Direct numerical simulation-based characterization of pseudo-random roughness in minimal channels

Abstract

Direct numerical simulations (DNS) are used to systematically investigate the applicability of the minimal-channel approach (Chung et al., J. Fluid Mech., vol. 773, 2015, pp. 418–431) for the characterization of roughness-induced drag on irregular rough surfaces. Roughness is generated mathematically using a random algorithm, in which the power spectrum (PS) and probability density function (p.d.f.) of the surface height can be prescribed. Twelve different combinations of PS and p.d.f. are examined, and both transitionally and fully rough regimes are investigated (roughness height varies in the range $k^+ = 25$ –100). It is demonstrated that both the roughness function ( ${\rm \Delta} U^+$ ) and the zero-plane displacement can be predicted with ${\pm }5\,\%$ accuracy using DNS in properly sized minimal channels. Notably, when reducing the domain size, the predictions remain accurate as long as 90 % of the roughness height variance is retained. Additionally, examining the results obtained from different random realizations of roughness shows that a fixed combination of p.d.f. and PS leads to a nearly unique ${\rm \Delta} U^+$ for deterministically different surface topographies. In addition to the global flow properties, the distribution of time-averaged surface force exerted by the roughness onto the fluid is calculated. It is shown that patterns of surface force distribution over irregular roughness can be well captured when the sheltering effect is taken into account. This is made possible by applying the sheltering model of Yang et al. (J. Fluid Mech., vol. 789, 2016, pp. 127–165) to each specific roughness topography. Furthermore, an analysis of the coherence function between the roughness height and the surface force distributions reveals that the coherence drops at larger streamwise wavelengths, which can be an indication that very large horizontal scales contribute less to the skin-friction drag.

Permeability and Turbulence Over Perforated Plates

“…The simulations are carried out in a rectangular box of size L x × L y × L z = 3 × 3 × 1.5 , where is the channel half-width and x, y and z are the streamwise, wall-normal and spanwise directions, respectively. This box size is smaller than the one typically recommended for achieving domain independence on smooth walls (Lozano-Durán and Jiménez 2014), however, even smaller box sizes have been used successfully for studying flows over rough walls (Chung et al 2015;Mac-Donald et al 2017;Di Giorgio et al 2020;Yang et al 2022). The main idea is that when studying the flow over roughness or porous surfaces, one is interested in comparing results with a baseline smooth configuration, therefore the effect of the box size is minimized if results are compared to smooth-wall simulations with the same computational domain.…”

The Wall-Jet Region of a Turbulent Jet Impinging on Smooth and Rough Plates

“…The application of the present forcing strategy coupled with a pseudo spectral method is reported in several works (Forooghi et al 2017Vanderwel et al 2019;Yang et al 2022). We validated our implementation by comparing our results with experimental measurements for turbulent jets impinging on smooth and rough surfaces.…”

“…Convergence is reached when both surfaces are characterized by the prescribed PDF and PS (although the two will always slightly differ for surfaces of finite size). In the context of turbulent flow research, the same approach for generating random rough surfaces is also used, for instance, in the work of Yang et al (2022). Further scaling of the wall height distribution designed with the method described above allows the characterization of various rough surfaces.…”

Turbulence and added drag over acoustic liners

“…2020; Yang et al. 2022) through comparison with smooth-wall simulations with the same box size. We use uniform mesh spacing in the streamwise and spanwise directions.…”

“…This box size is smaller than is usually recommended for DNS (Lozano-Durán & Jiménez 2014). However, similar and even smaller box sizes have been used previously to aid parametric analysis of rough-wall turbulent flows (Chung et al 2015;MacDonald et al 2017;Di Giorgio et al 2020;Yang et al 2022) through comparison with smooth-wall simulations with the same box size. We use uniform mesh spacing in the streamwise and spanwise directions.…”