Non-uniform flow modelling in compound channels with non-prismatic floodplains

Abstract

This research examines the flow in compound channels with non-prismatic floodplain through physical and mathematical modelling which are significant for understanding the non-uniform flow and its behaviour. Accounting the momentum exchange at the junctions of a non-prismatic compound channel is a complex task in order to develop an improved model for predicting stage-discharge relationship, distribution of the flow in subsections, resistance relationship, water surface profile variation and depth averaged velocity distribution.
In literature, much of experimental research works are found to be investigated on prismatic compound channels and less for non-prismatic cases whereas very rare works has been done particularly in non-prismatic compound channel with diverging floodplains. So experiments have been conducted on diverging compound channels in order to investigate the variation of depth averaged velocity distribution, boundary shear stress distribution, stage discharge relationships, flow resistance coefficient, water surface profile and flow distributions in floodplain and main channel (both upper and lower main channel) with different geometric and hydraulic parameters. With these channels, both converging and diverging compound channels have been analysed by studying the data of other researchers. The effectiveness of Manning’s n, Darcy- Weisbach f and Chezy’s C are analysed for the different flow configurations of a non-prismatic compound channel. Manning’s roughness coefficient considered to depend on the non-dimensional parameters like width ratio, aspect ratio, relative flow depth, angles (diverging and converging angles), relative distance, bed slope, Reynolds number and Froude number. A multivariable regression model has been developed by taking care of the aforementioned geometric and hydraulic parameters to predict the Manning’s roughness coefficient for non-prismatic compound channels. The non-linear regression models are developed using relevant experimental data obtained from laboratory experiments and the data from other researchers on the compound channel with non-prismatic floodplains. The present model is found to provide satisfactory results as compared to other approaches for different experimental channels and field data by providing less error.
In a compound channel, vertical apparent shear exists on the interface between the main channel and the floodplain, which generally accelerates the flow on the floodplain and resists the flow in the main channel. In addition, a horizontal apparent shear stress also occurs on the interface between the upper and lower main channels, which generally accelerates the flow in the lower one and resists the flow in the upper one. Therefore, it is essential to consider the exchanges of momentum at both vertical and horizontal shear layer regions. In this thesis, an attempt is made to extended the classical independent subsection method (ISM) to determine the magnitudes of flow and velocities in both upper and lower main channels. Four subsections are created in improved ISM according to the vertical and horizontal division lines that correspond to the vertical interface between the main channel and floodplain and the horizontal interface between upper and lower main channels respectively. The extended ISM consists in a set of four coupled 1D momentum equations (instead three equations of classical ISM) for subsections and a mass conservation equation for the total cross-section. The computed results show that the method is well capable of predicting the discharge distributions in the floodplain and main channel (both at upper and lower main channel) of non-prismatic compound channels.
The use of lateral distribution method (LDM) and its modifications in the computation of depth-averaged velocity distribution in a compound channel for both diverging and converging floodplains has also been performed. The modification of LDM has been done considering the friction slope and secondary current effect. Finite difference scheme has been used for discretizing the Modified LDM. MATLAB tool is used to write the code to compute the depth averaged velocity. Different non-prismatic compound channels having converging and diverging flood plains have been considered to evaluate the strength of Modified LDM over other numerical approaches like LDM and Shiono-Knight method (SKM).
Water level determination during flood is always a challenging task for river engineers. As the floodplain width of a non-prismatic compound channel, changes gradually and moves away from the main channel. Therefore, the prediction of water surface profile becomes complicated. The dependency of water surface profiles on five different non-dimensional parameters such as diverging angle, relative depth, relative distance, width ratio, and aspect ratio are analysed. A multivariable regression model has been developed to predict the water surface profile for diverging compound channels. Using the relevant experimental data, non-linear regression has been performed. The results obtained from the present water surface profile model shows good agreement with the observed data and the other researcher’s data-sets. Various statistical error analyses are performed to verify the reliability of the developed multivariable regression model. Water surface profile prediction is an important task in flood risk management in the urban area. In the present research, based on the principle of the momentum balance a numerical method is investigated to predict the water surface elevations in compound channels with both diverging and converging floodplains. Experimental data series of such channel are collected from literature for different geometry and flow conditions to verify the present model. Various existing flow distributions equations are used in the developed numerical method to estimate the water surface elevation. Finite difference method is used to solve the numerical model using MATLAB tool. The results obtained from the simulation show a good agreement with the experimental datasets. Statistical error analysis has been performed to verify the strength of the present model and the other prevailing water surface profile models. As in many cases the predictive capability of mathematical models fails especially in complicated river geometry cases, so the popular soft computing techniques such as ANN and ANFIS has also been successfully tested. Among these two models the ANFIS model is found to provide a higher value of coefficient of correlation and minimum error in terms of mean square error, mean absolute percentage error.