Equilibrium Near-Bed Concentration of Suspended Sediment

A new approach is presented for calculating the equilibrium near-bed concentration of suspended sediment in an alluvial channel flow. It is formulated from the balance between bed sediment entrainment and suspended sediment deposition across the near-bed boundary. The entrainment flux is determined making use of a turbulent bursting outer-scale-based function and the flux of deposition by the product of near-bed concentration and hindered settling velocity of sediment. A number of flume data records in the literature are analyzed to calibrate and verify the present approach. The observed near-bed concentrations for the data records are obtained by first isolating the suspended load transport rate from the observed total load transport rate using Engelund and Fredsoe's bed-load formula and then equating the suspended load transport rate to the shape integration of Dyer and Soulsby. The present approach is shown to perform satisfactorily compared to the results of data analysis. It is found that the near-bed concentration is evidently dependent on sediment particle size in addition to the Shields parameter due to skin friction. This finding seems to challenge previous relationships that simply represent the near-bed concentration as empirical functions of the purely skin-friction-related Shields parameter.     

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.     

Near-Bed Turbulence Characteristics at the Entrainment Threshold of Sediment Beds

This experimental study is devoted to quantification of the near-bed turbulence characteristics at an entrainment threshold of noncohesive sediments. Near the bed, the departure in the distributions of the observed time-averaged streamwise velocity from the logarithmic law is more for immobile beds than for entrainment-threshold beds. In the Reynolds shear stress distributions, a damping that occurs near the bed for sediment entrainment is higher than that for immobile beds. Quadrant analysis reveals that in the near-bed flow zone, ejections and sweeps on immobile beds cancel each other, giving rise to the outward interactions, whereas sweeps are the dominant mechanism toward sediment entrainment. The bursting duration for entrainment-threshold beds is smaller than that for immobile beds. On the other hand, the bursting frequency for entrainment-threshold beds is larger than that for immobile beds. The third-order correlations indicate that during sediment entrainment, a streamwise acceleration associated with a downward flux and advection of streamwise Reynolds normal stress is prevalent. The streamwise and the downward vertical fluxes of turbulent kinetic energy (TKE) increase with sediment entrainment. The TKE budget proves that for sediment entrainment, the pressure energy diffusion changes drastically to a negative magnitude, indicating a gain in turbulence production.     

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.     

Numerical Investigation of the Role of Turbulent Bursting in Sediment Entrainment

In this work we incorporate a Gram–Charlier-type joint probability distribution of near-bed two-dimensional instantaneous velocities into a simple mechanistic model to investigate the role of turbulent bursting in sediment entrainment. The results reveal that under typical values of bed-shear stress (>3?Pa), the time fractions of Quadrants 1–4 (Q1–Q4) remain constantly as 16, 34, 19, and 31%, respectively. Entrainment of the fine sediment mixtures is dominated by the lifting mode, whereas entrainment of the coarse ones is dominated by rolling. Sweeps (Q4) are consistently the most significant contributor to entrainment under various types of sediment mixtures. As the standard deviation of grain-size distribution increases, the hiding effect exerted on the finer grains of the mixture is reduced, leading to the elevated correction factors for effective hydrodynamic forces, and thus the reduced threshold velocities for entrainment. The reduced thresholds would, in turn, enhance the fractional contributions of ejections and inward interactions (Q2 and Q3), which are associated with negative longitudinal velocity fluctuations, such that the fractional contribution of outward interactions (Q1) would become less significant.     

Stochastic Incipient Motion Criterion for Spheres under Various Bed Packing Conditions

Incipient motion criteria based solely on time-averaged bed shear stress may underpredict sediment transport. The focus of this study is on the stochastic aspect of the problem of incipient motion. Specifically, the role of near-bed turbulent structures and bed packing density on the commencement of sediment motion is investigated. The cornerstone of the proposed model is based on the concept that the particle motion is governed by the intermittent nature of near-bed turbulence. Based on this mechanism, in this article we provide a quantitative model for predicting the commencement of sediment entrainment for the first time under three representative bed packing densities corresponding to the isolated, wake interference, and skimming flow regimes. The performance of the proposed model is compared to published experimental data and the “conventional” approach that is based on the consideration that flow parameters are statistically well represented by a normal distribution.     

Two-Phase Analysis of Vertical Sediment-Laden Jets

In this study, we investigated a vertical dilute sediment-laden jet both experimentally and theoretically. First, an instantaneous whole-field velocimetry tool, particle image velocimetry, was applied to measure the sediment and fluid mean and fluctuating velocities of a downward sediment-laden jet at the same time. Subsequently, an analysis was performed based on two-phase conservation equations for both downward and upward jets. The analysis shows that the mean sediment velocity can be taken as the sum of fluid velocity and the settling velocity in both cases. For the downward jets, the decay rate of the centerline sediment concentration increases with the sediment settling velocity while decreases with the initial discharge velocity. The zone of flow establishment for the sediment velocity is found to be longer than that of the fluid. For the upward jets, the maximum rise of the sediment particles and their deposition distribution on the ground were derived theoretically. The predicted results compare well to the experimental data in the literature.     

Entrainment Probabilities of Mixed-Size Sediment Incorporating Near-Bed Coherent Flow Structures

In this work we incorporate the effect of near-bed coherent flow structures into the entrainment of randomly configured mixed-size sediments. The fourth-order Gram–Charlier type probability density function (GC pdf) of near-bed streamwise velocity is employed to account for the higher-order correlations associated with turbulent bursting. A compilation of the published data over a wide range of bed roughness is used to analyze the near-bed coherent flow structures, including the second-, third-, and fourth-order moments of velocity fluctuation (i.e., turbulence intensity, skewness, and flatness factors) required in the fourth-order GC pdf. An important result of this study is a set of quantitative relations used to predict these higher-order moments as a function of the roughness Reynolds number. The random grain protrusion is parameterized with the exposure and friction heights, and an existing probabilistic approach is used to correct the hiding effect of mixed-size sediment. The above factors are all incorporated into the formulation of entrainment (rolling and lifting) probabilities. As compared to the previous normal and lognormal models, the present results demonstrate significantly improved agreement with the observed data for the unisize and mixed-size sediments under partial- and full-transport conditions. The results also reveal that the third-order GC pdf can be used to approximate the fourth-order one for the fully rough beds, however, for smooth beds the fourth-order GC pdf should be used to adequately incorporate the effects of higher-order correlations. This paper offers some new insights into the processes of sediment entrainment.     

Equivalent Roughness Height for Plane Bed under Steady Flow

This paper presents a new relationship between the roughness height and the main hydrodynamic and sediment parameters for plane beds under steady current conditions. In order to derive such a formula, a large data base involving plane-bed experiments was compiled from previous investigations and analyzed. Comparisons between the data and different existing predictive formulas for the bed roughness obtained from the literature were also made. A relationship with the Shields parameter only, which is commonly proposed, appeared to be insufficient. The roughness was also found to be a function of a Froude number and a dimensionless settling velocity. A critical Shields parameter was identified up to which the equivalent roughness ratio is proportional to the Shields parameter. The new empirical equation that was developed yields the best results for all conditions investigated, and should improve the understanding of the total shear stress.     

Experimental and Field Studies of Type I Settling for Particulate Matter Transported by Urban Runoff

Settling velocity is an important constitutive parameter of particulate matter (PM) transported by runoff. Settling velocity is either explicitly or implicitly utilized when designing or modeling unit operations, and in situ or watershed controls for urban rainfall-runoff. Utilizing two common settling devices, a settling column and an Imhoff cone, settling velocities of discrete noncolloidal particles in source area urban rainfall-runoff were measured. A comparison of settling models applicable to discrete (Type I) PM settling was developed. Models were compared to measured results across the noncohesive silt- and sand-size PM gradation from 2 to 2,000?μm, utilizing measured particle-size distributions (PSDs) and specific gravity. Results indicate that Newton’s Law can reproduce measured settling velocity when measured inputs of PM diameter, specific gravity, and temperature are utilized. Alternative models to Newton’s Law (in the Stokesian regime) did not improve agreement with measured settling velocities determined using PSDs from laser diffraction. Settling velocity distributions using Newton’s Law were applied for two limiting classes of storm events loading a screened hydrodynamic separator (HS) at an urban watershed. Results indicate that for a low flow and high flow event, Newton’s Law and a simple ideal overflow model of the HS could reproduce PM separation and the PSD of eluted PM (2 to ～ 250?μm) within 17% of measured results on a gravimetric basis.     

Rate of Deposition of Fine Sediment from Suspension

Standard depth-integrated models of sediment dynamics predict that concentrations of suspended fine sediment should decay at a characteristic rate that is controlled by the particle settling velocity and the depth of the water. In contrast, a model which resolves the processes of settling and dispersion in the water column has suggested that this decay rate should be independent of the settling velocity, and is controlled by dispersive processes in the water column. By revisiting the problem of sediment dispersion and settling following a point release of material, we resolve this discrepancy and confirm that depth-integrated models capture the correct physical behavior.     

Critical Flow Velocity in Slurry Transporting Horizontal Pipelines

A new empirical equation is proposed for predicting critical flow velocity in slurry-transporting horizontal pipelines. An analysis of the settling velocity of solid particles, including the effect of solid particle concentration, is undertaken because of this parameter's importance. This study builds on a previous study carried out to consider the settling velocity of a single solid particle in clear-water condition, which is actually different from the real physics of the hydrotransport phenomenon of the solid particles. Two earlier proposed methods are applied to the calculation of the settling velocity of a solid particle, including the effect of solid particle concentration within the suspending fluid. The most appropriate method for slurry transportation among these two methods is discussed and used in the analysis of critical flow velocity. The new proposed equation is based on analysis of data from the experiments as well as data from the earlier studies. A unique feature of the proposed equation is that it can be applied to noncohesive, uniform, and nonuniform coarse solid particles. In a comparison of prediction accuracy with four existing relationships, the proposed equation was found to give significantly better agreements with the observed data. Therefore, it can be stated that the new equation can safely be used by designers in the problems of slurry transportation.     

Clear-Water Scour at Abutments in Thinly Armored Beds

Experiments on local scour at short abutments (ratio of abutment length to approaching flow depth less than unity), namely vertical-wall, 45° wing-wall, and semicircular, embedded in a bed of relatively fine noncohesive sediment overlain by a thin armor-layer of coarser sediment, were conducted for different flow conditions, thickness of armor-layers, armor-layer, and bed sediments. The abutments were aligned with the approaching flow in a rectangular channel. The armor-layer and the bed underneath it were composed of different combinations of uniform sediments. In the experiments, the approaching flow velocities were restricted to the clear-water scour condition with respect to the armor-layer particles. Depending on the approaching flow conditions, three cases of scour at abutments in armored beds were identified. Effects of different parameters pertaining to scour at abutments are examined. The comparison of the experimental data shows that the scour depth at an abutment with an armor-layer in clear-water scour condition under limiting stability of the surface particles (approaching flow velocity nearly equaling critical velocity for the threshold motion of surface particles) is always greater than that without armor-layer for the same bed sediments. The characteristic parameters affecting the maximum equilibrium nondimensional scour depth (scour depth-abutment length ratio), identified based on the physical reasoning and dimensional analysis, are excess abutment Froude number, flow depth-abutment length ratio, armor-layer thickness-armor particle diameter ratio, and armor particle-bed sediment diameter ratio. The experimental data of clear-water scour condition in thinly armored beds under limiting stability of surface particles were used to determine the equation of maximum equilibrium scour depth through regression analysis. The estimated scour depths were in agreement with the experimental scour depths. Also, an equation of maximum equilibrium scour depth in uniform sediments was obtained.     

Stochastic Prediction of Sediment Transport in Sand-Gravel Bed Rivers

Classical deterministic bedload transport predictors are applied to sand-gravel bed rivers. The turbulent bed shear stress is modeled according to a probability distribution to obtain realistic bedload transport rates at incipient motion. In extending the predictors to stochastic predictors for nonuniform sediment, many parameters that represent near-bed turbulence and the particle size distribution must be chosen. The parameters that give realistic results are chosen by analyzing the results of a new experimental flume dataset with relatively large water depths. Choosing other combinations of parameters may give equal total bedload transport rates, but at the cost of large errors in fractional transport rates. Attention is given to the hiding-exposure phenomenon and a hindrance effect related to nonuniform sediment. Validation based on two independent field datasets shows that successful predictions of particle sizes near the threshold for motion are feasible using the stochastic approach, while the deterministic approach gives successful predictions well above incipient motion.     

Sediment Threshold under Stream Flow on Horizontal and Sloping Beds

A model is presented to determine the threshold shear stress for noncohesive sediment (uniform and nonuniform) motion on horizontal and stream-wise sloping sedimentary beds, under a unidirectional steady-uniform streamflow. Hydrodynamic and particle-mechanic forces on a solitary sediment particle, resting over a sedimentary bed under the slip-spinning condition, are analyzed including the effect of turbulent fluctuations. Hydrodynamic forces such as drag, shear lift, and Magnus lift are taken into consideration. The drag coefficient is determined using an empirical formula. The inclusion of Magnus lift is significant because spherical particles spin just before dislodging downstream from their original position due to the differential hydrodynamic force along the vertical. The experimental data of sediment threshold are used to calibrate the model making the lift coefficient as a free parameter. The dependency of normalized threshold shear stress on particle parameter for various angles of repose and stream-wise bed slopes is presented graphically. The results obtained using the present model are compared with the curves proposed by different investigators and the experimental data of sediment (uniform and nonuniform) threshold for horizontal and stream-wise sloping beds.     

Velocity and Concentration Fields in Uniform Flow with Coarse Sands

The vertical distributions of velocity and concentration for an open-channel flow mixed with coarse sands are investigated by using a mathematical model, taking account of the momentum transfer by the turbulent motion and the sediment mass balance by the diffusion and settling in a two-dimensional steady-state condition. An attempt is made here to obtain the horizontal time-mean velocity component and the sediment concentration quantitatively at a certain depth. An examination of measured velocity profiles plotted on semilogarithmic paper leads to the conclusion that the general characteristic of the flow is greatly affected by the increasing sediment load. The vertical distribution of the time-mean velocity is calculated by following the velocity gradient equation previously proposed. The concentration field is divided into the outer region and the inner region, since in each region the fall velocity varies according to the grain Reynolds number. For computing the concentration of suspended sediment, therefore, the writer proposes two formulas derived from Fick's diffusion equation. The theoretical results obtained by the velocity and concentration equations are found to be in good agreement with a set of experimental data, for the mean diameters of the sands ranged from 940 to 1,300 μm.     

Characteristics of Velocity and Excess Density Profiles of Saline Underflows and Turbidity Currents Flowing over a Mobile Bed

Turbidity currents in the ocean and lakes are driven by suspended sediment. The vertical profiles of velocity and excess density are shaped by the interaction between the current and the bed as well as between the current and the ambient water above. We present results of a set of 74 experiments that focus on the characteristics of velocity and fractional excess density profiles of saline density and turbidity currents flowing over a mobile bed. The gravity flows include saline density flows, hybrid saline/turbidity currents and a pure turbidity current. The use of dissolved salt is a surrogate for suspended mud that is so fine that it does not settle out readily. Thus, all the currents can be considered to be model turbidity currents. The data cover both Froude-subcritical and Froude-supercritical regimes. Depending on flow conditions, the bed remains flat or bed forms develop over time, which in turn affect vertical profiles. For plane bed experiments, subcritical flow profiles have velocity peaks located higher up in the flow, and display a sharper interface at the top of the current, than their supercritical counterparts. The latter have excess density profiles that decline exponentially upward from the bed, whereas subcritical flows show profiles with a region near the bed where excess density varies little. Wherever bed forms are present, they have a significant effect on the profiles. Especially for Froude-supercritical flow, bed forms push the location of peak velocity upward, and render the near-bed fractional excess density more uniform. In the case of subcritical flow, bed forms do not significantly affect fractional excess density profiles; velocity profiles are pushed farther upward from the bed than in the case of a plane bed, but to a lesser extent than for supercritical bed forms. Overall, the relative position of the velocity peak above the bed shows a dependence upon flow regime, being lowered for increasing Froude number Fd. Gradient Richardson numbers Rig in the near-bed region increase with increasing Fd, but are lower than the critical value of 0.25, indicating that near-bed turbulent structures are not notably suppressed. At the top interface, values of Rig are above the critical value for subcritical and mildly supercritical Fd, effectively damping turbulence. However as Fd increases, Rig goes below the critical value. Shape factors calculated from the profiles for use in the depth-averaged equation of motion are evaluated for different flow and bed conditions. Normalized experimental profiles for supercritical currents scale up well with observations of field-scale turbidity currents in the Monterey Canyon, and the range of average bed slopes and Froude numbers also compare favorably with estimated field-scale flow conditions for the Amazon canyon and fan. This suggests that the experimental results can be used to interpret the kinds of flows that are responsible for the shaping of major submarine canyon-fan systems.     

Two-Dimensional Numerical Simulation of Primary Settling Tanks by Hybrid Finite Analytic Method

In order to investigate the turbulent flow and mass transfer in primary settling tanks, numerical simulations are conducted by using a modified k?ε two-layer model based Boussinesq’s approximation to model the Reynolds stress in primary settling tanks, and solving the governing equations using a hybrid finite analytic method (HFAM). The simulation results obtained using the mathematical model are compared with the experimental data and simulation results available in the literature, and the results of comparison indicate that the profiles of the primary velocity field are in line with the experimental results and the flow-through curve obtained using the mathematical model are in good agreement with the curves based on experimental data. It is therefore concluded that the HFAM approach can be used to simulate the turbulent flow and mass transfer in a primary settling tank, and the modified k?ε two-layer model can be used to establish the velocity field distribution at the bottom of a primary settling tank.     

Unified View of Sediment Transport by Currents and Waves. II: Suspended Transport

The problem of suspended sediment transport in river and coastal flows is addressed. High-quality field data of river and coastal flows have been selected and clustered into four particle size classes (60–100, 100–200, 200–400, and 400–600?μm). The suspended sand transport is found to be strongly dependent on particle size and on current velocity. The suspended sand transport in the coastal zone is found to be strongly dependent on the relative wave height (Hs/h), particularly for current velocities in the range 0.2–0.5?m/s. The time-averaged (over the wave period) advection–diffusion equation is applied to compute the time-averaged sand concentration profile for combined current and wave conditions. Flocculation, hindered settling, and stratification effects are included by fairly simple expressions. The bed-shear stress is based on a new bed roughness predictor. The reference concentration function has been recalibrated using laboratory and field data for combined steady and oscillatory flow. The computed transport rates show reasonably good agreement (within a factor of 2) with measured values for velocities in the range of 0.6–1.8?m/s and sediments in the range of 60–600?μm. The proposed method underpredicts in the low-velocity range (<0.6?m/s). A new simplified transport formula is presented, which can be used to obtain a quick estimate of suspended transport. The modeling of wash load transport in river flow based on the energy concept of Bagnold shows that an extremely large amount of very fine sediment (clay and very fine silt) can be transported by the flow.     

Turbulent Effects on the Settling Velocity of Suspended Sediment

The mean settling velocities of suspended sediments in turbulence have been examined. The settling velocities in a flume are directly measured by using an acoustic Doppler velocimeter. The results indicate the same trend as previous work in homogeneous isotropic turbulence. In addition to the flume experiment, the numerical experiments were conducted in the velocity field of homogeneous isotropic turbulence simulated by Kraichnan’s technique. The experimental and numerical results show that at high turbulence intensity the relative settling velocity increases with the increasing relative turbulence intensity regardless of the Stokes number. At intermediate turbulence intensity, it seems that the settling data bifurcate, i.e., the particles at the large Stokes number tend to be slowed, whereas the settling velocity of particles is increased at the small Stokes number.