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.     

Hydrodynamics of Secondary Settling Tanks and Increasing Their Performance Using Baffles

Generally, the flow in settling tanks is stratified, but the effect of buoyancy force on the flow field depends on the inlet concentration of particles and flow bulk velocity. A common approach for increasing settling tanks performance is to use baffles which can reduce effects of the unfavorable phenomena such as short circuiting between inlet and outlet and density currents in primary and secondary settling tanks, respectively. The suitable position of the baffles is related to the importance of buoyancy force. As a result, effects of inlet Reynolds and Froude numbers on the strength of buoyancy force are studied for a secondary settling tank and the results show that neither Reynolds nor Froude numbers are sufficient to be considered alone. Effect of buoyancy force on the suitable baffle position is also investigated. Results show that in high Reynolds numbers, the flow field and baffle position are not affected by the inlet Froude number.     

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.     

Motions of alloying additions during furnace tapping in steelmaking processing operations

Numerical computations were carried out to describe the subsurface trajectories of spherically shaped particles (alloy additions) during simulated furnace to ladle tapping operations in steel-making. Complementing this, experiments in a 0.15 scale water model ladle of a 250 ton teeming ladle were also carried out so as to simulate the subsurface trajectories and total immersion times of various alloy additions as a function of (steel) jet orientation, jet entry locations, particle (alloy additions) entry location, particle shape, density,etc. Similarity criteria for model and prototype were deduced on the basis of Froude modeling. The possibilities of additions of various density being entrained into the bulk liquid and under-going prolonged subsurface motion were examined for a variety of operating conditions. It was found, however, that buoyant spherical particles with apparent densities ranging between 0.4 and 0.9 would, when projected into a recirculating water bath at velocities of 2.7 m/s, record total immersion times of only 0.1 to 40 seconds. The implications of the water model study, together with some idealized sets of computations for an industrial size 250 ton ladle, are analyzed from the viewpoint of industrial alloy addition practices. Finally, the results are examined with reference to different shaped particles and multi-particle addition procedures, since the latter are more typical of industrial practice. Formerly Doctoral Candidate, Department of Mining and Metallurgical Engineering, McGill University Formerly Assistant Professor, Department of Metallurgical Engineering, Indian Institute of Technology, Kanpur, 208016, India     

New Relation for the Computation of Settling Velocities and Diameters of Spheres

Single relations that can be used to calculate both the terminal settling velocities of spheres and the equivalent diameter of particles from their settling velocities are developed. The literature going back to Newton is reviewed and the relations developed tabulated. It is shown how the standard drag curve has developed into the dimensionless velocity versus dimensionless diameter curve. No relations that cover the full range that can conveniently be used for both velocity and diameter calculation were found, however a relation by Concha and Almendra covers most of the range.

The standard drag curve data are constructed by utilizing 535 data points available in the literature in a Reynolds number range of 2.4 × 10^?5 to 2 × 10⁵. The settling velocities are corrected for experiments in finite width columns that do not satisfy the infinite medium dimensions. The data are converted to the dimensionless diameter and dimensionless velocity terms, which is more convenient for calculation purposes.

The data are analyzed using piecewise cubic functions. Data from sources with excessive scatter and a few outliers are removed leaving 443 data points. The resulting piecewise cubic can be used to obtain velocity from diameter or diameter from velocity. To give an algebraic expression a hyperbola is fitted to the data giving an expression that can be solved to give explicit relations for both dimensionless velocity and dimensionless diameter. This provides an accuracy that compares well with expressions given in the literature.     

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.     

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.     

Subcritical 90° Equal-Width Open-Channel Dividing Flow

Based on experimental observations, for a subcritical, right-angled, equal-width, open-channel dividing flow over a horizontal bed, the contraction coefficient at the maximum width-contracted section in the recirculation region is almost inversely related to the main channel upstream-to-downstream discharge ratio. The energy heads upstream and downstream of the division in the main channel are found to be almost equal. Under the assumption that the velocities are nearly uniformly distributed at the considered boundaries, the depth-discharge relationship follows the commonly used energy equation. The predicted results correlate fairly with the experimental data from this and other studies. The energy-loss coefficient of a division is expressed in terms of discharge ratio, upstream Froude number, and depth ratio. An expression for practical engineering applications is to determine the maximum possible branch-channel discharge at a given upstream discharge with a prescribed downstream Froude number or the maximum possible downstream Froude number if both branch- and main-channel discharges are prescribed.     

基于固液两相流模拟的选矿循环水深度澄清装置优化

部分选矿循环水中含一定量的高分散性悬浮颗粒,仅依靠简单浓缩沉降难以澄清,无法达到回用要求。针对这一难题,提出了一种选矿循环水固体悬浮物澄清装置。为优化装置的结构参数与运行参数,建立了选矿循环水深度澄清装置的二维物理模型,基于计算流体力学（CFD）的方法,选用Mixture和RNG k?ε 模型对装置主要的结构参数与运行参数展开了数值模拟研究。研究发现适当降低水力循环区喷嘴长度,增加喉管与喷嘴管径比、颗粒沉降区开口尺寸、装置直径等结构,能够降低颗粒沉降区平均湍动能,由于湍动能为单位质量流体由于紊流脉动所具有的动能,故降低了颗粒沉降区流场的紊流程度,增加了水流的稳定性,提高了装置对悬浮颗粒的去除效果;同时发现降低入口流速、增加悬浮颗粒粒径有助于提高悬浮物的去除率,当进水流速为0.1 m·s?1、经过混凝的悬浮颗粒形成粒径大于100 μm时,装置对选矿循环水中的悬浮颗粒去除效果显著。      

Design of Secondary Settling Tanks Using a CFD Model

A computational fluid dynamics (CFD) model is presented and applied in the design of the secondary settling tanks of Psyttalia Wastewater Treatment Plant in Athens, Europe’s largest sewage treatment facility. The tanks are of the Gould Type II consisting of the following regions: an inlet-flocculation chamber with an inlet baffle, two zones of settling separated by an intermediate baffle, an outlet region, and a sludge collection region. The number of tanks and their dimensions were determined with an empirical design procedure. Then, theoretical considerations, information from similar existing tanks, and preliminary CFD calculations were combined to determine the dimensions of the main regions and the positions of the baffles. Finally, detailed CFD calculations were performed to examine the performance of the tanks for various design conditions. Computations showed that the flow in the inlet-flocculation region was completely mixed; while in the settling regions a “three-layer” structure with relatively constant layer heights was observed. CFD results were processed to determine parameters of practical interest, including the heights of the sludge blankets and the effluent suspended solids concentrations; these parameters were correlated satisfactorily with the Hazen number, which is used as a scaling parameter in primary settling tanks.     

Hydraulics of Rectangular Dropshafts

A dropshaft is an energy dissipator connecting two channels with a drop in invert elevation. The hydraulics of vertical rectangular shafts was systematically investigated in seven configurations. A particular emphasis was on the effects of shaft pool, outflow direction, and drop height, while geometrically similar shafts (scale 3.1:1) were studied using a Froude similitude. The results demonstrate that rectangular dropshafts with 90° outflow are the most efficient energy dissipators. The shaft pool and drop height have little effect on the rate of energy dissipation. Recirculation time results exhibited marked differences between flow regimes and the longest dimensionless residence times were observed at low flow rates. Although basic flow characteristics were similar between model and prototype, observations of dimensionless bubble penetration depths and recirculation times showed some discrepancy, highlighting limitations of the Froude similitude for studies of air entrainment and residence times in dropshafts.     

Residence time distribution of solid particles in liquid fluidised bed separator

Abstract

Residence time distribution (RTD) of coal particles in a floatex density separator (FDS) was investigated using stimulus response technique. The mean residence time of the underflow particles was observed to increase with a decrease in the particle size as well as density. The resistance to settling is enhanced at higher bed pressure and the residence time of the particles increases. A linear correlation of the mean residence time with the terminal settling velocity of the particles was observed. The mixing behaviour in the FDS was neither plug flow type nor fully mixed type. The n-tank in series model described the mixing pattern in the FDS well with ‘n’ values in the range of 3–5. The relatively low values of ‘n’ indicated that the flow behaviour in the FDS was closer to the well mixed state.     

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.     

The coarsening of liquid Al-Pb-dispersions

The behaviour of a dispersion with liquid Pb particles moving at their Stokes velocities relative to the liquid Al matrix has been investigated. In order to provide a stable dispersion a special experimental arrangement has been used that minimizes effects due to settling of the heavier Pb droplets. It is shown that the measured stationary droplet size distribution coincides with the authors′ theoretical prediction for Ostwald ripening by convective diffusion.     

Submerged liquid slag injection in steel melt: scaleup study using cold model and dimensional analysis

Abstract

Submerged injection of solid flux powder is used in the steel industry to eliminate impurities in an economical way. The efficiency of such an injection process is limited by the fact that only a fraction of the injected particles penetrate into the liquid melt, while the majority remain as bubble encapsulated solids, causing poor heat and mass transfer. Therefore, liquid slag injection can be considered a potential alternative technique in the refining of steel to improve the efficacy of mass transfer in such a process. In the present work, liquid slag injection in a steel melt has been simulated by means of laboratory scale cold model experiments in which, water, paraffin oil and benzoic acid have been used as low temperature analogues for liquid steel, slag and impurities, respectively. Through dimensional analysis it is observed that the modified Froude number can be considered as a criterion for scaling up such a process from a bench scale to a full scale system. A regression analysis has also been carried out to correlate the dimensionless mass transfer rate constant with the relevant dimensionless numbers, namely, dimensionless gas velocity, Froude number, aspect ratio and non-dimensional lance depth.     

Relationship between Hazen–William and Colebrook–White Roughness Values

Despite advances in computing technology and derivation of explicit approximation formulas, the experimentally verified and widely applicable Colebrook–White friction factor formula is often rejected in favor of the limited and less accurate Hazen–Williams equation. The general reluctance of practicing engineers to embrace the Colebrook–White formula may be due to the relatively large available database for Hazen–Williams C coefficient values versus a relatively small database of the equivalent sand roughness ks values required by the Colebrook–White equation. Until now, converting C to ks required knowledge of both the Reynolds number and pipe diameter originally used to determine C. The current effort derives implicit equations relating C to ks that do not require additional information and compare well with published data. The exact solution is approximated with a single explicit equation, accurate to within 4% error.     

Modified Hazen–Williams and Darcy–Weisbach Equations for Friction and Local Head Losses along Irrigation Laterals

In previous analytical approaches, the direct calculation of friction loss along a lateral is usually based on empirical power-form flow resistance equations, such as the Hazen–Williams and Blasius equations. The more generalized Darcy–Weisbach resistance equation is not usually applied since its friction coefficient varies along the lateral. In this paper, initially, the Darcy–Weisbach and Hazen–Williams equations are systematically compared, leading to a correction form for the Hazen–Williams coefficient. In addition, a more accurate procedure assuming a power function form for the Darcy–Weisbach equation along irrigation laterals is also proposed. The systematic analysis of various typical flow pipe irrigation situations (e.g., sprinkler irrigation laterals of linear or radial-center pivot displacement, trickle irrigation laterals, and manifolds) indicates that the friction loss along laterals calculated using the Darcy–Weisbach equation closely follows a discharge-power form function. The two empirical parameters of the power function depend on the specific pipe characteristics as well as the specific range of discharge values along the lateral. The proposed analytical solution is extended to incorporate the local head loss, the velocity head variation, and the outflow nonuniformity along sprinkler and trickle irrigation laterals. The suggested direct computation solution is demonstrated in two application examples of sprinkler and trickle irrigation laterals and compared with accurate numerical solutions.     

Side Outflow from Supercritical Channel Flow

Side flow on a flood plain from a side outlet of the main channel is investigated both theoretically and experimentally for supercritical main flow. The side outlet as a model simulates a failure of a river bank in a prototype. The discharge ratios of the side outflow to that of the main channel flow, the water depth, and the velocity at the side outlet are obtained. The theoretical discharge ratio is a function of the Froude number of the main channel flow. The theoretical spreading angle of the side flow and the theoretical relationship between the velocities and the distance from an upstream point of the side outlet are also compared and predicted. All the theoretical results are found to be in good agreement with the experimental data.     

Gravity segregation of complex intermetallic compounds in liquid aluminum-silicon alloys

Primary crystals of intermetallics that are rich in iron, manganese, and chromium form at temperatures above the liquidus, and because their density is higher than that of liquid alumi-num, they cause gravity segregation in the melt. Segregation may occur either in the mold at slow cooling rates or in the bulk liquid in furnaces or ladles. The kinetics of settling of these intermetallic compounds in a melt of Al-12.5 pct Si having 1.2 pct Fe, 0.3 pct Mn, and 0.1 pct Cr has been studied. Sedimentation was investigated at 630 ‡C for settling times of 30, 90, and 180 minutes in an electric resistance furnace. The effect of settling time and height of melt on the volume percent, number, and size of intermetallic compounds was studied by image anal-ysis. The volume percent of intermetallics increases with distance from the melt surface. Both the number of particles and the average size increase during sedimentation. The rate of settling varies with position in the melt due to depletion of intermetallics near the surface and an increase near the bottom. The settling velocities obtained experimentally were compared with terminal velocities calculated by Stokes’ law. Good agreement was generally found. The settling speed of intermetallics reaches the terminal velocity at very short times and very close to the liquid surface. Stokes’ law is therefore applicable to virtually all locations within the melt.     

Case Study: Particle Velocimetry in a Model of Lake Ogallala

In a case study of Lake Ogallala, a reservoir in central Nebraska, large scale particle tracking velocimetry (LSPTV) is used to measure surface velocities in a physical model of the lake. Knowledge of flow patterns in the lake is essential for predicting the transport of dissolved oxygen (DO). A preliminary comparison with acoustic Doppler velocimetery (ADV) measurements shows that both LSPTV and large scale particle image velocimetry (LSPIV) accurately measure surface velocities. In the present study, LSPTV works better near flow boundaries and in regions with high velocity gradients since smaller sampling areas are possible, and unlike LSPIV measurements, LSPTV measurements are unbiased. Discharges measured at eight different transects using LSPTV were within 6% of the discharge measured with an orifice, the worst correlation occurring where the bathymetry was slightly nonuniform (making application of the 1/7-power law suspect). In the prototype, DO content periodically drops to unacceptable levels throughout most of the Keystone Basin (a subbasin of Lake Ogallala). Predicted flow patterns suggest that low DO problems are exacerbated in regions with low velocities since oxygen consumed by macrophytes during nighttime hours is not quickly replenished.