Flow Modelling in Straight Compound Channels with Symmetrical, Asymmetrical and Unsymmetrical Floodplains

Abstract

This research examines the flow in both simple and compound channels through numerical and physical modeling which are significant for understanding the flow and its behavior. Accounting the momentum exchange at the junction of a 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, boundary shear stress and depth averaged velocity distribution. Analytical methodologies are proposed for assessing the discharge and its distribution in subsections of symmetric, asymmetric and unsymmetrical compound channels in terms of the zonal boundary shear stress and momentum transfer coefficients at junctions. Utilizing these outputs, the quantification of momentum exchange in terms of apparent shear force has been achieved.
The resistance to flow along the boundary of the compound channel is exhibited in the form of boundary shear stress. Distribution of this boundary shear stress is expressed in terms of geometric and hydraulic parameters for symmetrical, unsymmetrical and asymmetrical compound channels. Generally, the floodplains are rougher than the main channels. So, the influence of differential roughness on boundary shear distribution and flow distribution is examined by investigating a large number of experiments on heterogeneous compound channels. A improve relationship is derived for percentage shear force (%𝑆𝑓𝑝) carried by floodplain depending on width ratio, relative flow depth, relative roughness, Reynolds number and Froude number for symmetrical compound channels. Utilising this relationship, a modified formulation is developed for estimation of %𝑆𝑓𝑝 applicable for unsymmetrical cross sections. In addition to this, another model has also been proposed to predict %𝑆𝑓𝑝 for compound channels with asymmetric floodplains. Three phenomenological expressions are presented depending on %𝑆𝑓𝑝 for delivering the apparent shear at any possible interface of a compound channel. These expressions are capable of evaluating the intensity of momentum transfer at different interfaces and locating the zero shear interfaces for prediction of discharge by area method with reasonable accuracy.
In literature, much of experimental research works are found to be investigated on symmetrical compound channels and less for asymmetric cases. So experiments have been conducted on two-stage asymmetric compound channels in order to investigate the variation of depth averaged velocity distribution, boundary shear stress distribution, stage discharge relationships and turbulence characteristics with geometry and flow parameters. More data sets of boundary shear stress in asymmetric compound channels have also been extracted through numerical investigation. Utilising these wide ranges of data sets, an improved expression to predict the apparent shear stress in an asymmetrical compound channel is developed which is useful in deciding the choice of appropriate interface plane for developing stage-discharge relationship. Through multi variable regression analysis, another approach to estimate the discharge in asymmetric compound channels is developed by adopting zero shear interfaces at the junction. An unsymmetrical compound channel generally emulates a natural river. In an unsymmetrical compound channel, the magnitude of interaction at both shear layers is not equal due to its unequal floodplains at both sides. An analytical expression is proposed to predict boundary shear distribution as a function of geometric, roughness and hydraulic parameters for such channels. Magnitudes of momentum transfers at both the vertical interfaces are quantified and the inequality of flow distribution in the subsections is predicted. Momentum transfer in terms of interacting length at the interface between the main channel and adjoining floodplains has also been derived to predict discharge in compound channels. Further, based on dimensional analysis, simple design equations representing the mean velocities in main channel and in the floodplain are proposed to estimate the distribution of flow in both subsections. Though there are many models exist to predict the total flow and its distribution but few approaches are there who takes care for estimation of point to point boundary shear stress and depth averaged velocity. There is a certain level of uncertainty to predict these variables exceptionally at the shear layer region. As the shear layer width directly depends upon the mean velocity of the sub sections, reliable expressions are also developed to predict the mean velocity ratios and shear layer width for both symmetric and asymmetric compound channels.
Popular hydraulic software Conveyance Estimation System (CES) is based on Shiono and Knight Method (SKM) for predicting the flow variables. The analytical solution of the Shiono and Knight Method accounts three governing parameters i.e., lateral shear, bed friction and secondary flows. Secondary flow is more significant than the other two parameters in simple channel cases; so mathematical relationships have been developed to predict the secondary flow coefficients for constant and variable flow depth domains of a simple channel. In order to investigate the influence of these parameters on flow variables of asymmetric and symmetric compound channels, a number of experimental data sets have been utilised. The variation of three calibrating coefficients i.e., eddy viscosity coefficient (𝜆), friction factor (𝑓) and secondary flow coefficient (𝑘) against the geometric and hydraulic parameters have been studied and modelled for symmetric and asymmetric compound channels. An analytical solution to the depth-integrated turbulent form of the Navier-Stokes equation is also presented. A new secondary flow term is introduced and transverse shear stress in the mixing region is modelled using an effective eddy viscosity concept that contains horizontal coherent structures and three-dimensional bottom turbulence. The strength of the present methodology to predict depth averaged velocity and boundary shear distribution has been examined through some natural river cases with reasonable accuracy.