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Nonlinear feedback control of the wake past a plate with a suction point on the downstream wall

Published online by Cambridge University Press:  26 April 2006

Luca Cortelezzi
Luca Cortelezzi
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, CA 90095-1597, USA Department of Mathematics, University of California, Los Angeles, CA 90095-1555, USA e-mail: crtlz@math.ucla.edu
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Abstract

Active circulation control of the two-dimensional unsteady separated flow past a plate with a suction point on the downstream wall is considered. The rolling-up of the separated shear layer is modelled by a pair of point vortices whose time-dependent circulation is predicted by an unsteady Kutta condition. A nonlinear controller able to confine the wake to a single vortex pair of constant circulation is derived in closed form for any free-stream condition. Dynamical system analysis is used to explore the performance of the controlled system. Finally, the control strategy is applied to three different classes of unsteady flows and the results are discussed.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 327 , 25 November 1996 , pp. 303 - 324
Copyright
© 1996 Cambridge University Press

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References

Brown, C. E. & Michael, W. H. 1954 Effect of leading-edge separation on the lift of a delta wing. J. Aero. Sci. 21, 690–694.Google Scholar
Cao, N.-Z. & Aubry, N. 1993 Numerical simulation of a wake flow via a reduced system. Separated Flows ASME FED-Vol. 149.Google Scholar
Cheers, A. Y. 1979 A study of incompressible 2-d vortex flow past a circular cylinder. Lawrence Berkeley Laboratory LBL-9950.
Clements, R. R. 1973 An inviscid model of two-dimensional vortex shedding. J. Fluid Mech. 57, 321–336.Google Scholar
Cortelezzi, L. 1993 A theoretical and numerical study on active wake control. PhD thesis, California Institute of Technology.
Cortelezzi, L., Leonard, A. & Doyle, J. C. 1994 An example of active circulation control of the unsteady separated flow past a semi-infinite plate. J. Fluid Mech. 260, 127–154.Google Scholar
Doyle, J. C. Francis, B. A. & Tannenbaum, A. R. 1992 Feedback Control Theory. Macmillan.
Fan, M. K. H. Tits, A. L. & Doyle, J. C. 1991 Robustness in the presence of mixed parametric uncertainty and unmodeled dynamics. IEEE Auto. C. 36, 25–38.Google Scholar
Gad-el-Hak, M. & Bushnell, D. M. 1991 Separation control: review. Trans. ASME I: J. Fluids Engng 113, 5–30.Google Scholar
Graham, J. M. R. 1980 The forces on the sharp-edged cylinders in oscillatory flow at low Keulegan-Carpenter numbers. J. Fluid Mech. 97, 331–346.Google Scholar
Gopalkrishnan, R., Triantafyllou, M. S., Triantafyllou, G. S. & Barrett, D. 1994 Active vorticity control in a shear flow using a flapping foil. J. Fluid Mech. 274, 1–21.Google Scholar
Guckenheimer, J. & Holmes, P. 1983 Nonlinear Oscillations, Dynamical Systems, and Bifurcation of Vector Fields. Springer.
Koochesfahani, M. M. & Dimotakis, P. E. 1988 A cancelation experiment in a forced turbulent shear layer. First National Fluid Dynamics Congress July 25-28, 1988, Cincinnati, Ohio. AIAA Paper 88–3713-CP.
Lisoski, D. L. 1993 Nominally 2-dimensional flow about a normal flat plate. PhD Thesis, California Institute of Technology.
Ongoren, A. & Rockwell, D. 1988a Flow structure from an oscillating cylinder. Part 1. Mechanisms of phase shift and recovery in the near wake. J. Fluid Mech. 191, 197–223.Google Scholar
Ongoren, A. & Rockwell, D. 1988b Flow structure from an oscillating cylinder. Part 2. Mode competition in the near wake. J. Fluid Mech. 191, 225–245.Google Scholar
Rajaee, M., Karlsson, S. K. F. & Sirovich, L. 1994 Low-dimensional description of free-shear-flow coherent structures and their dynamical behaviour. J. Fluid Mech. 258, 1–29.Google Scholar
Rao, D. M. 1987 Vortical flow management techniques. Prog. Aerospace Sci. 24, 173–224.Google Scholar
Rossow, V. J. 1977 Lift enhancement by an external trapped vortex. 10th Fluid and Plasmadynamics Conference. June 27-29, 1977, Albuquerque, New Mexico. AIAA Paper 77–672.
Rott, N. 1956 Diffraction of a weak shock with vortex generation. J. Fluid Mech. 1, 111–128.Google Scholar
Roussopoulos, K. 1993 Feedback control of vortex shedding at low Reynolds numbers. J. Fluid Mech. 248, 267–296.Google Scholar
Shermer, R. 1992 Control of vortex shedding in a two-dimensional flow past a plate. Phys. Rev. A 46, 7614–7617.Google Scholar
Slomski, J. F. & Coleman, R. M. 1993 Numerical simulation of vortex generation and capture above an airfoil. 31st Aerospace Sciences Meeting and Exhibit, January 11–14, 1993, Reno, Nevada. AIAA Paper 93–864.
Tokumaru, P. T. & Dimotakis, P. E. 1991 Rotary oscillation control of a cylinder wake. J. Fluid Mech. 224, 77–90.Google Scholar