Hostname: page-component-669899f699-swprf Total loading time: 0 Render date: 2025-04-28T16:45:55.008Z Has data issue: false hasContentIssue false
  • English
  • Français

Impingement of a counter-rotating vortex pair on a wavy wall

Published online by Cambridge University Press:  21 May 2020

Sarah E. Morris Open the ORCID record for Sarah E. Morris [Opens in a new window]  and
C. H. K. Williamson
Sarah E. Morris*
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY14853-7501, USA
C. H. K. Williamson
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY14853-7501, USA
*
†Email address for correspondence: sem323@cornell.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper, we investigate the impingement of a two-dimensional (2-D) vortex pair translating downwards onto a horizontal wall with a wavy surface. A principal purpose is to compare the vortex dynamics with the complementary case of a wavy vortex pair (deformed by the long-wavelength Crow instability) impinging onto a flat surface. The simpler case of a 2-D vortex pair descending onto a flat horizontal ground plane leads to the well known ‘rebound’ effect, wherein the primary vortex pair approaches the wall but subsequently advects vertically upwards, due to the induced velocity of secondary vorticity. In contrast, a wavy vortex pair descending onto a flat plane leads to ‘rebounding’ vorticity in the form of vortex rings. A descending 2-D vortex pair, impinging on a wavy wall, also generates ‘rebounding’ vortex rings. In this case, we observe that the vortex pair interacts first with the ‘hills’ of the wavy wall before the ‘valleys’. The resulting secondary vorticity rolls up into a concentrated vortex tube, ultimately forming a vortex loop along each valley. Each vortex loop pinches off to form a vortex ring, which advects upwards. Surprisingly, these rebounding vortex rings evolve without the strong axial flows fundamental to the wavy vortex case. The present research is relevant to wing tip trailing vortices interacting with a non-uniform ground plane. A non-flat wall is shown to accelerate the decay of the primary vortex pair. Such a passive, ground-based method to diminish the wake vortex hazard close to the ground is consistent with Stephan et al. (J. Aircraft, vol. 50 (4), 2013a, pp. 1250–1260; CEAS Aeronaut. J., vol. 5 (2), 2013b, pp. 109–125).

JFM classification

Vortex Flows: Vortex dynamics Vortex Flows: Vortex instability Vortex Flows: Vortex interactions
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 895 , 25 July 2020 , A25
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Asselin, D. J. & Williamson, C. H. K. 2017 Influence of a wall on the three-dimensional dynamics of a vortex pair. J. Fluid Mech. 817, 339–373.CrossRefGoogle Scholar
Barker, S. J. & Crow, S. C. 1977 The motion of two-dimensional vortex pairs in a ground effect. J. Fluid Mech. 82 (04), 659–671.CrossRefGoogle Scholar
Bristow, N., Blois, G., Kim, T., Best, J. & Christensen, K. 2016 Refractive index matched PIV measurements of flow around interacting barchan dunes. In 69th Annual Meeting of the APS Division of Fluid Dynamics. American Physical Society.Google Scholar
Cantwell, B. J. 1981 Organized motion in turbulent flow. Annu. Rev. Fluid Mech. 13, 457–515.CrossRefGoogle Scholar
Chevalier, H. 1973 Flight test studies of the formation and dissipation of trailing vortices. J. Aircraft 10 (1), 14–18.CrossRefGoogle Scholar
Crouch, J. 2005 Airplane trailing vortices and their control. C. R. Phys. 6 (4–5), 487–499.CrossRefGoogle Scholar
Crouch, J. D. 1997 Instability and transient growth for two trailing-vortex pairs. J. Fluid Mech. 350, 311–330.CrossRefGoogle Scholar
Crouch, J. D., Miller, G. D. & Spalart, P. R. 2001 Active-control system for breakup of airplane trailing vortices. AIAA J. 39 (12), 2374–2381.CrossRefGoogle Scholar
Crow, S. C. 1970 Stability theory for a pair of trailing vortices. AIAA J. 8 (12), 2172–2179.CrossRefGoogle Scholar
Dee, F. W. & Nicholas, O. P.1968 Flight measurements of wing-tip vortex motion near the ground. Tech. Rep. 1065. British Aeronautical Research Council.Google Scholar
Duponcheel, M., Cottin, C., Daeninck, G., Leweke, T. & Winckelmans, G. 2007 Experimental and numerical study of counter-rotating vortex pair dynamics in ground effect. In 18e Congrès Français de Mécanique.Google Scholar
Eliason, B. G., Gartshore, I. S. & Parkinson, G. V. 1975 Wind tunnel investigation of crow instability. J. Aircraft 12 (12), 985–988.CrossRefGoogle Scholar
Fogg, J. G.2001 Vortex pair instabilities in ground effect. Master’s thesis, Cornell University, Ithaca, NY.Google Scholar
Green, S. I. 1995 Wing tip vortices. In Fluid Mechanics and Its Applications, pp. 427–469. Springer.Google Scholar
Harris, D. M. & Williamson, C. H. K. 2012 Instability of secondary vortices generated by a vortex pair in ground effect. J. Fluid Mech. 700, 148–186.CrossRefGoogle Scholar
Harvey, J. K. & Perry, F. J. 1971 Flowfield produced by trailing vortices in the vicinity of the ground. AIAA 9 (8), 1659–1660.CrossRefGoogle Scholar
Holzäpfel, F. N., Stephan, A., Misaka, T. & Körner, S. 2014 Wake vortex evolution during approach and landing with and without plate lines. In 52nd Aerospace Sciences Meeting. American Institute of Aeronautics and Astronautics.Google Scholar
Horowitz, M. & Williamson, C. H. K. 2010 The effect of Reynolds number on the dynamics and wakes of freely rising and falling spheres. J. Fluid Mech. 651, 251–294.CrossRefGoogle Scholar
Kazarin, P. & Golubev, V. V. 2017 Effects of ground surface conditions on aircraft wake vortex evolution. In 9th AIAA Atmospheric and Space Environments Conference. American Institute of Aeronautics and Astronautics.Google Scholar
Lamb, H. 1932 Hydrodynamics, 6th edn. Cambridge University Press.Google Scholar
Leweke, T., LeDizès, S. & Williamson, C. H. K. 2016 Dynamics and instabilities of vortex pairs. Annu. Rev. Fluid Mech. 48, 1–35.CrossRefGoogle Scholar
Leweke, T. & Williamson, C. H. K. 1998 Cooperative instability of a vortex pair. J. Fluid Mech. 360, 85–119.CrossRefGoogle Scholar
Leweke, T. & Williamson, C. H. K. 2011 Experiments on long-wavelength instability and reconnection of a vortex pair. Phys. Fluids 23, 024101.CrossRefGoogle Scholar
Luton, J. A. & Ragab, S. A. 1997 The three-dimensional interaction of a vortex pair with a wall. Phys. Fluids 9 (10), 2967–2980.CrossRefGoogle Scholar
Moin, P., Leonard, A. & Kim, J.1985 Evolution of a curved vortex filament into a vortex ring. Tech. Memo 86831. National Aeronautics and Space Administration, Ames Research Center.Google Scholar
Morris, S. E. & Williamson, C. H. K. 2017 Formation of mini vortex rings arising from a vortex pair impinging on a wavy wall. Phys. Rev. Fluids 2, 090508.CrossRefGoogle Scholar
Ortega, J. M., Bristol, R. L. & Savaş, Ö. 2002 Wake alleviation properties of triangular-flapped wings. AIAA J. 40 (4), 709–721.CrossRefGoogle Scholar
Ortega, J. M., Bristol, R. L. & Savaş, Ö. 2003 Experimental study of the instability of unequal-strength counter-rotating vortex pairs. J. Fluid Mech. 474, 35–84.CrossRefGoogle Scholar
Panton, R. L. 2001 Overview of the self-sustaining mechanisms of wall turbulence. Prog. Aerosp. Sci. 37, 341–383.CrossRefGoogle Scholar
Peace, A. J. & Riley, N. 1983 A viscous vortex pair in ground effect. J. Fluid Mech. 129, 409–426.CrossRefGoogle Scholar
Perry, A. E., Lim, T. T. & Teh, E. W. 1981 A visual study of turbulent spots. J. Fluid Mech. 104, 387–405.CrossRefGoogle Scholar
Quackenbush, T. R., Bilanin, A. J., Batcho, P. F., McKillip, R. M. J. & Carpenter, B. F. 1997 Implementation of vortex wake control using SMA-actuated devices. In Smart Structures and Materials 1997: Industrial and Commercial Applications of Smart Structures Technologies (ed. Sater, J. M.). SPIE.Google Scholar
Rennich, S. C. & Lele, S. K. 1999 Method for accelerating the destruction of aircraft wake vortices. J. Aircraft 36 (2), 398–404.CrossRefGoogle Scholar
Robinson, S. K. 1991 Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23 (1), 601–639.CrossRefGoogle Scholar
Savaş, Ö. 2005 Experimental investigations on wake vortices and their alleviation. C. R. Phys. 6 (4–5), 415–429.CrossRefGoogle Scholar
Spalart, P. R. 1998 Airplane trailing vortices. Annu. Rev. Fluid Mech. 30, 107–138.CrossRefGoogle Scholar
Stephan, A., Holzäpfel, F. & Misaka, T. 2013a Aircraft wake-vortex decay in ground proximity: physical mechanisms and artificial enhancements. J. Aircraft 50 (4), 1250–1260.CrossRefGoogle Scholar
Stephan, A., Holzäpfel, F., Misaka, T., Geisler, R. & Konrath, R. 2013b Enhancement of aircraft wake vortex decay in ground proximity. CEAS Aeronaut. J. 5 (2), 109–125.CrossRefGoogle Scholar
Stephan, A., Schrall, J. & Holzäpfel, F. 2017 Numerical optimization of plate-line design for enhanced wake-vortex decay. J. Aircraft 54 (3), 995–1010.CrossRefGoogle Scholar
Thielicke, W.2014 The flapping flight of birds – analysis and application. PhD thesis, Rijksuniversiteit Groningen.Google Scholar
Thielicke, W. & Stamhuis, E. J.2014a PIVlab – time-resolved digital particle image velocimetry tool for MATLAB Version 1.40.Google Scholar
Thielicke, W. & Stamhuis, E. J. 2014b PIVlab – towards user-friendly, affordable and accurate digital particle image velocimetry in MATLAB. J. Open Res. Softw. 2 (1), e30.Google Scholar
Wakim, A., Brion, V., Dolfi-Bouteyre, A. & Jacquin, L. 2020 A vortex pair in ground effect, dynamics and optimal control. J. Fluid Mech. 885, A26.CrossRefGoogle Scholar
Wang, C. H. J., Zhao, D., Schlüter, J., Holzäpfel, F. & Stephan, A. 2017 LES study on the shape effect of ground obstacles on wake vortex dissipation. Aerosp. Sci. Technol. 63, 245–258.CrossRefGoogle Scholar
Widnall, S. E. 1975 The structure and dynamics of vortex filaments. Annu. Rev. Fluid Mech. 7 (1), 141–165.CrossRefGoogle Scholar
Widnall, S. E., Bliss, D. B. & Tsai, C.-Y. 1974 The instability of short waves on a vortex ring. J. Fluid Mech. 66, 35–47.CrossRefGoogle Scholar
Williamson, C. H. K., Leweke, T., Asselin, D. J. & Harris, D. M. 2014 Phenomena, dynamics and instabilities of vortex pairs. Fluid Dyn. Res. 46, 061425.Google Scholar
Zheng, Z. C. & Wei, Z. 2013 Effects of surface roughness and patterns on a surface-approaching pair of aircraft wake vortices. In 51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition. American Institute of Aeronautics and Astronautics.Google Scholar