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published_or_final_version / Mechanical Engineering / Master / Master of Philosophy

Many free surface flow problems encountered in hydraulic engineering can be accurately analyzed by utilizing the depth-averaged equations of motion. A consequence of adopting this depth-averaged modeling approach is that closure approximations must be implemented to represent the so-called effective stresses. These effective stresses consist of the depth-averaged viscous stresses, which are usually small and therefore neglected, the depth-averaged turbulent Reynold's stresses, and additional stresses resulting from depth-averaging of the nonlinear 'convective acceleration terms (often called momentum dispersion terms). Attention is focused on examining closure for both the depth-averaged Reynold's stresses and the momentum dispersion terms. In the present study, the penalty function finite element technique is utilized to solve the governing hydrodynamic and turbulence model equations for a variety of flow domains. Alternative momentum dispersion and turbulence closure models are proposed and evaluated by comparing model predictions with experimental data for strongly curved open channel flow. The results of these simulations indicate that the depth-averaged (k-ε) turbulence model yields excellent agreement with experimental observations. In addition, it appears that neither the streamline curvature modification of the depth-averaged (k-ε) model, nor the momentum dispersion models based on the assumption of helicoidal flow in a curved channel, yield significant improvement in model predictions. Overall model predictions are found to be as good as those of a more complex and restricted three dimensional model. / Ph. D.

A numerical study of fundamental aspects of turbulent mixing has been performed,with emphasis on the behavior of passive scalars of low molecular diffusivity (high Schmidt number Sc). Direct Numerical Simulation is used to simulate incompressible, stationary and isotropic turbulence carried out at high grid resolution. Data analyses are carried out by separate parallel codes using up to 1024^3 grid points for Taylor-scale Reynolds number (R_lambda) up to 390 and Sc up to 1024.Schmidt number of order 1000 is simulated using a double-precision parallel code in a turbulent flow at a low Reynolds number of R_lambda 8 to reduce computational cost to achievable level. The results on the scalar spectrum at high Schmidt numbers appear to have a k^{-1} scaling range. In the presence of a uniform mean scalar gradient, statistics of scalar gradients are observed to deviate substantially from Kolmogorov's hypothesis of local isotropy, with a skewness factor remaining at order unity as the Reynolds number increases. However, this skewness decreases with Schmidt number suggesting that local isotropy for scalars at high Schmidt number is a better approximation. Intermittency exponents manifested by three types of two-point statistics of energy and scalar dissipation, i.e., the two-point correlator (chi(x)chi(x+r)), the second-order moment of local scalar dissipation (chi_r^2) and the variance of the logarithmic local scalar dissipation sigma^2_{lnchi_r} are discussed. Several basic issues in differential diffusion between two scalars of different molecular diffusivities transported by the same turbule nt flow, the physical process of scalar spectral transfer and subgrid-scale transfer are also briefly addressed.