Turbulence modeling for free-surface flows.

The structure and dynamics of free-surface turbulence at low Froude numbers has been studied using the DNS database (Mangiavacchi, 1994) of a temporally-growing, turbulent, round jet interacting with a free surface. The presence of the free surface is found to significantly modify the dynamics of turbulence within a thin 'surface layer' of thickness on the order of one-third the lateral Taylor microscale. Within this layer, the turbulence structure becomes strongly anisotropic and 'two-dimensional', with only one non-vanishing component of the vorticity, namely, the normal component. There is enhanced production of this component of vorticity within the 'surface layer'. However, the overall vorticity magnitude and hence the dissipation rate is lower than what would exist in 'three-dimensional' turbulence, resulting in a sharp rise in the kinetic energy within the surface layer. Examination of the dynamics of the energy-cascade show enhanced backscatter of energy and a pile-up of kinetic energy at the large scales within the surface layer. This pile-up of energy is maintained by the drop in the rate of kinetic energy combined with a reversal of the trends in the 'slow' pressure-strain correlation within the 'surface layer', which leads to a transfer of energy from the vertical to the horizontal components of motion. The ability of existing dynamic subgrid-scale (SGS) models in capturing these dynamics has been studied by a priori tests as well as actual LES runs of the free-surface turbulent jet. The SGS models studied include the Smagorinsky model (1963), the dynamic Smagorinsky model (DSM) of Germano et al. (1991), the dynamic two-component model (DTM) of Ansari et al. (1993), the dynamic mixed-model (DMM) of Zang et al. (1993), and the dynamic two-parameter (DTPM) model of Salvetti and Banerjee (1995) as well as an anisotropic dynamic Smagorinsky model (ADSM) developed in this work. Overall, the results are promising and indicate that existing dynamic SGS models can correctly capture the anisotropy in the turbulence structure and the rise in the turbulence kinetic energy within the surface layer. However, a more careful study is needed to definitively assess the performance of these models. We also evaluated the performance of a number of existing Reynolds-Averaged Navier-Stokes (RANS) models in free surface flows. A standard, unsteady $K-\epsilon$ model was not able to capture the anisotropy in the the turbulent stresses or the secondary flows which are driven by these anisotropies. Algebraic-stress RANS models represent the next higher level of closure. We have tested the classical Rotta (1951) model for the dissipation tensor, and the models of Swean et al. (1991) for the pressure-strain correlation and Perot and Moin (1995) and Rotta (1951) for the 'slow' pressure-strain in an a priori fashion using the DNS database of the free-surface jet. None of the models were fully successful in capturing the correct structure of the jet throughout its width. However, the overall trends predicted by the models were promising. Further developments, as well as tests in actual RANS computations are necessary before these models can be applied to free-surface flows.Ph.D.Applied SciencesMechanical engineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/130408/2/9722133.pd