Rough-wall turbulence in minimal flow units with rod-roughened walls

Abstract

Numerical simulation of minimal flow units (MFUs) can obtain “healthy turbulence” below a certain wall-normal height by limiting the effects of large-scale motions in the outer region. By “health,” it is meant that the mean velocity profile is consistent with the full-sized flow. In the present study, MFUs with rod-roughened walls at friction Reynolds numbers of 1000, 2000, and 4000 are studied by direct numerical simulation. For all the minimal channels, the domain size in streamwise and spanwise directions and the geometric parameters of roughness elements remain unchanged under the normalization of viscous units. The spurious spanwise uniform motions (SUM), induced by the narrow width of MFU, have significant contribution to turbulent fluctuations, especially to pressure. The spurious SUM are proved to be structures traveling downstream, holding strong relationship with the domain width. A new decomposition method is proposed to eliminate the spurious SUM. The results of MFU show that the roughness functions at different Reynolds numbers agree well with each other, implying that the effect of roughness on the main flow is independent of Reynolds numbers. In the context of the same wall roughness, the turbulent fluctuations and the roughness-induced fluctuations exhibit good Reynolds number independence. Additionally, the results of premultiplied spectra of the three velocity components suggest that the MFU could represent the near-wall small-scale motions within the full-sized domain. The universal signals extracted from the full-sized channel agree well with the near-wall velocity fluctuations in the MFU for all three velocity components.