Direct Numerical Simulation of Fully-Rough Open-Channel Flow Over Spherical Roughness Elements
1) Markus Uhlmann, 2) Marco Mazzuoli
1) Karlsruhe Institute of Technology/KIT (Germany), 2) University of Genoa (Italy)
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Open channel flow can be considered as a convenient "laboratory" for investigating the physics of the flow in rivers. One open questions in this field is related to the influence of a rough boundary (i.e. the sediment bed) upon the hydraulic properties, which to date is still unsatisfactorily modelled by common engineering-type formulae. The present project aims to provide the basis for enhanced models by generating high-fidelity data of shallow flow over a bed roughened with spherical elements in the fully rough regime. In particular, the influence of the roughness Reynolds number and of the spatial roughness arrangement upon the turbulent channel flow structure is being studied.
In shallow rivers, the effects of gravel or rocky beds on the flow persist through the whole water depth and they affect the turbulence structure even up to the free surface. Therefore, the relative submergence of roughness elements and their geometrical features cannot be neglected in this case when parameterizing rough-wall flow. Experimental investigations of such roughness effects are often limited by the size and the accuracy of measurement probes; similarly, numerical studies are typically limited by the extraordinary computational cost of direct numerical simulations at Reynolds numbers relevant for the problem of sediment transport. Much previous work has focused on a regular arrangement of the roughness elements which is statistically convenient, but tends to oversimplify natural flow configurations.
The main goal of the present project was to extend to the fully-rough wall case the earlier results obtained by Chan-Braun et al. (2011) for open-channel flow in the transitionally-rough regime. For this purpose, a team of researchers of the Karlsruhe Institute of Technology (KIT, Germany) and the University of Genova (Italy) have performed large-scale simulations (DNS, i.e. fully resolving all turbulent flow scales) on SuperMUC. The regularity of the arrangement of roughness elements (in a square pattern) was initially maintained in a first simulation (henceforth referred to as case D120) in order to compare with Chan-Braun et al. (2011) who considered closely-packed, spherical, mono-sized particles located at the vertices of a square grid adjacent to a plane wall.
The particle Reynolds number (based upon the friction velocity and particle diameter) was approximately equal to 120, while the values of the Reynolds numbers based on the channel height and bulk or friction velocities were 6900 and 540, respectively. The interested reader can find a detailed description of the simulation D120 in Mazzuoli and Uhlmann (2017 ).
Then, before running a second simulation (herein indicated by D140R), the spheres were preliminarily released from their positions, "shaken'' and then re-crystallized, thereby the bed displaying a "random'' pattern. Since the spheres were close, they tended to pack in patches with a hexagonal arrangement and orientation of the hexagons that changed "randomly'' patch by patch. The number of roughness elements, the relative submergence, as well as the size of the domain were preserved from the simulation D120. The bulk Reynolds number was also unchanged while particle Reynolds number reached the value 140 as an effect of the sphere arrangement. The simulation time (O(100) bulk time-units) allowed for a fair convergence of time-averages and, consequently, an accurate description of turbulent fluctuations.
Turbulent vortices of size comparable with that of the spheres can be recognized in the vicinity of sphere crests in both simulations, while the pattern associated with the regularity of the sphere arrangement is destroyed in the simulation D140R (cf. figure 1). However, at larger distances from the rough wall, the spatial scales of turbulent structures are controlled by the spatial distribution of the flow-blockage produced by the spheres. In fact, the number of spheres that can be counted along a stream-wise line is not independent of the span-wise coordinate. This non-homogeneity reflects, for instance, on the spacing of low- and high-speed streaks, as can be seen in figure 2, and on the generation of localized secondary flow. The sheltering effect produced by the spheres on their neighbours by virtue of their relative position was found to be well correlated with the fluctuations of the drag force.
The findings of the present project will contribute towards the improvement of engineering-type models for turbulent shallow river flows.
The researchers' goal for the near future is to investigate the turbulence structure and the distribution of hydrodynamic forces acting on the roughness elements when the inter-particle distance is progressively increased.
 C. Chan-Braun, M. García-Villalba, and M. Uhlmann. Force and torque acting on particles in a transitionally rough open channel flow. J. Fluid Mech., 684:441–474, 2011. doi:10.1017/jfm.2011.311.
 M. Mazzuoli and M. Uhlmann. Direct numerical simulation of open-channel flow over a fully-rough wall at moderate relative submergence. J. Fluid Mech., 824:722–765, 2017. doi:10.1017/jfm.2017.371.
Prof. Dr. Markus Uhlmann
Joint Head of Institute for Hydromechanics
Head of the Computational Fluid Dynamics group
Karlsruhe Institute of Technology (KIT)
Kaiserstraße 12, D-76131 Karlsruhe (Germany)
e-mail: markus.uhlmann [@] kit.edu