Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-05T05:03:41.310Z Has data issue: false hasContentIssue false
  • English
  • Français

The influence of harmonic wall motion on transitional boundary layers

Published online by Cambridge University Press:  03 November 2014

M. J. Philipp Hack  and
Tamer A. Zaki
M. J. Philipp Hack
Affiliation:
Department of Mechanical Engineering, Imperial College London, London SW7 2AZ, UK
Tamer A. Zaki*
Affiliation:
Department of Mechanical Engineering, Imperial College London, London SW7 2AZ, UK
*
†Present address: Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA. Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The influence of harmonic spanwise wall motion on bypass transition in boundary layers is investigated using direct numerical simulations. It is shown that the appropriate choice of the forcing parameters can achieve a substantial stabilization of the laminar flow regime. However, an increase of the forcing amplitude or period beyond their optimal values diminishes the stabilizing effect, and leads to breakdown upstream of the unforced case. For the optimal wall-oscillation parameters, the reduction in propulsion power substantially outweighs the power requirement of the forcing. The mechanism of transition delay is examined in detail. Analysis of the pre-transitional streaks shows that the wall oscillation substantially reduces their average amplitude, and eliminates the most energetic streaks. As a result, the secondary instabilities that precede breakdown to turbulence are substantially weakened – an effect demonstrated by linear stability analyses of flow fields from direct numerical simulations. The outcome is transition delay owing to a significant reduction in the frequency of occurrence of turbulent spots and a downstream shift in their average inception location. Finally, it is shown that the efficiency of the forcing can be further improved by replacing the sinusoidal time dependence of the wall oscillation with a square wave.

JFM classification

Boundary Layers: Boundary layer stability Instability: Transition to turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 760 , 10 December 2014 , pp. 63 - 94
Check for updates
Copyright
© 2014 Cambridge University Press 

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

Andersson, P., Berggren, M. & Henningson, D. S. 1999 Optimal disturbances and bypass transition in boundary layers. Phys. Fluids 11 (1), 134–150.Google Scholar
Arnal, D. & Michel, R. 1990 Laminar–Turbulent Transition, Vol. III. Springer.CrossRefGoogle Scholar
Barkley, D., Blackburn, H. M. & Sherwin, S. J. 2008 Direct optimal growth analysis for timesteppers. Intl J. Numer. Meth. Fluids 57, 1435–1458.Google Scholar
Baron, A. & Quadrio, M. 1996 Turbulent drag reduction by spanwise wall oscillations. Appl. Sci. Res. 55, 311–326.CrossRefGoogle Scholar
Blackburn, H. M. & Sherwin, S. J. 2004 Formulation of a Galerkin spectral element–Fourier method for three-dimensional incompressible flows in cylindrical geometries. J. Comput. Phys. 197, 759–778.Google Scholar
Boiko, A. V., Westin, K. J. A., Klingmann, B. G. B., Kozlov, V. V. & Alfredsson, P. H. 1994 Experiments in a boundary layer subjected to free stream turbulence. Part 2. The role of TS-waves in the transition process. J. Fluid Mech. 281, 219–245.Google Scholar
Bowles, R. G. A. & Smith, F. T. 1995 Short-scale effects on model boundary-layer spots. J. Fluid Mech. 295, 395–407.Google Scholar
Bradshaw, P. & Pontikos, N. S. 1985 Measurements in the turbulent boundary layer on an ‘infinite’ swept wing. J. Fluid Mech. 159, 105–130.Google Scholar
Brandt, L., Schlatter, P. & Henningson, D. S. 2004 Transition in boundary layers subject to free-stream turbulence. J. Fluid Mech. 517, 167–198.CrossRefGoogle Scholar
Breuer, K. S. & Haritonidis, J. H. 1990 The evolution of a localized disturbance in a laminar boundary layer. Part 1. Weak disturbances. J. Fluid Mech. 220, 569–594.Google Scholar
Butler, K. M. & Farrell, B. F. 1992 Three-dimensional optimal perturbations in viscous shear flow. Phys. Fluids A 4 (8), 1637–1650.Google Scholar
Choi, K.-S. 2002 Near-wall structure of turbulent boundary layer with spanwise-wall oscillation. Phys. Fluids 14 (7), 2530–2542.Google Scholar
Chong, T. P. & Zhong, S. 2005 On the three-dimensional structure of turbulent spots. Trans. ASME: J. Turbomach. 127, 545–551.Google Scholar
Cimarelli, A., Frohnapfel, B., Hasegawa, Y., De Angelis, E. & Quadrio, M. 2013 Prediction of turbulence control for arbitrary periodic spanwise wall movement. Phys. Fluids 25, 075102.Google Scholar
Cossu, C. & Brandt, L. 2004 On Tollmien–Schlichting-like waves in streaky boundary layers. Eur. J. Mech. (B/Fluids) 23, 815–833.Google Scholar
Dong, M. & Wu, X. 2013 On continuous spectra of the Orr–Sommerfeld/Squire equations and entrainment of free-stream vortical disturbances. J. Fluid Mech. 732, 616–659.Google Scholar
Driver, D. M. & Hebbar, S. K. 1987 Experimental study of a three-dimensional, shear-driven, turbulent boundary layer. AIAA J. 25 (1), 35–42.Google Scholar
Dryden, H. L.1936 Air flow in the boundary layer near a plate. NACA Report No. 562. National Advisory Committee for Aeronautics.Google Scholar
Duchmann, A., Grundmann, S. & Tropea, C. 2013 Delay of natural transition with dielectric barrier discharges. Exp. Fluids 54, 1461.Google Scholar
Durbin, P. A. & Wu, X. 2007 Transition beneath vortical disturbances. Annu. Rev. Fluid Mech. 39, 107–128.Google Scholar
Emmons, H. W. 1951 The laminar–turbulent transition in a boundary layer: part I. J. Aeronaut. Sci. 18 (7), 490–498.CrossRefGoogle Scholar
Fransson, J. H. M. & Alfredsson, P. H. 2003 On the disturbance growth in an asymptotic suction boundary layer. J. Fluid Mech. 482, 51–90.Google Scholar
Fransson, J. H. M., Brandt, L., Talamelli, A. & Cossu, C. 2005 Experimental study of the stabilization of Tollmien–Schlichting waves by finite amplitude streaks. Phys. Fluids 17, 054110.Google Scholar
Hack, M. J. P. & Zaki, T. A. 2012 The continuous spectrum of time-harmonic shear layers. Phys. Fluids 24 (3), 034101.Google Scholar
Hack, M. J. P. & Zaki, T. A. 2014 Streak instabilities in boundary layers beneath free-stream turbulence. J. Fluid Mech. 741, 280–315.Google Scholar
Hanson, R. E., Bade, K. M., Belson, B. A., Lavoie, P., Naguib, A. M. & Rowley, C. W. 2014 Feedback control of slowly-varying transient growth by an array of plasma actuators. Phys. Fluids 26, 024102.Google Scholar
Herbert, T. 1988 Secondary instability of boundary layers. Annu. Rev. Fluid Mech. 20, 487–526.CrossRefGoogle Scholar
Huang, J.-C. & Johnson, M. W. 2007 The influence of compliant surfaces on bypass transition. Exp. Fluids 42, 711–718.Google Scholar
Hunt, J. C. R. & Carruthers, D. J. 1990 Rapid distortion theory and the ‘problems’ of turbulence. J. Fluid Mech. 212, 497–532.Google Scholar
Hunt, J. C. R. & Durbin, P. A. 1999 Perturbed vortical layers and shear sheltering. Fluid Dyn. Res. 24, 375–404.Google Scholar
Jacobs, R. G. & Durbin, P. A. 1998 Shear sheltering and the continuous spectrum of the Orr–Sommerfeld equation. Phys. Fluids 10 (8), 2006–2011.Google Scholar
Jacobs, R. G. & Durbin, P. A. 2001 Simulations of bypass transition. J. Fluid Mech. 428, 185–212.CrossRefGoogle Scholar
Jung, W. J., Mangiavacchi, N. & Akhavan, R. 1992 Suppression of turbulence in wall-bounded flows by high-frequency spanwise oscillations. Phys. Fluids A 4 (8), 1605–1607.Google Scholar
Karniadakis, G. E. & Choi, K.-S. 2003 Mechanisms on transverse motions in turbulent wall flows. Annu. Rev. Fluid Mech. 35, 45–62.Google Scholar
Kendall, J.1985 Experimental study of disturbances produced in a pre-transitional laminar boundary layer by weak freestream turbulence. AIAA Paper 85-1695.CrossRefGoogle Scholar
Kerschen, E. J. 1991 Linear and nonlinear receptivity to vortical free-stream disturbances. In Boundary Layer Stability and Transition to Turbulence (ed. Reda, D., Reed, H. & Kobayashi, R.), ASME Fluid Engineering Division Conference, vol. 114, p. 43. ASME.Google Scholar
Kim, J. & Moin, P. 1985 Application of a fractional-step method to incompressible Navier–Stokes equations. J. Comput. Phys. 59, 308–323.Google Scholar
Klebanoff, P. S. 1971 Effect of freestream turbulence on the laminar boundary layer. Bull. Am. Phys. Soc. 16, 1323–1334.Google Scholar
Klebanoff, P. S., Tidstrom, K. D. & Sargent, L. M. 1962 The three-dimensional nature of boundary layer instability. J. Fluid Mech. 12 (1), 1–34.CrossRefGoogle Scholar
Kleiser, L. & Zang, T. A. 1991 Numerical simulation of transition in wall-bounded shear flows. Annu. Rev. Fluid Mech. 23, 495–537.Google Scholar
Kurian, T. & Fransson, J. H. M. 2009 Grid-generated turbulence revisted. Fluid Dyn. Res. 41, 021403.Google Scholar
Landahl, M. T. 1975 Wave breakdown and turbulence. SIAM J. Appl. Maths 28 (4), 735–756.Google Scholar
Landahl, M. T. 1980 A note on an algebraic instability of inviscid parallel shear flows. J. Fluid Mech. 98, 243–251.CrossRefGoogle Scholar
Lardeau, S. & Leschziner, M. A. 2013 The streamwise drag-reduction response of a boundary layer subjected to a sudden imposition of transverse oscillatory wall motion. Phys. Fluids 25, 075109.Google Scholar
Leib, S. J., Wundrow, D. W. & Goldstein, M. E. 1999 Effect of free-stream turbulence and other vortical disturbances on a laminar boundary layer. J. Fluid Mech. 380, 169–203.Google Scholar
Liu, Y., Zaki, T. A. & Durbin, P. A. 2008a Boundary-layer transition by interaction of discrete and continuous modes. J. Fluid Mech. 604, 193–233.Google Scholar
Liu, Y., Zaki, T. A. & Durbin, P. A. 2008b Floquet analysis of secondary instability of boundary layers distorted by Klebanoff streaks and Tollmien–Schlichting waves. Phys. Fluids 20, 124102.Google Scholar
Malik, S. V. & Hooper, A. P. 2005 Linear stability and energy growth of viscosity stratified flows. Phys. Fluids 17, 024101.Google Scholar
Mandal, A. C., Venkatakrishnan, L. & Dey, J. 2010 A study on boundary-layer transition induced by free-stream turbulence. J. Fluid Mech. 660, 114–146.Google Scholar
Matsubara, M. & Alfredsson, P. 2001 Disturbance growth in boundary layers subjected to free-stream turbulence. J. Fluid Mech. 430, 149–168.Google Scholar
Moin, P., Shih, T.-H., Driver, D. & Mansour, N. N. 1990 Direct numerical simulation of a three-dimensional turbulent boundary layer. Phys. Fluids 2 (10), 1846–1853.CrossRefGoogle Scholar
Nagarajan, S., Lele, S. K. & Ferziger, J. H. 2007 Leading-edge effects in bypass transition. J. Fluid Mech. 572, 471–504.Google Scholar
Nolan, K. P. & Zaki, T. A. 2013 Conditional sampling of transitional boundary layers in pressure gradients. J. Fluid Mech. 728, 306–339.Google Scholar
Ovchinnikov, V., Choudhari, M. M. & Piomelli, U. 2008 Numerical simulations of boundary-layer bypass transition due to high-amplitude free-stream turbulence. J. Fluid Mech. 613, 135–169.CrossRefGoogle Scholar
Phillips, O. M. 1969 Shear-flow turbulence. Annu. Rev. Fluid Mech. 1, 245–264.Google Scholar
Quadrio, M. & Ricco, P. 2004 Critical assessment of turbulent drag reduction through spanwise wall oscillations. J. Fluid Mech. 521, 251–271.Google Scholar
Quadrio, M., Ricco, P. & Viotti, C. 2009 Streamwise-travelling waves of spanwise wall velocity for turbulent drag reduction. J. Fluid Mech. 627, 161–178.CrossRefGoogle Scholar
Ricco, P. 2011 Laminar streaks with spanwise wall forcing. Phys. Fluids 22, 064103.Google Scholar
Roach, P. & Brierley, B. 1990 The influence of a turbulent freestream on zero pressure gradient transitional boundary layer development, Part I: Test cases T3A and T3B. In ERCOFTAC Workshop: Numerical Simulation of Unsteady Flows and Transition to Turbulence, Lausanne, Switzerland, pp. 319–347. Cambridge University Press.Google 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, 102–137.Google Scholar
Sameen, A. & Govindarajan, R. 2007 The effect of wall heating on instability of channel flow. J. Fluid Mech. 577, 417–442.Google Scholar
Saric, W. S., Reed, H. L. & Kerschen, E. J. 2002 Boundary-layer receptivity to freestream disturbances. Annu. Rev. Fluid Mech. 34, 291–319.Google Scholar
Schrader, L.-U., Brandt, L. & Henningson, D. S. 2009 Receptivity mechanisms in three-dimensional boundary-layer flows. J. Fluid Mech. 618, 209–241.Google Scholar
Schrader, L.-U., Subir, A. & Brandt, L. 2010 Transition to turbulence in the boundary layer over a smooth and rough swept plate exposed to free-stream turbulence. J. Fluid Mech. 646, 297–325.Google Scholar
Sorensen, D. C. 1992 Implicit application of polynomial filters in a $k$ -step Arnoldi method. SIAM J. Matrix Anal. Applics. 13 (1), 357–385.Google Scholar
Spalart, P. R. 1989 Theoretical and numerical study of a three-dimensional turbulent boundary layer. J. Fluid Mech. 205, 319–340.CrossRefGoogle Scholar
Suder, K. L., O’Brien, J. E. & Reshotko, E.1981 Experimental study of bypass transition in a boundary layer. NASA Rep. TM-100913. National Aeronautics and Space Administration.Google Scholar
Taylor, G. I. 1939 Some recent developments in the study of turbulence. In Proceedings of the 5th International Congress for Applied Mechanics (ed. Den Hartog, J. & Peters, H.), pp. 294–310. Wiley.Google Scholar
Touber, E. & Leschziner, M. A. 2012 Near-wall streak modification by spanwise oscillatory wall motion and drag-reduction mechanisms. J. Fluid Mech. 507, 1–51.Google Scholar
Vaughan, N. J. & Zaki, T. A. 2011 Stability of zero-pressure-gradient boundary layer distorted by unsteady Klebanoff streaks. J. Fluid Mech. 681, 116–153.Google Scholar
Viotti, C., Quadrio, M. & Luchini, P. 2009 Streamwise oscillation of spanwise velocity at the wall of a channel for turbulent drag reduction. Phys. Fluids 21, 115109.Google Scholar
White, F. M. 2005 Viscous Fluid Flow, 3rd edn. McGraw-Hill.Google Scholar
Wygnanski, I., Sokolov, M. & Friedman, D. 1976 On a turbulent ‘spot’ in a laminar boundary layer. J. Fluid Mech. 78, 785–819.Google Scholar
Zaki, T. A. 2013 From streaks to spots and on to turbulence: exploring the dynamics of boundary layer transition. Flow Turbul. Combust. 91, 451–473.Google Scholar
Zaki, T. A. & Durbin, P. A. 2005 Mode interaction and the bypass route to transition. J. Fluid Mech. 531, 85–111.CrossRefGoogle Scholar
Zaki, T. A. & Saha, S. 2009 On shear sheltering and the structure of vortical modes in single- and two-fluid boundary layers. J. Fluid Mech. 626, 111–147.CrossRefGoogle Scholar