On the numerical analysis of bed-load transport of saltating grains

The focus of this paper is on the analysis of the influence of particles’ velocity distribution and their concentration on the sediment transport rate in bed-load from the Lagrangian perspective.Such aims are addressed by use of the relevant Lagrangian model of spherical saltating particles in which turbulence plays a significant role.The Monte Carlo approach is employed in the simulations to obtain the velocity and concentration of the saltating particles.Numerical simulations using two saltating particle models:(1) with;and(2) without particle-particle collisions are carried out.Based on the numerical results,we address the hypothesis that instead of averaged characteristics,the distributions of particles’ velocity and sediment concentration should be taken into account in the calculation of sediment transport rate.Moreover,our results also show that the interaction between particles during their collisions is the key for better understanding of the physics of sediment transport.All results are compared with well-known experimental formulae i.e.Meyer-Peter and Muller and Fernandez Luque and van Beek.     

On the mechanisms of the saltating motion of bedload

Saltation of sediment particles is an important pattern of bedload transport.Based on force analysis for sediment particles,a Lagrangian model was proposed for the saltating motion of bedload in river flows,which was then solved with numerical method.Simulation results on the saltating trajectories neglecting particle rotation and turbulence effects compare fairly well with experimental observations.The mean values of the saltation parameters (saltation height,length and velocity) also agree well with the previous experimental data.Based on the numerical results,regression equations for the dimensionless saltation height,length and velocity were presented.Using the numerically achieved characteristics of the sediment saltation,we also obtained mathematical expression for the sediment transport rate.The studies in this paper are significant for its contribution to mechanism of the bedload motion and the computation of sediment transport rate.     

Particle velocity and concentration profiles in bedload experiments on a steep slope

Depth profiles of particle streamwise velocity, concentration and bedload sediment transport rate were measured in a turbulent and supercritical water flow. One‐size 6 mm diameter spherical glass beads were transported at equilibrium in a two‐dimensional 10% steep channel with a mobile bed. Flows were filmed from the side by a high‐speed camera. Particle tracking algorithms made it possible to determine the position, velocity and trajectory of a very large number of particles. Approximately half of the sediment transport rate was composed by rolling grains, and the other half by saltation. This revealed a complex structure, with several concentration and flux peaks due to rolling, and one peak due to saltation. With an increase of the sediment transport rate, the depth structure remained the same at the water/granular interface, with peak value increases but with no shift in elevations. The saltation region expanded towards higher elevations with an increase of the particle velocity commensurate to the water velocity. The proportion of the sediment transport rate in saltation did not vary significantly. The particle streamwise velocity profiles exhibited three segments: an exponential decay in the bed, a linear increase where rolling and saltation co‐existed, and above this, a logarithmic‐like shape due to saltating particles. These results are comparable to profiles measured and modelled in dry granular free surface flows and in more intense bedload such as sheet flows. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

Issues in Eulerian–Lagrangian modeling of sediment transport under saltation regime

The saltation regime is very important for understanding the sediment transport mechanism. However,there is no consensus on a model for the saltation regime. This study answers several questions raised with respect to the Eulerian-Lagrangian modeling of sediment transport. The first question is why the previous saltation models that use different combinations of hydrodynamic forces yielded acceptable results? The second question is which shear lift model(i.e. a shear lift expression and its coefficient) is more appropriate? Another important question is which hydrodynamic forces have greater contributions to the saltation characteristics of a sediment particle? The last question is what are the contributions of the turbulence fluctuations as well as effects of using two-and three-dimensional(2 D and 3 D) models on the simulation results? In order to fairly answer these questions, a systematic study was done by considering different scenarios. The current study is the first attempt to clearly discuss these issues. A comprehensive 3 D saltation model for non-cohesive sediment was developed that includes all the hydrodynamic forces acting on the particle. The random nature of sediment transport was included using turbulent flow and bed-particle collision models. The eddy interaction model was applied to generate a3 D turbulent flow field. Bed-particle collisions were considered using the concept of a contact zone and a corresponding contact point. The validation of the model was done using the available experimental data for a wide range of sediment size(0.03 to 4.8 cm). For the first question, the results indicated that some of the hydrodynamic effects show opposing trends and some have negligible effects. With these opposing effects it is possible to adjust the coefficients of different models to achieve acceptable agreement with the same experimental data while omitting some aspects of the physics of the process. A suitable model for the shear lift force was developed by linking the lift coefficient to the drag coefficient and the contributions of the hydrodynamic forces and turbulence fluctuations as well as the consequences of using of 2 D and 3 D models were studied. The results indicate that the shear lift force and turbulent flow fluctuations are important factors for the saltation of both sand and gravel, and they cannot be ignored.     

3D Lagrangian modelling of saltating particles diffusion in turbulent water flow

A 3D Lagrangian model of the saltation of solid spherical particles on the bed of an open channel flow, accounting for turbulence-induced mechanisms, is proposed and employed as the key tool of the study. The differences between conventional 2D models and a proposed 3D saltation model are discussed and the advantages of the 3D model are highlighted. Particularly, the 3D model includes a special procedure allowing generation of 3D flow velocity fields. This procedure is based on the assumption that the spectra of streamwise, vertical and transverse velocity components are known at any distance from the bed. The 3D model was used to identify and quantify effects of turbulence on particle entrainment and saltation. The analysis of particle trajectories focused on their diffusive nature, clarifying: (i) the effect of particle mobility parameter; (ii) the effect of bed topography; and (iii) the effect of turbulence. Specifically, the results of numerical simulations describing the abovementioned effects on the change in time of the variance are presented. In addition, the change in time of the skewness and kurtosis, which are likely to reflect the turbulence influence on the spread of particles, are also shown. Two different diffusion regimes (local and intermediate) for each of the investigated flow conditions are confidently identified.     

Particle transport mechanics and induced seismic noise in steep flume experiments with accelerometer-embedded tracers

Recent advances in fluvial seismology have provided solid observational and theoretical evidence that near-river seismic ground motion may be used to monitor and quantify coarse sediment transport. However, inversions of sediment transport rates from seismic observations have not been fully tested against independent measurements, and thus have unknown but potentially large uncertainties. In the present study, we provide the first robust test of existing theory by conducting dedicated sediment transport experiments in a flume laboratory under fully turbulent and rough flow conditions. We monitor grain-scale physics with the use of ‘smart rocks’ that consist of accelerometers embedded into manufactured rocks, and we quantitatively link bedload mechanics and seismic observations under various prescribed flow and sediment transport conditions. From our grain-scale observations, we find that bedload grain hop times are widely distributed, with impacts being on average much more frequent than predicted by existing saltation models. Impact velocities are observed to be a linear function of average downstream cobble velocities, and both velocities show a bed-slope dependency that is not represented in existing saltation models. Incorporating these effects in an improved bedload-induced seismic noise model allows sediment flux to be inverted from seismic noise within a factor of two uncertainty. This result holds over nearly two orders of magnitude of prescribed sediment fluxes with different sediment sizes and channel-bed slopes, and particle–particle collisions observed at the highest investigated rates are found to have negligible effect on the generated seismic power. These results support the applicability of the seismic-inversion framework to mountain rivers, although further experiments remain to be conducted at sediment transport near transport capacity. © 2018 John Wiley & Sons, Ltd.     

Three-dimensional saltating processes of multiple sediment particles

The purpose of this study was to investigate the interacting mechanism between the saltating particles near a channel bed. A three-dimensional real-time flow visualization technique was developed to measure the interparticle collision behaviors during the saltating process. Based on the experimental data, the distribution of the collision points was found to be symmetric. This confirms the assumption that the projections of the collision points onto the reasonable plane are uniformly distributed. A three-dimensional saltating model was also developed. This model produced satisfactory results. The model is able to simulate the continuous saltating trajectories of several particles. The simulated dimensionless saltating height, longitudinal and vertical saltation velocity components were found to increase as the dimensionless particle diameter and the dimensionless flow transport capacity parameter increase, while the simulated lateral saltation velocity component varies inversely with the dimensionless flow transport capacity parameter. A regression equation for the bed load transport rate was also obtained.     

Effect of sediment particles on the velocity profile of sediment-water mixtures in open-channel flow

The presence of sediment particles in open-channel flow has an important effect on turbulence; thus, an empirical, turbulent eddy viscosity formula was established for application in the limit for low concentrations. The current study establishes a theoretical relation for the mixture viscosity based on the two-phase mixture model. The percentage contribution of the three mechanisms of mixture viscosity,namely, fluid turbulence(FT), particle turbulence(PT), and inter-particle collisions(IPCs), w...     

Significance of particle interaction to the modelling of cohesive sediment transport in rivers

Aggregation processes of fine sediments have rarely been integrated in numerical simulations of cohesive sediment transport in riverine systems. These processes, however, can significantly alter the hydrodynamic characteristics of suspended particulate matter (SPM), modifying the particle settling velocity, which is one of the most important parameters in modelling suspended sediment dynamics. The present paper presents data from field measurements and an approach to integrate particle aggregation in a hydrodynamic sediment transport model. The aggregation term used represents the interaction of multiple sediment classes (fractions) with corresponding multiple deposition behaviour. The k–ε–turbulence model was used to calculate the coefficient of vertical turbulent mixing needed for the two‐dimensional vertical‐plane simulations. The model has been applied to transport and deposition of tracer particles and natural SPM in a lake‐outlet lowland river (Spree River, Germany). The results of simulations were evaluated by comparison with field data obtained for two levels of river discharge. Experimental data for both discharge levels showed that under the prevailing uniform hydraulic conditions along the river reach, the settling velocity distribution did not change significantly downstream, whereas the amount of SPM declined. It was also shown that higher flow velocities (higher fluid shear) resulted in higher proportions of fast settling SPM fractions. We conclude that in accordance with the respective prevailing turbulence structures, typical aggregation mechanisms occur that continuously generate similar distribution patterns, including particles that settle toward the river bed and thus mainly contribute to the observed decline in the total SPM concentration. In order to determine time‐scales of aggregation and related mass fluxes between the settling velocity fractions, results of model simulations were fitted to experimental data for total SPM concentration and of settling velocity frequency distributions. The comparison with simulations for the case of non‐interacting fractions clearly demonstrated the practical significance of particle interaction for a more realistic modelling of cohesive sediment and contaminant transport. Copyright © 2004 John Wiley & Sons, Ltd.     

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.     

Scouring of a granular bed by dam break: Experimental study and numerical simulation by a VOF-LPT coupling

The first part of the research reported here consists of an experimental campaign to study the scouring of a granular bed(glass beads, sand) induced by a dam break in an open channel. Two configurations are considered: with and without cylinders. In the second part of this study, the volume of fluid method coupled with the shear stress transport turbulent model and the lagrangian particle tracking method is used to simulate the local scour processes. The four-way coupling is realized by consider...     

A Bed-load function based on kinetic theory

Bed-load transport plays a fundamental role in morphological processes of natural rivers and human-made channels.This paper presents bed-load function derived on the basis of kinetic theory. The bed-load function is obtained by integrating the pick-up rate of bed sediment with respect to its longitudinal travel distance,following the basic concept on bed-load put forward by Einstein.The pick-up rate is expressed as an upwards flux of bed sediment and determined by invoking the particle velocity distribution function derived by solving the Boltzmann equation of kinetic theory. Comparisons of the present formula with six other bed-load formulas and the experimental data are also made in this paper.The results show that the present bed-load formula agrees well with the experimental data.In addition,the influences due to collision between particles on bed-load is discussed which shows that an appreciable damping of the intensities of bed-load is observed only when the shear acting on particles is large enough to increase the concentration and intensity of random motion of bed load particles so that the collisions between sediment particles can occur.     

Raindrop‐induced saltation and the enrichment of sediment discharged from sheet and interrill erosion areas

Sheet and interrill erosion areas are sources of soil material rich in nutrients and pollutants. The loss of soil, nutrients and other chemicals from these areas is a matter of concern both in terms of maintaining soil productivity and the health of offsite environments. Many experiments on rainfall erosion have shown enrichment of fine material, nutrients and other chemicals in the sediment discharged for sheet and interrill erosion areas, but often these results were obtained over short periods of time. A qualitative mechanistic model of raindrop‐induced saltation is used to illustrate how this transport mechanism influences the composition of sediment discharged by rain‐impacted flow. Initially, fast moving particles are enriched in the sediment discharge but, over time, during a rainfall event, slower moving particles become more represented. Raindrop‐induced saltation promotes the storage of material on the soil surface with a coarser composition than the original soil. Winnowing of material from this storage by the development of flow‐driven saltation during high‐intensity events can modify the composition of the sediment discharged later by raindrop‐induced saltation. Given stable soil particles, the composition of the sediment discharged at the steady state is the same as the original soil. Enrichment is a non‐steady‐state phenomenon and failure to recognize the transient nature of enrichment may lead to inappropriate interpretation of the implications of the results from short‐term experiments. Copyright © 2011 John Wiley & Sons, Ltd.     

Hindered settling with an apparent particle diameter concept

In this work a new expression has been developed to predict the settling velocity of a sediment particle which is dispersed in a sediment-fluid mixture during a turbulent flow. A concept of apparent particle diameter has been introduced and is defined by the diameter of the spherical volume in which the particle can move randomly after collision with other particles in suspension. The effect of suspension concentration is studied on the mass density of the sediment-fluid mixture. It has been shown that the settling velocity of sediment particle in a sediment-fluid mixture is a function of different characteristics of the sediment particle such as settling velocity in clear fluid, suspension concentration, relative mass density and Reynolds number. The model has shown good agreement when compared with previously published experimental data and it’s prediction accuracy is superior than the other existing models.     

Incompressible SPH scour model for movable bed dam break flows

In this study an incompressible smoothed particle hydrodynamics (ISPH) approach coupled with the sediment erosion model is developed to investigate the sediment bed scour and grain movement under the dam break flows. Two-phase formulations are used in the ISPH numerical algorithms to examine the free surface and bed evolution profiles, in which the entrained sediments are treated as a different fluid component as compared with the water. The sediment bed erosion model is based on the concept of pick-up flow velocity and the sediment is initiated when the local flow velocity exceeds a critical value. The proposed model is used to reproduce the sediment erosion and follow-on entrainment process under an instantaneous dam break flow and the results are compared with those from the weakly compressible moving particle semi-implicit (WCMPS) method as well as the experimental data. It has been demonstrated that the two-phase ISPH model performed well with the experimental data. The study shows that the ISPH modelling approach can accurately predict the dynamic sediment scouring process without the need to use empirical sediment transport formulas.     

Distribution characteristics of inertial sediment particles in the turbulent boundary layer of an open channel flow determined using Vorono? analysis

This paper presents the numerical investigation of the distribution of inertial sediment particles in the turbulent boundary layer of an open channel flow with the particle Stokes number ranging from 0.6 to 20.4. The methodology is a combination of three numerical approaches, i.e. direct numerical simulation of turbulent flow, the point-particle immersed boundary method, and the discrete particle method. By applying the Vorono? analysis, the preferential concentration characteristics of sediment particles were investigated quantitatively. It was found that the normalized area of the Vorono? cells follows a log-normal particle distribution. The inertial sediment particles distributed unevenly in the turbulent boundary layer and the unevenness, governed by the particle Stokes number, was more significant as the particle Stokes number approaches unity. The inertial sediment particles in the turbulent boundary layer accumulated preferentially in streamwise-aligned streaky structures and this pattern was less significant with increasing particle Stokes number.     

Distribution characteristics of inertial sediment particles in the turbulent boundary layer of an open channel flow determined using Voronoi analysis

This paper presents the numerical investigation of the distribution of inertial sediment particles in the turbulent boundary layer of an open channel flow with the particle Stokes number ranging from 0.6 to 20.4. The methodology is a combination of three numerical approaches, i.e. direct numerical simulation of turbulent flow, the point-particle immersed boundary method, and the discrete particle method. By applying the Vorono analysis, the preferential concentration characteristics of sediment particles were investigated quantitatively. It was found that the normalized area of the Voronoi cells follows a lognormal particle distribution. The inertial sediment particles distributed unevenly in the turbulent boundary layer and the unevenness, governed by the particle Stokes number, was more significant as the particle Stokes number approaches unity. The inertial sediment particles in the turbulent boundary layer accumulated preferentially in streamwise-aligned streaky structures and this pattern was less significant with increasing particle Stokes number.     

Changes in the saltation flux following a step‐change in macro‐roughness

The effect of a step change in macro‐roughness on the saltation process under sediment supply limited conditions was examined in the atmospheric boundary layer. For an array of roughness elements of roughness density λ = 0.045 (λ = total element frontal area/total surface area of the array) the horizontal saltation flux was reduced by 90% (±7%) at a distance of ≈150 roughness element heights into the array. This matches the value predicted using an empirical design model and provides confidence that it can be effectively used to engineer roughness arrays to meet sand flux reduction targets. Measurements of the saltation flux characteristics in the vertical dimension, including: saltation layer decay (e‐folding) height and particle size, revealed that with increasing distance into the array, the rate of mass flux change with increasing height decreased notably, and (geometric) mean particle diameter decreased. The distribution of the saltation mass flux in the vertical remains exponential in form with increasing distance into the roughness array, and the e‐folding height increases as well as increasing at a greater rate as particle diameter diminishes. The increase in e‐folding height suggests the height of saltating particles is increasing along with their mean speed. This apparent increase in mean speed is likely due to the preferential removal, or sequestration, of the slower moving particles across the size spectrum, as they travel through the roughness array. Copyright © 2018 John Wiley & Sons, Ltd.