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Turbulence in intermittent transitional boundary layers and in turbulence spots

Published online by Cambridge University Press:  05 December 2018

Olaf Marxen  and
Tamer A. Zaki Open the ORCID record for Tamer A. Zaki [Opens in a new window]
Olaf Marxen
Affiliation:
Department of Mechanical Engineering Sciences, University of Surrey, GuildfordGU2 7XH, UK
Tamer A. Zaki*
Affiliation:
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
*
†Email address for correspondence: [email protected]
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Abstract

Direct numerical simulation data of bypass transition in flat-plate boundary layers are analysed to examine the characteristics of turbulence in the transitional regime. When intermittency is 50 % or less, the flow features a juxtaposition of turbulence spots surrounded by streaky laminar regions. Conditionally averaged turbulence statistics are evaluated within the spots, and are compared to standard time averaging in both the transition region and in fully turbulent boundary layers. The turbulent-conditioned root-mean-square levels of the streamwise velocity perturbations are notably elevated in the early transitional boundary layer, while the wall-normal and spanwise components are closer to the levels typical for fully turbulent flow. The analysis is also extended to include ensemble averaging of the spots. When the patches of turbulence are sufficiently large, they develop a core region with similar statistics to fully turbulent boundary layers. Within the tip and the wings of the spots, however, the Reynolds stresses and terms in the turbulence kinetic energy budget are elevated. The enhanced turbulence production in the transition zone, which exceeds the levels from fully turbulent boundary layers, contributes to the higher skin-friction coefficient in that region. Qualitatively, the same observations hold for different spot sizes and levels of free-stream turbulence, except for young spots which do not yet have a core region of developed turbulence.

JFM classification

Boundary Layers: Boundary Layers Turbulent Flows: Intermittency Instability: Transition to turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 860 , 10 February 2019 , pp. 350 - 383
Copyright
© 2018 Cambridge University Press 

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References

Andersson, P., Brandt, L., Bottaro, L. & Henningson, D. S. 2001 On the breakdown of boundary layer streaks. J. Fluid Mech. 428, 29–60.Google Scholar
Anthony, R. J., Jones, T. V. & LaGraff, J. E. 2005 High frequency surface heat flux imaging of bypass transition. J. Turbomach. 127, 241–250.Google Scholar
Borrell, G. & Jimenez, J. 2016 Properties of the turbulent/non-turbulent interface in boundary layers. J. Fluid Mech. 801, 554–596.Google Scholar
Brandt, L. 2014 The lift-up effect: the linear mechanism behind transition and turbulence in shear flows. Eur. J. Mech. (B/Fluids) 47, 80–96.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.Google Scholar
Cantwell, B., Coles, D. & Dimotakis, P. 1978 Structure and entrainment in the plane of symmetry of a turbulent spot. J. Fluid Mech. 87 (04), 641–672.Google Scholar
Dhawan, S. & Narasimha, R. 1958 Some properties of boundary layer flow during the transition from laminar to turbulent motion. J. Fluid Mech. 3 (04), 418–436.Google Scholar
Durbin, P. & Wu, X. 2007 Transition beneath vortical disturbances. Annu. Rev. Fluid Mech. 39 (1), 107–128.Google Scholar
Ge, X., Arolla, S. & Durbin, P. A. 2014 A bypass transition model based on the intermittency function. Flow Turbul. Combust. 93 (1), 37–61.Google Scholar
Hack, M. J. P. & Zaki, T. A. 2014 The influence of harmonic wall motion on transitional boundary layers. J. Fluid Mech. 760, 63–94.Google Scholar
Hack, M. J. P. & Zaki, T. A. 2016 Data-enabled prediction of streak breakdown in pressure-gradient boundary layers. J. Fluid Mech. 801, 43–64.Google Scholar
Herbert, T. 1988 Secondary instability of boundary layers. Annu. Rev. Fluid Mech. 20, 487–526.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
Itsweire, E. C. & Atta, C. W. V. 1984 An experimental investigation of coherent substructures associated with turbulent spots in a laminar boundary layer. J. Fluid Mech. 148, 319–348.Google Scholar
Jacobs, R. G. & Durbin, P. A. 2001 Simulations of bypass transition. J. Fluid Mech. 428, 185–212.Google Scholar
Kachanov, Y. S. 1994 Physical mechanisms of laminar-boundary-layer transition. Annu. Rev. Fluid Mech. 26 (1), 411–482.Google Scholar
Kendall, J. 1991 Studies on laminar boundary layer receptivity to free stream turbulence near a leading edge. In Boundary Layer Stability and Transition to Turbulence (ed. Reda, X.), vol. 114, pp. 23–30. ASME-FED.Google Scholar
Klebanoff, P. S. 1971 Effect of freestream turbulence on the laminar boundary layer. Bull. Am. Phys. Soc. 16, 1323.Google Scholar
Landahl, M. T. 1980 A note on an algebraic instability of inviscid parallel shear flows. J. Fluid Mech. 98, 243–251.Google Scholar
Lee, J., Sung, H. J. & Zaki, T. A. 2017 Signature of large-scale motions on turbulent/non-turbulent interface in boundary layers. J. Fluid Mech. 819, 165–187.Google Scholar
Lee, S. J. & Zaki, T. A. 2017 Simulations of natural transition in viscoelastic channel flow. J. Fluid Mech. 820, 232–262.Google Scholar
Liu, Y., Zaki, T. A. & Durbin, P. A. 2008 Boundary-layer transition by interaction of discrete and continuous modes. J. Fluid Mech. 604, 199–233.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
Narasimha, R. 1957 On the distribution of intermittency in the transition region of a boundary layer. J. Aerosp. Sci. 24, 711–712.Google Scholar
Narasimha, R. 1985 The laminar-turbulent transition zone in the boundary layer. Prog. Aerosp. Sci. 22 (1), 29–80.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
Otsu, N. 1979 A threshold selection method from grey-level histograms. IEEE Trans. Syst. Man Cybern. 9 (1), 62–66.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.Google Scholar
Park, G. I., Wallace, J. M., Wu, X. & Moin, P. 2012 Boundary layer turbulence in transitional and developed states. Phys. Fluids 24 (3), 035105.Google Scholar
Perry, A. E., Lim, T. T. & Teh, E. W. 1981 A visual study of turbulent spots. J. Fluid Mech. 104, 387–405.Google Scholar
Phillips, O. M. 1969 Shear-flow turbulence. Annu. Rev. Fluid Mech. 1, 245–264.Google Scholar
Renard, N. & Deck, S. 2016 A theoretical decomposition of mean skin friction generation into physical phenomena across the boundary layer. J. Fluid Mech. 790, 339–367.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 (1), 102–137.Google Scholar
Sandham, N. D. & Kleiser, L. 2006 The late stages of transition to turbulence in channel flow. J. Fluid Mech. 245, 319.Google Scholar
Sayadi, T. & Moin, P. 2012 Large eddy simulation of controlled transition to turbulence. Phys. Fluids 24, 114103.Google Scholar
Schmid, P. J. & Henningson, D. S. 2000 Stability and Transition in Shear Flows. Springer.Google Scholar
Simon, F. & Ashpis, D.1996 Progress in modeling of laminar to turbulent transition on turbine vanes and blades. Tech. Rep. NASA-TM-107180.Google Scholar
Spalart, P. R. 1988 Direct simulation of a turbulent boundary layer up to R 𝜃 = 1410. J. Fluid Mech. 187, 61–98.Google Scholar
Steelant, J. & Dick, E. 2001 Modeling of laminar-turbulent transition for high freestream turbulence. J. Fluids Engng 123 (1), 22.Google Scholar
Trefethen, L. N., Trefethen, A. E., Reddy, S. C. & Driscoll, T. A. 1993 Hydrodynamic stability without eigenvalues. Science 261, 578–584.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
Wu, X. & Moin, P. 2009 Direct numerical simulation of turbulence in a nominally zero-pressure-gradient flat-plate boundary layer. J. Fluid Mech. 630, 5–41.Google Scholar
Wu, X., Moin, P., Wallace, J. M., Skarda, J., Lozano-Durán, A. & Hickey, J.-P. 2017 Transitional–turbulent spots and turbulent–turbulent spots in boundary layers. Proc. Natl Acad. Sci. USA 114 (27), E5292–E5299.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.Google Scholar
Zaki, T. A. & Durbin, P. A. 2006 Continuous mode transition and the effects of pressure gradients. J. Fluid Mech. 563, 357–358.Google 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.Google Scholar
Zaki, T. A., Wissink, J. G., Rodi, W. & Durbin, P. A. 2010 Direct numerical simulations of transition in a compressor cascade: the influence of free-stream turbulence. J. Fluid Mech. 665, 57–98.Google Scholar