Numerical modeling of flow distribution and sediment transport for channel contractions

Abstract

The main objective of this dissertation is to determine the flow distribution in channel contractions and to model the corresponding sediment transport. In channel contractions, the flow area is reduced, flow velocity is increased, and as a result the scour process is significantly increased. The intensity of local scour is amplified at locations where the velocity gradient is large. For the safety assessment of manmade hydraulic structures such as bridge abutments and coffer dam structures, the accurate assessment of scour problem is of great importance. In the dissertation, first, using a numerical model flow distribution at contracted reaches investigated. This model solves the Reynolds and continuity equations for fully developed turbulent flows. Employing the streamlined upwind scheme in the finite element formulation, the algorithm provides numerical stability. In order to achieve computational efficiency, the penalty function is incorporated to satisfy the continuity condition automatically without solving an additional equation. The hydrodynamic analysis investigates velocity and shear distributions in channel contractions due to the skewed abutments with angle variations from 30° to 150° with 10° increments. The analysis is conducted for both single and double abutments. Following series of numerical simulations, a semi-empirical equation was derived for expressing maximum velocity as a function of the contraction ratio, friction, and the skewness angle. Using this empirical equation, it is possible to determine the approximate maximum velocities and the corresponding shear stresses in contracted zones for different skewness angles. In designing footing depth and bank protection for hydraulic structures placed at angle to oncoming flows, this equation provides the magnitude of maximum velocities and the corresponding shear stresses without the use of complex numerical modeling. Next in the dissertation, a bed load transport model is developed for scour analysis in contracted reaches; this model is applied to estimate scour in the Mississippi River. During Phase I of the Lock & Dam No. 26 replacement project, a cofferdam was constructed to reduce the width of Mississippi by approximately 50 %. Increases in flow velocities in the contracted region resulted in the significant lowering (erosion) of the channel bed. The numerical model solves the sediment continuity equation to investigate scour and deposition process in the vicinity of channel contractions. In an effort to achieve the benefit of matrix diagonalization, lumped matrix formulation was introduced and incorporated to the model. The proposed model is verified and its applicability is evaluated through the comparison with measured data. Finally, the unsteady 2-dimensional convection and diffusion equation is solved numerically for the real-time simulation of suspended sediment propagation. The streamlined upwind scheme efficiently reduces numerical oscillations in convection dominated flows due to the high Peclet number. By using the mixed boundary condition to express the external source terms or externally induced suspended load as a function of time in the algorithm, the model is capable of handling not only continuous load cases but also non-continuous suspended load influx. The suspended load transport model was verified using a case study for which an analytical exact solution is available and was applied to the real-time simulation of a suspended load influx case on the Mississippi River. The model algorithm provides a framework upon which water quality as well as contaminant transport models can be built.