Large Eddy Simulation of Sediment Deformation in a Turbulent Flow by Means of Level-Set Method Susanne Kraft 1 ; Yongqi Wang 2 ; and Martin Oberlack 3 Abstract: Sediment transport in a turbulent channel flow over the sediment bed with a ripple structure is numerically simulated by means of a large eddy simulation. The filtered Navier-Stokes equations for the channel flow and the filtered advection-diffusion equation with a settling term for the suspended sediment are numerically solved, in which the unresolved subgrid-scale processes are modeled by the dynamic subgrid-scale model of Germano et al. The migration and deformation of the interface between the sediment bed and the fluid flow is captured by the level-set method. The sediment erosion is approached by means of three different pickup relations postulated by van Rijn, Einstein, and Yalin, respectively, partly modified by the authors. Generally, the sediment is entrained into the flow from locations where the shear stress exceeds a critical value—on the upstream slopes of ripple crests—and is advected downstream in suspension by the flow, until it settles again when the local flow condition cannot further transport it, e.g., on the lee sides of ripples. A global effect of these local processes is the migration of ripples. The numerical results on the fluid flow field and the sediment concentration distribution are discussed. The computed migration speed of the ripples, which is only a fraction of the free stream velocity, is compared with known experimental data and a good agreement is demonstrated. DOI: 10.1061/(ASCE)HY.1943-7900.0000439. © 2011 American Society of Civil Engineers. CE Database subject headings: Channel flow; Velocity; Simulation; Eddies; Sediment. Author keywords: Ripple; Channel flow; Migration velocity; Large eddy simulation; Level-set method. Introduction The bed of a flowing water body is usually composed of fine co- hesionless loose sediments and thus its form is not stable. When the bed cannot resist the wall shear stress caused by the fluid flow, sediment is entrained and transported downstream (erosion). On the contrary, in weaker flow areas in which the force of gravity of the particles prevails, the suspended sediment settles at the bed surface (sedimentation). The erosion and sedimentation deform the river bed, which affects the fluid flow and the associated sediment trans- port in a strongly coupled manner. Under certain flow conditions, e.g., when a wave passes over sand or silt in shallow water, or an initial nonsmooth geometry structure of the sediment bed exists, ripple structures may be developed (Zanke 1999). Rows of ripples form perpendicular to the flow direction of the water. Ripple struc- tures have a dynamic state of equilibrium, i.e., they keep the shape but are not spatially fixed. They move downstream by erosion of sediment from the upstream side of the ripple, and deposition on the lee side. For given flow conditions, the ripples move with a certain migration velocity, which is small compared with the mean fluid velocity (Kühlborn 1993). Ripple formation occurs ubiquitously as natural processes both in interior and in marine flows. There exists a large scientific and economic interest to model this phe- nomenon exactly, hence to predict the effect of anthropogenic interferences in water bodies. The fundamental understanding of sedimentation and erosion as well as the metastable equilibrium of these processes are not only of theoretical interest, but also particularly of special importance for the description of large-scale sedimentation. Small-scale local sed- imentation and erosion are responsible for global spacious changes both in inland water bodies and in coastal regions. In many fields, erosion and sedimentation lead to problems. Erosion of coastal regions and also the sedimentation of river and channel beds are examples. The phenomenon of the ripple emergence and migration has been experimentally analyzed in many works (e.g., Fürböter 1983; Kühlborn 1993). In recent years the numerical investigation has also gained significance because of the increase of computer achievement. Most of the works focus mainly on the sediment transport rather than on the ripple movement. Chang and Scotti (2003) examined the influence of coherent structures on particle transport in suspension over a fixed wavelike surface with the help of the large eddy simulation (LES). They used a Lagrangian ansatz for the modeling of the particle movement and computed the movement of each individual particle. In a further work, Chang and Scotti 2004 compared numerical results of the LES with those of the Reynolds-averaged Navier-Stokes (RANS) modeling, for which the k  ω closure model was employed. It was demonstrated that the RANS modeling could not reproduce the most important coherent structures near the flow bed and the transport in suspension correctly. Similarly, Zedler and Street (2001) examined the influence of ripples on the sediment transport by means of the LES. They also used a sinusoidal wave as the 1 Chair of Fluid Dynamics, Dept. of Mechanical Engineering, Technische Universität at Darmstadt, Petersenstrasse 30, 64287 Darmstadt, Germany. 2 Chair of Fluid Dynamics, Dept. of Mechanical Engineering, Technische Universität at Darmstadt, Petersenstrasse 30, 64287 Darmstadt, Germany. (corresponding author). E-mail: wang@fdy.tu-darmstadt.de 3 Chair of Fluid Dynamics, Dept. of Mechanical Engineering, Technische Universität at Darmstadt, Petersenstrasse 30, 64287 Darmstadt, Germany.; Center of Smart Interfaces, Technische Universität at Darmstadt, Petersenstrasse 32, 64287 Darmstadt, Germany; Graduate School of Com- putational Engineering, Technische Universität at Darmstadt, Dolivostrasse 15, 64293 Darmstadt, Germany. Note. This manuscript was submitted on September 14, 2010; approved on April 11, 2011; published online on April 13, 2011. Discussion period open until April 1, 2012; separate discussions must be submitted for indi- vidual papers. This paper is part of the Journal of Hydraulic Engineering, Vol. 137, No. 11, November 1, 2011. ©ASCE, ISSN 0733-9429/2011/11- 1394–1405/$25.00. 1394 / JOURNAL OF HYDRAULIC ENGINEERING © ASCE / NOVEMBER 2011 Downloaded 26 Jan 2012 to 130.83.248.188. Redistribution subject to ASCE license or copyright. Visit http://www.ascelibrary.org