Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-19T15:43:15.274Z Has data issue: false hasContentIssue false

A generalized mean-field model of the natural and high-frequency actuated flow around a high-lift configuration

Published online by Cambridge University Press:  06 March 2009

DIRK M. LUCHTENBURG*
Affiliation:
Department of Fluid Dynamics and Engineering Acoustics, Berlin Institute of Technology MB1, Straße des 17. Juni 135, D-10623 Berlin, Germany
BERT GÜNTHER
Affiliation:
Department of Fluid Dynamics and Engineering Acoustics, Berlin Institute of Technology MB1, Straße des 17. Juni 135, D-10623 Berlin, Germany
BERND R. NOACK
Affiliation:
Department of Fluid Dynamics and Engineering Acoustics, Berlin Institute of Technology MB1, Straße des 17. Juni 135, D-10623 Berlin, Germany
RUDIBERT KING
Affiliation:
Department of Plant and Process Technology, Berlin Institute of Technology ER2-1, Hardenbergstraße 36a, D-10623 Berlin, Germany
GILEAD TADMOR
Affiliation:
Department of Electrical and Computer Engineering, Northeastern University, 440 Dana Research Building, Boston, MA 02115, USA
*
Email address for correspondence: [email protected]

Abstract

A low-dimensional Galerkin model is proposed for the flow around a high-lift configuration, describing natural vortex shedding, the high-frequency actuated flow with increased lift and transients between both states. The form of the dynamical system has been derived from a generalized mean-field consideration. Steady state and transient URANS (unsteady Reynolds-averaged Navier–Stokes) simulation data are employed to derive the expansion modes and to calibrate the system parameters. The model identifies the mean field as the mediator between the high-frequency actuation and the low-frequency natural shedding instability.

Type
Papers
Copyright
Copyright © Cambridge University Press 2009

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.)

References

REFERENCES

Amitay, M. & Glezer, A. 2002 Controlled transients of flow reattachment over stalled airfoils. Intl J. Heat Transfer and Fluid Flow 23, 690699.CrossRefGoogle Scholar
Aubry, N., Holmes, P., Lumley, J. L. & Stone, E. 1988 The dynamics of coherent structures in the wall region of a turbulent boundary layer. J. Fluid Mech. 192, 115173.CrossRefGoogle Scholar
Ausseur, J. M. & Pinier, J. T. 2005 Towards closed-loop feedback control of the flow over NACA-4412 airfoil. AIAA Paper 2005–0343.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 (6), 13821392.Google 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 (097101), 121.Google Scholar
Collis, S. S., Joslin, R. D., Seifert, A. & Theofilis, V. 2004 Issues in active flow control: theory, control, simulation, and experiment. Prog. Aerosp. Sci. 40, 237289.Google Scholar
Couplet, M., Sagaut, P. & Basdevant, C. 2003 Intermodal energy transfers in a proper orthogonal decomposition – Galerkin representation of a turbulent separated flow. J. Fluid Mech. 491, 275284.Google Scholar
Dusek, J., Le Gal, P. & Fraunié, P. 1994 A numerical and theoretical study of the first Hopf bifurcation in a cylinder wake. J. Fluid Mech. 264, 5980.CrossRefGoogle Scholar
Favier, J., Cordier, L. & Kourta, A. In press Accurate POD reduced-order models of separated flows. Phys. Fluids.Google Scholar
Fletcher, C. A. J. 1984 Computational Galerkin Methods. Springer-Verlag.CrossRefGoogle Scholar
Gad-el-Hak, M. 1996 Modern developments in flow control. Appl. Mech. Rev. 49, 365379.Google Scholar
Gad-el-Hak, M. 2000 Flow Control: Passive, Active and Reactive Flow Management. Cambridge University Press.Google Scholar
Galletti, G., Bruneau, C. H., Zannetti, L. & Iollo, A. 2004 Low-order modelling of laminar flow regimes past a confined square cylinder. J. Fluid Mech. 503, 161170.CrossRefGoogle 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.CrossRefGoogle Scholar
Graham, W. R., Peraire, J. & Tang, K. Y. 1999 Optimal control of vortex shedding using low-order models. Part I: Open-loop model development. Int. J. Num. Meth. Eng. 44, 945972.Google Scholar
Günther, B., Thiele, F., Petz, R., Nitsche, W., Sahner, J., Weinkauf, T. & Hege, H. C. 2007 Control of separation on the flap of a three element high-lift configuration. AIAA Paper 2007-0265.CrossRefGoogle Scholar
Henning, L., Pastoor, M., Noack, B. R., King, R. & Tadmor, G. 2007 Feedback control applied to the bluff body wake. In Active Flow Control (ed. King, R.), Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol. 95, pp. 369390. Springer-Verlag.Google Scholar
Holmes, P., Lumley, J. L. & Berkooz, G. 1998 Turbulence, Coherent Structures, Dynamical Systems and Symmetry. Cambridge University Press.Google Scholar
Hu, G.-H., Sun, D.-J., Yin, X.-Y. & Tong, B.-G. 1996 Hopf bifurcation in wakes behind a rotating and translating circular cylinder. Phys. Fluids 8, 19721974.CrossRefGoogle Scholar
Kaepernick, K., Koop, L. & Ehrenfried, K. 2005 Investigation of the unsteady flow field inside a leading edge slat cove. AIAA Paper 2005–2813.CrossRefGoogle Scholar
King, R. (Ed.) 2007 Active Flow Control, Notes on Numerical Fluid Mechanics and Interdisciplinary Design, vol. 95. Springer-Verlag.Google Scholar
Ladyzhenskaya, O. A. 1963 The Mathematical Theory of Viscous Incompressible Flow. Gordon and Breach.Google Scholar
Luchtenburg, D. M., Tadmor, G., Lehmann, O., Noack, B. R., King, R. & Morzyński, M. 2006 Tuned POD Galerkin models for transient feedback regulation of the cylinder wake. AIAA Paper 2006-1407.Google Scholar
Maurel, A., Pagneux, V. & Wesfreid, J. E. 1995 Mean-flow correction as a non-linear saturation mechanism. Europhysics Lett. 32, 217222.Google Scholar
Monin, A. S. & Yaglom, A. M. 1971 Statistical Fluid Mechanics I. The MIT Press.Google Scholar
Noack, B. R. 2006 Niederdimensionale Galerkin-Modelle für laminare und transitionelle freie Scherströmungen (transl. Low-dimensional Galerkin models of laminar and transitional free shear flows). Habilitation thesis, Fakultät V – Verkehrs- und Maschinensysteme, Berlin Institute of Technology, Germany.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, 335363.Google Scholar
Noack, B. R. & Copeland, G. S. 2000 On a stability property of ensemble-averaged flow. Tech. Rep. 03/2000. Hermann-Föttinger-Institut für Strömungsmechanik, Berlin Institute of Technology.Google Scholar
Noack, B. R. & Eckelmann, H. 1994 A low-dimensional Galerkin method for the three-dimensional flow around a circular cylinder. Phys. Fluids 6, 124143.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, 339365.CrossRefGoogle Scholar
Noack, B. R., Pelivan, I., Tadmor, G., Morzyński, M. & Comte, P. 2004 a Robust low-dimensional Galerkin models of natural and actuated flows. In Proceedings of the Fourth Aeroacoustics Workshop, RWTH Aachen, February 26–27, 2004 (ed. Schröder, W. & Tröltzsch, P.). Institut für Akustik und Sprachkommunikation, Technical University of Dresden.Google Scholar
Noack, B. R., Schlegel, M., Ahlborn, B., Mutschke, G., Morzyński, M., Comte, P. & Tadmor, G. 2008 A finite-time thermodynamics of unsteady fluid flows. J. Non-Equilib. Thermodyn. 33 (2), 103148.Google Scholar
Noack, B. R., Tadmor, G. & Morzyński, M. 2004 b Actuation models and dissipative control in empirical Galerkin models of fluid flows. In Proceedings of the 2004 American Control Conference, pp. 5722–5727. American Automatic Control Council (AACC), Dayton, OH, USA.Google Scholar
Noack, B. R., Tadmor, G. & Morzyński, M. 2004 c Low-dimensional models for feedback flow control. Part I. Empirical Galerkin models. AIAA Paper 2004-2408.Google Scholar
Pastoor, M., Henning, L., Noack, B. R., King, R. & Tadmor, G. 2008 Feedback shear layer control for bluff body drag reduction. J. Fluid Mech. 608, 161196.CrossRefGoogle Scholar
Pastoor, M., Noack, B. R., King, R. & Tadmor, G. 2006 Spatiotemporal waveform observers and feedback in shear layer control. AIAA Paper 2006-1402.Google Scholar
Raju, R. & Mittal, R. 2002 Towards physics based strategies for separation control over an airfoil using synthetic jets. AIAA Paper 2007-1421.Google Scholar
Rediniotis, O. K., Ko, J. & Kurdila, A. J. 2002 Reduced order nonlinear Navier–Stokes models for synthetic jets. J. Fluids Engng 124, 433443.CrossRefGoogle Scholar
Rempfer, D. & Fasel, F. H. 1994 Dynamics of three-dimensional coherent structures in a flat-plate boundary-layer. J. Fluid Mech. 275, 257283.Google Scholar
Reynolds, W. C. & Hussain, A. K. M. F. 1972 The mechanics of an organized wave in turbulent shear flow. Part 3. Theoretical model and comparisons with experiments. J. Fluid Mech. 54, 263288.Google Scholar
Rowley, C. W. & Juttijudata, V. 2005 Model-based control and estimation of cavity flow oscillations. In Proceedings of the 44th IEEE Conference on Decision and Control and European Control Conference, pp. 512–517. European Union Control Association (EUCA), Saint-Martin d'Hères, France.Google Scholar
Rummler, B. 2000 Zur Lösung der instationären inkompressiblen Navier-Stokesschen Gleichungen in speziellen Gebieten (transl. On the solution of the incompressible Navier–Stokes equations in special domains). Habilitation thesis. Fakultät für Mathematik, Otto-von-Guericke-Universität Magdeburg.Google Scholar
Rung, T. & Thiele, F. 1996 Computational modelling of complex boundary layer flows. In Proceedings of the 9th International Symposium on Transport Phenomena in Thermal-Fluids Engineering, pp. 321–326. Singapore.Google Scholar
Samimy, M., Debiasi, M., Caraballo, E., Serrani, A., Yuan, X., Little, J. & Myatt, J. 2007 Feedback control of subsonic cavity flows using reduced-order models. J. Fluid Mech. 579, 315346.Google Scholar
Schatz, M., Günther, B. & Thiele, F. 2006 Computational investigation of separation control over high-lift airfoil flows. In Active Flow Control (ed. King, R.), Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol. 95, pp. 260278. Springer-Verlag.Google Scholar
Seifert, A., Darabi, A. & Wygnanski, I. 1996 On the delay of airfoil stall by periodic excitation. J. Aircraft 33 (4), 691699.Google Scholar
Siegel, S., Cohen, K. & McLaughlin, T. 2003 Feedback control of a circular cylinder wake in experiment and simulation. AIAA Paper 2003-3569.Google Scholar
Siegel, S. G., Seidel, J., Fagley, C., Luchtenburg, D. M., Cohen, K. & McLaughlin, T. 2008 Low-dimensional modelling of a transient cylinder wake using double proper orthogonal decomposition. J. Fluid Mech. 610, 142.CrossRefGoogle Scholar
Stuart, J. T. 1958 On the non-linear mechanics of hydrodynamic stability. J. Fluid Mech. 4, 121.Google Scholar
Tadmor, G., Gonzalez, J., Lehmann, O., Noack, B. R., Morzyński, M. & Stankiewicz, W. 2007 Shift modes and transient dynamics in low order, design oriented Galerkin models. AIAA Paper 2007-0111.Google Scholar
Tadmor, G., Noack, B. R., Morzyński, M. & Siegel, S. 2004 Low-dimensional models for feedback flow control. Part II. Controller design and dynamic estimation. AIAA Paper 2004-2409.CrossRefGoogle Scholar
Ukeiley, L., Cordier, L., Manceau, R., Delville, J., Bonnet, J. P. & Glauser, M. 2001 Examination of large-scale structures in a turbulent plane mixing layer. Part 2. Dynamical systems model. J. Fluid Mech. 441, 61108.Google Scholar
Zielinska, B. J. A., GoujonDurand, S., Dusek, J. & Wesfreid, J. 1997 Strongly nonlinear effect in unstable wakes. Phys. Rev. Lett. 79, 38933896.Google Scholar