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

• Published in: Journal of fluid mechanics Vol. 630; pp. 5 - 41
• Main Authors: WU, XIAOHUA, MOIN, PARVIZ
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 10.07.2009
• Subjects: Boundary layers; Exact sciences and technology; Fluid dynamics; Fluid mechanics; Fundamental areas of phenomenology (including applications); Physics; Shear stress; Transition to turbulence; Turbulence simulation and modeling; Turbulent flows, convection, and heat transfer; Skin friction; Digital simulation; Modelling; Isotropic turbulence; Velocity distribution; Transition flow; Incompressible fluid; Boundary layers; Turbulence structure; Turbulent laminar transition; Pressure gradients; Flat plate
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/S0022112009006624

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.