Numerical investigations of turbulent free surface flows using level set method and large-eddy simulation

A numerical model for large eddy simulation of free-surface flows is developed by coupling level set method with the filtered incompressible Navier-Stokes equations. The level set method transforms a free-surface flow problem into an air-water two-phase flow on a fixed grid. The free surface is implicitly captured by the zero level set function. The incompressible Navier-Stokes equations are discretized on a non-staggered boundary-fitted grid based on the finite volume method, advanced with a four-step fractional step method in time. The level set equations are solved with the high-order Essentially Non-Oscillatory schemes. The numerical model is validated and verified by some benchmark free-surface flows, such as a two-dimensional travelling solitary wave and two- and three-dimensional broken-dams.; The turbulent flows in an open-channel, with a train of two-dimensional fixed dunes on the bottom wall, are numerically studied. The free surface is treated in two different ways. First, it is modelled as a fixed undisturbed plane surface. Next, it is simulated as a freely deformable interface of air-water. The former case is studied by the single-phase large eddy simulation, establishing a baseline for the latter case. In the latter case, the model coupling the level set method and large eddy simulation is employed to simulate the air-water two-phase flow. The numerical predictions by both cases are in good agreement with the experimental data. Complex flow patterns on the free surface are revealed in both cases, such as surface-upwellings and downdrafts. Both cases show that the quadrant-two events dominate the production of the Reynolds shear stress and streaky structures appear in the wall layer. The secondary peaks in the profiles of the streamwise component of turbulence intensities, measured by the experiment, are predicted in the latter case while absent in the first case. Three SGS models, namely Smagorinsky model, dynamic Smagorinsky model, and dynamic two-parameter model, are applied for the latter case. The effects of flow depth on the free surface are investigated. A prominent phenomenon in the shallow-water flow is the absence of near-wall streaky structures.*; *This dissertation is compound (contains both a paper copy and CD as part of the dissertation). The CD requires the following system applications: QuickTime, Windows MediaPlayer or RealPlayer.