The large-eddy simulation of incompressible flows in simple and complex geometries
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LES results using the damped SGS model verified the published experimental evidence as well as uncovered new flow features within the cavity. LES computations were also carried-out of the three-dimensional shear driven cavity flow at a high Reynolds number where the SGS turbulent field was represented by a dynamic model. Lilly's least-squares expression was tested for determining Smagorinsky's coefficient in the model without ad hoc measures such as ensemble-averaging or filtering. However, zero cutoff of negative total viscosity (kinematic plus turbulent eddy viscosity) was necessary to maintain stable solutions. A discretized filter function was derived for the test filter. Both qualitative and quantitative comparisons to experimental data show that the dynamic model performed quite well. The dynamic model gave better comparisons to the experimental evidence than the damped model did. Vortex formation in the wake of a circular cylinder and their subsequent downstream transport was also numerically investigated by LES. Here however, the curvilinear form of the governing equations was necessary to perform the computations. A new generalized dynamic model was derived to represent the SGS stress field in the curvilinear space. This new model introduced the contravariant velocity components as part of the field variables.
New downstream boundary conditions were also formulated to permit the shed vortices to exit with minimum disturbance. The focus of the investigation was at Re = 5600 with some verification of the computations at Re = 200 and Re = 3000. At all of these Reynolds numbers. the upstream boundary layer was laminar but the wake was fully turbulent at Re = 3000 and Re = 5600. The LES results of the many interesting characteristics of the wake showed good comparisons to the experimental data.
- Doctoral Dissertations