Turbulent drag induced by low surface roughness at transonic speeds: Experimental/numerical comparisons

Abstract

This paper gives the main results of an experimental test campaign aimed at quantifying the effects of very low roughness levels on the flat plate turbulent drag in transonic conditions. This work, in a field not completely understood yet, the one of the transitionally rough regime, has revealed its importance by showing that some surfaces considered as hydrodynamically smooth in past studies might not have been. This issue can be strongly critical in the delicate exercise of experimental/numerical comparisons, and more specifically, when it comes to absolute drag predictions, if the fluid dynamics computations use only, as they almost always do, infinitely smooth surfaces. The experiments on the S8Ch wind tunnel have involved high-level measurement techniques, such as micro-drag evaluation with a three-component balance and near-wall laser Doppler velocimetry, for Mach numbers from 0.55 to 0.8 and maximum Reynolds numbers based on the sample length and the boundary layer thickness of about 2.6 × 106 and 0.13 × 106, respectively, the highest friction Reynolds number being close to 5000. A dozen surface samples were tested, with average roughness values from less than 0.25 μm (mirror-polished aluminum) to more than 10 μm (commercial sandpapers), and in between standard-machined or painted samples (including pressure sensitive paintings). A pragmatic computational fluid dynamics study reproducing this test campaign was completed. It is based on the well-known equivalent sand grain roughness height approach and also on the Musker correlation, which was adapted. The results and validity of such Reynolds-averaged Navier–Stokes simulations in that particular regime are discussed. Anyway, both experimental and numerical outcomes of this work are in agreement to indicate that drag can be significantly impacted even for roughness Reynolds numbers potentially below the usual threshold values often considered in the engineering world (i.e., about 3.5–5). And the cross-analysis of surface drag production and roughness characteristics has allowed the decisive role played by the rms (or average) roughness height, the skewness and kurtosis coefficients, and especially the slope parameter to be confirmed.