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Feedback shear layer control for bluff body drag reduction

Published online by Cambridge University Press:  11 July 2008

MARK PASTOOR ,
LARS HENNING ,
BERND R. NOACK ,
RUDIBERT KING  and
GILEAD TADMOR
MARK PASTOOR*
Affiliation:
Berlin Institute of Technology ER2-1, Department of Process Engineering, Chair of Measurement and Control, Hardenbergstraße 36a, D-10623 Berlin, Germany
LARS HENNING
Affiliation:
Berlin Institute of Technology ER2-1, Department of Process Engineering, Chair of Measurement and Control, Hardenbergstraße 36a, D-10623 Berlin, Germany
BERND R. NOACK
Affiliation:
Berlin Institute of Technology MB1, Department of Fluid Dynamics and Technical Acoustics, Straße des 17. Juni 135, D-10623 Berlin, Germany
RUDIBERT KING
Affiliation:
Berlin Institute of Technology ER2-1, Department of Process Engineering, Chair of Measurement and Control, Hardenbergstraße 36a, D-10623 Berlin, Germany
GILEAD TADMOR
Affiliation:
Northeastern University, Department of Electrical and Computer Engineering, 440 Dana Research Building, Boston, MA 02115, USA
*
†Author to whom correspondence should be addressed: [email protected]
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Abstract

Drag reduction strategies for the turbulent flow around a D-shaped body are examined experimentally and theoretically. A reduced-order vortex model describes the interaction between the shear layer and wake dynamics and guides a path to an efficient feedback control design. The derived feedback controller desynchronizes shear-layer and wake dynamics, thus postponing vortex formation. This actuation is tested in a wind tunnel. The Reynolds number based on the height of the body ranges from 23000 to 70000. We achieve a 40% increase in base pressure associated with a 15% drag reduction employing zero-net-mass-flux actuation. Our controller outperforms other approaches based on open-loop forcing and extremum-seeking feedback strategies in terms of drag reduction, adaptivity, and the required actuation energy.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 608 , 10 August 2008 , pp. 161 - 196
Copyright
Copyright © Cambridge University Press 2008

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References

REFERENCES

Ahlborn, B. K. 2004 Zoological Physics. Springer.Google Scholar
Ariyur, K. & Krstić, M. 2003 Real-Time Optimization by Extremum-Seeking Control. John Wiley & Sons.CrossRefGoogle Scholar
Beale, J. T. & Majda, A. 1982 Vortex methods I: Convergence in three dimensions. Math. Comput. 39, 1–27.Google Scholar
Bearman, P. W. 1965 Investigation of the flow behind a two-dimensional model with a blunt trailing edge and fitted with splitter plates. J. Fluid Mech. 21, 241–255.Google Scholar
Bearman, P. W. 1967 The effect of base bleed on the flow behind a two-dimensional model with a blunt trailing edge. Aeronaut. Q. 18, 207–224.CrossRefGoogle Scholar
Beaudoin, J. F., Cadot, O., Aider, J.-L., & Wesfreid, J.-E. 2006 Drag reduction of a bluff body using adaptive control methods. Phys. Fluids 18, 08510.CrossRefGoogle Scholar
Becker, R., Garwon, M., Gutknecht, C., Bärwolff, G. & King, R. 2005 Robust control of separated shear flows in simulation and experiment. J. Process Control 15, 691–700.Google Scholar
Becker, R., King, R., Petz, R. & Nitsche, W. 2007 Adaptive closed-loop separation control on a high-lift configuration using extremum seeking. AIAA J. 45, 1382–1392.CrossRefGoogle Scholar
Bergmann, M., Cordier, L. & Brancher, J.-P. 2005 Optimal rotary control of the cylinder wake using proper orthogonal decomposition reduced order model. Phys. Fluids 17, 1–21.CrossRefGoogle Scholar
Birkhoff, G. 1962 Helmholtz and Taylor instability. In Proc. Symp. Appl. Maths XII, pp. 55–76. AMS.Google Scholar
Cattafesta, L., Williams, D. R., Rowley, C. W. & Alvi, F. 2003 Review of active control of flow-induced cavity resonance. AIAA Paper 2003-3567.CrossRefGoogle Scholar
Clements, R. R. 1973 An inviscid model of two-dimensional vortex shedding. J. Fluid Mech. 57, 321–336.Google Scholar
Coller, B. D., Noack, B. R., Narayanan, S., Banaszuk, A. & Khibnik, A. I. 2000 Reduced-basis model for active separation control in a planar diffuser flow. AIAA Paper 2000-2563.Google Scholar
Collis, S. S., Joslin, R. D., Seifert, A. & Theofilis, V. 2004 Issues in active flow control: theory, control, simulation, and experiment. Prog. Aerospace Sci. 40, 237–289.Google Scholar
Cooper, K. R. 1985 The effect of front-edge rounding and rear edge shaping on the aerodynamic drag of bluff vehicles in proximity. SAE Paper 850288.CrossRefGoogle Scholar
Cordier, L. & Bergmann, M. 2003 Proper Orthogonal Decomposition: An Overview. VKI Lecture Series 2003–04. Von Kármán Institut for Fluid Dynamics.Google Scholar
Cortelezzi, L. 1996 Nonlinear feedback control of the wake past a plate with a suction point on the downstream wall. J. Fluid Mech. 327, 303–324.Google Scholar
Cottet, G. H. & Koumoutsakos, P. 2000 Vortex Methods – Theory and Practice. Cambridge University Press.CrossRefGoogle Scholar
Detemple-Laake, E. & Eckelmann, H. 1989 Phenomenology of Kármán vortex streets in oscillatory flow. Exps. Fluids 7, 217–227.Google Scholar
Evans, R. A. & Bloor, M. I. G. 1977 The starting mechanism of wave-induced flow through a sharp-edged orifice. J. Fluid Mech. 82, 115–128.CrossRefGoogle Scholar
Fiedler, H.-E. & Fernholz, H. H. 1990 On management and control of turbulent shear flows. Prog. Aeronaut. Sci. 27, 305–387.Google Scholar
Fletcher, C. A. J. 1988 Computational Techniques for Fluid Dynamics; Volume II: Specific Techniques for Different Flow Categories. Springer.Google Scholar
Gad-el-Hak, M., Pollard, A. & Bonnet, J.-P. 1998 Flow Control - Fundamentals and Practices. Springer.Google Scholar
Garwon, M., Darmadi, L. H., Urzynicok, F., Bärwolff, G. & King, R. 2003 Adaptive control of separated flow. In Proc. European Control Conf. ECC'03, ECC Paper 543.Google Scholar
Gelb, A. 1986 Applied Optimal Estimation. The MIT Press.Google Scholar
Gerhard, J., Pastoor, M., King, R., Noack, B. R., Dillmann, A., Morzyński, M. & Tadmor, G. 2003 Model-based control of vortex shedding using low-dimensional Galerkin models. AIAA Paper 2003-4262.Google Scholar
Ghoniem, A. F. & Gagnon, Y. 1987 Vortex simulation of laminar recirculating flow. J. Comput. Phys. 68, 346–377.Google Scholar
Giesing, J. P. 1969 Vorticity and Kutta condition for unsteady multi-energy flows. Trans. ASME: J. Appl. Mech. 36, 608–613.Google Scholar
Grosche, F. R. & Meier, G. E. A. 2001 Research at the DLR Göttingen on bluff body aerodynamics, drag reduction by wake ventilation and active flow control. J. Wind. Engng Ind. Aerodyn. 89, 1201–1218.CrossRefGoogle Scholar
Helmholtz, H. 1858 Über Integrale der hydrodynamischen Gleichungen, welche den Wirbel-bewegungen entsprechen. Crelles J. 55, 25–55.Google Scholar
Henning, L. & King, R. 2005 a Multivariable closed-loop control of the reattachement length downstream of a backward-facing step. In Proc. 16th IFAC World Congress. IFAC Paper 02575.Google Scholar
Henning, L. & King, R. 2005 b Drag reduction by closed-loop control of a separated flow over a bluff body with a blunt trailing edge. In Proc. 44th IEEE Conf. on Decision and Control and European Control Conference CDC-ECC'05, pp. 494–499.Google Scholar
Henning, L. & King, R. 2007 Robust multivariable closed-loop control of a turbulent backward-facing step flow. J. Aircraft 40, 201–208.CrossRefGoogle Scholar
Henning, L., Pastoor, M., King, R., Noack, B. R. & Tadmor, G. 2007 Feedback control applied to bluff body wake. In Active Flow Control (ed. King, R.). Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol. 95. Springer.Google Scholar
Hucho, W.-H. 2002 Aerodynamik der stumpfen Körper. Physikalische Grundlagen und Anwendungen in der Praxis. Vieweg.CrossRefGoogle Scholar
Huerre, P. & Monkewitz, P. A. 1990 Local and global instabilities in spatially developing flows. Annu. Rev. Fluid Mech. 22, 473–537.Google Scholar
von Kármán, T. 1911 Über den Mechanismus des Widerstandes, den ein bewegter Körper in einer Flüssigkeit erfährt. Nachrichten der Kaiserlichen Gesellschaft der Wissenschaften zu Göttingen, pp. 324–338.Google Scholar
Kim, J., Hahn, S., Lee, D., Choi, J., Jeon, W.-P. & Choi, H. 2004 Active control of turbulent flow over a model vehicle for drag reduction. J. Turb. 5, 1–25.CrossRefGoogle Scholar
King, R., Becker, R., Garwon, M. & Henning, L. 2004 Robust and adaptive closed-loop control of separated shear flows. AIAA Paper 2004-2519.Google Scholar
King, R., Seibold, M., Lehmann, O., Noack, B. R., Morzyńksi, M. & Tadmor, G. 2005 Nonlinear flow control based on a low dimensional model of fluid flow. In Control and Observer Design for Nonlinear Finite and Infinite Dimensional Systems (ed. Meurer, T. et al. ). Lecture Notes in Control and Information Sciences, vol. 322, pp. 369–386. Springer.CrossRefGoogle Scholar
Krasny, R. 1986 Desingularization of periodic vortex sheet roll-up. J. Comput. Phys. 65, 292–313.Google Scholar
Krstić, M. & Wang, H.-H. 2000 Stability of extremum seeking feedback for general nonlinear dynamic systems. Automatica 36, 595–601.Google Scholar
Leder, A. 1992 Abgelöste Strömungen – Physikalische Grundlagen. Vieweg.Google Scholar
Leonard, A. 1985 Computing three-dimensional incompressible flows with vortex elements. Annu. Rev. Fluid Mech. 17, 523–559.Google Scholar
Little, J., Debiasi, M., Caraballo, E., & Samimy, M. 2007 Effects of open-loop and closed-loop control on subsonic cavity flows. Phys. Fluids 19, 065104.Google Scholar
Lugt, H. J. 1996 Introduction to Vortex Theory. Vortex Flow Press.Google Scholar
Lumley, J. L. & Blossey, P. N. 1998 Control of turbulence. Annu. Rev. Fluid Mech. 30, 311–327.Google Scholar
Meiburg, E. 1995 Three-dimensional vortex dynamics simulation. In Fluid Vortices (ed. Green, S.), pp. 651–685. Kluwer.CrossRefGoogle Scholar
Mercker, E. 1980 Eine Blockierungskorrektur für aerodynamische Messungen in offenen und geschlossenen Unterschallwindkanälen. PhD Thesis, Technische Universität Berlin.Google Scholar
Milne-Thomson, L. M. 1968 Theoretical Hydrodynamics. Macmillan.Google Scholar
Noack, B. R, Afanasiev, K., Morzyński, M., Tadmor, G. & Thiele, F. 2003 A hierarchy of low-dimensional models for the transient and post-transient cylinder wake. J. Fluid Mech. 497, 335–363.CrossRefGoogle Scholar
Noack, B. R., Papas, P. & Monkewitz, P. A. 2005 The need for a pressure-term representation in empirical Galerkin models of incompressible shear flows. J. Fluid Mech. 523, 339–365.Google Scholar
Noack, B. R., Tadmor, G. & Morzyński, M. 2004 Low-dimensional models for feedback flow control. Part I: Empirical Galerkin models (Invited). AIAA Paper 2004-2408.Google Scholar
Park, H., Lee, D., Jeon, W.-P., Hahn, S., Kim, J., Kim, J., Choi, J. & Choi, H. 2006 Drag reduction in flow over a two-dimensional bluff body with a blunt trailing edge using a new passive device. J. Fluid Mech. 563, 389–414.Google Scholar
Pastoor, M., King, R., Noack, B. R., Dillmann, A. & Tadmor, G. 2003 Model-based coherent-structure control of turbulent shear flows using low-dimensional vortex models. AIAA Paper 2003–4261.Google Scholar
Protas, B. 2004 Linear feedback stabilization of laminar vortex shedding based on a point vortex model. Phys. Fluids 16, 4473–4488.CrossRefGoogle Scholar
Protas, B. 2006 Higher-order Föppl models of steady wake flows. Phys. Fluids 18, 117109.Google Scholar
Protas, B. & Wesfreid, J.-E. 2002 Drag force in the open-loop control of the cylinder wake in the laminar regime. Phys. Fluids 14, 810–826.Google Scholar
Rosenhead, L. 1931 The formation of vortices from a surface of discontinuity. Proc. R. Soc. Lond. 134, 170–192.Google Scholar
Roussopoulos, K. 1993 Feedback control of vortex shedding at low Reynolds numbers. J. Fluid Mech. 248, 267–296.Google Scholar
Rowley, C. W., Williams, D. R., Colonius, T., Murray, R. M., MacMartin, D. G. & Fabris, D. 2002 Model-based control of cavity oscillations. Part II: System identification and analysis. AIAA Paper 2002-0972.Google Scholar
Seidel, J., Siegel, S., Cohen, K., Becker, V. & McLaughlin, T. 2007 Simulations of three dimensional feedback control of a circular cylinder wake. AIAA Paper 2006-1404.CrossRefGoogle Scholar
Siegel, S., Aradag, S., Seidel, J., Cohen, K. & McLaughlin, T. 2007 Low diimensional POD based estimation of a 3D turbulent separated flow. AIAA Paper 2007-0112.Google Scholar
Siegel, S., Cohen, K. & McLaughlin, T. 2003 Feedback control of a circular cylinder wake in experiment and simulation. AIAA Paper 2003-3571.Google Scholar
Siegel, S., Cohen, K., Seidel, J., Luchtenburg, M. & McLaughlin, T. 2008 Low dimensional modelling of a transient cylinder wake using double proper-orthogonal decomposition. J. Fluid Mech. (in press).CrossRefGoogle Scholar
Soteriou, M. 2003 Vortex element method – expansion about incompressible flow computation of noise generation by subsonic shear flows – the impact of external forcing. J. Turb. 4, 1–9.CrossRefGoogle Scholar
Tadmor, G. 2004 Observers and feedback control for a rotating vortex pair. IEEE Trans. Control Systems Technol. 12, 36–51.Google Scholar
Tadmor, G., Noack, B. R., Morzyński, M. & Siegel, S. 2004 Low-dimensional models for feedback flow control. Part II: Observer and controller design (Invited). AIAA Paper 2004-2409.CrossRefGoogle Scholar
Tang, S. & Aubry, N. 2000 Suppression of vortex shedding inspired by a low-dimensional model, J. Fluids Struct. 14, 443–468.CrossRefGoogle Scholar
Tanner, M. 1972 A method of reducing the base drag of wings with blunt trailing edges. Aeronaut. Q. 23, 15–23.Google Scholar
Thomson, W. 1869 On vortex motion. Trans. R. Soc. Edin. 25, 217–260.Google Scholar
Tombazis, N. & Bearman, P. W. 1997 A study of three-dimensional aspects of vortex shedding from a bluff body with a mild geometric disturbance. J. Fluid Mech. 330, 85–112.Google Scholar
Wu, C.-J., Wang, L. & Wu, J.-Z. 2007 Suppression of the von Kármán vortex street behind a circular cylinder by a travelling wave generated by a flexible surface. J. Fluid Mech. 574, 365–391.Google Scholar
Wu, C.-J., Xie, Y. & Wu, J.-Z. 2003 Fluid roller bearing effect and flow control. Acta Mechanica Sinica 19 (5), 476–484.Google Scholar
Wygnanski, I. 2004 The variables affecting the control of separation by periodic excitation. AIAA Paper 2004-2505.Google Scholar
Zhang, H.-Q., Fey, U., Noack, B. R., König, M. & Eckelmann, H. 1995 On the transition of the cylinder wake. Phys. Fluids 7, 779–794.Google Scholar