Highly-resolved Numerical Simulations of Bed Load Transport in a Turbulent Open Channel Flow
Prediction of turbulence-induced erosion and near-bed transport of sediment particles in turbulent flow is important for many processes in environmental engineering. Beyond its relation to sediment transport, the results of the present study are relevant as well for numerous industrial applications, particularly in the field of process technology, where solid particles are conveyed by a carrier flow. Traditional methods for the prediction of sediment transport are empirical and based on averaged bulk quantities. The predictive power of these formulae is low, because homogeneity of the sediment is postulated. A detailed understanding of sediment stability and the physical mechanisms involved in sediment transport is still missing due to the lack of highly-resolved data under controlled flow conditions.
The presented study employs Direct Numerical Simulations (DNS) of a turbulent flow laden with a large number of particles with parameters of the disperse phase chosen similar to laboratory experiments. A systematic study with different runs was carried out on the supercomputer JUQUEEN at the Jülich Supercomputing Centre (JSC) using up to 16,384 processors. The runs comprise a variation of the number of mobile particles and the particle density to investigate the impact of these two key parameters on sediment transport and to cover a wide range of patterns reflecting the state of equilibrium between forces of the fluid and the particles. The highly-resolved simulations provide detailed and physically reliable instantaneous information on bed-load transport at medium Reynolds number, covering parameter ranges so far not reached. The reference run contains one full layer of mobile particles with a specific density slightly above the threshold of incipient motion. This simulation produced dune-like structures with a typical streamwise distance of 12 H, where H is the water depth (Fig. 1). Reducing the mass loading results in streamwise oriented ridges with a typical distance of 2 H (Fig. 2). Increasing the number of mobile particles yields two distinct dunes with unstable clusters in between (Fig. 3). Increasing the specific density, a more or less closed plane bed is observed with only a few particles eroded individually from this inactive layer (Fig. 4). Reducing the particle density, the particles form a bed-load layer with large clusters that have a finite life time (Fig. 5). Note that in the simulations described the background grid is made of 1.4 109 regular cubical cells which are so small that each of the particles is resolved by 22 cells per diameter.
The findings of this study provide benchmark data and will help to improve the understanding of particle-fluid interaction and the related patterns. This knowledge can in the long run help to improve existing simulations of particle-laden flows and in particular to improve engineering models for the prediction of erosion.
Fig. 1: Snapshot of a flow laden with 13500 particles with a mobility slightly above the mobilisation threshold. Iso-surfaces of fluid fluctuations blue: u’ /Ub = −0.3, particles in yellow: fixed, white: |up | < 1.5 uτ , black: |up | ≥ 1.5 uτ
Fig. 2: Same as Fig. 1, but with 6750 particles.
Fig. 3: Same as Fig. 1, but with 27000 particles.
Fig. 4: Same as Fig. 1, but with heavy particles.
Fig. 5: Same as Fig. 1, but with light particles.
Dipl.-Hydrol. Bernhard Vowinckel, Dr.-Ing. Tobias Kempe, Prof. Dr.-Ing. habil. Jochen Fröhlich
Institut für Strömungsmechanik, TU Dresden