THE FLUCTUATING CHARACTERISTICS OF HYDRODYNAMIC FORCES ON BED PARTICLE

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Numerical simulation of incipient particle motion

A two-dimensional(2 D) computational model for simulation of incipient sediment motion for noncohesive uniform and non-uniform particles on a horizontal bed was developed using the Discrete Element Method(DEM).The model was calibrated and verified using various experimental data reported in the literature and compared with different theories of incipient particle motion.Sensitivity analysis was done and the effects of relevant parameters were determined.In addition to hydrodynamic forces such as drag,shear lift and Magnus force,the particle-particle interaction effects were included in the model.The asymptotic critical mobility number was evaluated for various critical particle Reynolds numbers(R*) in the range of very small and very large R*.The obtained curve is classified into four regions.It was found that in the linear region,the drag force has the principal role on the initiation of motion.Moreover,the critical mobility number is independent of particle diameter.A procedure for estimating the critical shear velocity directly from the information on particle diameter and roughness height was developed.Finally,the mechanism of incipient motion for the different regions was studied and the effect of different forces on the incipient particle motion was obtained.It was found that the maximum effects of lift and Magnus forces were,respectively,less than ten and twenty percent of the total force.The drag force,however,was typically the dominant force accounting for majority of the net hydrodynamic force acting on sediment particles at the onset of incipient motion.     

INCIPIENT MOTION OF COARSE PARTICLES IN HIGH GRADIENT RIVERS

1 INTRODUCTION To data, there are about 100 formulae for the incipient motion of sediment, among which, only about ten are convenient and practical. In 1936, using nondimensional drag force and the sediment’s Reynolds number, Shields (1936) presented the…     

On the influence of bed roughness on saltation in inertial regime

In extreme tidal environment, occurrences of saltating pebbles have been observed. The ambition to instal hydrokinetic turbines in such environment requires knowledge on the presence of pebbles in saltation in the water column because they can damage the structures. An experimental study is realized in a free-surface flume with no slope and different bed roughnesses as in marine environment. With fast camera the trajectories of hundreds of spherical particles are analysed. Our study deals with saltation in the inertial regime (i.e., large Stokes number) over fixed beds with various roughnesses. In inertial regime, the bed roughness has more influence on the collision process and the trajectory of the particles than for non-inertial motion where viscous forces play a key role. Jump height and length increase with bed roughness, with height increasing quicker than length leading to a more vertical trajectory for higher bed roughness. The vertical restitution coefficient is shown to increase with bed roughness leading to higher jumps. The initiation of the motion is shown to depend on the bed roughness as well. Power laws of the excess shear stress are proposed for jump height and length, taking into account the bed roughness. The dataset and analysis proposed in this study is a key ingredient for developing quantitative models for particle transport.     

A probabilistic model for sediment entrainment:The role of bed irregularity

A generalized probabilistic model is developed in this study to predict sediment entrainment under the incipient motion, rolling, and pickup modes. A novelty of the proposed model is that it incorporates in its formulation the probability density function of the bed shear stress, instead of the near-bed velocity fluctuations, to account for the effects of both flow turbulence and bed surface irregularity on sediment entrainment. The proposed model incorporates in its formulation the collective effects of three para-meters describing bed surface irregularity, namely the relative roughness, the volumetric fraction and relative position of sediment particles within the active layer. Another key feature of the model is that it provides a criterion for estimating the lift and drag coefficients jointly based on the recognition that lift and drag forces acting on sediment particles are interdependent and vary with particle protrusion and packing density. The model was validated using laboratory data of both fine and coarse sediment and was compared with previously published models. The study results show that all the examined models perform adequately for the fine sediment data, where the sediment particles have more uniform gra-dation and relative roughness is not a factor. The proposed model was particularly suited for the coarse sediment data, where the increased bed irregularity was captured by the new parameters introduced in the model formulation. As a result, the proposed model yielded smaller prediction errors and physically acceptable values for the lift coefficient compared to the other models in case of the coarse sediment data.     

FORCES ON PARTICLES AND THEIR EFFECTS ON VERTICAL SEDIMENT SORTING IN SOLID-LIQUID TWO-PHASE FLOWS

1 INNDUCTIONMes on prtcles are of significance to understand the motion of pwhcles in solid-liquid two-Phaseflows (Ni, et aI, l991). Early in l85l, Stokes (l85l) stUdied the simple harmonic linear motion of a singlesphere using a cylinder and a long flat plate. As a result, a simPle mathematical expression was given.Later on, Boussineaq (l885), Basset (1888), and Oseen (1927) stUdied the Iinear motion of a singIesphere that was accelotd in viscous fluid. It was fOund that the forces …     

Determining drag coefficients and their application in modelling of turbulent flow with submerged vegetation

Vegetation is a key aspect of water resources and ecology in natural rivers, floodplains and irrigation channels. The hydraulic resistance of the water flow is greatly changed when submerged vegetation is present. Three kinds of drag coefficients, i.e., the drag coefficient for an isolated cylinder, the bulk drag coefficient of an array of cylinders and the vertically distributed or local drag coefficient, have been commonly used as parameters to represent the vegetation drag force. In this paper, a comprehensive experimental study of submerged stems in an open channel flow is presented. Empirical formulae for the three drag coefficients were obtained based on our experimental results and on data from previous studies. A two-layer model was developed to solve the mean momentum equation, which was used to evaluate the vertical mean velocity profile with each of the drag coefficients. By comparing the velocity distribution model predictions and the measurement results, we found that the model with the drag coefficient for an isolated cylinder and the local drag coefficient was good fit. In addition, the model with the bulk drag coefficient gave much larger velocity values than measurements, but it could be improved by adding the bed friction effect and making choice of the depth-averaged velocity within the canopy layer.     

An improved formula for incipient sediment motion in vegetated open channel flows

Quantifying incipient sediment motion in vegetated open channel flow is pivotal for estimating bed load transport and the aquatic ecological environment in rivers.A new formula is developed to predict the critical flow velocity for incipient sediment motion in the presence of emergent vegetation,by incorporating the influence of vegetation drag that characterizes the effects of mean flow and turbulence on sediment movement.The proposed formula is shown to agree with existing experimental data.Mo...     

Experimental study of bed-load transport using particle motion tracking

A series of experiments were conducted in a flume to study bed-load transport.The motion of bed-load particles was captured by a series of images taken by a high-speed camera.A novelparticle motion tracking method was developed to automatically detect all the moving particles and calculate the instantaneous particle velocities.The instantaneous bed load transport rate was calculated based on particle velocity and the volume of moving particles.To verify this method,bed load transport rate based on the image processing technique was compared to the manually measured ones as well as data from other experiments.Results showed that the new technique made it possible to quantify the spatial and temporal variations of bed load transport rate at the individual particle scale.     

Sediment transport in high‐speed flows over a fixed bed: 1. Particle dynamics

Particle dynamics are investigated experimentally in supercritical high‐speed open channel flow over a fixed planar bed of low relative roughness height simulating flows in high‐gradient non‐alluvial mountain streams and hydraulic structures. Non‐dimensional equations were developed for transport mode, particle velocity, hop length and hop height accounting for a wide range of literature data encompassing sub‐ and supercritical flow conditions as well as planar and alluvial bed configurations. Particles were dominantly transported in saltation and particle trajectories on planar beds were rather flat and long compared with alluvial bed data due to (1) increased lift forces by spinning motion, (2) strongly downward directed secondary currents, and (3) a planar flume bed where variation in particle reflection and damping effects were minor. The analysis of particle saltation trajectories revealed that the rising and falling limbs were almost symmetrical contradicting alluvial bed data. Furthermore, no or negligible effect of particle size and shape on particle dynamics were found. Implications of experimental findings for mechanistic saltation‐abrasion models are briefly discussed. Copyright © 2017 John Wiley & Sons, Ltd.     

Representing the bed roughness of coarse‐grained streams in computational fluid dynamics

Computational fluid dynamics (CFD) applications are increasingly utilized for modelling complex flow patterns in natural streams and rivers. Although CFD has been successfully implemented to model many complex flow situations in natural stream settings, adequately characterizing the effects of gravel and cobble beds on flow hydraulics in CFD is a difficult challenge due to the scale of roughness lengths and the inadequacy of traditional roughness representations to characterize flow profiles in situations with large roughness elements. An alternative method of representing gravel and cobble beds is presented. Appropriate drag forces associated with different grain sizes are computed and included in the momentum equations to account for the influence of a hydraulically rough bed. Comparisons with field measurements reveal reasonable agreement between measured and modelled profiles of spatially averaged velocity and turbulent kinetic energy, and model fidelity to the non‐logarithmic behaviour of the velocity profiles. The novel method of representing coarse beds expands the utility of CFD for investigating physical processes in natural channels with large bed roughness. Copyright © 2005 John Wiley & Sons, Ltd.     

Flume experiments on wood entrainment in rivers

A flume experiment on entrainment of woody debris is carried out. Woody debris is modeled using smooth, cylindrical dowels, in touch with the flume bed. The water depth and velocity are evaluated that initiate the motion of the partially submerged dowels. On the basis of the experimental finding, a theoretical model of log entrainment is developed, providing in dimensionless form the equilibrium equation for incipient motion. The experiment shows that the equilibrium equation must keep into account the modification of the local water profile, affecting the force balance at incipient motion. This issue has been apparently neglected in the wood entrainment models so far developed. The entrainment model is less sensitive to the choice of the apparent drag coefficient. The capability of the model in predicting the critical log diameter for initiation of motion is discussed and compared with that from the recent entrainment model from Braudrick and Grant, 2000. The comparison shows interesting results and provide evidence of the needs for further studies on wood entrainment in rivers.     

Modeling depth-averaged velocity and bed shear stress in compound channels with emergent and submerged vegetation

This paper presents an approach to modeling the depth-averaged velocity and bed shear stress in compound channels with emergent and submerged vegetation. The depth-averaged equation of vegetated compound channel flow is given by considering the drag force and the blockage effect of vegetation, based on the Shiono and Knight method (1991) [40]. The analytical solution to the transverse variation of depth-averaged velocity is presented, including the effects of bed friction, lateral momentum transfer, secondary flows and drag force due to vegetation. The model is then applied to compound channels with completely vegetated floodplains and with one-line vegetation along the floodplain edge. The modeled results agree well with the available experimental data, indicating that the proposed model is capable of accurately predicting the lateral distributions of depth-averaged velocity and bed shear stress in vegetated compound channels with secondary flows. The secondary flow parameter and dimensionless eddy viscosity are also discussed and analyzed. The study shows that the sign of the secondary flow parameter is determined by the rotational direction of secondary current cells and its value is dependent on the flow depth. In the application of the model, ignoring the secondary flow leads to a large computational error, especially in the non-vegetated main channel.     

Parameterization of near-bed processes under collinear wave and current flows from a two-phase sheet flow model

Sediment transport models require appropriate representation of near-bed processes. We aim here to explore the parameterizations of bed shear stress, bed load transport rate and near-bed sediment erosion rate under the sheet flow regime. To that end, we employ a one-dimensional two-phase sheet flow model which is able to resolve the intrawave boundary layer and sediment dynamics at a length scale on the order of the sediment grain. We have conducted 79 numerical simulations to cover a range of collinear wave and current conditions and sediment diameters in the range 210–460 μm$\mathrm{\mu }\mathrm{m}$. The numerical results confirm that the intrawave bed shear stress leads the free stream velocity, and we assess an explicit expression relating the phase lead to the maximum velocity, wave period and bed roughness. The numerical sheet flow model is also used to provide estimates for the bed load transport rate and to inspect the near-bed sediment erosion. A common bed load transport rate formulation and two typical reference concentration approaches are assessed. A dependence of the bed load transport rate on the sediment grain diameter is observed and parameterized. Finally, the intrawave near-bed vertical sediment flux is further investigated and related to the time derivative of the bed shear stress.     

纵波质点的运动与界面的反射

在原有波动学的基础上,通过对波传播质点的运动和作用进行研究,提出了波传播的力学作用不仅有因形变产生的应力,还存在着另一种由速度决定的不同形式的力——“动作用力”.动作用力才是波传播的根本动力.由“动作用力"和形变应力确立波的动力学方程,由这个方程,又可确定质点的运动规律.质点在波传播中一般并不作弹性振动,质点沿一个方向运动进行能量传递后,只作微弱的回复运动.质点这种运动特点才符合能量守恒.质点这种运动特点决定不同的界面性状有不同形态的反射波.     

Evaluation of the saltation process of bed materials by video imaging under altered bed roughness

The purpose of this paper is to examine the nature of particle saltation and movement over the beds of fixed roughness from flume experiments. A series of experiments are carried out to study the saltation of individual sand particles of different sizes over rough beds under different flow conditions. A 3‐D acoustic Doppler velocimeter is used to record the fluid velocity components; subsequently, under different flow conditions, the images of released sand particles are recorded using high‐speed video imaging technique. Systematic analysis is made with regard to the forces acting on the grains and the variation of their magnitudes along the saltation trajectories of the grains. Relations between the saltation parameters, flow intensity and bed roughness are developed. The distributions of the angle of orientations during a single saltation follows almost a Gaussian distribution. The shape of the Gaussian distribution depends on the particle size and bed roughness. Particle collisions with rough beds and the resulting coefficients of restitution are also discussed. A theoretical framework is developed to compute the mean particle velocity considering the spin in the energy balance equation. Results of the detailed analysis using the imaging technique are much better than in previously reported studies. Copyright © 2013 John Wiley & Sons, Ltd.     

Aeolian sediment flux decay: Non-linear behaviour on developing deflation lag surfaces

Wind tunnel simulations of the effect of non-erodible roughness elements on sediment transport show that the flux ratio q/q_s, shear velocity U*, and roughness density λ are co-dependent variables. Initially, the sediment flux is enhanced by kinetic energy retention in relatively elastic collisions that occur at the roughness element surfaces, but at the same time, the rising surface coverage of the immobile elements reduces the probability of grain ejection. A zone of strong shearing stress develops within 0·03 to 0·04 m of the rough bed because of a relative straightening of velocity profiles which are normally convex with saltation drag. This positive influence on fluid entrainment is opposed by declining shear stress partitioned to the sand bed. Similarly, because the free stream velocity U_f is fixed while U_* increases, velocity at height z and particle momentum gain from the airstream decline, leading eventually to lower numbers of particles ejected on average at each impact. When the ratio of the element basal area to frontal area σ is approximately equal to 3·5, secondary flow effects appear to become significant, so that the dimensionless aerodynamic roughness parameter Z₀/h and shear stress on the exposed sand bed T_s decrease. It is at this point that grain supply to the airstream and saltation drag appear to be significantly reduced, thereby intensifying the reduction in U_*. The zone of strong fluid shear near the bed dissipates.     

Effects of vegetation on flow and sediment transport: comparative analyses and validation of predicting models

The presence of vegetation modifies flow and sediment transport in alluvial channels and hence the morphological evolution of river systems. Plants increase the local roughness, modify flow patterns and provide additional drag, decreasing the bed‐shear stress and enhancing local sediment deposition. For this, it is important to take into account the presence of vegetation in morphodynamic modelling. Models describing the effects of vegetation on water flow and sediment transport already exist, but comparative analyses and validations on extensive datasets are still lacking. In order to provide practical information for modelling purposes, we analysed the performance of a large number of models on flow resistance, vegetation drag, vertical velocity profiles and bed‐shear stresses in vegetated channels. Their assessments and applicability ranges are derived by comparing their predictions with measured values from a large dataset for different types of submerged and emergent vegetation gathered from the literature. The work includes assessing the performance of the sediment transport capacity formulae of Engelund and Hansen and van Rijn in the case of vegetated beds, as well as the value of the drag coefficient to be used for different types of vegetation and hydraulic conditions. The results provide a unique comparative overview of existing models for the assessment of the effects of vegetation on morphodynamics, highlighting their performances and applicability ranges. Copyright © 2014 John Wiley & Sons, Ltd.     

Estimating depth‐averaged velocities in rough ­channels

Profiles of streamwise velocity obtained from North Boulder Creek, Colorado, typically are non‐logarithmic in form and exhibit the strong influence of form drag associated with coarse bed roughness. The spatially averaged profile is consistent with recent theoretical profile forms suggested for rough channels that are based on a partitioning of the total stress between a fluid part and a part associated with form drag on bed particles. Estimates of local depth‐averaged velocity using algorithms that are based on several measurements in the flow column improve with explicit Riemann averaging, versus simple averaging, of the measurements. Estimates based on a single‐point measurement at 0·6 of the flow depth, assuming a logarithmic or approximately logarithmic velocity profile, are the least reliable. Copyright © 2000 John Wiley & Sons, Ltd.