## Abstract

The present paper reports a numerical study of fully developed turbulent flow over a flat plate with a step change from a smooth to a rough surface. The Reynolds number based on momentum thickness for the smooth flow was $Reθ=5950$. The focus of the study was to investigate the capability of the Reynolds-averaged Navier–Stokes (RANS) equations to predict the internal boundary layer (IBL) created by the flow configuration. The numerical solution used a two-layer $k−ε$ model to implement the effects of surface roughness on the turbulence and mean flow fields via the use of a hydrodynamic roughness length $y0$. The prediction for the mean velocity field revealed a development zone immediately downstream of the step in which the mean velocity profile included a lower region affected by the surface roughness below and an upper region with the characteristics of the smooth-wall boundary layer above. In this zone, both the turbulence kinetic energy and Reynolds shear stress profiles were characterized by a significant reduction in magnitude in the outer region of the flow that is unaffected by the rough surface. The turbulence kinetic energy profile was used to estimate the thickness of the IBL, and the resulting growth rate closely matched the experimental results. As such, the IBL is a promising test case for assessing the ability of RANS models to predict the discrete roughness configurations often encountered in industrial and environmental applications.

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