Depth-averaged turbulence model and applications
This paper presents the developments and applications of a turbulence depth-averaged (depth-integrated) two-equation closure model, symbolised by model depth-averaged turbulent kinetic energy parameter; depth-averaged vorticity fluctuation parameter of turbulence). The model, different from the well-known turbulence depth-averaged model depth-averaged dissipation rate parameter of turbulent kinetic energy), was stemmed from the revised version of kw model (k: turbulent kinetic energy; w: time-mean-square vorticity fluctuations of turbulence). In the model, the depth-averaged partial differential and w? -equations are solved with the mean flow equations together in order to determine the distribution of turbulence eddy viscosity and diffusivity as well as other physical variables. Three computational examples, two steady and one unsteady, have been carried out for investigating and applying the established model. They are: (1) the side jet with temperature difference is discharged vertically into a rectangular open channel; (2) the cooling water is simultaneously discharged from three submerged outlets of an electric power plant into the Rhine River and (3) the waste-heat and pollutants are discharged from seven sources, two of which were submerged, into the south estuary of the Yangtse River. In these three examples, the distributions and variations of velocity, temperature and concentration fields were numerically simulated and the velocity and temperature fields computed by different turbulence two-equation closure models also compared with experimental results and field data. It was found that the results computed by model are closer to experimental data than those computed by using the model, when the width or flow rate of the side-discharge outlet is relatively small to compare the corresponding width or flow rate of cross-section flow, a situation frequently encountered in environmental engineering. The computed temperature distributions by using model, model as well as other simple, low-order turbulence model are different; the results calculated by depth-averaged model are better than those computed by using model and much better than those from simple constant coefficient diffusivity model even at the lower reach far from the discharging outlet. The numerical simulation by use of the advanced turbulence two-equation model provided indispensable information for the tidal patterns and the distributions of depth-averaged temperature, the chemical oxygen demand (COD) concentration and biochemical oxygen demand (BOD) concentration and is much more reliable than those by use of the phenomenological algebraic formulae of eddy viscosity and diffusivity.
turbulence model turbulence two-equation closure numerical model simulation and prediction contaminant transport waste heat discharge tidal modelling concentration distribution