Direkte numerische Simulation der Ausbildung von Dünen in Gewässern
Zusammenfassung der Projektergebnisse
When a macroscopically flat bed of non-cohesive sediment grains is subjected to a shear flow, patterns with significant amplitude will form under certain conditions of instability. Some previous works have linked the onset of the instability to a critical Reynolds number (apart from the basic condition of super-critical Shields number for particle motion), and the parameter space has been explored by previous laboratory experiments. However, these experiments have the drawback that a full characterization of the dynamics of the particle phase and of the fluid phase in time and space is currently not possible. Therefore, the mechanisms by which sediment patterns form and evolve in time are still largely unexplored. On the other hand, in the context of a continuum approach, linear stability analysis has been successfully performed for this type of system, albeit under some far-reaching assumptions, in particular on the particle flux expressed as a function of the bed shear stress. In the present work we have approached this problem with the aid of direct numerical simulation of the fluid flow, coupled with an immersed boundary method for the representation of fully-resolved, finite-size particles, and further coupled with a discrete element method for the treatment of solidsolid contact. This numerical representation of the sediment erosion problem is largely free of modelling assumptions, allowing us for the first time ever to perform “ab initio” computations of the pattern formation. Our simulation results in both the (laminar) small-dune regime and in the (turbulent) vortex-dune regime have confirmed the proposed pattern regime classification in terms of the Reynolds number. The observed pattern wavelengths were in line with experimental results in comparable systems. By varying the length of the computational domain we were able to determine the lower limit of unstable wavelengths, which turns out to be equal to four clear fluid heights (or equivalently 100 particle diameters). Conversely, by increasing the domain length we have found that the process of initial pattern formation is well represented if a few multiples of the minimal domain length are chosen. Our results have also revealed the details of the modification of the flow due to the sediment patterns, namely the emergence of a recirculation region (in the vortex-dune regime), and the resulting strong streamwise variability of most quantities in the near-wall region. A careful analysis of the momentum budget in a frame moving with the average dune velocity has allowed us to determine the streamwise variation of the bed shear-stress. It is found that this quantity exhibits a phase lag of approximately 15 particle diameters with respect to the pattern contour. This quantity is typically an input parameter for stability analyses; however, it is very difficult to obtain experimentally, which makes this a highly valuable result. We have further performed a decomposition of the particle forces into the contributions from hydrodynamics and from solid-solid contact, which reveals the subtle imbalance between the two that gives rise to the net force profile. This data, which is totally complementary to what can be measured in laboratory experiments, can feed into different classes of reduced-order models, such as two-fluid/rheological approaches or LES.
Projektbezogene Publikationen (Auswahl)
- Direct numerical simulation of pattern formation in subaqueous sediment. J. Fluid Mech., 750:R2, 2014
A.G. Kidanemariam and M. Uhlmann
(Siehe online unter https://doi.org/10.1017/jfm.2014.330) - Interface-resolved direct numerical simulation of the erosion of a sediment bed sheared by laminar flow. Int. J. Multiphase Flow, 67:174–188, 2014
A.G. Kidanemariam and M. Uhlmann
(Siehe online unter https://doi.org/10.1016/j.ijmultiphaseflow.2014.08.008) - The formation of patterns in subaqueous sediment. PhD Thesis, Karlsruhe Institute of Technology, 2015 [Award of the “da Vinci prize” 2015 from ERCOFTAC]
A.G. Kidanemariam
(Siehe online unter https://dx.doi.org/10.5445/IR/100005373)
