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Leading-edge vortex dynamics on plunging airfoils and wings

Published online by Cambridge University Press:  11 April 2022

O. Son
Affiliation:
Department of Mechanical Engineering, University of Bath, Bath, BA2 7AY, UK
A.-K. Gao
Affiliation:
Department of Aeronautics, Imperial College London, London, SW7 2AZ, UK
I. Gursul*
Affiliation:
Department of Mechanical Engineering, University of Bath, Bath, BA2 7AY, UK
C.D. Cantwell
Affiliation:
Department of Aeronautics, Imperial College London, London, SW7 2AZ, UK
Z. Wang
Affiliation:
Department of Mechanical Engineering, University of Bath, Bath, BA2 7AY, UK
S.J. Sherwin
Affiliation:
Department of Aeronautics, Imperial College London, London, SW7 2AZ, UK
*
Email address for correspondence: ensiag@bath.ac.uk

Abstract

The vortex dynamics of leading-edge vortices on plunging high-aspect-ratio (AR = 10) wings and airfoils were investigated by means of volumetric velocity measurements, numerical simulations and stability analysis to understand the deformation of the leading-edge vortex filament and spanwise instabilities. The vortex filaments on both the wing and airfoil exhibit spanwise waves, but with different origins. The presence of a wing-tip causes the leg of the vortex to remain attached to the wing upper surface, while the initial deformation of the filament near the wing tip resembles a helical vortex. The essential features can be modelled as the deformation of an initially L-shaped semi-infinite vortex column. In contrast, the instability of the vortices is well captured by the instability of counter-rotating vortex pairs, which are formed either by the trailing-edge vortices or the secondary vortices rolled-up from the wing surface. The wavelengths observed in the experiments and simulations are in agreement with the stability analysis of counter-rotating vortex pairs of unequal strength.

Type
JFM Papers
Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

Anderson, J., Streitlien, K., Barrett, D. & Triantafyllou, M. 1998 Oscillating foils of high propulsive efficiency. J. Fluid Mech. 360, 4172.CrossRefGoogle Scholar
Benton, S. & Visbal, M.R. 2019 The onset of dynamic stall at a high, transitional Reynolds number. J. Fluid Mech. 861, 860885.CrossRefGoogle Scholar
Bernal, L.P. & Roshko, A. 1986 Streamwise vortex structure in plane mixing layers. J. Fluid Mech. 170, 499525.CrossRefGoogle Scholar
Bull, S., Chiereghin, N., Gursul, I. & Cleaver, D.J. 2021 Unsteady aerodynamics of a plunging airfoil in transient motion. J. Fluids Struct. 103, 103288.CrossRefGoogle Scholar
Calderon, D., Wang, Z. & Gursul, I. 2013 a Lift enhancing vortex flows generated by plunging rectangular wings with small amplitude. AIAA J. 51 (12), 29532964.CrossRefGoogle Scholar
Calderon, D., Wang, Z., Gursul, I. & Visbal, M.R. 2013 b Volumetric measurements and simulations of the vortex structures generated by low aspect ratio plunging wings. Phys. Fluids 25, 067102.CrossRefGoogle Scholar
Cantwell, C.D., Moxey, D., Comerford, A., Bolis, A., Rocco, G., Mengaldo, G. & de Grazia, D. 2015 Nektar++: an open-source spectral/hp element framework. Comput. Phys. Commun. 192, 205219.CrossRefGoogle Scholar
Chiereghin, N., Bull, S., Cleaver, D.J. & Gursul, I. 2020 Three-dimensionality of leading-edge vortices on high aspect ratio plunging wings. Phys. Rev. Fluids 5 (6), 064701.CrossRefGoogle Scholar
Chiereghin, N., Cleaver, D.J. & Gursul, I. 2019 Unsteady lift and moment of a periodically plunging airfoil. AIAA J. 57, 208222.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), 20182033.CrossRefGoogle Scholar
Ekaterinaris, J. & Platzer, M. 1998 Computational prediction of airfoil dynamic stall. Prog. Aerosp. Sci. 33, 759846.CrossRefGoogle Scholar
Eldredge, J.D. & Jones, A.R. 2019 Leading-edge vortices: mechanics and modelling. Annu. Rev. Fluid Mech. 51 (1), 75104.CrossRefGoogle Scholar
Fabre, D. 2002 Instabilité et instationnarités dans les tourbillons: application aux sillages d'avions. PhD dissertation, Université Pierre et Marie Curie–Paris VI.Google Scholar
Fischer, P.F. 1998 Projection techniques for iterative solution of Ax = b with successive right-hand sides. Comput. Meth. Appl. Mech. Engng 163 (1–4), 193204.CrossRefGoogle Scholar
Gao, A., Sherwin, S.J. & Cantwell, C.D. 2020 Three-dimensional instabilities of vortices shed from a plunging wing: computations. In The 73rd Annual Meeting of the APS Division of Fluid Dynamics (APS DFD 2020), Bulletin of the American Physical Society. 22–24 November 2020. Virtual Meeting.Google Scholar
Gardner, A., Klein, C., Sachs, W., Henne, U., Mai, H. & Richter, K. 2014 Investigation of three-dimensional dynamic stall on an airfoil using fast-response pressure-sensitive paint. Exp. Fluids 55, 1807.CrossRefGoogle Scholar
Geuzaine, C. & Remacle, J.-F. 2009 Gmsh: a 3-D finite element mesh generator with built-in pre- and post-processing facilities. Intl J. Numer. Meth. Engng 79 (11), 13091331.CrossRefGoogle Scholar
Hammer, P.R., Garmann, D.J. & Visbal, M.R. 2021 Effect of aspect ratio on finite wing dynamic stall. AIAA Paper 2021-1089, AIAA SciTech Forum, 11–15, 19–21 January 2021. Virtual event.CrossRefGoogle Scholar
Heathcote, D.J., Gursul, I. & Cleaver, D.J. 2018 Aerodynamic load alleviation using minitabs. J. Aircraft 55 (5), 20682077.CrossRefGoogle Scholar
von Karman, T. & Sears, W.R. 1938 Airfoil theory for non-uniform motion. J. Aeronaut. Sci. 5, 379.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), 414443.CrossRefGoogle Scholar
Kaufmann, K., Merz, C. & Gardner, A. 2017 Dynamic stall simulations on a pitching finite wing. J. Aircraft 54, 13031316.CrossRefGoogle Scholar
Leweke, T., Le Dizes, S. & Williamson, C.H.K. 2016 Dynamics and instabilities of vortex pairs. Annu. Rev. Fluid Mech. 48, 507541.CrossRefGoogle Scholar
Leweke, T. & Williamson, C.H.K. 1998 Cooperative elliptic instability of a vortex pair. J. Fluid Mech. 360, 85119.CrossRefGoogle Scholar
Mccroskey, W.J. 1982 Unsteady airfoils. Annu. Rev. Fluid Mech. 14 (1), 285311.CrossRefGoogle Scholar
Moura, R.C., Aman, M., Peiro, 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
Mueller, T.J. & Delaurier, J.D. 2003 Aerodynamics of small vehicles. Annu. Rev. Fluid Mech. 35, 89111.CrossRefGoogle Scholar
Schreck, S. & Helin, H. 1994 Unsteady vortex dynamics and surface pressure topologies on a finite wing. J. Aircraft 31, 899907.CrossRefGoogle Scholar
Sherwin, S.J. & Casarin, M. 2001 Low-energy basis preconditioning for elliptic substructured solvers based on unstructured spectral/hp element discretization. J. Comput. Phys. 171 (1), 394417.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), 284327.CrossRefGoogle Scholar
Smits, A.J. 2019 Undulatory and oscillatory swimming. J. Fluid Mech. 874, P1.CrossRefGoogle Scholar
Son, O., Wang, Z. & Gursul, I. 2020 Three-dimensional instabilities of vortices shed from a plunging wing: experiments. In The 73rd Annual Meeting of the APS Division of Fluid Dynamics (APS DFD 2020), Bulletin of the American Physical Society, 22–24 November 2020. Virtual meeting.Google Scholar
Son, O., Wang, Z. & Gursul, I. 2021 Three-dimensional instabilities of vortices on a periodically plunging wing. AIAA 2021-1211. AIAA Science and Technology Forum and Exposition (SciTech 2021). Nashville, Tennessee, USA, 11–15 January 2021.Google Scholar
Spentzos, A., Barakos, G., Badcock, K., Richards, B., Coton, F., Galbraith, R.A., Berton, E. & Favier, D. 2007 Computational fluid dynamics study of three-dimensional dynamic stall of various planform shapes. J. Aircraft 44, 11181128.CrossRefGoogle Scholar
Spentzos, A., Barakos, G., Badcock, K., Richards, B., Wernert, P., Schreck, S. & Raffel, M. 2005 Investigation of three-dimensional dynamic stall using computational fluid dynamics. AIAA J. 43, 10231033.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
Theodorsen, T. 1935 General theory of aerodynamic instability and the mechanism of flutter. NACA Rep. TR496.Google Scholar
Tudball Smith, D., Rockwell, D., Sheridan, J. & Thompson, M. 2017 Effect of radius of gyration on a wing rotating at low Reynolds number: a computational study. Phys. Rev. Fluids 2, 064701.CrossRefGoogle Scholar
Tufo, H.M. & Fischer, P.F. 2001 Fast parallel direct solvers for coarse grid problems. J. Parallel Distrib. Comput. 61 (2), 151177.CrossRefGoogle Scholar
Visbal, M.R. & Garmann, D. 2019 Dynamic stall of a finite-aspect-ratio wing. AIAA J. 57, 962977.CrossRefGoogle Scholar
Visbal, M.R., Yilmaz, T.O. & Rockwell, D. 2013 Three-dimensional vortex formation on a heaving low-aspect ratio wing: computations and experiments. J. Fluids Struct. 38, 5876.CrossRefGoogle Scholar
Weihs, D. & Katz, J. 1983 Cellular patterns in post-stall flow over unswept wings. AIAA J. 21, 17571759.CrossRefGoogle Scholar
Williamson, C.H.K. 1996 Three-dimensional wake transition. J. Fluid Mech. 328, 345407.CrossRefGoogle Scholar
Wolfinger, M. & Rockwell, D. 2014 Flow structure on a rotating wing: effect of radius of gyration. J. Fluid Mech. 755, 83110.CrossRefGoogle Scholar
Yilmaz, T.O. & Rockwell, D. 2012 Flow structure on finite-span wings due to pitch-up motion. J. Fluid Mech. 691, 518545.CrossRefGoogle Scholar
Zhang, K., Hayostek, S., Amitay, M., He, W., Theofilis, V. & Taira, K. 2020 On the formation of three-dimensional separated flows over wings under tip effects. J. Fluid Mech. 895, A9.CrossRefGoogle Scholar