Estimating Turbulent Wall Shear and Boundary Layer Thickness for Hydro-dynamically Rough Surfaces by Perturbing Known Smooth Results

Abstract

[Abstract] It is not uncommon when utilizing hydrodynamically smooth experimental or computational results that one would like to estimate the additional effect of wall roughness without performing either new experiments or computations. Here we consider a simple analytical model based on inner law methods which extends smooth wall skin friction and boundary layer thickness to be valid for rough wall flows. The approach described here uses a formal perturbation model of the compressible (adiabatic) skin friction, the rough wall equivalent (Van-Driest) log-law boundary layer thickness. Though perturbation-based approaches provide a correction expression, they are not valid for many physically interesting problems where the roughness is more significant. For these flows we solve the appropriate roughness expressions using an approximate procedure that is valid for a wider range of roughness. Though useful to demonstrate behaviors associated with roughness and providing a connection to smooth expressions, this approximate method is of less value when one requires compressibility corrections, whereby it is perhaps more appropriate to dispense with approximation and simplly solve the full expression numerically. We also note that the empirically based expression described by Fang et. al. (2003) 1 is in excellent agreement with the inner law based model described here.