Three-dimensional unsteady modeling of clear-water scour in the vicinity of hydraulic structures: Lagrangian and Eulerian perspectives

Abstract

The complex interaction between turbulence and sediment dynamics in aquatic environments is the most important mechanism of sediment transport and bed erosion in multiple geophysical, environmental, and engineering flows. Scour around hydraulic structures is an example in which this relation acquires great relevance. The bed erosion in the vicinity of bridge foundations is controlled by the dynamically rich horseshoe vortex system (HSV) that develops in front of the structures and increases the near-bed turbulent stresses by one order of magnitude compared to the approaching turbulent boundary layer flow.

Advances in numerical simulations designed to understand the physical mechanisms of sediment transport and bed erosion in turbulent flows, however, have been limited by the ability of the models to capture the large-scale coherent vortical structures with adequate resolution, and by the level of description and assumptions of the sediment transport models utilized to predict the sediment flux.

In this thesis we develop an advanced computational fluid dynamics (CFD) model to simulate the flow, bed-load transport, and scour in the vicinity of hydraulic structures. To handle arbitrarily complex multi-connected geometries, the numerical solver employs domain decomposition techniques with structured Chimera overset grids. An Arbitrary Lagrangian-Eulerian (ALE) approach is also incorporated to consider the effects of moving boundaries in the flowfield solution. We carry out numerical simulations of the turbulent flow past a cylindrical pier using the detached-eddy simulation (DES) approach as the turbulence model. DES is a hybrid method that combines an unsteady Reynolds-averaged Navier-Stokes (URANS) model in regions of the computational domain near the wall, with large-eddy simulation (LES) in regions away from solid boundaries This numerical method is capable of capturing the dynamics of the HSV and reproducing for the first time, along with the recent study of Paik, Escauriaza, and Sotiropoulos [Phys. Fluids 19, 045107, 2007], all the experimental trends observed in junction flows at high Reynolds numbers.

Two models of sediment transport are developed in the present investigation to study the initiation of motion, transport processes, and clear-water scour by the large-scale vortical structures of the HSV system: (1) A Lagrangian model for sediment grains to simulate the transport of individual particles. The trajectory and momentum of the sediment particles are computed to evaluate the effects of the instantaneous hydrodynamic forces induced by the HSV system. Since the magnitude of the particle stresses are near the threshold of motion, the transport is characterized by intermittent displacement events of varying magnitudes. Groups of sediment grains move continuously, saltating or sliding on the bed, and streaks aligned with near-wall vortices are formed around the cylindrical pier. The global transport of particles past the cylinder is studied by performing a statistical analysis of the flux to reveal scale-invariance of the process and multifractality of particle transport as the overall effect of the flow around the pier. (2) A new unsteady bed-load transport model based on the momentum equation of the sediment in an Eulerian framework. The evolution of scour is obtained from the solution of the Exner equation, computing the bed elevation from the instantaneous flowfield. The model reproduces scour in non-equilibrium conditions, giving information of the spatial distribution and time evolution of erosion and deposition in the vicinity of the pier. A remarkable process captured for the first time by our model is the development of bed-forms along the legs of the HSV system. The interaction of the vortical structures with the wall produces the bed instability that grows and propagates, generating ripples that travel and merge in the downstream direction showing the same dynamic features observed in experiments.^ The model constitutes a powerful simulation tool to investigate the relation between sediment and bed processes with coherent structures in turbulent flows, and it can also serve as a general framework for developing three-dimensional non-equilibrium sediment transport models that can be used in the future for engineering design and optimization. The model also highlights the importance of integrating high-resolution numerical simulations with laboratory experiments to understand and be able to predict the complex physics of sediment transport in nature.