-dimensional effects on plunging airfoils at low Reynolds numbers. AIAA J. 59 (1), 65–74.CrossRefGoogle Scholar
Moriche, M., Sedky, G., Jones, A.R., Flores, O. & García-Villalba, M. 2021 b Characterization of aerodynamic forces on wings in plunge maneuvers. AIAA J. 59 (2), 751–762.CrossRefGoogle Scholar
Moura, R.C., Aman, M., Peiró, J. & Sherwin, S.J. 2020 Spatial eigenanalysis of spectral/HP continuous Galerkin schemes and their stabilisation via DG-mimicking spectral vanishing viscosity for high Reynolds number flows. J. Comput. Phys. 406, 109112.CrossRefGoogle Scholar
Moxey, D., et al. 2020 Nektar++: enhancing the capability and application of high-fidelity spectral/HP element methods. Comput. Phys. Commun. 249, 107110.CrossRefGoogle Scholar
Orszag, S.A., Israeli, M. & Deville, M.O. 1986 Boundary conditions for incompressible flows. J. Sci. Comput. 1 (1), 75–111.CrossRefGoogle Scholar
Quartapelle, L. & Napolitano, M. 1983 Force and moment in incompressible flows. AIAA J. 21 (6), 911–913.CrossRefGoogle Scholar
Shyy, W., Aono, H., Chimakurthi, S.K., Trizila, P., Kang, C.-K., Cesnik, C.E.S. & Liu, H. 2010 Recent progress in flapping wing aerodynamics and aeroelasticity. Prog. Aerosp. Sci. 46 (7), 284–327.CrossRefGoogle Scholar
Son, O., Gao, A.-K., Gursul, I., Cantwell, C.D., Wang, Z. & Sherwin, S.J. 2022 Leading-edge vortex dynamics on plunging airfoils and wings. J. Fluid Mech. 940, A28.CrossRefGoogle Scholar
Sun, L., Deng, J. & Shao, X. 2018 Three-dimensional instabilities for the flow around a heaving foil. Phys. Rev. E 97 (1), 013110.CrossRefGoogle ScholarPubMed
Triantafyllou, G.S., Triantafyllou, M.S. & Grosenbaugh, M.A. 1993 Optimal thrust development in oscillating foils with application to fish propulsion. J. Fluids Struct. 7 (2), 205–224.CrossRefGoogle Scholar
Visbal, M.R. 2009 High-fidelity simulation of transitional flows past a plunging airfoil. AIAA J. 47 (11), 2685–2697.CrossRefGoogle Scholar
Visbal, M.R. 2011 Numerical investigation of deep dynamic stall of a plunging airfoil. AIAA J. 49 (10), 2152–2170.CrossRefGoogle Scholar
Wang, Z.J. 2000 Vortex shedding and frequency selection in flapping flight. J. Fluid Mech. 410, 323–341.CrossRefGoogle Scholar
Wu, J.Z., Ma, H.Y. & Zhou, M.D. 2006 Vorticity and Vortex Dynamics. Springer.CrossRefGoogle Scholar
Zhang, J. 2017 Footprints of a flapping wing. J. Fluid Mech. 818, 1–4.CrossRefGoogle Scholar
Zurman-Nasution, A.N., Ganapathisubramani, B. & Weymouth, G.D. 2020 Influence of three-dimensionality on propulsive flapping. J. Fluid Mech. 886, A25.CrossRefGoogle Scholar