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Direct numerical simulation of turbulence in a nominally zero-pressure-gradient flat-plate boundary layer

Published online by Cambridge University Press:  10 July 2009

XIAOHUA WU  and
PARVIZ MOIN
XIAOHUA WU
Affiliation:
Department of Mechanical Engineering, Royal Military College of Canada, Kingston, Ontario, Canada, K7K 7B4
PARVIZ MOIN*
Affiliation:
Centre for Turbulence Research, Stanford University, Stanford, CA 94305-3035, USA
*
†Email address for correspondence: [email protected]
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Abstract

A nominally-zero-pressure-gradient incompressible boundary layer over a smooth flat plate was simulated for a continuous momentum thickness Reynolds number range of 80 ≤ Reθ ≤ 940. Transition which is completed at approximately Reθ = 750 was triggered by intermittent localized disturbances arising from patches of isotropic turbulence introduced periodically from the free stream at Reθ = 80. Streamwise pressure gradient is quantified with several measures and is demonstrated to be weak. Blasius boundary layer is maintained in the early transitional region of 80 < Reθ < 180 within which the maximum deviation of skin friction from the theoretical solution is less than 1%. Mean and second-order turbulence statistics are compared with classic experimental data, and they constitute a rare DNS dataset for the spatially developing zero-pressure-gradient turbulent flat-plate boundary layer. Our calculations indicate that in the present spatially developing low-Reynolds-number turbulent flat-plate boundary layer, total shear stress mildly overshoots the wall shear stress in the near-wall region of 2–20 wall units with vanishing normal gradient at the wall. Overshoots as high as 10% across a wider percentage of the boundary layer thickness exist in the late transitional region. The former is a residual effect of the latter. The instantaneous flow fields are vividly populated by hairpin vortices. This is the first time that direct evidence (in the form of a solution of the Navier–Stokes equations, obeying the statistical measurements, as opposed to synthetic superposition of the structures) shows such dominance of these structures. Hairpin packets arising from upstream fragmented Λ structures are found to be instrumental in the breakdown of the present boundary layer bypass transition.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 630 , 10 July 2009 , pp. 5 - 41
Copyright
Copyright © Cambridge University Press 2009

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