Mathematical Model Of The Lateral And Longitudinal Mixing Processes In Open Channels PDF Download

The present research investigates the numerical and experimental modelling aspects of flow in compound channels, with special interest in the transport of inert pollutant aspects. This is examined through developing a 2-D finite difference mathematical model, (CHAT: Compound-channel Hydraulics And Transport), to solve the flow and transport equations for open channels having compound cross-sections. The numerical computation of open-channel flows requires preparing and processing larger volumes of boundary and bathymetry data for computer inputs and the development of numerical algorithms for treating complex boundary condition, channel properties, and free surface effects. Derivation of the basic differential equations is based on the Navier-Stokes equations of continuity and fluid motion, in addition to the convection-dispersion equation. These equations are derived in three dimensions (3-D), however, in order to simplify the problem and ease the computational effort, the equations are integrated over the depth (depth-averaged). Most finite difference methods for calculating the convection portion of the transport equation are plagued by artificial (numerical) diffusion. This is sometimes stronger than the physical diffusion and can render the calculations useless. Therefore, as far as reliability of the results is concerned, selection of the numerical scheme is critical. Data for the verification and validation of the developed mathematical model was obtained through dye-tracer experiments performed in a large concrete channel of the Hydraulics Laboratory, University of Ottawa. Consideration was limited to conservative, non-buoyant material. The study investigates the impact on the mixing processes of strong lateral momentum transfer effects associated with severely compound flow fields. The experiments include measurements of dye concentrations downstream from slug-injection or steady-injection point source(s). Longitudinal and transverse mixing coefficients were calculated using the method of moments and by estimation using empirical relationships. In general, it is not possible to obtain analytical solutions to the dispersion equation in natural waterways with arbitrary boundary conditions. However, a variety of exact solutions exists for idealized situations, which can be useful in obtaining order-of-magnitude estimates. These exact simplified solutions were applied to our experimental data. The comparison between measured and predicted concentration curves by the developed model shows a level of agreement in the general shape, peak concentrations and time to peak. Different statistical methods were considered in evaluating the simulated results.