Simultaneous Particle Image Velocimetry and Laser Doppler Velocimetry Measurements of Periodical Oscillatory Horseshoe Vortex System near Square Cylinder-Base Plate Juncture

This paper presents simultaneous measurements using particle image velocimetry (PIV) and laser Doppler velocimetry (LDV) techniques on the study of a horseshoe vortex system. The horseshoe vortex system is generated near the juncture of a vertical square cylinder and a horizontal base plate. The combination of PIV and LDV not only gives the spatial distribution and time history of velocity near the juncture for spatial and time domain analyses, it also allows phase averaging the PIV velocity data to reduce noise and, in a turbulent flow, result in turbulence statistics. A flow visualization technique displaying particle streaklines has also been used to help the classification of the vortex system and visualize the flow motion and vortex evolution. The classification of the horseshoe vortex was briefly categorized as steady, periodical oscillatory, and turbulence-like chaotic vortex systems through the use of the flow visualization technique and time-domain spectral analysis. Phase-averaged flow characteristics of the periodical oscillatory vortex system with a Reynolds number of 2,250 are presented in detail through the use of PIV and LDV as well as the flow visualization technique.     

Using CFD Modeling to Improve the Inlet Hydraulics and Performance of a Storm-Water Clarifier

The feasibility of high-rate treatment of storm water achieving total suspended solids (TSS) removals in the range from 60 to 80% was studied using an available clarifier. The clarifier (3?m long, 1.4?m wide, and 2?m deep) was fitted with a removable lamella pack and had a limited flow capacity (surface load rate of 35?m/h). To achieve the desired removals of TSS, the clarifier required polymer feed (4?mg/L), which caused maintenance problems during intermittent storm-water treatment—laborious and costly cleaning of lamella plates after individual storm events. This problem posed the following challenge: was it feasible to avoid costly maintenance by removing the lamella pack and at the same time to retain the high TSS removals by improving the clarifier hydraulics by internal structural changes? The purpose of the paper is to evaluate such changes by focusing on different inlet configurations designed using computational fluid dynamics (CFD) simulations. This analysis resulted in adopting a U-tube duct inlet (inserted into the outer box of the original clarifier) with two special features: (1) three horizontal slot openings (width = 0.1?m) releasing flow into the clarifier and (2) a narrow slot opening in the bottom U bend allowing removal of grit. The flow release slots in the rising leg of the U tube were fitted, along the upper edge, with horizontal trailing plates protruding 0.15?m into the clarifier and forcing the flow to move horizontally. This clarifier design performed well, but storm-water grit accumulated at the bottom of the U tube, which had to be cleaned out after individual storms to avoid plugging. This issue was resolved by allowing grit to move into the sludge storage compartment of the clarifier through a narrow tilted slot opening in the U-tube bottom. The final clarifier design with polymer feed, without lamellas, produced TSS removals comparable to those in the original lamella clarifier (almost 80%), but at a higher surface loading rate (43?m/h, which was limited by the feed pump capacity). CFD modeling, in comparison to conventional methods of hydraulic design, served as a flexible and powerful tool providing distinct advantages with respect to the speed, efficiency and reduced cost of analysis, and a better understanding of the clarifier operation.     

Settling Velocity Grading of Particle Bound PAHs: Case of Wet Weather Flows within Combined Sewer Systems

The elaboration, management, and design of the sedimentation devices require an improved knowledge not only on the suspended solids (SS) settling velocity but also on the distributions of these particulate pollutants by category of SS settling velocity. Nevertheless, there is currently a lack of available data regarding the settling velocity grading of particle bound pollutants. As a consequence, this study investigating the settling velocity grading of particle bound polycyclic aromatic hydrocarbons (PAHs) in wet weather flows within combined sewers was launched. The pursed objectives were to compare the SS and PAH settling velocity grading curves and hence to assess whether or not PAHs were associated with a specific settling velocity category. Investigations were carried out for three storms at two sampling sites within the Parisian combined sewer. Results indicate that most of PAHs seem to be preferentially associated with particles with a settling velocity >0.3?mm?s?1.     

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.     

Urban Particle Capture in Bioretention Media. I: Laboratory and Field Studies

Bioretention is a novel stormwater best-management practice that uses a mixture of soil/sand/mulch as adsorptive filtration media that can capture both urban particulates and dissolved pollutants while promoting infiltration. This study conducted a series of laboratory column experiments and field observations, which showed that: (1) bioretention media stratification occurs with runoff percolation due to particulate deposition; (2) bioretention filter media are clogging limited, instead of breakthrough limited; and (3) both depth filtration and cake filtration significantly contribute to urban particle capture. Because of the fine size of bioretention media, incoming suspended solids cannot significantly penetrate below 5–10?cm of the media in the column tests and approximately 20?cm in the monitored field facility. Bioretention filters under intermittent flow conditions exhibited higher solids loading capacity (in kg/m2) before clogging than under continuous flow conditions. The clay components in incoming total suspended solids assume critical responsibility for bioretention media clogging. The media resistance due to solids deposition was estimated through Darcy’s law. The hydraulic conductivity of two media types decreased from 54±23 and 72±46?cm/h to less than 10?cm/h due to particle capture. Experimental results suggest that a 20-cm media depth is sufficient for bioretention design and maintenance procedures (media replacement) for runoff particle capture.     

Urban Particle Capture in Bioretention Media. II: Theory and Model Development

As a novel stormwater best-management practice, using a soil/sand/mulch mixture to capture urban pollutants while promoting infiltration, the unique media composition renders bioretention significantly different from conventional sand filters. In this work, a three-layer model is presented to describe particulate capture in bioretention media employing parameter calibration and presensitivity analysis. Since the fine size of bioretention media strictly limits the particulate penetration distance, the media column is modeled as a pristine zone (bottom), a working zone (middle), and a cake zone (top). Mechanisms of both depth filtration and cake filtration are examined through mass balances, which show that both are significant. The developed resistance of each layer due to solid deposition was also estimated. Experimental data for different media/TSS-type combinations of selected experimental trials were used in parameter calibration. The calibrated model successfully predicted the effluent TSS and media hydraulic conductivity of subsequent trials with appropriate boundary and initial conditions as input. A weighted combination of calibrated parameters from different TSS types also agreed well with media behavior for treating a complex TSS mixture. The results of media replacement (top removal and refill) simulation also reasonably fit experimental data. Using proper assumptions, a long-term scenario analysis for permeability reduction was performed for a field bioretention facility. Based on modeling results, this study recommends a shallow bioretention media depth design, an annual or biannual field inspection schedule, and periodic media replacement maintenance.     

Three-Dimensional and Depth-Averaged Large-Eddy Simulations of Some Shallow Water Flows

Three-dimensional (3D) and two-dimensional (2D) depth-averaged (DA) large-eddy simulations (LES) are presented for three different shallow-water flows involving large-scale horizontal structures: a mixing layer, the flow around a circular cylinder, and the flow in a groyne field. The results are compared with each other and also with experiments. In the 3D-LES, most of the energy-containing turbulent motions, including the larger subdepth-scale motions, are resolved, while in the 2D-DA-LES the effect of the 3D subdepth-scale turbulence is represented by a quadratic bottom-friction model and a simple eddy-viscosity model. In the case of the mixing layer, an additional stochastic backscatter model is necessary to account for the energy transfer from the subdepth-scale turbulence to the 2D structures in order to generate the latter. The 3D-LES results are generally in good agreement with the experiments, including the evolution of the horizontal structures. The much more economic 2D-DA-LES are somewhat less realistic in detail but also produce results that are generally of sufficient accuracy for practical purposes.     

Convection Velocity of Vortex Structures in the Near Wake of a Circular Cylinder

The convection velocity of vortex structures in the near wake of a circular cylinder was experimentally investigated over the region 1.6–2.5 ? x/D ? 12.0 for R = 160–12,000. Dye injection technique of flow visualization and two completely noninvasive laser Doppler velocimeters were employed for R ? 320 and ?400, respectively. The convection velocity, Uc, is defined as the mean traveling velocity of vortex cores passing a streamwise separation during a mean elapsed time. For R ? 320, Uc was determined directly from the motion of dye-marked vortex cores filmed by a video camera. In the cases of R ≥ 400, the positions of peak vorticity and half of the half-velocity-defect width at each downstream section were first used to identify the mean path of vortex cores (i.e., the most probable trajectory of the vortex structures), along which spatial correlation measurements were then performed to determine the mean elapsed time corresponding to the maximum cross correlation. The present results show that, in laminar and transitional wakes, the ratio Uc/Uo increases from 0.53 to 0.84 over a region of 1.6 ? x/D ? 6.0 and then tends to be a constant of 0.84 for x/D ≥ 6.0. In a turbulent wake, Uc/Uo also increases from a certain value at a point downstream from the position of vortex formation to a mean value of about 0.86 at x/D ≥ 5.0–6.0, and then changes little with the increase of x/D. In addition, it is found that the dependence of Uc/Uo on R almost disappears for x/D ≥ 5.0.     

Utility of Suspended Solid Measurements for Storm-Water Runoff Treatment

In this paper alternative solutions are presented to solve problems associated with the measurement of total suspended solids (TSS) in storm-water runoff. Results revealed that the accuracy of TSS measurement is largely related to sample representativeness, particle size distribution (PSD), sampling pipette position, and sample mixing. In general, when the PSD in the runoff was mostly larger than 75?μm, the most accurate and reproducible results were obtained when samples were collected from a position of mid-depth and midway between the walls of the beaker and the vortex and mixed at speeds in the range of 600–700?rpm. For runoff samples with a PSD smaller than 75?μm, mixing at a higher rpm is not a significant factor. As long as the PSD in the TSS subsample is representative of the original sample, a strong correlation between TSS and suspended solid concentration can be achieved. The results showed that density was largely correlated with the organic content of the particles, and, in general, smaller particles tended to have a lower density. The density results revealed that assuming a single sand size density of 2.6?g/cm3 for storm-water runoff produced a large error in the computation of sediment load and particle settling velocity.     

Characteristics of Steady Horseshoe Vortex System near Junction of Square Cylinder and Base Plate

This paper presents an experimental investigation on the characteristics of a horseshoe vortex system near the juncture of a square cylinder and a horizontal base plate, using particle image velocimetry and flow visualization technique. Experiments were conducted for Reynolds numbers (based on the free stream velocity and the width of square cylinder) ranging from 2.0×102 to 6.0×103. The flow patterns are first classified into four major regimes: Steady horseshoe vortex system, periodic oscillation vortex system with small displacement, periodic breakaway vortex system, and irregular vortex system. The classifications can be demonstrated as a figure of Reynolds number versus the ratio of the height of square cylinder to undisturbed boundary layer thickness. The study then mainly focused on the characteristics of steady horseshoe vortex system (corresponding to Reynolds numbers ranging from 2.0×102 to 2.5×103). The nondimensional characteristics, including the horizontal and vertical distances from the primary vortex core to frontal face of the vertical square cylinder and bottom boundary of the base plate, respectively, the height of stagnation point at frontal face of the square cylinder, and the down-flow discharge as well as circulation of the primary vortex, all increase with increase of the ratio of the height of square cylinder to undisturbed boundary layer thickness. However, they all decrease with the increase of the aspect ratio (i.e., the height-to-width ratio) of the square cylinder. The study provides essential properties of a steady horseshoe vortex system and gives an insight for related engineering applications. It can be served as a basis for more complicated horseshoe vortex systems occurring at high Reynolds numbers.     

Method of Fundamental Solutions for Three-Dimensional Stokes Flow in Exterior Field

The main purpose of the present paper is to provide practical and numerical implementations of the method of fundamental solutions for three-dimensional exterior Stokes problems with quiet far-field condition and discuss the issues therein. The solutions of the steady Stokes problems are obtained by utilizing the boundary collocation method as well as the expansion of Stokeslets, which are the fundamental solutions of the steady Stokes equations. To validate the proposed model, numerical results of a lid-driven cavity flow, uniform flow passing a sphere, and a rotating dumbbell-shaped body show good agreement with the numerical and analytical solutions available in the literature. Also, a hypothetical problem with both vorticity and velocity boundary conditions is solved and compared with the analytical solution. The proposed model is then properly exploited to obtain the flow results of uniform flow passing a pair of vertical spheres in tandem and uniform flow passing a pair of horizontal spheres in tandem. Furthermore, the accuracy of the present numerical scheme is addressed and the detail flow characteristics, such as pressure distribution, streamline contour, velocity field, and vorticity fields are sketched.     

Three-Dimensional Simulation on the Water Flow Field and Suspended Solids Concentration in the Rectangular Sedimentation Tank

A 3D computational fluid dynamics model for describing the water flow and suspended solids (SS) concentration distribution in a rectangular sedimentation tank is presented. The interfacial momentum transfer, buoyant forces, and the effect of sediment-induced density currents are considered. A convection-diffusion equation, which is extended to incorporate the sedimentation of activated sludge in the field of gravity, governed the mass transfer in the clarifier. The double-exponential law is used to describe the dependence of the settling velocity on the concentration. The results show that during the dynamic settling process of the sludge, the mud surface rose slowly, and a period of time later, the mud surface kept stability and reached dynamic equilibrium in the tank. The distribution of velocity along the z axis in the rectangular tank is not uniform, and the surface return flow is found. The turbulent kinetic energy is larger and dropped drastically in the inlet zone, while in the settling zone the turbulent kinetic energy is relatively small. Density current is formed, and the clear water zone, flocculation zone, lamella zone, and compression zone are found. Furthermore, under certain operational conditions, the influence of inlet baffle length on SS settling in the rectangular sedimentation tank is discussed. The prediction by the present model for liquid flow and SS concentration is confirmed by the experimental measurement in a rectangular sedimentation tank in Sweden reported by Larsen in 1977.     

Analytic Solution on Critical Suspended Particle Size and Minimum Collection Efficiency in Deep Bed Filtration

Deep bed filtration is one of the most frequently employed water treatment techniques, and is routinely applied in the clarification of dilute particle suspensions. The prediction of critical suspended particle size is important due to the fact that the corresponding minimum collection efficiency is one of the primary considerations in the design of facilities based on filtration mechanisms. In this study, critical suspended particle size was studied analytically for the case of the Rajagopalan and Tien (RT) filtration model using a harmonic mean type of approximation, as well as a calculation of minimum collection efficiency. The obtained analytic solutions were then compared with the experimental and numerically calculated results, showing good agreement. This analytic solution for critical suspended particle size appears to be applicable to the determination of optimal conditions in deep-bed filtration protocols.     

Measurement of Particle Dynamics in Rapid Granular Shear Flows

Micromechanics of rapid granular flows is studied in a two-dimensional planar granular Couette flow apparatus. The device is capable of generating particulate flows at different shearing rates and solid fractions. Monosize plastic disks are sheared across an annular test section for several shear rates. The motion of particles is recorded through a high speed digital camera and analyzed by image processing techniques. The average and fluctuation velocity profiles are obtained and granular temperature relations with shear rate are investigated. Average streaming velocity across the shear cell decays slightly faster than exponential, and is rather Gaussian when not too close to the wall. Fluctuation velocities and granular temperature across the shear cell are related to effective shear rate. Interparticle collisions are estimated from the particle trajectories and probability distribution of collision angles obtained from particle collision data. In dense flows, three peaks of collision angles are observed, which signal the onset of triangular structure formulation and cause crystallization. It is found that the distribution of collision angles is anisotropic.     

Computational Fluid Dynamics Modeling for the Design of Large Primary Settling Tanks

Settling tanks are used to remove solids at wastewater treatment plants. Many numerical models have been proposed to simulate the settling process and to improve tank efficiency. In this research, a three-dimensional (3D) numerical model is developed to simulate large primary settling tanks. In the proposed model, the non-Newtonian properties of the sludge flow in the settling tank are described by a Bingham plastic rheological model. To eliminate the singularity inherited in the rheological model, a modified constitutive relation is used in both the yielded and unyielded regions. Hindered settling of particles in the settling tank is also modeled. Tracer study, where a massless scalar is injected and transported, is done to investigate the tank’s residence time. This numerical model is used to improve the design of the primary settling tanks, which will be built in Chicago. The Metropolitan Water Reclamation District of Greater Chicago (MWRDGC) is in the process of building new preliminary treatment facilities at their Calumet Water Reclamation Plant (CWRP), including twelve 155-ft-diameter primary settling tanks (PSTs) designed to treat flows up to (480?million?gal./day (MGD). The computational fluid dynamics (CFD) model simulated solids removal efficiencies based on a particle size distribution similar to the one observed in the CWRP influent. The results were used to establish the design basis for tank side-water depth, inlet feedwell dimensions, etc., resulting in improved performance and substantial reduction in construction costs.     

Case Study: Refinement of Hydraulic Operation of a Complex CSO Storage/Treatment Facility by Numerical and Physical Modeling

The performance of a combined sewer overflow (CSO) storage/treatment facility in North Toronto, Ont., Canada, was investigated by conjunctive numerical and physical (hydraulic) modeling. The main objectives of the study were to (1) assess the feasibility of increasing the hydraulic loading of the CSO facility without bypassing; and (2) establish a verified numerical model of the facility for future work. The numerical model [a commercial computational fluid dynamics (CFD), PHOENICS] was validated and verified using results from a hydraulic scale model (1:11.6). The results obtained show that the CFD model can simulate hydraulic conditions in the facility well, as demonstrated by accurate reproduction of the filling rate, water levels at various locations, flow velocities in feed pipes, and overflows from the inflow channel. Numerical simulations identified excessive local head losses and helped select structural changes to reduce such losses. The analysis of the facility showed that with respect to hydraulic operation, the facility is a complex, highly nonlinear hydraulic system. Within the existing constraints, a few structural changes examined by numerical simulation could increase the maximum treatment flow rate in the CSO storage/treatment facility by up to 31%.     

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.     

Simple and General Formula for the Settling Velocity of Particles

A simple, robust, and general formula for the settling velocity of a particle is presented, taking into account the shape and roundness of the particles. It is based on the two asymptotic behaviors of the drag coefficient for low and high Reynolds numbers, respectively. The three coefficients in the proposed equation were fitted for different shape and roundness using explicit relationships. The proposed relationship yields the best results among the studied formulas for many kind of particles with various sizes, shapes, roundnesses, and densities. This formula could therefore be applied to any particle.     

VICAS—An Operating Protocol to Measure the Distributions of Suspended Solid Settling Velocities within Urban Drainage Samples

To meet the need for an operating protocol to measure the distributions of suspended solid settling velocities within urban drainage, the CEREVE research laboratory has developed and validated the VICAS protocol. This procedure makes it possible, through the use of a compact, inexpensive and easy-to-operate settling column, to measure the settling velocity of suspended solids conveyed by either storm water or combined sewage, immediately after collecting a reduced volume sample (4.5 L), and without any pretreatment steps. Two measurement data processing methods were developed and may be easily implemented by means of a series of macros written in Excel. Tests were also conducted for the purpose of evaluating the level of measurement uncertainty specific to the protocol.