Effects of Reynolds number and adverse pressure gradient on a turbulent boundary layer developing on a rough surface

Abstract

A detailed experimental study of turbulent boundary layers developing over rough surfaces subjected to both zero and adverse pressure gradients was undertaken. Two rough surfaces constituted by distributed random elements have been chosen. The experiments were conducted in the range of the Reynolds number R _θ based upon the momentum thickness varying from 2200 to 5800 and 3200 to 3800, respectively, with and without pressure gradient. The roughness Reynolds number h ⁺ characteristic of the rough surfaces grew from about 25 to 80 in both zero and adverse pressure gradient, which corresponds to Reynolds number based upon the equivalent sand grain ranging from 75 to 225. The boundary layer was probed with a single hot wire. Skin friction coefficient was obtained from the semi-logarithmic profiles of the mean velocity. The aim of this work is to assess the relevance of the “equivalent sand grain” concept, and more precisely if the equivalent sand grain height only depends upon the surface characteristics or also upon the flow regime. The present study confirms that the equivalent sand grain height is far from being constant for a given surface, although this is often assumed in computational fluid dynamics. Significant changes in the equivalent sand grain height are evidenced as well for zero pressure gradient, transitional flow as for adverse pressure gradient, fully rough flow. Therefore, the roughness topology as well as the nature of flow should be accounted for to evaluate an equivalent sand grain roughness.

Keywords:

• adverse pressure gradient
• equivalent sand grain
• rough surface
• skin friction coefficient
• logarithmic law