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.     

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.     

Near-Bed Sediment Concentration Distribution and Basic Probability of Sediment Movement

Sediment concentration distribution and the basic probability of sediment movement near the channel bed are two of the most important and fundamental issues in the study of sediments. Based on statistical analysis and considering the transport mechanisms, the rules of sediment concentration distribution near a channel bed are studied. Analytical expressions for the near-bed sediment concentration distribution and mean sediment concentration are derived, and the expression for the mean sediment concentration near the bed is verified by measured data, which were obtained from previous experiments. With the help of statistical theory, the expressions of basic probabilities, i.e., rolling, saltating, and suspending probabilities, for sediment movement near the bed are also derived. The expression for starting probability is verified by the measured data. The verification shows that the results from the proposed expression agree well with the measured data. This research has both theoretical and practical significance for further investigation concerning rules of bed load and suspended sediment transport.     

Bayesian Updating of Parameters for a Sediment Entrainment Model via Markov Chain Monte Carlo

A Bayesian framework incorporating Markov chain Monte Carlo (MCMC) for updating the parameters of a sediment entrainment model is presented. Three subjects were pursued in this study. First, sensitivity analyses were performed via univariate MCMC. The results reveal that the posteriors resulting from two- and three-chain MCMC were not significantly different; two-chain MCMC converged faster than three chains. The proposal scale factor significantly affects the rate of convergence, but not the posteriors. The sampler outputs resulting from informed priors converged faster than those resulting from uninformed priors. The correlation coefficient of the Gram–Charlier (GC) probability density function (PDF) is a physical constraint imposed on MCMC in which a higher correlation would slow the rate of convergence. The results also indicate that the parameter uncertainty is reduced with increasing number of input data. Second, multivariate MCMC were carried out to simultaneously update the velocity coefficient C and the statistical moments of the GC PDF. For fully rough flows, the distribution of C was significantly modified via multivariate MCMC. However, for transitional regimes the posterior values of C resulting from univariate and multivariate MCMC were not significantly different. For both rough and transitional regimes, the differences between the prior and posterior distributions of the statistical moments were limited. Third, the practical effect of updated parameters on the prediction of entrainment probabilities was demonstrated. With all the parameters updated, the sediment entrainment model was able to compute more accurately and realistically the entrainment probabilities. The present work offers an alternative approach to estimating the hydraulic parameters not easily observed.     

Discrete Particle Modeling of Entrainment from Flat Uniformly Sized Sediment Beds

The stability of randomly deposited sediment beds is examined using a discrete particle model in which individual grains are represented by spheres. The results indicate that the threshold shear stress for flat beds consisting of cohesionless uniformly sized grains cannot be adequately described by a single-valued parameter; rather, it is best represented by a distribution of values. Physically, this result stems from the localized heterogeneity in the arrangement of surface grains. For uniformly sized beds, geometric similarity exists such that the critical entrainment shear stress distributions scale directly with grain size. A Shields parameter of 0.06 is commonly used to define “threshold conditions,” and it was found that this corresponds to a point on the distributions where approximately 1.4% by weight of the surface is mobile. Furthermore the analysis includes a comparison of the contributions of sheltering to variation in critical entrainment shear stress. It was found that remote sheltering, induced by prominent upstream grains, has a significant effect in increasing the apparent critical entrainment shear stress of exposed surface grains.     

Parameter Identifiability for Three Sediment Entrainment Equations

A process-based erosion model is used to study parameterization problems of sediment entrainment equations in overland flow areas. One of the equations for entrainment by flow is developed based on a theory of excess stream power, while the other two relate to excess hydraulic shear. The investigation is conducted in two steps. The first step examines parameter optimization for simulated data sets where the parameter values are known. In the second step, parameter optimization for the most robust equation is examined using experimental data from rainfall simulator plots. Results demonstrate that although the model is capable of estimating total sediment yields with relatively small errors in parameter estimates, the converse is true when the optimization is performed for sediment concentrations. Although sediment yields calculated from simulated sediment concentrations match well with observed data, the parameter estimates generally underestimate sediment concentrations on the rising limb of the sediment graphs, and they overestimate them on the falling limb. This difficulty might be related to structural problems in the model, and unique solutions for parameter estimates cannot be obtained.     

Transition between Two Bed-Load Transport Regimes: Saltation and Sheet Flow

In the saltation regime where bed-shear stress is low, bed load moves by sliding, rolling, and saltating along the bed, while in the sheet-flow regime where bed-shear stress is high, it travels by a combination of saltation and sheet flow. In this paper a theoretical model is developed for predicting the onset of the sheet-flow regime as shear stress increases. This model is based on a new variable Pb representing the proportion of grains on the bed that are entrained as bed load. The model yields the equation Pb = 2.56θG3 in which G = 1?θc/θ, θ = dimensionless bed-shear stress; and θc = critical value of θ at which grains begin to move. The equation shows that θt, which is the value of θ at the onset of the sheet-flow regime and is assumed to occur when Pb = 1, is around 0.5 with the exact value controlled by θc. For example, when θc = 0.045, θt = 0.52. The theoretical model is verified by performing a nonlinear regression analysis on data from 285 flume experiments. Additional flume experiments with a high-speed video (HSV) system result in consistent values of θ for the onset of the sheet-flow regime, which support the theoretical model. The HSV images further reveal that: (1) the sheet-flow regime is characterized by granular sheets or laminations; and (2) a zone of mixed saltation and rolling grains exists not only in the saltation regime but also in the sheet-flow regime.     

Density Functions for Entrainment and Deposition Rates of Uniform Sediment

A model has been developed for the prediction of the density functions of bed-elevation and entrainment and deposition rates of sediment in sand bed streams within the lower regime flow condition. The model incorporates both statistical and deterministic parameters in its form. A total of 46 experimental runs have been carried out in a recirculating tilting flume under the equilibrium flow condition using three grain sizes of uniform gradation to validate the model and estimate its parameters. The model parameters are related to the hydraulic conditions of flow and fluid and sediment properties through dimensional and regression analyses. The study has shown that the density functions of bed elevation and entrainment and deposition rates can be approximated quite satisfactorily with the normal distribution curve. Transformation of the density functions into the standardized normal distribution curve provides a unique pattern for all the experimental runs regardless of the sediment grain size, flow condition, and shapes and dimensions of the bed forms. The developed density functions have been utilized to provide a closure for the probabilistic Exner equation for uniform sediment.     

Probability of Individual Grain Movement and Threshold Condition

A new criterion for the experimental characterization of the threshold of motion of sediment as bed load is introduced and this criterion is implemented in an experimental investigation of the role of sediment packing density on bed behavior near the threshold of motion. The new criterion, which may be interpreted as the probability of individual grain movement, accounts for the statistical nature of sediment movement in turbulent flow and the time scale of the flow. The threshold of motion is specified by a fixed value of the probability. The criterion represents an objective, quantitative and consistent approach to the threshold condition for sediment of uniform size, shape, and density. The experimental investigation demonstrates that this criterion leads to results that are comparable to those of other approaches, for nearly isolated grains; however, it is found that a threshold criterion based upon the probability of grain movement can yield relatively active sediment beds where the level of activity is strongly dependent upon sediment packing density.     

CSP工艺冷轧微碳钢组织演变研究

采用CSP热轧板为原料,设计了两个成分的微碳钢,对其生产加工过程中的热轧样、冷硬样、退火样及平整后的样板进行了金相显微镜和扫描电镜观察,研究了各个加工过程中金相组织变化、晶粒度变化及Fe3C的析出演变规律。结果表明:CSP热轧板组织均由铁素体和不连续链状碳化物组成,冷轧退火后链状碳化物逐渐均匀,并成连续链状分布在晶界上;碳含量对组织晶粒度有一定影响。     

Flow-Induced Failure of Cable-Tied Blocks

An experimental study of flow-induced failure of cable-tied blocks is presented. The particular failure mechanism studied is overturning and rolling up of the leading edge of a cable-tied block mat. Individual blocks were investigated also. The block size, flow depth, and block (mat) protrusion above the surrounding bed were systematically varied. The results are presented in terms of the critical dimensionless shear stress θc for block (mat) failure. A relationship between θc, block size and block protrusion, and flow depth is given.     

Fluvial Entrainment of Protruding Fractured Rock

Fluvial entrainment of fractured rock assessed in terms of bed shear stress, stream power, and time-averaged bed uplift pressures indicates that rock-block stability reduces with increasing protrusion and decreasing surface length (in the direction of flow), with protrusion of only a nominal portion of the block required to significantly decrease block stability. Variations in block uplift pressure coefficient with normalized block protrusion and block surface length can be used to predict the height of a block (of protrusion P and known surface lengths) at the point of entrainment for an open-channel flow (of average depth h and velocity U). Alternatively, entrainment of prismoidal particles of square section in plan by fully turbulent open-channel flows (of R?>100) can be predicted using (θC?0.002) = 0.0015?(Pvb/L)?1, where θC is the critical dimensionless shear stress, R? is the grain Reynolds number, L is the particle upper-surface side length, and Pvb is the particle protrusion relative to the virtual-bed level at which the average flow velocity is zero (approximately the tops of the supporting or surrounding particles for the present prismoidal blocks). Owing to the potential occurrence of cavitation on prototype block surfaces, it is recommended that quantitative scaling of the present results be conservatively limited to prototype average velocities (U) of less than approximately 6 m/s (with scale ratios λU2 = λL = 29). In contrast to existing practice, particle protrusion needs to be accounted for when assessing the erodibility of a channel bed using stream-power-based methods such as the erodibility index method reported by Annandale in 1995.     

Sedimentation from Buoyant Jets

An integral model is developed to describe sedimentation from a turbulent, buoyant jet injected at an angle into a stationary, uniform ambient fluid. Entrainment is modeled using the standard entrainment assumption and sediment is assumed to fall from the jet where the outward component of the fall velocity normal to the jet boundary exceeds the inward entrainment velocity. When appropriately scaled by source momentum and buoyancy fluxes, turbulent, buoyant jets may be described in terms of a single parameter: the angle θ0 between the flow and the horizontal at the virtual origin (which is close to the actual source for large initial densimetric Froude numbers). Including sedimentation in the model introduces a further parameter ws, which is the ratio of the fall speed of the sedimenting particles to a typical entrainment velocity (and so wS is a nondimensional fall speed). An important result is that this ratio is independent of the source speed, so that the proportion of the sediment load deposited near the source is independent of the flow rate. Sediment remaining in the plume beyond the near-source region is deposited when the plume spreads horizontally once it reaches the free surface. Results for plume shapes, deposition patterns, and the proportion of sediment load deposited in the near-source region (as functions of θ and ws) are given. The results are supported by some preliminary laboratory experiments. The effects of flow in the ambient fluid are discussed briefly and a further parameter uF is introduced, which is the ratio of the ambient flow speed to a typical entrainment velocity (again this ratio is independent of the flow rate).     

Bed Sediment Entrainment Function Based on Kinetic Theory

Bed sediment entrainment function is derived based on kinetic theory. The entrainment rate is expressed as an upward flux by integrating the particle velocity over all possible upward motions. The possibility of upward motion is determined by a sediment particle velocity distribution function, which is obtained by solving the Boltzmann equation instead of using a prior assumed distribution. External forces and turbulence intensity of the flow are shown to exert significant influences on the velocity distribution function and, in turn, the entrainment rate. Comparisons between available laboratory data and the entrainment function show that the calculated entrainment rates agree well with the observations. Applications of the entrainment function to the specification of the bottom boundary condition for convection-diffusion equation of suspended load are also presented, which show that the calculated concentration profiles are in good agreement with observations. The study also suggests that kinetic theory is a promising analytical approach for the study of sediment motion near a riverbed.     

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.     

Hydrodynamic Forces Generated on a Spherical Sediment Particle during Entrainment

The objective of this research is to study the relationship between the coherent flow structures and the hydrodynamic forces leading to entrainment of a spherical bed sediment particle for a rough bed uniform turbulent flow. Two types of experiments, namely, movable and fixed balls, were conducted using spherical roughness-element beds with particle image velocimetry to measure the instantaneous flow-velocity field. Miniature piezoelectric pressure sensors were used to capture the instantaneous pressure on the surface of the sphere. Movable ball experiments reveal the predominance of large sweep structures at the instant of entrainment. Fixed ball experiments carried out at entrainment conditions show the importance of both vertical and horizontal pressure gradients on the ball leading to entrainment. Probability distribution function plots of pressures based on quadrant analysis of velocities also reveal the higher probability of occurrence of high magnitude force induced by sweep (Q4) events.     

带钢冷轧润滑形膜的特征

提出了一种建立于流体动力学及塑性变形原理基础上的带钢冷轧润滑模型,可用于预测分析轧制变表区内油膜厚度,前滑、轧制压力及摩擦力分布等。该模型首先求解入口速度,然后得到油膜厚度,另外,本作还进行了高运动粘度矿物油带钢轧制、实测了不同压下率下变形区入口处油膜厚度,结果表明：实测值与计算机值吻合很好。该模型为进一步研究带钢冷轧及其润滑过程、优化生产工艺提供了依据。     

Computer Vision Technique for Tracking Bed Load Movement

An advanced image analysis system, called Khoros, was used to investigate the bed load movement of sediment particles in a laboratory flume. Incipient flow conditions prevailed throughout the experiments. Painted glass balls of identical diameter and density were used to simulate the sediment particles. They were uniformly placed on top of a tightly packed flat porous bed. Experiments were performed with two distinct surface packing configurations. A video camera was used to monitor their motion within a specified area of view. The resulting video record was converted to digital images using a frame grabber. These digital images were downloaded to a workstation for analysis. The outcome of this analysis provided quantitative information about the frequency of the entrainment of the glass beads, their displacement distance, and the mode of their motion. Such information, when used in conjunction with laser Doppler velocimeter measurements of the fluid velocity, can elucidate the physical mechanisms that are responsible for the entrainment of sediment. During the analysis of the tests, it was observed that the displacement of the beads was sporadic and occurred typically by rolling. The glass beads moved predominately along the flow direction, while on some occasions they were displaced in the transverse direction. For the two packing density tests that were examined, the minimum traveling distance in the longitudinal direction was found to be equal to one bead diameter and the maximum was equal to 10 bead diameters. In the transverse direction, the maximum particle traveling distance was equal to four bead diameters. Finally, it is shown that the existing imaging workspace can be used to accurately identify the displacements of small particles, which are typically encountered near incipient flow conditions and are not easily detectable with the bare eye. The imaging method described here is dynamic in nature and may prove to be a valuable tool for studying two-phase flows, as well as for visualizing flow structures taking place near the boundary in turbulent flows.     

Probabilistic Modeling of Bed-Load Composition

This paper proposes that the changes which occur in composition of the bed load during the transport of mixed-grain-size sediments are largely controlled by the distributions of critical entrainment shear stress for the various size fractions. This hypothesis is examined for a unimodal sediment mixture by calculating these distributions with a discrete particle model and using them in a probabilistic calculation of bed-load composition. The estimates of bed-load composition compare favorably with observations of fractional transport rates made in a laboratory flume for the same sediment, suggesting that the hypothesis is reasonable. The analysis provides additional insight, in terms of grain mechanics, into the processes that determine bed-load composition. These insights strongly suggest that better prediction methods will result from taking account of the variation of threshold within size fractions, something that most previous studies have neglected.