Mean Parameters of an Incompressible Turbulent Boundary Layer on the Wind Tunnel Wall at Very High Reynolds Numbers

Abstract

The mean parameters of a two-dimensional incompressible turbulent boundary layer with zero pressure gradient were measured on the smooth wall of the TsAGI T-128 transonic wind tunnel in the range Reθ = 5.3 × 104–2.9 × 105 velocity profiles, skin friction coefficient, and shape factor. Novel data were obtained in the range Reθ ≈ 2.35 × 105–2.9 × 105. At the maximum Reynolds number, the record value of the von Karman number Reτ ∼1 × 105 was reached and the logarithmic law was maintained up to y+ ≈ 1.3 × 104. The equilibrium state of the boundary layer was estimated using Clauser’s equilibrium parameter, which was G = 6.4–6.8 for high Reynolds numbers. The results of the investigation confirm the conclusions of other studies on the universality of dimensionless velocity profile in the boundary layer outer region. The results were compared with semi-empirical dependencies, direct numerical simulation (DNS) results and the results of other studies performed both on wind tunnel walls and on a flat plate. At high Reynolds numbers the agreement between the shape factor was within ΔH = ± 0.012 (± 1%), with a skin friction coefficient—Δcf= ± 0.00006 (± 3.7%).