Three-Dimensional Modeling of Sediment Transport in a Narrow 90° Channel Bend

A three-dimensional numerical model was used for calculating the velocity and bed level changes over time in a 90° bended channel. The numerical model solved the Reynolds-averaged Navier-Stokes equations in three dimensions to compute the water flow and used the finite-volume method as the discretization scheme. The k-ε model predicted the turbulence, and the SIMPLE method computed the pressure. The suspended sediment transport was calculated by solving the convection diffusion equation and the bed load transport quantity was determined with an empirical formula. The model was enhanced with relations for the movement of sediment particles on steep side slopes in river bends. Located on a transversally sloping bed, a sediment particle has a lower critical shear stress than on a flat bed. Also, the direction of its movement deviates from the direction of the shear stress near the bed. These phenomenona are considered to play an important role in the morphodynamic process in sharp channel bends. The calculated velocities as well as the bed changes over time were compared with data from a physical model study and good agreement was found.     

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.     

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.     

Numerical Modeling of Bed Evolution in Channel Bends

A two-dimensional numerical model is developed to predict the time variation of bed deformation in alluvial channel bends. In this model, the depth-averaged unsteady water flow equations along with the sediment continuity equation are solved by using the Beam and Warming alternating-direction implicit scheme. Unlike the present models based on Cartesian or cylindrical coordinate systems and steady flow equations, a body-fitted coordinate system and unsteady flow equations are used so that unsteady effects and natural channels may be modeled accurately. The effective stresses associated with the flow equations are modeled by using a constant eddy-viscosity approach. This study is restricted to beds of uniform particles, i.e., armoring and grain-sorting effects are neglected. To verify the model, the computed results are compared with the data measured in 140° and 180° curved laboratory flumes with straight reaches up- and downstream of the bend. The model predictions agree better with the measured data than those obtained by previous numerical models. The model is used to investigate the process of evolution and stability of bed deformation in circular bends.     

Effect of Bed Armoring on Bed Topography of Channel Bends

The two-dimensional numerical model previously developed by the writers for modeling the bed variations in a channel bend with uniform sediment is upgraded to incorporate the nonuniformity of sediment particles as well as bed armoring. In this model, the two-dimensional, depth-averaged, unsteady flow equations along with the bed-load mass conservation equation are solved in a body-fitted coordinate system by using the Beam and Warming alternating-direction implicit (ADI) scheme. A one-dimensional bed surface armoring approach is extended herein for application to a two-dimensional domain. The model is applied to a 180° bend with a constant radius under unsteady flow conditions. Numerical simulations are carried out to study the effect of bed armoring on the bed deformations in channel bends. Results show that bed armoring reduces scour in channel bends.     

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.     

Three-Dimensional Numerical Model for Flow and Bed Deformation around River Hydraulic Structures

This paper describes a numerical model developed to simulate flow and bed deformation around river hydraulic structures. The model solved the fully three-dimensional, Reynolds-averaged Navier–Stokes equation expressed in a moving boundary-fitted coordinate system to calculate the flow field with water and bed surfaces varying in time. A nonlinear k-ε turbulence model was employed in order to predict flow near the structure where three-dimensional flow is dominant. The temporal change in bed topography was calculated by coupling a stochastic model for sediment pickup and deposition using a momentum equation of sediment particles in order to account for the effect of nonequilibrium sediment transport. In validating the numerical model, a spur dike and a bridge pier, which are considered to be typical river-engineering structures, were selected. By comparing the numerical results with observed laboratory experimental data, the model was found to reproduce flow and scour geometry around these structures with sufficient accuracy.     

Three-Dimensional Numerical Simulation of Compound Channel Flows

A three-dimensional numerical study is presented for the calculation of turbulent flow in compound channels. The flow simulations are performed by solving the three-dimensional Reynolds-averaged continuity and Navier–Stokes equations with the k?ε turbulence model for steady-state flow. The flow equations are solved numerically with a general-purpose finite-volume code. The results are compared with the experimental data obtained from the UK Flood Channel Facility. The simulated distributions of primary velocity, bed shear stress, turbulent kinetic energy, and Reynolds stresses are used to investigate the accuracy of the model prediction. The results show that, using an estimated roughness height, the primary velocity distributions and the bed shear stress are predicted reasonably well for inbank flows in channels of high aspect ratio (width/depth ≥ 10) and for high overbank flows with values of the relative flow depth greater than 0.25.     

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.     

Three-Dimensional CFD Modeling of Self-Forming Meandering Channel

A three-dimensional CFD model was used to compute the formation of the meandering pattern in an initially straight alluvial channel. The numerical model was based on the finite volume method using an unstructured grid with dominantly hexahedral cells. The k-ε model was used to predict turbulence and the SIMPLE method was used to compute the pressure. The sediment transport was computed as bed load in addition to solving the convection-diffusion equation for suspended sediment transport. The bed changes were calculated and the grid was altered during the computation as channel erosion and deposition caused wetting and drying. The model was tested by comparing with results from physical model studies carried out at Colorado State Univ., Fort Collins, Colo. The results showed successfully the replication of many of the meander characteristics, including secondary currents, cross-sectional profiles, meander planform, meander wavelength, downstream meander migration, and chute formation.     

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.     

Modeling of a Rough-Wall Oscillatory Boundary Layer Using Two-Equation Turbulence Models

The standard k?ω turbulence model and two versions of blended k?ω/k?ε models have been used to study the characteristics of a one-dimensional oscillatory boundary layer on a rough surface. The wall boundary condition for the specific dissipation rate of turbulent kinetic energy at the wall is specified in terms of a function based on wall roughness. A detailed comparison has been made for mean velocity, turbulent kinetic energy, Reynolds stress, and wall shear stress with the available experimental data. The three models predict the above properties reasonably well. In particular, the prediction of turbulent kinetic energy for the rough case by the blended models is much better than that for smooth oscillatory boundary layers as reported in previous studies. As a result of the present study, the use of one of the blended models in calculating the sediment transport in coastal environments may be recommended.     

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.     

Three-Dimensional Modeling of Nonuniform Sediment Transport in an S-Shaped Channel

A three-dimensional numerical model was applied to compute uniform and nonuniform sediment transport and bed deformation in an S-shaped laboratory channel located at the University of Innsbruck, where detailed measurements of the velocity field and bed elevation changes were made. The channel had two bends, a trapezoidal cross section, and a slope of S = 0.005. Gravel with a mean diameter of 4.2?mm was used as movable bed material and for sediment feeding. Wu’s formula for multiple grain sizes was compared with van Rijn’s formula using one grain size. Fairly good agreement was found between the computed and measured bed elevations for both approaches, whereas Wu’s formula could further improve the numerical results. Looking at the physics of the erosion pattern, the computed scour areas were located slightly more downstream than what was observed in the physical model. The current study also includes several parameter tests: grid distribution in vertical, lateral, and longitudinal direction; time step; number of inner iterations/time step; active sediment layer thickness; and the Shields coefficient. The variation of those parameters gave some differences in the results, but the overall pattern of bed elevation changes remained the same.     

Turbulent Flow Over and Within a Porous Bed

The characteristics of turbulent flow in open channels with a porous bed are studied numerically and experimentally. The “microscopic” approach is followed, by which the Reynolds-averaged Navier-Stokes equations are solved numerically in conjunction with a low-Re k-ε turbulence model above and within the porous bed. The latter is represented by a bundle of cylindrical rods of certain diameter and spacing, resulting in permeability K ranging from 5.5490×10?7 to 4.1070×10?4?m2 and porosity ? from 0.4404 to 0.8286. Mean velocities and turbulent stresses are measured for ? = 0.8286 using hot-film anemometry. Emphasis is given to the effect of Darcy number Da on the flow properties over and within the porous region. Computed and experimental velocities in the free flow are shown to decrease with increasing Da due to the strong momentum exchange near the porous medium/free flow interface and the corresponding penetration of turbulence into the porous layer for highly permeable beds. Computed discharge indicates the significant reduction of the channel capacity, compared to the situation with an impermeable bed. On the contrary, laminar flow computations, along with analytical solutions and measurements, indicate opposite effects of the porous medium on the free flow.     

A 3-D numerical prediction of turbulent flow,heat transfer and solidification in a continuous slab caster for steel

This study describes the numerical modeling of three-dimensional coupled turbulent flow, heat transfer, and solidification in a continuous slab caster for stainless steel. The model uses generalized transport equations which are applicable to the liquid, mushy and solid regions within the caster. The turbulent characteristics in the melt pool and mushy region are accounted for using the low-Reynolds number k–ε turbulence model by Launder and Sharma. This version of the low-Reynolds number turbulence model is found to be more easily adaptable to the coupled flow and mushy region solidification caster problem compared to the standard high-Reynolds number and other low-Reynolds number turbulence models. The macroscopic solidification process itself is based on the enthalpy-porosity scheme. The governing transport equations are solved employing the primitive variables and using the control volume based finite-difference scheme on a staggered grid. The process variables considered are the casting speed and the inlet superheat of the melt. The effects of these process variables on the velocity and temperature distributions and on the extent of the solidification and mushy regions are reported and discussed. The numerical predictions of solidification profile are compared with the limited experimental data available in the literature, and very good agreement was found.     

Dissolved Oxygen Demand at the Sediment-Water Interface of a Stream: Near-Bed Turbulence and Pore Water Flow Effects

A microbial dissolved oxygen (DO) uptake model was developed for a stream bed, including the effect of turbulence in the flow over the bed and pore water flow in the porous bed. The fine-grained sediment bed has hydraulic conductivities 0.01 ≤ k ≤ 1??cm/s, i.e., sediment particle diameter 0.006 ≤ ds ≤ 0.06??cm. The pore water flow is driven by pressure fluctuations at the sediment-water interface, mostly attributable to near-bed coherent motions in the turbulent boundary layer above the sediment bed. An effective mass transfer coefficient (De) coupled to a pore water flow model was used in the DO transport and DO uptake model. DO flux across the sediment-water interface and into the sediment, i.e., sedimentary oxygen demand (SOD), was related to hydraulic conductivity and microbial oxygen uptake rate in the sediment and shear velocity at the sediment-water interface. Simulated SOD values were validated against experimental data. For hydraulic conductivities of the sediment bed up to k ≈ 0.01??cm/s, the pore water flow effect on SOD was found negligible. Above this threshold, the effective mass (DO) transfer coefficient in the sediment bed (De) becomes larger as the hydraulic conductivity (k) becomes larger as the interstitial flow velocities increase; consequently, DO penetration depth increases with larger hydraulic conductivity of the sediment bed (k), and SOD increases as well. The enhancement of vertical DO transport into the sediment bed is strongest near the sediment-water interface, and rapidly diminishes with depth into the sediment layer. An increase in shear velocity at the sediment-water interface also enhances DO transfer. Shear velocity increases at the sediment-water interface will raise SOD regardless of the maximum oxidation rate if the hydraulic conductivity is above the threshold of k ≈ 1??cm/s. The relationship is nearly linear when U*<0.8??cm/s. At shear velocity U* = 1.6??cm/s, SOD for oxidation rates μ = 1000 and 2000??mg?l-1?d-1 are almost five times larger than those with no pore water flow. When pore water transport of DO is not limiting, SOD is a linear function of oxygen demand rate μ in the sediment when 0 ≤ μ ≤ 200??mg?l-1?d-1.     

One-Dimensional Modeling of Dam-Break Flow over Movable Beds

A one-dimensional model has been established to simulate the fluvial processes under dam-break flow over movable beds. The hydrodynamic model adopts the generalized shallow water equations, which consider the effects of sediment transport and bed change on the flow. The sediment model computes the nonequilibrium transport of bed load and suspended load. The effects of sediment concentration on sediment settling and entrainment are considered in determining the sediment settling velocity and transport capacity. In particular, a correction factor is proposed to modify the Van Rijn formulas of equilibrium bed-load transport rate and near-bed suspended-load concentration for the simulation of sediment transport under high-shear flow conditions. The governing equations are solved by an explicit finite-volume method with the first-order upwind scheme for intercell fluxes. The model has been tested in two experimental cases, with fairly good agreement between simulations and measurements. The sensitivities of the model results to parameters such as the sediment nonequilibrium adaptation length, Manning’s roughness coefficient and the proposed correction factor have been verified. The proposed model has also been compared to an existing model and the results indicate the new model is more reliable.