Sensitivity of incipient particle motion to fluid flow penetration depth within a packed bed

A discrete element method is applied to a three‐dimensional analysis related to sediment entrainment on a micro‐scale. Sediment entrainment is the process by which a fluid medium accelerates particles from rest and advects them upward until they are either transported as bedload or suspended by the flow. Modelling of the entrainment process is a critically important aspect for studies of erosion, pollutant resuspension and transport, and formation of bedforms in environmental flows. Previous discrete element method studies of sediment entrainment have assumed the flow within the particle bed to be negligible and have only allowed for the motion of the topmost particles. At the same time, micro‐scale experimental studies indicate that there is a small slip of the fluid flow at the top of the bed, indicating the presence of non‐vanishing fluid velocity within the topmost bed layers. The current study demonstrates that the onset of particle incipient motion, which immediately precedes particle entrainment, is highly sensitive to this small fluid flow within the topmost bed layers. Using an exponential decay profile for the inner‐bed fluid flow, the discrete element method calculations are repeated with different fluid penetration depths within the bed for several small particle Reynolds numbers. For cases with slip velocity corresponding to that observed in previous experiments with natural sediment, the predicted particle velocity is found to be a few percent of the fluid velocity at the top of the viscous wall layer, which is a reasonable range of velocities for observation of incipient particle motion. This method for prescribing the fluid flow within the particle bed allows for the current discrete element method to be extended in future studies to the analysis of sediment entrainment under the influence of events such as turbulent bursting. Additionally, predictions for the slip velocities and fluid flow profile within the bed suggest the need for further experimental studies to provide the data necessary for additional improvement of the discrete element method models.     

Applications of grain-pivoting and sliding analyses to selective entrapment of gravel and to flow-competence evaluations

Models of sediment threshold by grain pivoting or sliding over underlying particles are examined in order to explore their application to evaluations of selective entrainment of gravel by flowing water. Of special interest is whether such process-based models provide satisfactory evaluations of flow competence and the movement of large clasts by floods. A detailed derivation is undertaken, focusing first on the fluid flow and forces at the particle level. The resulting threshold equation for the particle-level velocity is then modified to yield the mean entrainment stress for the flow as a whole. This approach is appropriate for considerations of selective entrainment of grains of varying sizes within a deposit, the sorting being due to their relative projection distances above the bed and the dependence of their pivoting angles on grain size and shape. The resulting threshold equations contain a number of coefficients (e.g. drag and lift) whose values are poorly known, but can be constrained by requiring agreement with the Shields curve for the threshold of grains in uniform deposits. If pivoting coefficients based on laboratory measurements with tetrahedral arrangements of particles are used in the models, smaller degrees of selective sorting are predicted than found in the field measurements of gravel entrainment. However, if reasonable modifications of those coefficients are made for expected field conditions, then the models yield good agreement with the data. Sliding models, where sorting is due entirely to projection distances of the grains above the bed, yield somewhat poorer agreement with the field data; however, the sliding models may have support from laboratory experiments on gravel entrainment in that the data and theoretical curves have similar concave trends. The existing measurements lack documentation of the mechanisms of grain movement, so it is not possible to conclusively determine the relative importance of grain pivoting versus sliding. In spite of such uncertainties, the results are encouraging and it is concluded that pivoting and sliding models for grain entrainment do have potential for field computations of selective entrainment and flow competence.     

Threshold for particle entrainment into suspension

ABSTRACT Laboratory observations regarding the limit conditions for particle entrainment into suspension are presented. A high‐speed video system was used to investigate conditions for the entrainment of sediment particles and glass beads lying over a smooth boundary as well as over a rough bed. The results extend experimental conditions of previous studies towards finer particle sizes. A criterion for the limit of entrainment into suspension is proposed which is a function of the ratio between the flow shear velocity and particle settling velocity. Observations indicate that particles totally immersed within the viscous sublayer can be entrained into suspension by the flow, which contradicts the conclusions of previous researchers. A theoretical analysis of the entrainment process within the viscous sublayer, based on force–balance considerations, is used to show that this phenomenon is related to turbulent flow events of high instantaneous values of the Reynolds stress, in agreement with previous observations. In the case of experiments with a rough bed, a hiding effect was observed, which tends to preclude the entrainment of particles finer than the roughness elements. This implies that, as the ratio between particle and roughness element sizes becomes smaller, progressively higher bed shear stresses are required to entrain particles into suspension. On the other hand, an overexposure effect was also observed, which indicates that a particle moving on a smooth bed is more prone to be entrained than the same particle moving on a bed formed by identical particles.     

The hydrodynamics of particle clusters and sediment entrapment in coarse alluvial channels

ABSTRACT Particles projecting from the bed of an alluvial channel distort the fluid stream to produce a distinctive pressure field. This has considerable significance for both the entrapment and entrainment of other particles and is a primary cause of the widespread occurrence of pebble clusters and boulder shadows. Lift and drag forces are determined on clustered hemispherical particles of varying size. In the wake of an obstructing particle both forces are shown to vary directly with particle separation in a linear fashion. On the stoss side of the cluster, drag is uniform regardless of the separation of the component particles, but lift is shown to increase when particle separation is small, so affecting stability. This mutual interference of neighbouring clustered bed particles is a vital consideration of incipient motion and is shown by field evidence to cause a wide range in transport stage for particles of similar size and shape. On average, 46% of clustered particles are entrained by flood flow compared to 87% of particles in open plane-beds. The influence of clusters is a major determinant of sedimentary sorting.     

Direct numerical simulation of bedload transport using a local, dynamic boundary condition

ABSTRACT Temporally and spatially averaged models of bedload transport are inadequate to describe the highly variable nature of particle motion at low transport stages. The primary sources of this variability are the resisting forces to downstream motion resulting from the geometrical relation (pocket friction angle) of a bed grain to the grains that it rests upon, variability of the near‐bed turbulent velocity field and the local modification of this velocity field by upstream, protruding grains. A model of bedload transport is presented that captures these sources of variability by directly integrating the equations of motion of each particle of a simulated mixed grain‐size sediment bed. Experimental data from the velocity field downstream and below the tops of upstream, protruding grains are presented. From these data, an empirical relation for the velocity modification resulting from upstream grains is provided to the bedload model. The temporal variability of near‐bed turbulence is provided by a measured near‐bed time series of velocity over a gravel bed. The distribution of pocket friction angles results as a consequence of directly calculating the initiation and cessation of motion of each particle as a result of the combination of fluid forcing and interaction with other particles. Calculations of bedload flux in a uniform boundary and simulated pocket friction angles agree favourably with previous studies.     

The entrainment factor in froth flotation: Model for particle size and other operating parameter effects

Accurately estimating entrainment is crucial when predicting flotation performance as it is essential for determining the concentrate grade achieved. It has been found previously that the amount of gangue entrained is proportional to the water recovery; this proportionality is referred to as the entrainment factor. Experimentally it has been found that entrainment is a strong function of particle size, as well as being dependent on other cell operating parameters such as froth depth and air rate.A simplified theoretical model for entrainment is developed which includes the effects of liquid motion and content, particle settling and particle dispersion. First, a detailed one-dimensional differential model for the entrainment factor is developed and solved numerically. Thereafter, a simplified analytical expression for the entrainment factor is produced which is a good approximation to the more detailed one-dimensional model. Both these models are shown to predict closely experimental trends for entrainment as a function of particle size and froth depth.     

Interrelationships between bed morphology and bed-material transport for a small,gravel-bed channel*

Bed conditions (micro-relief, textural associations and packing structural arrangements) in the gravel-bed channel of Seale's Brook are shown to be closely interrelated; various categories are identified and related to mode of bed material transport and deposition. Entrainment of bed material, commonly treated as a simple function of particle weight and channel hydraulics, is also shown to be strongly affected by varying and variable bed conditions. In particular, the classic concept of competence appears to be of restricted utility in such channels; resistance of bed material to fluid drag and to particle impact is augmented, over large parts of the channel bed, by its interlocking structure, made possible by the wide range in particle calibre, and by the characteristic disc and blade shapes of the slate debris. Particle mobility, as indicated by distance of travel of labelled bed material, is only partly a function of particle weight; indeed, although particle mobility decreases from small pebbles to large cobbles, it also decreases for the finest bed material (very small pebbles). This appears to be explicable, partly in terms of the ease of entrainment (and duration of travel), and, partly in relation to the ease of transport of material over an uneven channel bed surface. Particle mobility is greatest for material in open and infilled structures and smallest for sediment in tight structural arrangements. Local bed slope also exerts an influence on the probability of particle entrainment and on particle mobility. The findings emphasize the need for combining sedimentological and engineering approaches to bed material transport in coarse-bedded channels, and, at the same time, illustrate some of the reasons for the existence of indeterminacy in the modelling of bed-material transporting processes.     

The structure and kinematics of substrate entrainment into high-concentration sandy turbidites: a field example from the Gorgoglione 'flysch' of southern Italy

Sandy turbidites commonly show evidence for significant dynamic coupling with their substrate. The resulting deformation can be described using structural kinematic methods, linked to palaeoflow indicators, to better understand the links between flow and entrainment processes. A field example from the syn‐orogenic Gorgoglione Flysch, a succession of upper Miocene turbidites deposited into a deforming array of thrust‐top basins in the southern Apennine thrust belt, Italy, is described. The succession contains metre‐scale packages of alternating sandy turbidites and shales but is notable for containing > 100 m thick, massive sandbodies. These are structureless apart from sporadic horizons of aligned mud clasts. Commonly, the substrate beneath the massive sandbodies is deformed, with minor folds and thrusts verging in the direction of palaeoflow determined from tool marks and flutes at the base of these sandbodies. Structural studies from the base of a selected massive sandbody have identified that the substrate mud has been injected upwards, with flames sheared over in the direction of palaeoflow. Thus the substrate has deformed and become entrained during emplacement of the massive sandy body. At some locations, the substrate can be traced into the overlying deposit, with substrate clay beds becoming boudinaged and entrained into the sandbody. Analysis of the orientation of the mud clasts indicates that this bed disruption and incorporation into the sandy massive‐bed turbidite was an organized, viscous process. These features indicate that significant shear stress was partitioned out of the flow and onto the substrate. The incorporation and disruption of substrate into the sandbody suggest that post‐disruption strains increase upwards – implying that displacement gradients increased into the flow. These behaviours, showing variations in strain partitioning between the flow and its substrate, are explored in terms of evolving flow dynamics and substrate rheology.     

Effects of bed longitudinal inflexion and sediment porosity on basal entrainment mechanism: insights from laboratory debris flows

Channel morphology and bed sediment erodibility are two crucial factors that significantly affect debris flow entrainment processes. Current debris flow entrainment models mostly hypothesize the erodible beds are infinite with uniform slopes. In this study, a series of small-scale flume experiments were conducted to investigate the effects of bed longitudinal inflexion and sediment porosity on basal entrainment characteristics. Experimental observations revealed that sediment entrainment is negligible at early stages and accelerates rapidly as several erosion points appear. Continual evolution of flow-bed interfaces changes interactions between debris flows and bed sediments, rendering the interfacial shear action involved into a mixed shear and frontal collisional action. Lower bed sediment porosity will change the spatial arrangement and orientation of particle mixture, strengthen the interlocking and anti-slide forces of adjacent sediment particles, and promote the formation of particle clusters, all of which will increase bed sediment resistance to erosion. By examining the post-experimental bed morphology, the slope-cutting amounts and topographic reliefs are determined to positively correlate with longitudinal transition angles. These high topographic reliefs may indicate the propensity of triangular slab erosion, rather than strip-shaped slab erosion, in non-uniform channels with relatively steep erodible beds. Empirical formulas are obtained that denote the relationships among bed sediment strength, channel curvature radius, and sediment porosity through a multi-parameter regression analysis. This study may aid in clarifying the complex coupling effects of spatial variations in debris flow dynamics as well as sediment erodibility and bed morphology in non-uniform channels with abundant seismic loose material.

     

基底侵蚀对高速流动性滑坡运动性影响的模拟分析

高速流动性滑坡运动距离远,破坏性强。这类滑坡在运动过程中常裹挟大量的松散物质,导致滑坡的体积和致灾范围增大,该现象被称为基底侵蚀效应。以往的研究指出基底侵蚀效应对这类滑坡的运动性有显著的影响,但却很少有研究考虑其对滑体性质的影响,以及如何对其进行量化。因此,本文基于动量守恒原理建立了考虑基底侵蚀效应的滑坡运动模型,利用有限差分法求解,并依据滑坡的侵蚀深度来计算侵蚀导致的滑坡性质变化。利用改进的模型对陕西泾河南岸的西庙店滑坡进行模拟分析。结果表明,滑坡运动可分为启动加速阶段（0~5 s）和运动减速阶段（5~14 s）。在启动加速阶段,基底侵蚀程度低,对滑体运动的影响较弱。而在运动减速阶段,基底侵蚀效应降低了滑带土强度,对该滑坡的运动产生了明显的促进作用,致使其发生远程运动。此外,对比考虑和不考虑基底侵蚀两种工况的模拟结果还发现,考虑这种影响时,模拟所得的运动范围及地形与实测吻合良好,而未考虑时模拟所得运动范围明显偏小。因此,本文的模型可对这类滑坡的运动过程进行更为有效的模拟。     

泥沙起动概率的高速摄影测量方法

为了通过实验测量泥沙起动概率,基于封闭槽道内开展的泥沙起动实验,系统论述了基于高速摄影的起动概率测量方法所涉及的起动概率定义、相机采样频率、图像处理方法、起动比例与运动比例的关系等关键问题.根据泥沙在水流紊动猝发作用下起动的物理机制,定义实测起动概率为单个紊动猝发周期内,从一定面积床面上冲刷外移的泥沙比例.根据推移质运动概念模型,提出高速图片拍摄间隔应小于推移质运动的中间时间尺度,以捕获泥沙的每一次起动.在高速图像处理时,通过连续两帧图片之间的灰度差实现运动比例的无偏差提取.进一步分析表明,运动泥沙可处于起动、止动或滑翔状态,运动比例等于起动比例、止动比例和滑翔比例之和,起动比例与运动比例之比等于两张图片之间的时间间隔除以推移质运动的中间时间尺度.基于上述关键技术,将高速摄影测量方法用于泥沙起动概率的测量,结果表明,临界起动水流条件时,床沙处于少量起动现象,对应的临界起动概率与窦国仁所推导的2.28%接近.     

Clast ploughing, lodgement and glacier sliding over a soft glacier bed

Rarely-preserved features indicative of clast lodgement are exceptionally well preserved near Peoria, Illinois, on the contact surface between Illinoian till and underlying glacifluvial sand due to synsedimentary cementation of the substrate contact. Features preserved on the cemented contact surface record a history of particle transport, lodgement by ploughing into a deformable substrate, and subsequent overriding by abrasive debris-rich ice. Linear grooves and frontal sediment prows suggest that clasts embedded in the glacier sole ploughed through the soft, deformable bed. Increasing form resistance by the enlargement of sediment prows that developed on the lee side of clasts and deeper penetration of the clasts into the substrate eventually exceeded the force exerted on the clasts by ice flow, and the clasts lodged. Subsequently, clasts were abraded on their up-ice flanks and plucked on their down-ice flanks, resulting in stoss-lee morphology. These features offer direct information on the nature of the interface between aglacier and a soft, deformable substrate such as characterized large areas of former ice sheets.     

黑龙江镜泊湖地区蛤蟆塘火山空落堆积物形成机制研究

火山碎屑物的粒度、粒形和分布特征蕴含着其形成机制和喷发的环境信息。基于镜泊湖地区蛤蟆塘火山的一个空落堆积剖面的野外地质和岩相学,以粒度分析和分形理论定量研究了火山碎屑物的粒度分布、粒形几何及其分形特征。蛤蟆塘火山空落碎屑粒度分布均为单峰式,由岩浆爆炸形成的空落浮岩粒度峰值较小,而由射气岩浆喷发形成的含细花岗岩碎屑夹层的碎屑粒度峰值较大。空落浮岩颗粒的类球度、长宽比和凸度都小于含细花岗岩碎屑夹层的数值,表明空落浮岩颗粒相对不规则的特点。利用多段幂律方法拟合了蛤蟆塘火山空落碎屑颗粒分布规律,发现空落浮岩颗粒存在四个幂律分布段（即对应四个分形维数）,这是由于岩浆初始破碎、火山通道内的二次破碎以及风力筛选作用等造成的;含细花岗岩碎屑夹层的碎屑分布有两个幂律分布段（对应两个明显不同的分形维数）,即浮岩和花岗岩碎屑的形成是因不同破碎机制造成的。     

Bed sediment entrainment by streamflow: State of the science

In fluvial sedimentology, bed sediment entrainment by streamflow has a decisive role in controlling several fluvial processes. Owing to its huge practical importance, the subject has been painstakingly explored for over a century. However, a detailed understanding of the mechanism of the bed sediment entrainment phenomenon achieved hitherto is far from complete. The central theme of bed sediment entrainment is occupied by the sediment entrainment threshold, which varies enormously in its qualitative definition, identification and quantification encompassing a broad range of spatiotemporal scales. This article presents the state of the science of the entrainment of non‐cohesive bed sediments under a steady‐unidirectional streamflow. It begins with the diverse definitions and representations of the entrainment threshold criterion from both qualitative and quantitative perspectives, scrutinising its suitability and ambit of applicability. Then, the effects of energetic factors that drive the entrainment threshold criterion are critically appraised. The indispensable mechanisms of bed sediment entrainment, including the theoretical background and modelling strategies, the role of turbulent bursting phenomenon and the phenomenological perspective into the origin of the scaling laws of sediment entrainment, are explained. Throughout the article, special emphasis is given to the strengths and weaknesses of the current state of the science. In addition, a deliberate attempt is made to invoke the thought‐provoking ideas on the multifarious features of bed sediment entrainment. Finally, the innovative perspectives on the bed sediment entrainment are provided and the concluding remarks are made, elucidating the major challenges and suggesting the prospective ways to resolve them as a future scope of research.     

The separation mechanism and application of a tapered diameter separation bed

Research on recycling waste printed circuit boards is at the forefront of preventing environmental pollution and finding ways to recycle resources. A wet process for reclaiming metals from printed circuit boards applying a tapered diameter separation bed is described, and the separation mechanism of the device is proposed. The motion of a particle in the tapered diameter fluid flow field and particle separation within this field were studied. As the material passes through the fluid field, along with the water, differences in particle density, granularity, and shape cause particles to follow at different trajectories. A tapered diameter separation bed was used to process 1?C0.074?mm-sized crushed material from discarded printed circuit boards. The separation efficiency of 91.77?% and the recovery rate of 95.79?% for recovered metal were achieved with a discharge water flow rate of 4.5m³/h, a material feed rate of 300?g/min, and an obliquity of 30°. For ?0.074?mm printed circuit boards, the metal recovery is 93.42?% and the separation efficiency is 77.63?% when the water discharge is 2?m³/h, the obliquity is 35o, and the material feed rate is 450?g/min. The superfine products in a size range of ?0.074?mm can be recovered effectively under suitable operating condition using the tapered diameter separation bed. It indicates that the lower separation limit of the tapered diameter separation bed can be close to zero. The technique will prevent environmental pollution from waste printed circuit boards and allow efficient recovery.     

Origin of the vertically orientated clasts in brecciated shallow‐marine limestones of the Chaomidian Formation (Furongian,Shandong Province,China)

Numerous shallow‐marine limestone layers of the Furongian (Late Cambrian) Chaomidian Formation in the Jiulongshan section (Shandong Province, China) are breccias. Some of these breccias show abundant vertical to sub‐vertical clasts. Typically, these clasts end abruptly at the contact plane with the overlying deposit, either abutting the overlying sedimentary bed or via an erosional plane that truncates the clasts. A few exposures show concentrations of clasts that must have been uplifted to the extent that they transgressed the then sedimentary surface or (possibly) penetrated the overlying sediment which, in this case, consists of muds or marls. The clasts tend to show clusters with respect to the enclosing fabric. All clasts are parallel to each other in a specific cluster, while the various clusters may show different orientations of the clasts. It is deduced that both the exceptional position and the exceptional orientation of the clasts must be ascribed to the upward movement of the clasts under the influence of pore water escaping under high pressure through fluidized sediment.     

Fine particle deposition to initially starved,stationary, planar beds

Reported here are results from new flume experiments examining deposition and entrainment of inert, silt‐sized particles (with spherical diameters in the range from 20 to 60 μm) to and from planar, impermeable and initially starved beds underlying channel flows. Bed surfaces comprised smooth or fixed sand‐size granular roughness and provided hydraulically smooth to transitionally rough boundaries. Results of these experiments were analysed with a simple model that describes the evolution of vertically averaged concentration of suspended sediment and accommodates the simultaneous delivery to and entrainment of grains from the bed. The rate of particle arrival to a bed diminishes linearly, and the rate of particle entrainment increases by the 5/2 power, as the value of the dimensionless Saffman parameter S = u_*³/g’ν approaches a threshold value of order unity, where u is the conventional friction velocity of the turbulent channel flow, g’ is the acceleration due to gravity adjusted for the submerged buoyancy of individual particles and ν is the kinematic viscosity of the transporting fluid. This transport behaviour is consistent with the notion that non‐cohesive, silt‐sized particles can neither reach nor remain on an impermeable bed under flow conditions where mean lift imposed on stationary particles in the viscous sublayer equals or exceeds the submerged weight of individual particles. Within the size range of particles used in these experiments, particle size and the characteristic size of granular roughness, up to that of medium sand, did not affect rates of dimensionless arrival or entrainment to a significant degree. Instead, a new but consistent picture of fine‐particle transport is emerging. Silt‐sized material, at least, is subject to potentially significant interaction with the bed during intermittent suspension transport at intermediate flow speeds greater than the value required for initiation of transport (ca 20 cm sec^?1) but less than the value (ca 50 cm sec^?1) required by the Saffman criterion ensuring transport in fully passive suspension or, equivalently, ‘wash‐load’.     

非均匀沙运动特性试验

天然河流床沙通常为非均匀沙,准确把握非均匀沙颗粒运动规律是模拟和预测天然河流河床演变的基础。开展了恒定均匀流条件下的非均匀沙推移质运动水槽试验,床沙粒径范围为0.10~20 mm。利用摄像机从顶部拍摄了粗化条件下的推移质颗粒运动,获取大量非均匀沙颗粒的运动轨迹,提取了颗粒运动速度、走停时间等基本运动参数,推移质运动颗粒粒径范围为0.74~8.19 mm。试验结果表明,非均匀沙床面聚集体或大颗粒使推移质颗粒运动方向发生改变,与均匀沙成果相比,非均匀沙推移质颗粒的纵向运动速度减小,横向运动速度增大;推移质颗粒纵向运动速度遵循指数分布,单次运动速度遵循Γ分布,横向运动速度及运动速度矢量角则遵循正态分布。     

床面附近泥沙运动的分析

基于水、沙两相的分相测量试验结果,分析了床面附近泥沙颗粒的脉动和力学特性,指出床面附近的泥沙运动有着特殊的力学机制:颗粒相具有较强的非湍流脉动,其产生的脉动应力对颗粒的运动起着重要作用。论述了沙粒在水流中从推移运动到扬起悬浮的物理过程,讨论了过去一些理论中存在的问题和不足,概括了泥沙颗粒在水流中从床面扬起的基本模式,运用两相流理论分析了沙粒在水流中扬起的动力学机理。根据颗粒运动的垂向动量平衡原理,对泥沙颗粒的垂向浓度分布规律作了新的分析解释。证实了除浓度梯度之外,颗粒相的垂向脉动强度梯度也是泥沙扩散的重要扩散势,进一步揭示了悬移质浓度垂线分布存在两种类型的内在机理。