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Optimal suppression of a separation bubble in a laminar boundary layer

Published online by Cambridge University Press:  06 April 2020

Michael Karp
Affiliation:
Center for Turbulence Research, Stanford University, Stanford, CA94305, USA
M. J. Philipp Hack
Affiliation:
Center for Turbulence Research, Stanford University, Stanford, CA94305, USA
Corresponding
E-mail address:

Abstract

By means of nonlinear optimization, we seek the velocity disturbances at a given upstream position that suppress a laminar separation bubble as effectively as possible. Both steady and unsteady disturbances are examined and compared. For steady disturbances, an informed guess based on linear analysis of transient perturbation growth leads to significant delay of separation and serves as a starting point for the nonlinear optimization algorithm. It is found that the linear analysis largely captures the suppression of the separation bubble attained by the nonlinear optimal perturbations. The mechanism of separation delay is the generation of a mean flow distortion by nonlinear interactions during the perturbation growth. The mean flow distortion enhances the momentum close to the wall, counteracting the deceleration of the flow in that region. An examination of the effect of the disturbance spanwise wavenumber reveals that perturbations maximizing the mean flow distortion also approximately maximize the peak wall pressure, which is beneficial for lowering form drag. The optimal spanwise wavenumber leading to maximal peak wall pressure is significantly larger than the one maximizing the shift in separation onset. For unsteady disturbances, the mechanism of separation delay relies on enhancing wall-normal momentum transfer by triggering instabilities of the separated shear layer. It is found that Tollmien–Schlichting waves obtained from linear stability theory provide accurate estimates of the nonlinearly optimal disturbances. Comparison of optimal steady and unsteady perturbations reveals that the latter are able to obtain a higher time-averaged peak wall pressure.

Type
JFM Papers
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

Abdessemed, N., Sherwin, S. J. & Theofilis, V. 2009 Linear instability analysis of low-pressure turbine flows. J. Fluid Mech. 628, 5783.CrossRefGoogle Scholar
Åkervik, E., Brandt, L., Henningson, D. S., Hœpffner, J., Marxen, O. & Schlatter, P. 2006 Steady solutions of the Navier–Stokes equations by selective frequency damping. Phys. Fluids 18, 068102.CrossRefGoogle Scholar
Alam, M. & Sandham, N. D. 2000 Direct numerical simulation of ‘short’ laminar separation bubbles with turbulent reattachment. J. Fluid Mech. 410, 128.CrossRefGoogle Scholar
Andersson, P., Berggren, M. & Henningson, D. S. 1999 Optimal disturbances and bypass transition in boundary layers. Phys. Fluids 11, 134150.CrossRefGoogle Scholar
Boiko, A. V., Dovgal, A. V. & Hein, S. 2008 Control of a laminar separating boundary layer by induced stationary perturbations. Eur. J. Mech. (B/Fluids) 27, 466476.CrossRefGoogle Scholar
Butler, K. M. & Farrell, B. F. 1992 Three-dimensional optimal perturbations in viscous shear flow. Phys. Fluids A 4, 16371650.CrossRefGoogle Scholar
Cho, M., Choi, S. & Choi, H. 2016 Control of flow separation in a turbulent boundary layer using time-periodic forcing. Trans. ASME: J. Fluids Engng 138, 101204.Google Scholar
Cossu, C. & Brandt, L. 2002 Stabilization of Tollmien–Schlichting waves by finite amplitude optimal streaks in the Blasius boundary layer. Phys. Fluids 14, L57L60.CrossRefGoogle Scholar
Ellingsen, T. & Palm, E. 1975 Stability of linear flow. Phys. Fluids 18, 487488.CrossRefGoogle Scholar
Fransson, J. H. M. & Talamelli, A. 2012 On the generation of steady streamwise streaks in flat-plate boundary layers. J. Fluid Mech. 698, 211234.CrossRefGoogle Scholar
Fransson, J. H. M., Talamelli, A., Brandt, L. & Cossu, C. 2006 Delaying transition to turbulence by a passive mechanism. Phys. Rev. Lett. 96, 064501.CrossRefGoogle ScholarPubMed
Greenblatt, D. & Wygnanski, I. J. 2000 The control of flow separation by periodic excitation. Prog. Aerosp. Sci. 36, 487545.CrossRefGoogle Scholar
Gustavsson, L. H. 1991 Energy growth of three-dimensional disturbances in plane Poiseuille flow. J. Fluid Mech. 224, 241260.CrossRefGoogle Scholar
Hack, M. J. P. & Moin, P. 2017 Algebraic disturbance growth by interaction of Orr and lift-up mechanisms. J. Fluid Mech. 829, 112126.CrossRefGoogle Scholar
Hack, M. J. P. & Zaki, T. A. 2015 Modal and non-modal stability of boundary layers forced by spanwise wall oscillations. J. Fluid Mech. 778, 389427.CrossRefGoogle Scholar
Karp, M. & Hack, M. J. P. 2018 Transition to turbulence over convex surfaces. J. Fluid Mech. 855, 12081237.CrossRefGoogle Scholar
Kerho, M., Hutcherson, S., Blackwelder, R. F. & Liebeck, R. H. 1993 Vortex generators used to control laminar separation bubbles. J. Aircraft 30, 315319.CrossRefGoogle Scholar
Kim, J. & Moin, P. 1985 Application of a fractional-step method to incompressible Navier–Stokes equations. J. Comput. Phys. 59, 308323.CrossRefGoogle Scholar
Kotapati, R. B., Mittal, R., Marxen, O., Ham, F., You, D. & Cattafesta, L. N. 2010 Nonlinear dynamics and synthetic-jet-based control of a canonical separated flow. J. Fluid Mech. 654, 6597.CrossRefGoogle Scholar
Landahl, M. T. 1980 A note on an algebraic instability of inviscid parallel shear flows. J. Fluid Mech. 98, 243251.CrossRefGoogle Scholar
Levinsky, E. S. & Schappelle, R. H. 1975 Analysis of separation control by means of tangential blowing. J. Aircraft 12, 1826.CrossRefGoogle Scholar
Mao, X., Zaki, T. A., Sherwin, S. J. & Blackburn, H. M. 2017 Transition induced by linear and nonlinear perturbation growth in flow past a compressor blade. J. Fluid Mech. 820, 604632.CrossRefGoogle Scholar
Marxen, O., Kotapati, R. B., Mittal, R. & Zaki, T. 2015 Stability analysis of separated flows subject to control by zero-net-mass-flux jet. Phys. Fluids 27, 024107.CrossRefGoogle Scholar
Marxen, O., Lang, M., Rist, U., Levin, O. & Henningson, D. S. 2009 Mechanisms for spatial steady three-dimensional disturbance growth in a non-parallel and separating boundary layer. J. Fluid Mech. 634, 165189.CrossRefGoogle Scholar
Marxen, O. & Rist, U. 2010 Mean flow deformation in a laminar separation bubble: separation and stability characteristics. J. Fluid Mech. 660, 3754.CrossRefGoogle Scholar
Marxen, O., Rist, U. & Wagner, S. 2004 Effect of spanwise-modulated disturbances on transition in a separated boundary layer. AIAA J. 42, 937944.CrossRefGoogle Scholar
Na, Y. & Moin, P. 1998 Direct numerical simulation of a separated turbulent boundary layer. J. Fluid Mech. 374, 379405.CrossRefGoogle Scholar
Pearcey, H. H. 1961 Shock-induced separation and its prevention. In Boundary Layer and Flow Control, Its Principle and Applications (ed. Lachmann, G. V.). Pergamon Press.Google Scholar
Polak, E. & Ribière, G. 1969 Note sur la convergence de directions conjugées. Rev. Fr. Inform. Rech. O. 16, 3543.Google Scholar
Pujals, G., Depardon, S. & Cossu, C. 2010 Drag reduction of a 3D bluff body using coherent streamwise streaks. Exp. Fluids 49, 10851094.CrossRefGoogle Scholar
Ran, W., Zare, A., Hack, M. J. P. & Jovanovic, M. R. 2019 Modeling mode interactions in boundary layer flows via the parabolized Floquet equations. Phys. Rev. Fluids 4, 023901.Google Scholar
Rist, U. & Augustin, K. 2006 Control of laminar separation bubbles using instability waves. AIAA J. 44, 22172223.CrossRefGoogle Scholar
Rosenfeld, M., Kwak, D. & Vinokur, M. 1991 A fractional step solution method for the unsteady incompressible Navier–Stokes equations in generalized coordinate systems. J. Comput. Phys. 94, 102137.CrossRefGoogle Scholar
Schmid, P. J. & Henningson, D. S. 2001 Stability and Transition in Shear Flows. Springer.CrossRefGoogle Scholar
Schubauer, G. B. & Spangenberg, W. G. 1960 Forced mixing in boundary layers. J. Fluid Mech. 8, 1032.CrossRefGoogle Scholar
Seo, J. H., Cadieux, F., Mittal, R., Deem, E. & Cattafesta, L. 2018 Effect of synthetic jet modulation schemes on the reduction of a laminar separation bubble. Phys. Rev. Fluids 3, 033901.Google Scholar
Theofilis, V., Hein, S. & Dallmann, U. 2000 On the origins of unsteadiness and three-dimensionality in a laminar separation bubble. Phil. Trans. R. Soc. Lond. A 358, 32293246.CrossRefGoogle Scholar
Xu, H., Mughal, S. M., Gowree, E. R., Atkin, C. J. & Sherwin, S. J. 2017 Destabilisation and modification of Tollmien–Schlichting disturbances by a three-dimensional surface indentation. J. Fluid Mech. 819, 592620.CrossRefGoogle Scholar

Karp and Hack supplementary movie

Instantaneous streamwise component for the nonlinearly optimal case ω = 0.10.

Video 273 KB

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