Errors in the Bed Shear Stress as Estimated from Vertical Velocity Profile

In this study, errors in determining bed shear stress caused by errors in theoretical bed surface data or roughness size selection using one-point velocity, two-point velocity, or a group of velocity measurements within the log-velocity region are systematically and quantitatively analyzed. The smaller the roughness element, the smaller the error in the bed shear stress estimate. For a fixed roughness size and absolute error in selecting the theoretical bed data, the closer to the bed the velocity measurement is taken, the larger the error in the friction velocity estimate. The velocity profile near the bed is very sensitive to the selection of the theoretical bed surface data. The velocity profile near the bed will deviate significantly from the true log profile if the theoretical bed surface data is over- or underestimated by 5?mm or more. This study shows conclusively that using the upper measurement data points, instead of the near-bed measurement, in the regression analysis yields better roughness size and bed shear stress estimates.     

Wall Shear Stress in Transient Turbulent Pipe Flow by Local Velocity Measurement

The modeling of unsteady wall shear stress plays a crucial role in the analysis of fast transients in pressurized pipe systems, since it allows to evaluate transient energy dissipation properly. The main aim of this paper is to give a contribution to the understanding of transient pressurized flow dynamics in turbulent regime by measuring not only pressure but also the instantaneous axial velocity profile at two sections of the laboratory pipe. Specifically, by means of ultrasonic Doppler velocimetry—a completely nonintrusive technique—instantaneous velocity gradients at pipe wall are measured allowing to evaluate the time history of the actual wall shear stress by coupling velocity measurements to a two-zone stress model. As a result, the behavior of accelerating and decelerating flows with respect to the corresponding steady ones, i.e., with the same value of the discharge, is pointed out. Due to the characteristics of the laboratory pipe—a 352-m long high density polyethylene pipe—transients phenomena are investigated both at short and long time scales.     

Shear Stress Distribution in Partially Filled Pipes

Boundary shear stresses have been calculated for circular pipes with a flat sediment bed using computational fluid dynamics (CFD). First of all, CFD simulations were carried out for rectangular channels in order to check the software package for its ability to reproduce experimental (literature) results. The influence of the applied turbulence model (isotropic or anisotropic) was also studied for rectangular channels. The simulations for circular pipes, using an isotropic turbulence model, were done for different filling ratios, mean flow velocities, and roughness heights. For validation, the numerical results were compared with former experimental work. With the help of the detailed shear stress distribution, sediment transport can be calculated more accurately than using the global shear stress, as is traditionally done. This method was applied to a simple flume experiment, subjected to a triangular inflow hydrograph, and the comparison with the traditional approach was made.     

Critical Shear Stress of Bimodal Sediment in Sand-Gravel Rivers

A new model for the critical shear stress and the transport of graded sediment is presented. The model is based on the size distribution of the bed surface and can be used to compute sediment transport rates in numerical simulations with an active layer model. This model makes a distinction between unimodal and bimodal sediments. It is assumed that all size fractions of unimodal sediments have the same critical shear stress while there is selective transport for the gravel fractions of bimodal sediments. A recently published laboratory transport data set is used to calibrate our model.     

Critical Bed Shear Stress for Unisize Sediment

The overall, spatially averaged, mean magnitude of local, spatially averaged (over a small area enclosing the particles’ projected area), instantaneous, critical Shields shear-stress parameters required for incipient motion of uniform-sized sand grains, independent of the bed shear-velocity particle Reynolds number, equal to 0.16, is obtained from calibration of a theory for bed load sediment transport, by minimizing the sum of the squares of the deviations between theoretical and experimental bed load rates. Additionally, optimized expressions for a proposed probability density distribution of the bed shear stresses, for its standard deviation, for finite, maximum, and minimum bed shear stresses, and a bed load rate are obtained. In terms of the mean fluid shear stress, a dimensionless, critical, shear-stress parameter equal to 0.0513 is obtained. Investigation of the probability density distribution of the spatially varying, critical shear stresses would allow a more accurate formulation for the case of low transport rates.     

Incipient Motion of Riverbank Sediments with Outflow Seepage

Based on a force analysis, an expression is derived to describe the critical Shields number for incipient motion of uniform cohesionless sediment particles on a riverbank slope in terms of flow parameters, outflow seepage, and physical and mechanical properties of sediments. Parametric studies were conducted to investigate quantitatively the effects of hydraulic gradient of seepage, slope angle, and flow direction on the critical Shields number. The results show that the critical Shields number decreases with an increase in the hydraulic gradient. Where bank collapse is concerned, the most dangerous direction of hydraulic gradient of outflow seepage is at an angle equal to the effective internal angle of friction of the sediment mass with respect to slope surface. At a certain value of hydraulic gradient, the critical Shields number decreases with increasing slope angle. Open flow becomes more erosive when the current direction changes from horizontally parallel with the riverbank line to turning downward.     

Depth-Averaged Shear Stress and Velocity in Open-Channel Flows

Turbulent momentum and velocity always have the greatest gradient along wall-normal direction in straight channel flows; this has led to the hypothesis that surplus energy within any control volume in a three-dimensional flow will be transferred toward its nearest boundary to dissipate. Starting from this, the boundary shear stress, the Reynolds shear stress, and the velocity profiles along normal lines of smooth boundary may be determined. This paper is a continuous effort to investigate depth-average shear stress and velocity in rough channels. Equations of the depth-averaged shear stress in typical open channels have been derived based on a theoretical relation between the depth-averaged shear stress and boundary shear stress. Equation of depth mean velocity in a rough channel is also obtained and the effects of water surface (or dip phenomenon) and roughness are included. Experimental data available in the literature have been used for verification that shows that the model reasonably agrees with the measured data.     

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.     

Viscous Flow Past a Porous Spherical Shell—Effect of Stress Jump Boundary Condition

Using the stress jump boundary condition for the tangential stresses at the porous liquid interface along with the continuity of the velocity components and normal stress, the uniform viscous flow past a porous spherical shell with external radius r1, internal radius r2 is studied. The flow inside the porous region is governed by Brinkman equation. The flow in the liquid region is governed by the Stokes equation. The flow field is computed by matching the boundary conditions at the porous-fluid interface. The effect of stress jump coefficient β on the flow field is very much felt. An increase in the drag with permeability is found for different R, different ratio of r1/r2, and also a change in magnitude of the drag for different values of stress jump coefficient β is observed. Also, the variation of torque and shear stress with permeability and the stress jump coefficient is discussed.     

Measuring Velocity and Shear Stress over Dunes with Acoustic Doppler Profiler

This study evaluates the use of an acoustic Doppler profiler (ADP) for measurement of velocity profiles over dunes in an estuary. The ADP can be deployed from a moving launch and provides three-dimensional velocity profiles that can be used to describe flow structure and to provide rough estimates of shear stress. Quadratic stress models are recommended for shear stress because they estimate skin friction and form stress whereas the law of the wall only reliably estimates total stress over dunes. The most serious limitation of the ADP is a beam geometry that results in a large sampling diameter close to the bed that does not adequately measure velocity in dune troughs.     

Probability Density Function of Instantaneous Drag Forces and Shear Stresses on a Bed

A probability density function (PDF) of the instantaneous bed shear stress in a turbulent flow is derived in this paper. It is argued that the shape of the PDF is similar to the PDF of the instantaneous drag forces on bed roughness elements. The influence of the near-bed relative turbulence intensity is included in the PDF. The shape of the distribution compares well with our measurements of the instantaneous drag force on a protruding bed element for a range of turbulence intensities. However, deviations are apparent at high turbulence intensities. The PDF also compares well with measurements of shear stresses on a smooth wall.     

Fluid-Particle Interactions and Resuspension in Simple Shear Flow

The lattice Boltzmann method (LBM) is used to simulate the particle resuspension process in a two-dimensional simple shear flow. At first, the lift force on a single disk-shaped particle attached at the channel wall is computed. It is found that when the particle is allowed to freely move in the viscous fluid, the resulting lift force is smaller than that when the particle is constrained to be stationary. The bulk properties of fluids with particles suspended under various concentrations are numerically calculated. The results agree reasonably well with analytical results by Batchelor when the volume fraction is lower than 50%. The resuspension process of a group of particles (up to 500) is simulated at different particle-to-fluid density ratios. It is found that the height and shape of particle bed depend on the particle density ratio and flow conditions. Interactions of groups of particles as well as the final shape of the bedform of the particles were studied during this resuspension process. Finally, the pressure distribution and flow above the bedform of particles was examined. The results obtained agree well with those observed in naturally occurring bedforms of sediments.     

Bed Shear Stress Boundary Condition for Storage Tank Sedimentation

Computational fluid dynamics-based (CFD) software tools enable engineers to simulate flow patterns and sediment transport in ancillary structures of sewer systems. Lagrangian particle tracking represents a computationally efficient technique for modeling sediment transport. In order to represent the process of sedimentation in storage tanks, careful consideration must be given to the boundary condition at the bottom of the tanks. None of the boundary conditions currently available in the FLUENT CFD software appears to represent the observed behavior of sediment particles, which may become resuspended after first contact with the bed if the local flow velocity is sufficiently high. In this study, a boundary condition based on bed shear stress has been implemented in FLUENT and evaluated against laboratory data. A particle is trapped if the local bed shear stress is below the critical bed shear stress; otherwise, the particle is resuspended. The approach gives satisfactory agreement with measured sedimentation efficiency data, and the simulated spatial distribution is very similar to the sediment distribution observed in a laboratory tank.     

Fall Cone Test to Characterize Shear Strength of Organic Sediments

In this paper, the results of the standard percussion cup test, the penetration cone test, and the laboratory vane test performed on organic sediments and kaolin are discussed. First, the relationship between the water content and the cone penetration depth is explored. Second, the relationship between the shear strength, using the laboratory vane apparatus, and the water content is investigated. Finally, the relationship between the shear strength and the penetration depth of the cone, at different levels of water content, is explored.     

Rapid Increase in Suspended Load at High Bed Shear

When the dimensionless shear stress θ exceeds 0.8 a plane shear layer develops on the top of a granular bed. This layer is stabilized by the mixture density gradient within it. Its thickness typically increases linearly with θ, and so does the ratio of the effective roughness size to particle diameter, ks/d. If the ratio of shear velocity U* to particle fall velocity Vf is sufficiently large, the shear layer may be destabilized, giving a rapid increase in turbulent suspension. New closed-conduit experiments with 0.11?mm sand show that for U*/Vf>6.5 the ratio ks/d has a pronounced increase above the typical shear-layer trend, and so does the suspended-load concentration (measured at the mid-height between the stationary bed and the top of the flow). These observations differ significantly from the sediment pick-up function in common use, indicating that the latter must be reconsidered. The present experiments also show a tie-in with hyperconcentrated flow as observed in the rivers of Northern China.     

宝钢宽厚板试样剪液压回路及剪切缸剪切能力分析计算

介绍宝钢宽厚板试样剪的主要技术参数、构成及工作原理;着重对主剪切缸液压回路特点进行了分析,对主剪切缸剪切能力进行了详细校核。本文对厚板厂类似的压平机设备的维护及改造也有指导意义。     

Fluctuations of Turbulent Bed Shear Stress

With the assumption that the bed shear stress fluctuates in a lognormal fashion, the probability density function (PDF) of the standardized bed shear stress is derived as a function of the relative shear stress intensity. The PDF is more skewed with larger relative intensities, but approaches a Gaussian function when the relative intensity is small. The computed PDF agrees well with the reported experimental data for flows over a smooth boundary. The higher-order moments of the bed shear stress, skewness, and kurtosis, are shown analytically to be also dependent on the relative intensity. The theoretical dependencies are then compared to a number of measurements available in the literature. The Reynolds number effect on the relative intensity is also discussed.     

Numerical Model for Sediment Transport and Bed Degradation in the Yangtze River Channel Downstream of Three Gorges Reservoir

This paper presents a two-dimensional morphological model for unsteady flow and both suspended-load and bed-load transport of multiple grain size to simulate transport of graded sediments downstream from the Three Gorges Reservoir. The model system includes a hydrodynamic module and a sediment module. The hydrodynamic module is based on the depth-averaged shallow water equations in orthogonal curvilinear coordinates. The sediment module describing nonuniform sediment transport is developed to include nonequilibrium transport processes, bed deformation, and bed material sorting. The model was calibrated using field observations through application to a 63-km-long alluvial river channel on the middle Yangtze River in China. A total of 16 size groups and a loose layer method of three sublayers were considered for the transport of the nonuniform bed materials in a long-term simulation. Predictions are compared with preliminary results of field observations and factors affecting the reliability of the simulated results are discussed. The results may be helpful to the development of more accurate simulation models in the future.     

Evaluation of Unsteady Wall Shear Stress by Zielke’s Method

The method used in the classical paper by Zielke to estimate the unsteady component of shear stress in unsteady pipe flows is revisited. It is found that the method is undesirably sensitive to the size of the integration time step. The sensitivity is shown to be caused dominantly by the first term in the integration when inadequate allowance is made for the infinite value of the weighting function. A simple method of avoiding the error without requiring the use of small grid sizes is presented.     

Effects of Lifting Force on Bed Topography and Bed-Surface Sediment Size in Channel Bend

In bed-load sediment transport, the lifting force plays an important role in reducing the friction between sediment particles and the bed surface, and it makes particle transportation by the shear force easier. Because the lifting force is related to vorticity, a three-dimensional (3D) numerical model incorporating large eddy simulations was applied to simulate the vorticity field in a channel bend. The results show that the distribution of vorticity is highly nonuniform, and it can lead to significant variations in lifting force and bed-load sediment transport per unit width in a channel bend. Relevant theories are modified on the basis of physical reasoning and then incorporated into numerical models to investigate the lifting-force effects on the bed topography and bed-surface sediment size gradation in a channel bend. With the lifting-force effects considered, it is shown that the errors in simulated bed topography can be reduced by approximately 40% and in bed-surface sediment size by 50%.