Depth-Averaged Two-Dimensional Numerical Modeling of Unsteady Flow and Nonuniform Sediment Transport in Open Channels

A depth-averaged two-dimensional (2D) numerical model for unsteady flow and nonuniform sediment transport in open channels is established using the finite volume method on a nonstaggered, curvilinear grid. The 2D shallow water equations are solved by the SIMPLE(C) algorithms with the Rhie and Chow’s momentum interpolation technique. The proposed sediment transport model adopts a nonequilibrium approach for nonuniform total-load sediment transport. The bed load and suspended load are calculated separately or jointly according to sediment transport mode. The sediment transport capacity is determined by four formulas which are capable of accounting for the hiding and exposure effects among different size classes. An empirical formula is proposed to consider the effects of the gravity on the sediment transport capacity and the bed-load movement direction in channels with steep slopes. Flow and sediment transport are simulated in a decoupled manner, but the sediment module adopts a coupling procedure for the computations of sediment transport, bed change, and bed material sorting. The model has been tested against several experimental and field cases, showing good agreement between the simulated results and measured data.     

Numerical Simulation of Contraction Scour in an Open Laboratory Channel

A finite-volume computer code developed at the Institute for Hydromechanics, University of Karlsruhe, has been used to calculate the flow and sediment transport in a laboratory channel with constriction and movable bed. The flow is calculated by solving the fully three dimensional Reynolds-averaged Navier-Stokes equations with k?ε turbulence model. The bed deformation is obtained from an overall mass-balance equation for sediment transport and the bed-load transport is simulated with a nonequilibrium model. The calculated results for flow and scour development in the laboratory channel are compared with experimental measurements. The sensitivity of the simulated results to the nonequilibrian adaptation-length parameter in the nonequilibrium bed-load transport model is investigated systematically, which represents the main contribution of this paper.     

Numerical Modeling of Bed Deformation in Laboratory Channels

A depth-average model using a finite-volume method with boundary-fitted grids has been developed to calculate bed deformation in alluvial channels. The model system consists of an unsteady hydrodynamic module, a sediment transport module and a bed-deformation module. The hydrodynamic module is based on the two-dimensional shallow water equations. The sediment transport module is comprised of semiempirical models of suspended load and nonequilibrium bedload. The bed-deformation module is based on the mass balance for sediment. The secondary flow transport effects are taken into account by adjusting the dimensionless diffusivity coefficient in the depth-average version of the k–ε turbulence model. A quasi-three-dimensional flow approach is used to simulate the effect of secondary flows due to channel curvature on bed-load transport. The effects of bed slope on the rate and direction of bed-load transport are also taken into account. The developed model has been validated by computing the scour hole and the deposition dune produced by a jet discharged into a shallow pool with movable bed. Two further applications of the model are presented in which the bed deformation is calculated in curved alluvial channels under steady- and unsteady-flow conditions. The predictions are compared with data from laboratory measurements. Generally good agreement is obtained.     

One-Dimensional Numerical Model for Nonuniform Sediment Transport under Unsteady Flows in Channel Networks

In this study, the proposed one-dimensional model simulates the nonequilibrium transport of nonuniform total load under unsteady flow conditions in dendritic channel networks with hydraulic structures. The equations of sediment transport, bed changes, and bed-material sorting are solved in a coupling procedure with a direct solution technique, while still decoupled from the flow model. This coupled model for sediment calculation is more stable and less likely to produce negative values for bed-material gradation than the traditional fully decoupled model. The sediment transport capacity is calculated by one of four formulas, which have taken into consideration the hiding and exposure mechanism of nonuniform sediment transport. The fluvial erosion at bank toes and the mass failure of banks are simulated to complement the modeling of bed morphological changes in channels. The tests in several cases show that the present model is capable of predicting sediment transport, bed changes, and bed-material sorting in various situations, with reasonable accuracy and reliability.     

Aspect Ratio to Maximize Sediment Transport in Rigid Bank Channels

The continuity equation, Manning’s equation, Einstein’s wall correction procedure and sediment transport equations are combined to indicate channel aspect ratios which maximize sediment transport for a given water discharge in rigid-bank trapezoidal and rectangular channels with fixed slope. Higher aspect ratios are required to maximize sediment transport for channels conveying bed load than for those with a dominant suspended load. A total load equation predicts optimum aspect ratios lying in between those for bed load and suspended load channels. The equations imply that the optimum aspect ratio increases markedly as the channel bank to channel bed roughness ratio increases. The resulting optimum ratios are smaller than the aspect ratios of many natural rivers.     

Unified View of Sediment Transport by Currents and Waves. III: Graded Beds

The problem of suspended load and bed load transport in river and coastal flows over graded beds is addressed. Two effects are important: the degree of exposure of the sediment particles of unequal size within a mixture (hiding of smaller particles resting or moving between the larger particles) and the nonlinear dependence of transport on particle diameter. The former effect can be modeled by modifying the critical bed-shear stress through a correction factor and by modifying the effective grain roughness through another correction factor. The modeling of the effective bed-shear stress parameter is studied by using various alternative methods. Based on comparison with suspended load and bed load transport data for graded beds in steady and oscillatory flow, the most promising method is selected. The proposed prediction method is found to work well for the fine sand bed range as well as the coarse sand-gravel bed range.     

3D Numerical Simulation for Water Flows and Sediment Deposition in Dam Areas of the Three Gorges Project

This paper presents a three-dimensional (3D) mathematical model for suspended load transport in turbulent flows. Based on the stochastic theory of turbulent flow proposed by Dou, numerical schemes of Reynolds stresses for anisotropic turbulent flows are obtained. Instead of a logarithmic law, a specific wall function is used to describe the velocity profile close to wall boundaries. The equations for two-dimensional suspended load motion and sorting of bed material have been improved for a 3D case. Numerical results are in good agreement with the measured data of the Gezhouba Project. The present method has been employed to simulate sediment erosion and deposition in the vicinity of the Three Gorges Dam. The size distribution of the deposits and bed material, and flow and sediment concentration at different times and elevations, are predicted. The results agree well with the observations in physical experiments. Thus, a new method is established for 3D simulation of sediment motion in the vicinity of dams.     

Two-Dimensional Total Sediment Load Model Equations

An unsteady total load equation is derived for use in depth-averaged sediment transport models. The equation does not require the load to be segregated a priori into bed and suspended but rather automatically switches to suspended load, bed load, or mixed load depending on a transport mode parameter consisting of local flow hydraulics. Further, the sediment transport velocity, developed from available data, is explicitly tracked, and makes the equation suitable for unsteady events of sediment movement. The equation can be applied to multiple size fractions and ensures smooth transition of sediment variables between bed load and suspended load for each size fraction. The new contributions of the current work are the consistent treatment of sediment concentration in the model equation and the empirical definition of parameters that ensure smooth transitions of sediment variables between suspended load and bed load.     

Experimental Study of Bed Load Transport through Emergent Vegetation

Vegetation is an important agent in fluvial geomorphology and sedimentary processes, through its influence on the local hydraulics that determine sediment transport. Within stands of emergent vegetation, bed shear is substantially reduced through the absorption of momentum by drag on the stems. This stimulates deposition of sediment and reduces capacity for bed load transport. The effect of emergent vegetation on hydraulic parameters (including equilibrium bed gradient, flow depth, and velocity) and on bed load transport rate has been investigated experimentally for one sediment size, stem diameter, and stem spacing. Bed load transport rate was found to be closely related to bed-shear stress, which must be estimated by partitioning total flow resistance between stem drag and bed shear.     

3D Numerical Modeling of Flow and Sediment Transport in Open Channels

A 3D numerical model for calculating flow and sediment transport in open channels is presented. The flow is calculated by solving the full Reynolds-averaged Navier-Stokes equations with the k ? ε turbulence model. Special free-surface and roughness treatments are introduced for open-channel flow; in particular the water level is determined from a 2D Poisson equation derived from 2D depth-averaged momentum equations. Suspended-load transport is simulated through the general convection-diffusion equation with an empirical settling-velocity term. This equation and the flow equations are solved numerically with a finite-volume method on an adaptive, nonstaggered grid. Bed-load transport is simulated with a nonequilibrium method and the bed deformation is obtained from an overall mass-balance equation. The suspended-load model is tested for channel flow situations with net entrainment from a loose bed and with net deposition, and the full 3D total-load model is validated by calculating the flow and sediment transport in a 180° channel bend with movable bed. In all cases, the agreement with measurements is generally good.     

Applicability of Sediment Transport Capacity Formulas to Dam-Break Flows over Movable Beds

In this paper, we investigate the extent to which well-known sediment transport capacity formulas can be used in one-dimensional (1D) numerical modeling of dam-break waves over movable beds. The 1D model considered here is a one-layer model based on the shallow-water equations, a bed update (Exner) equation, a space-lag equation for the nonequilibrium sediment transport and an empirical formula calculating the sediment transport capacity of the flow. The model incorporates a variety of sediment transport capacity formulas proposed by Meyer-Peter and Müller, Bagnold, Engelund and Hansen, Ackers and White, Smart and Jaeggi, van Rijn, Rickenmann, Cheng, Abrahams and Camenen, and Larson. We examine the performance of each formula by simulating four idealized laboratory cases on dam-break waves over sandy beds. Comparisons between numerical results and measurements show that for each case better predictions are obtained using a particular formula, but overall, formulas proposed by Meyer-Peter and Müller (with the factor 8 being replaced by 12), Smart and J?ggi, Cheng, Abrahams and Camenen, and Larson rank as the best predictors for the entire range of conditions studied here. Moreover, results show that in the cases where a bed step exists, implementing a mass failure mechanism in the numerical modeling plays an important role in reproducing the bed and water profiles.     

Modeling Sediment Transport Using Depth-Averaged and Moment Equations

A 1D mathematical model to calculate bed variations in alluvial channels is presented. The model is based on the depth-averaged and moment equations for unsteady flow and sediment transport in open channels. Particularly, the moment equation for suspended sediment transport is originally derived by the assumption of a simple vertical distribution for suspended sediment concentration. By introducing sediment-carrying capacity, suspended sediment concentration can be solved directly from sediment transport and its moment equations. Differential equations are then solved by using the control-volume formulation, which has been proven to have good convergence. Numerical experiments are performed to test the sensitivity of the calibrated coefficients α and k in the modeling of the bed deposition and erosion. Finally, the computed results are compared with available experimental data obtained in laboratory flumes. Comparisons of this model with HEC-6 and other numerical models are also presented. Good agreement is found in the comparisons.     

3D Numerical Modeling of Flow and Sediment Transport in Laboratory Channel Bends

The development of a fully three-dimensional finite volume morphodynamic model, for simulating fluid and sediment transport in curved open channels with rigid walls, is described. For flow field simulation, the Reynolds-averaged Navier–Stokes equations are solved numerically, without reliance on the assumption of hydrostatic pressure distribution, in a curvilinear nonorthogonal coordinate system. Turbulence closure is provided by either a low-Reynolds number k?ω turbulence model or the standard k?ε turbulence model, both of which apply a Boussinesq eddy viscosity. The sediment concentration distribution is obtained using the convection-diffusion equation and the sediment continuity equation is applied to calculate channel bed evolution, based on consideration of both bed load and suspended sediment load. The governing equations are solved in a collocated grid system. Experimental data obtained from a laboratory study of flow in an S-shaped channel are utilized to check the accuracy of the model’s hydrodynamic computations. Also, data from a different laboratory study, of equilibrium bed morphology associated with flow through 90° and 135° channel bends, are used to validate the model’s simulated bed evolution. The numerically-modeled fluid and sediment transportation show generally good agreement with the measured data. The calculated results with both turbulence models show that the low-Reynolds k?ω model better predicts flow and sediment transport through channel bends than the standard k?ε model.     

Influence of Vertical Resolution and Nonequilibrium Model on Three-Dimensional Calculations of Flow and Sediment Transport

This note, using a three-dimensional model of river flow and sediment transport, examines the effect of the vertical resolution and the choice a nonequilibrium adaptation length Ls in predicting flow and sediment transport around groins in China’s Yongding River. The results show that a fine vertical grid and nonequilibrium sediment transport model provide good predictions, especially on the river bed profile with an obvious main channel and flood plain.     

Validation of Existing Bed Load Transport Formulas Using In-Sewer Sediment

Granular sediment in pipe inverts has been reported in a number of sewer systems in Europe. Given the range of flow conditions and particle characteristics of inorganic sewer sediments the mode of transport may normally be considered as bed load. Current commercial software for modeling the erosion and transport of sediments in sewer pipes still utilizes well-known, or modified versions of transport equations that were derived for transport of noncohesive sediment in alluvial streams. In this paper the performances of the equations of Ackers and White (originally developed for the transport of river sediments) and of May (derived from laboratory pipe experiments) are examined against two separate data sets. One set is from laboratory erosion experiments on sewer sediment obtained in Paris. A second data set has bed load transport rate measurements recorded in a sewer inlet pipe. The formulas were selected because of their widespread use in the prediction of in-sewer sediment transport both in commercial software and in the latest United Kingdom design guidance for new sewers. The results indicated that both the relationships performed poorly, even in such well-controlled conditions. These formulas have significant difficulties in predicting the erosion thresholds and fractional transport rates for non-uniformly sized in-sewer sediments. An empirical formula to adjust the threshold of motion for individual grain size fractions was developed which significantly improved predictions. Although such techniques have been used in gravel bed rivers, the threshold adjustment function for in-sewer deposits was significantly different from these previously published for fluvial gravels, indicating that a direct transfer of fluvial relationships to sewers may be inappropriate without further research.     

Unified View of Sediment Transport by Currents and Waves. II: Suspended Transport

The problem of suspended sediment transport in river and coastal flows is addressed. High-quality field data of river and coastal flows have been selected and clustered into four particle size classes (60–100, 100–200, 200–400, and 400–600?μm). The suspended sand transport is found to be strongly dependent on particle size and on current velocity. The suspended sand transport in the coastal zone is found to be strongly dependent on the relative wave height (Hs/h), particularly for current velocities in the range 0.2–0.5?m/s. The time-averaged (over the wave period) advection–diffusion equation is applied to compute the time-averaged sand concentration profile for combined current and wave conditions. Flocculation, hindered settling, and stratification effects are included by fairly simple expressions. The bed-shear stress is based on a new bed roughness predictor. The reference concentration function has been recalibrated using laboratory and field data for combined steady and oscillatory flow. The computed transport rates show reasonably good agreement (within a factor of 2) with measured values for velocities in the range of 0.6–1.8?m/s and sediments in the range of 60–600?μm. The proposed method underpredicts in the low-velocity range (<0.6?m/s). A new simplified transport formula is presented, which can be used to obtain a quick estimate of suspended transport. The modeling of wash load transport in river flow based on the energy concept of Bagnold shows that an extremely large amount of very fine sediment (clay and very fine silt) can be transported by the flow.     

Formation Processes and Configuration of Channel-Flow Dominated Alluvial Deltas by Numerical Simulation

A horizontal two-dimensional mobile bed model for simulating the formation of river-dominated deltas in the river mouth or reservoir is presented, which is composed of shallow water equations, sediment transport formula, and a sediment continuity equation. Geometry similarity of river deltas during the processes of formation is discussed. Stability analysis and sensitivity analysis of parameters in the model are analyzed, which indicates that bed configuration is sensitive to the incipient-motion criteria of bed–load particles. The effect of gravity component on the initiation of sediment movement, therefore, is recommended to be considered in the modeling. The bed configuration including the reverse slope in the longitudinal profile and concave in the transverse profiles are correctly simulated with help from the correction of incipient-motion criteria. Simulation results are verified with a series of experiments and are consistent with series geometric functions and dimensionless profiles inducted from experimental data. This reflects the great reliability of the model. Historical topographical records of two typical in-land deltas depicting their earlier developmental stages are discussed to show the usefulness of this study.     

Simulation of Scour Process in Plunging Pool of Loose Bed-Material

The scouring process in a plunge pool of loose bed with uniform bed-materials due to a two-dimensional plane impinging jet was simulated computationally. The finite-element-based unsteady three-dimensional model, CCHE3D, with k-ε turbulence closure was employed to solve the flow field. It has long been recognized that the unsteady behavior of the turbulent jet fluctuation plays an important role in scouring and transporting sediment in the plunge pool. In order to model this phenomenon realistically, one has to consider the effects of both shear stress and the life force on sediment particles due to pressure fluctuation. The latter has been taken into account by using empirical relationships of flume data. Both of these effects have been incorporated in the nonequilibrium sediment transport model consisting of sediment pickup rate and step length adopted for the jet scour problem. The model constant relating to the fluctuating lift force was calibrated using an empirical equation to predict the quasi-equilibrium scour depth. The results simulated by the model proposed here agree reasonably well with experimental data.     

Simulating Bed-Load Transport in a Complex Gravel-Bed River

An existing two-dimensional mobile-bed hydrodynamic model has been modified to simulate bed-load transport in a complex gravel-bed river. We investigated the sensitivity of predicted bed load to control parameters, and compared model predictions of flow depth, shear stress, and gravel transport with field measurements made from the river. The predictions are based on concurrent field data of flow discharge, water level, and sediment for model input. The model takes into account multiple-fraction transport rates, and continuously updates the river bed and surface grain-size distribution. The model predictions are in reasonable agreement with field measurements.     

Method for Estimating Sediment Transport in Ice-Covered Channels

A method is proposed for estimating rates of sediment transport in ice-covered alluvial channels. The method extends existing, open-water procedures for estimating rates of sediment transport to conditions of ice-covered flow. A key aspect of the method is the assessment of flow resistance attributable to bed-surface drag. That assessment is used to estimate rates of bed load and suspended load, and thereby total bed-sediment transport rate. Estimation of ice-covered suspended load additionally entails an approximation whereby open-water suspended load is scaled in proportion to the ratio of a reference sediment concentration for ice-covered flow relative to that for open-water flow. The reference concentration is calculated in terms of bed-load rate and shear velocity attributed to bed-surface drag. Flume data are used to develop the method and tentatively verify it. Field verification of the method presently is hampered by the absence of field data on bed sediment transport in ice-covered channels.