Skip to main content Accessibility help
×
Home

A vortex pair in ground effect, dynamics and optimal control

  • Arnold Wakim (a1), Vincent Brion (a1), Agnès Dolfi-Bouteyre (a2) and Laurent Jacquin (a1)

Abstract

The dynamics and control of a vortex pair in ground effect are investigated in a planar, incompressible and laminar setting. The evolution of the vortices obtained numerically shows vortex rebound as a consequence of the separation of the boundary layer induced at the wall by the vortices. An optimal control approach is developed and employed for vortex Reynolds numbers of 200 and 1000 in order to identify the optimal Dirichlet boundary condition at the wall to counteract this rebound and allow for an increased lateral displacement of the vortex, similarly to the inviscid evolution of the flow, which features hyperbolic trajectories. The work is primarily a conceptual approach to deal with aircraft separation distances in airport airspace by moving the vortices laterally, away from the runway but may also apply to the control of coherent structures in wall bounded turbulence. The most efficient control is able to double the lateral position and yields mostly vertical in and outflow at the wall. An optimal horizon time is found, equal to 5 characteristic time units of the vortex system, beyond which control is not able to further displace the vortices. The control is shown to delay the separation of the boundary layer at the origin of vortex rebound by applying suction ahead of the vortex, and to generate a vorticity flux at the wall, leading to a pusher vortex of sign opposite to that of the primary vortex, that attenuates the effect of the no-slip boundary condition at the wall by pushing the vortex outward.

Copyright

Corresponding author

Email address for correspondence: arnold.wakim@gmail.com

References

Hide All
Airbus SAS 2015 Flying by numbers-global market forecast 2015–2034. Tech. Rep. 2. Airbus SAS.
Airiau, C., Bottaro, A., Walther, S. & Legendre, D. 2003 A methodology for optimal laminar flow control: application to the damping of Tollmien–Schlichting waves in a boundary layer. Phys. Fluids 15 (5), 11311145.
Akhavan, R., Jung, W. J. & Mangiavacchi, N. 1993 Turbulence control in wall-bounded flows by spanwise oscillations. In Advances in Turbulence IV, pp. 299303. Springer.
Barker, S. J. & Crow, S. C. 1977 The motion of two-dimensional vortex pairs in a ground effect. J. Fluid Mech. 82 (4), 659671.
Bewley, T. R. 2001 Flow control: new challenges for a new renaissance. Prog. Aerosp. Sci. 37 (1), 2158.
Bewley, T. R., Moin, P. & Temam, R. 2001 Dns-based predictive control of turbulence: an optimal benchmark for feedback algorithms. J. Fluid Mech. 447, 179225.
Bricteux, L., Duponcheel, M., De Visscher, I. & Winckelmans, G. 2016 Les investigation of the transport and decay of various-strengths wake vortices in ground effect and subjected to a turbulent crosswind. Phys. Fluids 28 (6), 065105.
Choi, H., Hinze, M. & Kunisch, K. 1999 Instantaneous control of backward-facing step flows. Appl. Numer. Maths 31 (2), 133158.
Choi, H., Moin, P. & Kim, J. 1994 Active turbulence control for drag reduction in wall-bounded flows. J. Fluid Mech. 262, 75110.
Clercx, H. J. H. & Van Heijst, G. J. F. 2002 Dissipation of kinetic energy in two-dimensional bounded flows. Phys. Rev. E 65 (6), 066305.
Coutsias, E. A. & Lynov, J.-P. 1991 Fundamental interactions of vortical structures with boundary layers in two-dimensional flows. Physica D: Nonlinear Phenomena 51 (1–3), 482497.
Davies, C. & Carpenter, P. W. 1997 Instabilities in a plane channel flow between compliant walls. J. Fluid Mech. 352, 205243.
Dee, F. W. & Nicholas, O. P. 1968 Flight Measurements of Wing-Tip Vortex Motion Near the Ground. Royal Aircraft Establishment.
Endo, T. & Himeno, R. 2002 Direct numerical simulation of turbulent flow over a compliant surface. J. Turbul. 3 (007), 110.
European Commission, UFO Consortium Parters 2015 Ufo 2015 web page. www.ufo-wind-sensors.eu/home.
Fischer, P. F., Lottes, J. W. & Kerkemeier, S. G.2008 nek5000 web page. http://nek5000.mcs.anl.gov.
Flinois, T. L. B. & Colonius, T. 2015 Optimal control of circular cylinder wakes using long control horizons. Phys. Fluids 27 (8), 087105.
Furukawa, M., Inoue, M., Saiki, K. & Yamada, K. 1999 The role of tip leakage vortex breakdown in compressor rotor aerodynamics. Trans. ASME J. Turbomach. 121 (3), 469480.
Gerz, T., Holzäpfel, F. & Darracq, D. 2002 Commercial aircraft wake vortices. Progr. Aerosp. Sci. 38 (3), 181208.
Guégan, A., Schmid, P. J. & Huerre, P. 2006 Optimal energy growth and optimal control in swept hiemenz flow. J. Fluid Mech. 566, 1145.
Hallermeyer, A.2017 Traitement du signal dun lidar doppler scannant dédié á la surveillance aéroportuaire. PhD thesis, Université Paris-Saclay.
Harris, D. M. & Williamson, C. H. K. 2012 Instability of secondary vortices generated by a vortex pair in ground effect. J. Fluid Mech. 700, 148186.
Harvey, J. K. & Perry, F. J. 1971 Flowfield produced by trailing vortices in the vicinity of the ground. AIAA J. 9 (8), 16591660.
Hoepffner, J., Bottaro, A. & Favier, J. 2010 Mechanisms of non-modal energy amplification in channel flow between compliant walls. J. Fluid Mech. 642, 489507.
Holzäpfel, F., Stephan, A., Heel, T. & Körner, S. 2016 Enhanced wake vortex decay in ground proximity triggered by plate lines. Aircraft Engng Aerosp. Technol: An International Journal 88 (2), 206214.
Homescu, C., Navon, I. M. & Li, Z. 2002 Suppression of vortex shedding for flow around a circular cylinder using optimal control. Intl J. Numer. Methods Fluids 38 (1), 4369.
Hunt, J. C. R., Wray, A. A. & Moin, P.1988 Eddies, streams, and convergence zones in turbulent flows. Center for Turbulence Research Report CTR-S88 pp. 193–208.
Iverson, K. E. 1962 A programming language. In Proceedings of the May 1–3, 1962, Spring Joint Computer Conference, pp. 345351. ACM.
Jiménez, J. & Pinelli, A. 1999 The autonomous cycle of near-wall turbulence. J. Fluid Mech. 389, 335359.
Kolář, V. 2007 Vortex identification: new requirements and limitations. Intl J. Heat Fluid Flow 28 (4), 638652.
Koumoutsakos, P. 1997 Active control of vortex–wall interactions. Phys. Fluids 9 (12), 38083816.
Kravchenko, A., Choi, H. & Moin, P. 1993 On the relation of near-wall streamwise vortices to wall skin friction in turbulent boundary layers. Phys. Fluids A 5 (12), 33073309.
Lachmann, G. V. 2014 Boundary Layer and Flow Control: Its Principles and Application. Elsevier.
Lamb, H. 1932 Hydrodynamics. Cambridge University Press.
Lee, C., Kim, J., Babcock, D. & Goodman, R. 1997 Application of neural networks to turbulence control for drag reduction. Phys. Fluids 9 (6), 17401747.
Leweke, T., Le Dizes, S. & Williamson, C. H. K. 2016 Dynamics and instabilities of vortex pairs. Annu. Rev. Fluid Mech. 48, 507541.
Leweke, T. & Williamson, C. H. K. 1998 Cooperative elliptic instability of a vortex pair. J. Fluid Mech. 360, 85119.
Lin, J. C. 2002 Review of research on low-profile vortex generators to control boundary-layer separation. Prog. Aerosp. Sci. 38 (4–5), 389420.
Luhar, M., Sharma, A. S. & McKeon, B. J. 2015 A framework for studying the effect of compliant surfaces on wall turbulence. J. Fluid Mech. 768, 415441.
Önder, A. & Meyers, J. 2016 Optimal control of a transitional jet using a continuous adjoint method. Comput. Fluids 126, 1224.
Orlandi, P. 1990 Vortex dipole rebound from a wall. Phys. Fluids A 2 (8), 14291436.
Pailhas, G., de Saint, X. & Touvet, Y. 2002 Behaviour of trailing vortices in the vicinity of the ground. In Laser Techniques for Fluid Mechanics, pp. 323338. Springer.
Peace, A. J. & Riley, N. 1983 A viscous vortex pair in ground effect. J. Fluid Mech. 129, 409426.
Robins, R. E. & Delisi, D. P. 1993 Potential hazard of aircraft wake vortices in ground effect with crosswind. J. Aircraft 30 (2), 201206.
Sipp, D. & Jacquin, L. 2003 Widnall instabilities in vortex pairs. Phys. Fluids 15 (7), 18611874.
Skybrary 2019 Parallel runway operation. https://www.skybrary.aero/index.php/Parallel_Runway_Operation.
Sorvig, K. & Thompson, J. W. 2018 Quietly defend silence. In Sustainable Landscape Construction, pp. 363372. Springer.
Storer, J. A. & Cumpsty, N. A. 1991 Tip leakage flow in axial compressors. Trans. ASME J. Turbomach. 113 (2), 252259.
Türk, L., Coors, D. & Jacob, D. 1999 Behavior of wake vortices near the ground over a large range of Reynolds numbers. Aerosp. Sci. Technol. 3 (2), 7181.
Walther, S., Airiau, C. & Bottaro, A. 2001 Optimal control of Tollmien–Schlichting waves in a developing boundary layer. Phys. Fluids 13 (7), 20872096.
Widnall, S. E., Bliss, D. B. & Tsai, C. 1974 The instability of short waves on a vortex ring. J. Fluid Mech. 66 (1), 3547.
Williamson, C. H. K., Leweke, T., Asselin, D. J. & Harris, D. M. 2014 Phenomena, dynamics and instabilities of vortex pairs. Fluid Dyn. Res. 46 (6), 061425.
Yeo, K. S. 1992 The three-dimensional stability of boundary-layer flow over compliant walls. J. Fluid Mech. 238, 537577.
Zheng, Z. C. & Ash, R. L. 1993 Prediction of turbulent wake vortex motion near the ground. ASME-PUBLICATIONS-FED 151, 195195.
Zheng, Z. C. & Ash, R. L. 1996 Study of aircraft wake vortex behavior near the ground. AIAA J. 34 (3), 580589.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

A vortex pair in ground effect, dynamics and optimal control

  • Arnold Wakim (a1), Vincent Brion (a1), Agnès Dolfi-Bouteyre (a2) and Laurent Jacquin (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed