Direct numerical simulation of turbulent channel flow over a surrogate for Nikuradse-type roughness

Abstract

A tiled approach to rough surface simulation is used to explore the full range of roughness Reynolds numbers, from the limiting case of hydrodynamic smoothness up to fully rough conditions. The surface is based on a scan of a standard grit-blasted comparator, subsequently low-pass filtered and made spatially periodic. High roughness Reynolds numbers are obtained by increasing the friction Reynolds number of the direct numerical simulations, whereas low roughness Reynolds numbers are obtained by scaling the surface down and tiling to maintain a constant domain size. In both cases, computational requirements on box size, resolution in wall units and resolution per minimum wavelength of the rough surface are maintained. The resulting roughness function behaviour replicates to good accuracy the experiments of Nikuradse (1933 VDI-Forschungsheft, vol. 361), suggesting that the processed grit-blasted surface can serve as a surrogate for his sand-grain roughness, the precise structure of which is undocumented. The present simulations also document a monotonic departure from hydrodynamic smooth-wall results, which is fitted with a geometric relation, the exponent of which is found to be inconsistent with both the Colebrook formula and an earlier theoretical argument based on low-Reynolds-number drag relations.

Modulation of near-wall turbulence in the transitionally rough regime

“…However, Bradshaw (2000) proposes a gradual transition between these regimes, without a defined, hard boundary. A recent work by Thakkar et al (2018) also seems to point in this direction. The interest in transitional roughness resides in understanding the effects that small surface texture starts having on the flow; effects that, as size increases, will lead to the departure from its smooth-wall behaviour and eventually to the fully rough regime.…”

Direct numerical simulations of Taylor–Couette turbulence: the effects of sand grain roughness

“…An intriguing feature of the data from Nikuradse (1933) is at k + s ≈ 5, where roughness effects suddenly result in an inflectional increase of ∆u + , as compared to the gradual increase of the roughness function found by Colebrook (1939) who extracted an empirical relationship from many industrial surfaces (Shockling et al 2006). Later, this inflectional behavior was also observed for tightly packed spheres (Ligrani & Moffat 1986), honed surfaces (Shockling et al 2006), and grit-blasted surfaces (Thakkar et al 2018). Chan-Braun et al (2011) had too few points to find the inflectional behavior; however, their two simulations of monodisperse spheres in regular arrangement collapsed on the Nikuradse curve.…”

Moving beyond Moody

“…Correlations are presented considering roughness heights, slopes, density and moments of the surface elevation p.d.f. Thakkar et al (2018) are the first to use DNS to study a realistic irregular roughness, similar to the sand grain roughness of Nikuradse (1933), for the entire range of roughness Reynolds numbers from hydraulically smooth to fully rough. This is an extension of their previous work (Thakkar, Busse & Sandham 2017) where they presented roughness results in the upper part of the transitionally rough regime and the fully rough regime for grit blasted and graphite surfaces.…”

“…This filter should also be based on a roughness scale. There are a number of issues that need to be addressed before developing a robust engineering correlation, hence the reason that the contributions by Thakkar, Busse & Sandham (2018) (for example, dispersive sheer stress as shown in the figure by the title) and other recent simulations of rough wall flows are so important. Realistic rough surfaces at relevant Reynolds numbers are being computed and there is hope in making headway towards identifying roughness scales to inform engineering predictions of surface drag.…”