Direct numerical simulation (DNSs) are used to systematically investigate applicability of minimal channel approach for characterization of roughness-induced drag in irregular rough surfaces. Roughness is generated mathematically using a random algorithm, in which the power spectrum (PS) and probability density function (PDF) of surface height function can be prescribed. 12 different combinations of PS and PDF are examined and both transitionally and fully rough regimes are investigated (roughness heights varies in the range $k^+$ = 25 -- 100). It is demonstrated that both roughness function ($\Delta U^+$) and zero-plane displacement can be predicted within $\pm5\%$ accuracy using DNS in properly sized minimal channels. Notably, the predictions do not deteriorate when a limited range of large horizontal roughness scales are filtered out due to the small channel size (here up to 10\% of original roughness height spectral energy based on 2D PS). Additionally, examining the results obtained from different random realizations of roughness shows that a certain combination of PDF and PS leads to a nearly unique $\Delta U^+$ 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 and compared for different cases. It is shown that patterns of surface force distribution over irregular rough surfaces can be well captured when the sheltering effect is taken into account. This is made possible applying the sheltering model proposed by Yang et al. to each specific roughness topography. Furthermore, an analysis of the coherence function between roughness height and surface force distributions reveals that the coherence drops at larger streamwise wavelengths, which can be an indication that very large horizontal scales are less dominant in contributing to the skin friction drag. Finally, some existing roughness correlations are assessed using the present roughness dataset, and it is shown that the correlation predictions for the values of equivalent sand-grain roughness mainly lie within $\pm30\%$ error in comparison to the DNS results.

These files contain the data used in the publication:

“DNS-based characterization of pseudo-random roughness in minimal channels” J. Yang, A. Stroh, D. Chung and P. Forooghi published in Journal of Fluid Mechanics doi:10.1017/jfm.2022.331

Numerical Details:

The carried out DNS is based on a pseudo-spectral solver for incompressible boundary layer flows developed at KTH/Stockholm. The Navier-Stokes equations are numerically integrated using the velocity-vorticity formulation by a spectral method with Fourier decomposition in the horizontal directions and Chebyshev discretization in the wall-normal direction. For temporal advancement, the convection and viscous terms are discretized using the 3rd order Runge-Kutta and Crank-Nicolson methods, respectively. The simulation domain represents an turbulent channel flow with periodic boundary conditions applied in streamwise and spanwise directions, while the wall-normal extension of the domain is bounded by no-slip boundary conditions at the upper and lower domain wall. The flow is driven by a prescribed constant pressure gradient (CPG). The friction Reynolds number for the present case is fixed to Re_τ = 500. The structured surface is introduced through an immersed boundary method (IBM) based on the method proposed by Goldstein et al. (1993) and is essentially a proportional controller which imposes zero velocity in the solid region of the numerical domain.

Data Files:

The data files are saved and labeled in *.mat files. Each file contains MATLAB data consisting of the roughness height distribution and corresponding coordinates. The roughness structures are non-dimensionalized with the channel half height δ.

Reference:

Please provide a reference to the article above when using this data. Please direct questions regarding numerical setup/data to Jiasheng Yang (jiasheng.yang@kit.edu)