Three-Dimensional Numerical Modeling of Local Scouring in Open Channel Flow

Abstract

In the present study the three-dimensional numerical model SSIIM is used to investigate local scouring in open channel flow. Based on an implicit finite-volume scheme, the transient Reynolds-averaged Navier-Stokes equations are solved in all three dimensions. The non-hydrostatic pressure is calculated with the SIMPLE method. A pressure-based algorithm is used to compute the location of the free surface. For turbulence modeling both the k − and the k −ω models are applied and their effect on the scour development is studied. A transport equation is solved for the suspended sediment concentration. Sediment continuity in combination with an empirical formula is used to capture the bed load transport and the resulting bed changes. When modeling local scour, steep bed slopes up to the angle of repose occur. In order to be able to predict the depth and the shape of the local scour correctly, the reduction of the critical shear stress due to the sloping bed has to be taken into account. Several formulas for the shear stress reduction in combination with a sandslide algorithm are studied. The numerical results of local abutment and pier scour show, that the inclusion of these mechanism are vital for the prediction of the correct shape and size of the local scour. Further investigations suggest that the hydrodynamics play a prominent role in local scouring. More sophistication is demanded from the turbulence model and the free surface algorithm. This realization leads to the implementation of an Explicit Algebraic Reynolds stress model into SSIIM, which is validated through the calculation of secondary currents in straight channel flow and in flumes with longitudinal bedforms. It also initiated the development of a new numerical model REEF3D with an interface-capturing algorithm.

REEF3D uses the level set method in addition with Lagrangian particle correction for the calculation of the free water level. With this front-capturing method the free surface is modeled as the zero level set of a scalar signed distance function. In order to maintain this property and to ensure mass conservation, the level set function is reinitialized after each time step. Surface tension is taken into account with the continuum surface force method. The convective terms including the level set function and the equations of the k-ω turbulence model are discretized with the fifth-order finite difference WENO scheme. It ensures a smooth and oscillation free solution for large gradients and even shocks while maintaining a high order discretization at the same time. The pressure is discretized with the projection method. The Poisson equation for the pressure is solved with the preconditioned BiCGStab algorithm. The staggered grid configuration leads to a tight velocity-pressure coupling. For time discretization a second-order Adams-Bashforth scheme is used. Parallelization of the numerical scheme is achieved by using the domain decomposition framework together with the MPI library. Since the numerical model employs a Cartesian grid, an immersed boundary method based on ghost cell extrapolation is used. In the present study the model is used to predict the flow over a backward facing step and flow in a channel with a long contraction. The numerical results are encouraging, and further development of REEF3D is planned.