Effect of roughness on mean flow properties for turbulent boundary layer

Abstract

The roughness sublayer beneath a turbulent boundary layer has been investigated analytically and experimentally, and the effect has been discussed on the mean velocity profile throughout the layer. The rough surface consists of two-dimensional square roughness elements. The roughness height is proportional to streamwise distance. It is one of conditions of an equilibrium boundary layer proposed by Rotta J.C. The roughness pitch ratio is 4. The measurement within/outside the roughness sublayer was made using LDV and CTA, respectively. The Reynolds number based on the momentum thickness is 6000. The roughness Reynolds number is 149 and the roughness is in complete rough regime. The analytical solutions of streamwise mean velocity and Reynolds shear stress profiles were derived from the space averaged Reynolds equation in the cavity region between roughness elements and the mixing length model. The solutions were well consistent with the experimental results. By use of the solutions and experimental results, the center height of drag moment and the constant of the roughness function can be represented as a function of the roughness pitch ratio for the equilibrium boundary layer. Also, from the momentum integral equation, Coles's wake law, solution and experimental results, the wake parameter will be given as a function of the friction parameter and relative roughness height. Finally, the local skin friction coefficient will be formulated with a function of the roughness pitch ratio and relative roughness height.

Keywords

• boundary layer
• shear flow
• turbulent flow
• roughness sublayer
• friction law