The Effect of Non-Equilibrium Coefficients on Sediment Transport in Rivers Using Numerical Model

Document Type : Research Article

Authors

• sabah mohamadi ¹
• Rasool Ghobadian ²
• mahmood kashefipoor

¹ Razi university

² Razi University

https://doi.org/10.22067/jsw.v32i1.65319

Abstract

Introduction: It is so important for engineers to be able to predict the places in which deposition and scouring occurs. In recent two decades using the numerical models arecommon for simulating flow and sediment transport. Numerical models are valuable tools for estimating flow conditions and sediment transport, and are widely applied in water resources management. For this reason, many researches focus on modeling and simulation of flow on a mobile bed in natural and alluvial rivers. Analyzer of sediment transport is one of the most complicated topics in sediment and river hydraulic.
Material and Methods: In this research a one dimensional, unsteady, hydrodynamic model is developed which can be used for simulating flow and sediment transport as semi-coupled model in river systems. In this research, the Saint- Venant’s first order partial differential hyperbolic equations are numerically solved using the Visual Basic program for river systems. In this research study a semi implicit finite difference scheme is developed to solve the Saint- Venant equations for unsteady flow. The linear equations are produced based on the partial differential equations and the staggered technique, so it is possible to employ the tri-angular matrix algorithm (TDMA) to solve them, with this algorithm the time of running model being minimum due to the least mathematical computations. The matrix form of the linearized momentum and continuity equations for a channel with upstream and downstream boundary conditions is provided. Another technique used to solve the matrix of the linear equations is Influence Line Technique (ILT). Base flow discharge and depth in each branch are introduced into the model as the initial conditions. To avoid divergence in numerical calculations, the downstream end discharge of each branch is calculated using initial flow depth and stage-discharge or Manning’s relationship. At the junctions, the upstream discharge is calculated using the algebraic sum of the discharges of the downstream branches and vice-versa; this process is continued up to the last branches at the upstream of the river system. After solving the above equations, the computed hydraulic parameters in this part are sent to the sediment transport segment. In the sediment subroutine the bed and suspended dynamic equations are discretized by finite volume method, and solved with flow equations as semi-coupled scheme. In this study the bed and suspended load rates are individually solved. The dynamic advection- dispersion equation and the bed load differential equation were applied to calculate the suspended sediment concentration and bed load transport, respectively. The Exner equation is then used to predict the changes in the river bed elevations innon-equilibrium conditions. Because ofthe nature, the sediment transport is often in non-equilibrium form, in this study, the non-equilibrium Exner equation is used to compute the bed elevations, unlike many of the known models. The use of non-equilibrium method due to the complexity of the solution and the presence of non-equilibrium parameters such as coefficients of the adaptation length and recovery is very difficult.
Results and Discussion: In non-equilibrium conditions, the numerical models have high sensitivity to two parameters including, the adaptation length coefficient for bed load and recovery coefficient for suspended load, with the sensitivity analysis for these coefficients being carried out in this research. In this study, a sensitivity analysis was performed on these parameters using developed numerical model. The developed model has this ability to simulate flow and sediment transport in complex and loop river systems. Finally, the model was simulated for the Chaudhry loop river systems. Thisriver system has 9 branches that form the loop. All channels have rectangular sections and their flows are sub-critical. The upstream boundary condition is an unsteady hydrograph with peak discharge of 250 cubic meters per seconds and base time of 8 hours. The calculated stage and discharge by the model (using Manning’s equation) was supplied to the model as a downstream boundary condition at last node. The model outputs are discharged hydrographs on different sections of each channel. The developed model has good ability to simulate the flow and sediment transport in river systems. The result showed that by selecting the adaptation length coefficient, equivalent to a multiple of 1 to 3 times the distance between cross sections, the results of the numerical model can be more realistic. Also it was concluded that empirical equation of Lin(1984) used for the recovery factor of the suspended load.

Keywords

• River System
• Semi-Coupled
• Exner equation
• One dimensional

20.1001.1.20084757.1397.32.1.1.5

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