Aerodynamic Characterization of Irregular Undulating (Stochastic) Surface Roughness

Aerodynamic characterization of the roughness is essential to enable computation of flows over rough surfaces. Most roughness of practical interest is stochastic, that is, irregular and undulating. Examples include corrosion or deposits on turbomachinery blading or contamination on aircraft wings. This paper presents the first available method for aerodynamic characterization of stochastic surface roughness. A semi-empirical correlation approach is used. Simple physically meaningful roughness-topography characterization parameters that are suitable for both stochastic and deterministic (i.e., regular arrays of simple elements) roughness are proposed. These parameters can be evaluated from profilometer traces or laser scans of rough surfaces. Measurements of boundary-layer development along five stochastically rough surfaces are presented and are used, together with data from the literature for standard-sand roughness and deterministic roughness, to develop a unified characterization scheme that predicts the aerodynamic effects of both stochastic and deterministic roughness. The characterization scheme yields the effect of the roughness on the law-of-the-wall; this can easily be converted to an equivalent standard-sand roughness height for input to computational fluid dynamics codes.