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.

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Recent developments in neural networks have shown the potential of estimating drag on irregular rough surfaces. Nevertheless, the difficulty of obtaining a large high-fidelity dataset to train neural networks is deterring their use in practical applications. In this study, we propose a transfer learning framework to model the drag on irregular rough surfaces even with a limited amount of direct numerical simulations. We show that transfer learning of empirical correlations, reported in the literature, can significantly improve the performance of neural networks for drag prediction. This is because empirical correlations include ‘approximate knowledge’ of the drag dependency in high-fidelity physics. The ‘approximate knowledge’ allows neural networks to learn the surface statistics known to affect drag more efficiently. The developed framework can be applied to applications where acquiring a large dataset is difficult but empirical correlations have been reported.

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In the present study we investigate an incompressible turbulent channel flow with heat transfer at Re τ = 180 with a deterministic surface topography consisting of truncated cones. Two solvers for each of the two boundary handling strategies are considered. With Nek5000 and OpenFOAM the influence of the roughness elements is directly accounted for by an unstructured body fitted mesh, whereas Xcompact3d and SIMSON utilize the immersed boundary method (IBM) to deal with the 3D geometry. The main focus of this work is on an evaluation of the usability of the IBM and a comparison of the parallel performance of the different solvers. Since usability is an ambiguous definition, various quantities are compared: global statistics like Nusselt number and friction coefficient, one-dimensional wall-normal profiles for first and second order statistics, as well as three-dimensional averages over roughness sections. In addition, the computational effort for each method is documented.