Thermal and hydrodynamic characteristics of boundary layers developing over uniform spheres roughness with momentum thicknesses as large as 1.43 cm are presented. To obtain thick hydrodynamic boundary layers, an artificial thickening device is employed. The normalized velocity and turbulence profiles produced using this device are two-dimensional and self-preserving. The turbulent transport and structural characteristics are representative of normal behavior to the level of spectra of the longitudinal velocity fluctuations. In the artificially thickened layers, the effect of the unheated starting length (ξ > 0, Δ < δ) on thermal boundary layer properties is present. Turbulent Prandtl number profiles are generally unaffected by the magnitude of the unheated starting length, whereas measured Stanton numbers, show different behavior as the unheated starting length varies. In thermal boundary layers which would have the same thickness as the augmented hydrodynamic layers (Δ ≃ δ), Stanton numbers are shown to be the same as skin friction coefficients, and are then provided for boundary layers much thicker than those previously studied. As fully rough boundary layers develop downstream and δ/ks increases, Cf/2 is proportional to δ2−b where b = 0.175. In order for such U∞ = constant, thick, rough wall layers to develop far enough downstream to reach smooth behavior where b = 0.250, ks Uτ/ν must become small, and b must increase from 0.175 to become greater than 0.250 in the transitionally rough regime.
A robust post-processing method to determine skin friction in turbulent boundary layers from the velocity profile
