Numerical study of Fourier-filtered rough surfaces

Abstract

Rough surfaces are common in engineering applications, where a priori estimations of drag for a given flow are needed based on knowledge of the surface topography. It is likely that length-scale information is required, in addition to standard statistical quantities such as solidity or effective slope, root-mean-square height and skewness. In this work we consider a set of rough surfaces that are derived from a physical scan of a grid-blasted rough surface. Different surfaces are generated by applying Fourier band-pass filters to the surface scan, including complementary cases, for example, where a midrange of wave numbers are included or excluded. This enables comparisons as to how the roughness spectral content affects the mean flow and turbulence properties. In total, turbulent flow over five surfaces with different wave-number spectra is investigated by direct numerical simulation, with resulting variations in the roughness function of over a factor of 3. It is found that, except for the low-pass filtered surface which has very small effective slope, the roughness function scaled by the viscous proportion of total drag remains remarkably constant, while the pressure counterpart is largest for high-pass filtered surfaces. Existing correlations for the roughness function are found, at best, to reproduce only the qualitative effects, suggesting that the correlations would benefit from introducing additional parameters to account for the wave-number spectrum of the rough surfaces. Besides the friction effect, it is also of interest to determine the extent to which the turbulence in the roughness layer is influenced by the spectral characteristics of the surface. The location of the peak streamwise velocity fluctuations moves outwards in wall units as the roughness function increases, whereas wall-normal and spanwise velocity fluctuations are found to be insensitive to the surface filtering, down to a region below the maximum roughness height. A trend towards spanwise organization of the mean flow is observed for low-pass filtered surfaces, but otherwise the effect of the roughness wave-number spectrum appears to vanish rapidly above the maximum roughness elevation. Instead, significant differences are found in the profiles of the various dispersive stresses which are highly dependent on (local) topographical features of the roughness; for some quantities differences between surfaces persist well into the log layer.

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