Two-dimensional simulation models of shallow recirculating flows

Shallow recirculating flows dominated by bed-friction effect are numerically simulated in this thesis using two-dimensional models. A two-length-scale k-epsilon turbulence model which is based on Reynolds averaged procedure, and a two-dimensional Large Eddy Simulation (2DLES) model based on subgrid stress are employed. The performance of these models is evaluated by comparing the numerical results with the available laboratory experimental data for a range of conditions from deep to shallow water depth.In the two-length-scale k-epsilon model simulations, the small-scale turbulence is treated as a background component locally in equilibrium, while the large-scale turbulence is modeled by a second-order closure model. Two versions of wall-function models, a high-Reynolds number and a low-Reynolds number wall model, are considered in the implementation of the k-epsilon model. The reattachment length, the recirculation flow rate, and the tracer concentration distribution of shallow recirculating flows are correctly predicted by the k-epsilon model for all of the conducted tests. However, the secondary eddy observed in the experiments in the corner of the main recirculating region is reproduced only when the low-Reynolds-number wall model is implemented. The length of the secondary eddy is ≃25% of the length of the recirculating eddy.In the 2DLES model, the Smagorinsky model for the subgrid stress is modified taking into account the bed-friction effect. A series of numerical simulations are conducted to determine the Smagorinsky coefficient, Cs, for shallow recirculating flows. The results show that the value of the Smagorinsky coefficient is not constant but it is related to a dimensionless parameter (the bed-friction number, S) and to the size of the numerical mesh. For a mesh size 180 x 60, the Cs ranges from 0.1 to 0.25 for shallow to deep recirculating flows respectively. This range of Cs becomes 0.13 to 0.30 for a mesh size 360 x 120. The secondary (corner) eddy as well as the mean flow characteristics are predicted by the 2DLES model when fine mesh sizes of 180 x 60 and 360 x 120 are used in the simulations. Using the optimum Cs values, the numerical results obtained for all parameters (such as the mean flow, the Reynolds stresses, the mean tracer concentration, and the tracer concentration fluctuations) are in agreement with the laboratory observations. The Strouhal number for the oscillations of the shallow recirculating flows is also obtained from the 2DLES.Unlike the k-epsilon model which needs a pair of differential equations for k and epsilon, the 2DLES relates stress and strain at the subgrid scale using an algebraic relation. Provided that a correct Cs is selected, the 2DLES model is more stable, easier to implement and hence would be a more suitable simulation scheme for engineering applications