| In this investigation, the incompressible zero-pressure-gradient turbulent boundary layers are investigated in light of the effect of the Reynolds number, the upstream conditions, and roughness. The experiments at very high Reynolds number were performed using cross hot-wire technique at the University of Western Ontario (UWO) on both a smooth surface and a rough surface. The range of the Reynolds number based on the momentum thickness was achieved from 30,000 up to 120,000. Wind tunnel speeds of 10 m/s and 20 m/s were set up in order to investigate the effect of the upstream conditions, the local Reynolds number effect and roughness effect on the downstream flow. Also, the experimental data from various researchers was collected and analyzed in order to study the effect of the Reynolds number, the upstream conditions, and the roughness in outer flow and inner flow.; Here, the scalings of George and Castillo (1997) for the mean velocity profiles and the Reynolds stress are used for analysis and compared with the results of the classical scalings determined by the log-law. It is shown that the mean deficit profiles in outer scaling are affected by the upstream conditions and they collapse in one curve for a given set of the upstream conditions even at very high Reynolds number. This result is contrary to the common belief about the true asymptotic state. Furthermore, the shape of the curve depends on the upstream conditions. On the other hand, it is shown that there is no apparent upstream condition effect in inner flow. Moreover, the true asymptotic profile (self-preserving) solution for the outer flow is found when the profiles are normalized by the Zagarola/Smits (1998) scaling, U ∞δ*/δ. This scaling successfully remove all the effects of the Reynolds number, the upstream conditions, and the roughness.; The Reynolds stress profiles are investigated in order to search the effect of the Reynolds number and the upstream conditions and it is found that the cross wise component of normal stress, < υ2 > /U∞, in the outer variables is affected mostly by the upstream conditions among other Reynolds stress components. For fixed upstream conditions the cross wise component of the Reynolds stress tend to collapse in one curve. However, the Reynolds stresses profiles in the inner variables are shown to be dependent on the Reynolds number not the upstream conditions.; More importantly, the analytical form of the skin-friction law for rough surface turbulent boundary layer, which is also applicable for smooth surface, is found as a function of the local Reynolds number, δ+, and the roughness parameter, κ+. Furthermore, the boundary layer parameters and the growth rate of the boundary layer can be represented in analytical form as functions of δ+ and κ +. This results were induced using the composite velocity profiles for rough surface and Near-Asmyptotics method of George and Castillo (1997). The predictability of the skin-friction and the boundary layer parameters will provide great tools for the practical engineering design and turbulence modeling. |
