Simplified Model of Tractive-Force Distribution in Closed Conduits

A simplified model for the computation of boundary shear stress distributions acting on the flow perimeter of closed ducts is presented. The model assumes that the surplus energy within any control volume in a three-dimensional flow will be transferred towards the nearest boundary to be dissipated. Based on this model, the flow cross sectional area in the closed duct is divided into subflow regions corresponding to the side walls and bed, and the shear distributions over the wetted perimeter within each subflow area are assessed. Analytical equations, valid for all channel aspect ratios, for the prediction of local and mean shear stresses along the bed and side walls in smooth rectangular duct flow are derived. The formulae give good predictions of the shear stress distributions when compared with existing experimental data in the literature. The possible applications of the model to nonrectangular duct flows are also discussed.     

Numerical Modeling of Three-Dimensional Flow Field Around Circular Piers

A three-dimensional numerical model FLUENT is used to simulate the separated turbulent flow around vertical circular piers in clear water. Computations are performed using different turbulence models and results are compared with several sets of experimental data available in the literature. Despite commonly perceived weakness of the k-ε model in resolving three-dimensional (3D) open channel and geophysical flows, several variants of this turbulence model are found to have performed satisfactorily in reproducing the measured velocity profiles. However, model results obtained using the k-ε models show some discrepancy with the measured bed shear stress. The Reynolds stress model performed quite well in simulating velocity distribution on flat bed and scour hole as well as shear stress distribution on flat bed around circular piers. The study demonstrates that a robust 3D hydrodynamic model can effectively supplement experimental studies in understanding the complex flow field and the scour initiation process around piers of various size, shape, and dimension.     

Modeling Depth-Averaged Velocity and Boundary Shear in Trapezoidal Channels with Secondary Flows

The Shiono and Knight method (SKM) offers a new approach to calculating the lateral distributions of depth-averaged velocity and boundary shear stress for flows in straight prismatic channels. It accounts for bed shear, lateral shear, and secondary flow effects via 3 coefficients—f,λ, and Γ—thus incorporating some key 3D flow feature into a lateral distribution model for streamwise motion. The SKM incorporates the effects of secondary flows by specifying an appropriate value for the Γ parameter depending on the sense of direction of the secondary flows, commensurate with the derivative of the term Hρ(UV)d. The values of the transverse velocities, V, have been shown to be consistent with observation. A wide range of boundary shear stress data for trapezoidal channels from different sources has been used to validate the model. The accuracy of the predictions is good, despite the simplicity of the model, although some calibration problems remain. The SKM thus offers an alternative methodology to the more traditional computational fluid dynamics (CFD) approach, giving velocities and boundary shear stress for practical problems, but at much less computational effort than CFD.     

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.     

Distribution of Bed Shear Stress in Rotating Circular Flume

Distributions of bed shear stress across the width of a rotating circular flume with smooth and rough bed surfaces were obtained by measurement and model prediction. Results with flows over smooth beds showed that the flow in the central part may be considered to be two-dimensional and that effects of flow depth over the operating range of the flume are minor for flow depths not exceeding 0.14 m. For rough beds, the bed shear stress distributions were found to be skewed toward the inner wall. This can be corrected if a compensating roughness is added to the bottom of the ring. Such measures are also effective for flumes with smooth beds. Measured bed shear stress distributions agreed well with the predicted distributions for smooth beds and reasonably well for rough beds. The modified Preston tube, for measurement of bed shear stress in flows over rough beds, was found to give promising results. Further tests are required to completely define the uncertainty in bed shear stress measurements made with this instrument.     

Reynolds Stress and Bed Shear in Nonuniform Unsteady Open-Channel Flow

Expressions for the Reynolds stress and bed shear stress are developed for nonuniform unsteady flow in open channels with streamwise sloping beds, assuming universal (logarithmic) velocity distribution law and using the Reynolds and continuity equations of two-dimensional open-channel flow. The computed Reynolds stress distributions are in agreement with experimental data.     

Flow Field at a Vertical-Wall Abutment

Experiments were conducted to measure the three-dimensional turbulent flow field, using the acoustic Doppler velocimeter, at a short vertical-wall abutment (ratio of abutment length to approach flow depth less than unity) before and after the development of a scour hole under a clear water scour condition. In the upstream, the presentation of flow field through vectors at vertical sections shows a primary vortex associated with the downflow. In the downstream, the upward flow is comprised of with irregularities owing to the vortex shedding. The flow separation near the bed and within the scour hole is evident from the turbulent kinetic energy distribution. Using Reynolds stresses, the bed shear stresses are calculated.     

Flow Heterogeneity over 3D Cluster Microform: Laboratory and Numerical Investigation

The present study examines the flow around a self-occurring cluster bed form and the use of general computation fluid dynamics methods for hydraulic and geophysical flow applications. This is accomplished through a comprehensive experimental/numerical investigation. In the laboratory, cluster bed forms are first formed from movable sediment, and laser Doppler velocimeter measurements of two-dimensional fluid velocity are then taken around a formed cluster. A three-dimensional (3D) Reynolds averaged Navier-Stokes simulation of the physical cluster and flow conditions is then conducted using near-wall, shear stress transport (SST) turbulence modeling with the inclusion of hydraulic roughness, ks (R = 31,150, ks/h = 0.1, ks+ = 274, i.e., in the fully rough regime). SST near-wall modeling is advantageous compared to the more widely used wall functions approach for flows with significant roughness and flow separation because the model equations can be integrated down to the wall. Therefore, SST near-wall modeling makes no a priori assumption that the law of the wall is valid throughout the wall region of the flow. Additionally, it has the ability to intrinsically handle boundary roughness through the boundary condition for turbulent specific dissipation at the wall, allowing for wall functions to be bypassed in accounting for roughness effects. The study shows that in the wall region surrounding the cluster, flow is 3D and quite complex, with different scales of embedded flow structures dominating the cluster wake and leading to flow heterogeneities in pressure and bed-shear stress. Results also indicate that near-wall modeling with SST compared favorably with the experimental flow data without tuning of model constants.     

Numerical Modeling of Abutment Scour with the Focus on the Incipient Motion on Sloping Beds

A three-dimensional computational fluid dynamics model is applied to predict local scour around an abutment in a rectangular laboratory flume. When modeling local scour, steep bed slopes up to the angle of repose occur. To predict the depth and the shape of the local scour correctly, the reduction of the critical shear stress due to the sloping bed must be taken into account. The focus of this study is to investigate different formulas for the threshold of noncohesive sediment motion on sloping beds. Some formulas only take the transversal angle (perpendicular to the flow direction) into account, but others also consider the longitudinal angle (streamwise direction). The numerical model solves the transient Reynolds-averaged Navier-Stokes equations in all three dimensions to compute the water flow. Sediment continuity in combination with an empirical formula is used to capture the bed load transport and the resulting bed changes. When the sloping bed exceeds the angle of repose, the bed slope is corrected with a sand-slide algorithm. The results from the numerical simulations are compared with data from physical experiments. The reduction of the bed shear stress on the sloping bed improves the results of the numerical simulation distinctly. The best results are obtained with the formulas that use both the transversal and the longitudinal angle for the reduction of the critical bed shear stress.     

Turbulence Characteristics in Gradual Channel Transition

A field study was conducted to determine the effects of a channel transition on turbulence characteristics. Detailed three-dimensional (3D) flow measurements were collected at a cross section that is located downstream of a gradual channel expansion. These measurements were obtained via an acoustic doppler velocimeter and include the 3D velocity field, the mean local velocities, the turbulent intensities, the frictional characteristics of the flow, the secondary velocity along the transverse plane, and the instantaneous shear stress components in the streamwise and transverse directions. Analysis of the 3D flow data indicates that the turbulent flow on the outer bank of the channel is anisotropic. Such anisotropy of turbulence, which is attributed to the gradual expansion in the channel and bed roughness, yields the development of a secondary flow of Prandtl’s second kind as reported in 1952. In particular, it was found that turbulent intensities in the vertical and transverse directions on the outer bank section are different in magnitude creating turbulence anisotropy in the cross-sectional plane and secondary flows of the second kind. Turbulent intensities increase toward the free surface indicating the transfer of a higher-momentum flux from the channel bed to the free surface, which contradicts common wisdom. Results for the normalized stress components in the streamwise and transverse direction show similar behavior to the intensities. Moreover, the nonlinear distribution of stresses is indicative of the oscillatory nature of the flow induced by the secondary flows of Prandtl’s second kind. A similar behavior was found for flows in straight rectangular channels over different roughness. Finally, a comparison between the secondary current velocity with the mainstream velocity indicates that secondary flow of Prandtl’s second kind is present within the right half of the measured cross section.     

Turbulent Flow over a Channel with Fluid-Saturated Porous Bed

The characteristics of fully developed turbulent flow in a hybrid domain channel, which consists of a clear fluid region and a porous bed, are examined numerically using a model based on the macroscopic Reynolds-averaged Navier–Stokes equations. By adopting the classical continuity interface conditions, the present model treats the hybrid domain problem with a single domain approach, and the simulated results are noted to coincide with the existing experimental data and microscopic data. The effects of porosity ? and Darcy number Da on the flow properties over and inside the porous bed are further investigated in the selected ranges of 0.6 ? ? ? 0.8, and 1.6×10?4 ? Da ? 1.6×10?2. It has been demonstrated that the presence of the porous bed causes the significant reduction of the flow velocities inside the clear fluid region relative to that of a smooth impermeable bed, and also reduces the magnitude of the integral constant B of the velocity logarithmic distributions from its traditional value 5.25. Moreover, turbulent shear stress within the upper part of the porous bed increases significantly with the porosity ? and Darcy number Da. The thickness of turbulence penetration remains proportional to the values of porosity ? and Darcy number Da.     

Validation of a Three-Dimensional Numerical Code in the Simulation of Pseudo-Natural Meandering Flows

Validation of a three-dimensional finite volume code solving the Navier–Stokes equations with the standard k-ε turbulence model is conducted using a high quality and high spatial resolution data set. The data set was collected from a large-scale meandering channel with a self-formed fixed bed, and comprises detailed bed profiling and laser Doppler anemometer velocity measurements. Comparisons of the computed primary and secondary velocities are made with those observed and it is found that the lateral momentum transfer is generally under predicted. At the apices this results in the predicted position of the primary velocity maximum having a bias towards the channel center, compared to the position where it has been measured. Using a simplified two zone roughness distribution whereby a separate roughness height was prescribed for the channel center and channel sides relative to a single distributed roughness height, generally led to a slightly improved longitudinal velocity distribution; the higher velocities were located nearer to the outside of the bend. Improving both the free surface calculation and scheme for discretization of the convection terms led to no appreciable difference in the computed velocity distributions. A more detailed study involving turbulence measurements and bed form height distribution should discriminate whether using distributed roughness height is a precursor to using an anisotropic turbulence representation for the accurate prediction of three-dimensional river flows.     

Measured and Simulated Flow near a Submerged Spur Dike

To improve knowledge of the flow and scour processes associated with spur dikes, three-dimensional flow velocities were measured at 2,592 points using an acoustic Doppler velocimeter over a fixed flat bed with a trapezoidal shaped submerged spur dike in a laboratory flume. General velocity distribution and detailed near field flow structures were revealed by the measurements and numerical simulations performed using a free surface turbulent flow model with a k–ε closure scheme. The three-dimensional flow separation characterized in this study was found to yield forces on the bed that were significantly different from nonsubmerged vertical obstructions that have been measured in other studies. Values of bed shear stress derived from both measured and simulated values were similar but indicated that local scour would be initiated in one rather than in the two locations of initial local scour measured in previous experiments with a similar flow.     

Numerical Investigation into Secondary Currents and Wall Shear in Trapezoidal Channels

This paper presents the use of computational fluid dynamics (CFD) to determine the distribution of the bed and sidewall shear stresses in trapezoidal channels. The impact of the variation of the slant angle of the side walls, aspect ratio, and composite roughness on the shear stress distribution is analyzed. The shear stress data can be directly output from the CFD models at the boundaries, but they can also be derived using the Guo and Julien equations for the average bed and side wall shear stresses. These equations compute the shear stress as a function of three components; gravitational, secondary flows, and interfacial shear stress, and are hence used to gauge the respective merits of the different components of wall shear. The results show a significant contribution from the secondary currents and internal shear stresses on the overall shear stress at the boundaries. This work also extends previous work of the authors on rectangular channels.     

Vertical Dispersion of Fine and Coarse Sediments in Turbulent Open-Channel Flows

Through using a kinetic model for particles in turbulent solid–liquid flows, underlying mechanisms of sediment vertical dispersion as well as sediment diffusion coefficient are investigated. Four hydrodynamic mechanisms, namely gravitational settling, turbulent diffusion, effect of lift force, and that of sediment stress gradient, coexist in two-dimensional (2D) uniform and steady open-channel flows. The sediment diffusion coefficient consists of two independent components: one accounts for the advective transport of sediment probability density distribution function due to sediment velocity fluctuations, and the other results from sediment–eddy interactions. Predictions of the kinetic model are in good agreement with experimental data of 2D open-channel flows. In such flows, it is shown that: (1) the parameter γ (i.e., the inverse of the turbulent Schmidt number) may be greater than unity and increases toward the bed, being close to unity for fine sediments and considerably large for coarse ones; (2) effects of lift force and sediment stress gradient become significant and need to be considered below the 0.1 flow depth; and (3) large errors may arise from the traditional advection–diffusion equation when it is applied to flows with coarse sediments and/or high concentrations.     

Analytic Stage-Discharge Formulas for Flow in Straight Prismatic Channels

Three analytic stage-discharge formulas, suitable for hand calculation, have been derived for prismatic open channels. The three types of prismatic geometry investigated are: simple rectangular, symmetric, and asymmetric rectangular compound channels. The formulas include three key parameters that govern the local friction factor, eddy viscosity, and secondary flow. The discharge results and the corresponding analytic depth-averaged velocity and bed shear stress distributions show good agreement with the experimental data, even when constant parameter values are assumed. The influence of these three parameters on the stage-discharge relationships is explored.     

Effect of Applying Different Distribution Shapes for Velocities and Pressure on Simulation of Curved Open Channels

Most of the computational models of curved open channel flows use the conventional depth averaged De St. Venant equations. De St. Venant equations assume uniform velocity and hydrostatic pressure distributions. They are thus applicable only to cases of meandering rivers and curved open channels where vertical details are not of importance. The two-dimensional vertically averaged and moment equations model, developed by the writers, is used to study the effect of applying different distribution shapes for velocities and pressure on the simulation of curved open channels. Linear and quadratic distribution shapes are proposed for the horizontal velocity components, while a quadratic distribution shape is considered for the vertical velocity. Linear hydrostatic and quadratic nonhydrostatic distribution shapes are proposed for the pressure. The proposed model is applied to problems involved in curved open channels with different degrees of curvature. The implicit Petrov–Galerkin finite element scheme is applied in this study. Computed values for depth averaged longitudinal and transverse velocities across the channel width and vertical profiles of longitudinal and transverse velocities are compared to the observed experimental data. A fairly good agreement is attained. Predictions of overall flow characteristics suggest that the results are not very sensitive to different approximations of the preassumed applied velocity and pressure distribution shapes.     

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.     

Shear Stress in Smooth Rectangular Open-Channel Flows

The average bed and sidewall shear stresses in smooth rectangular open-channel flows are determined after solving the continuity and momentum equations. The analysis shows that the shear stresses are function of three components: (1) gravitational; (2) secondary flows; and (3) interfacial shear stress. An analytical solution in terms of series expansion is obtained for the case of constant eddy viscosity without secondary currents. In comparison with laboratory measurements, it slightly overestimates the average bed shear stress measurements but underestimates the average sidewall shear stress by 17% when the width–depth ratio becomes large. A second approximation is formulated after introducing two empirical correction factors. The second approximation agrees very well (R2>0.99 and average relative error less than 6%) with experimental measurements over a wide range of width–depth ratios.