Hindered Settling Velocity Research Articles

Hindered Settling Velocity in Particle-Fluid Mixture: A Theoretical Study Using the Entropy Concept

AbstractIn the study of mechanics of sediment transport, settling velocity is one of the important parameters because it is needed to solve the governing equations. It has been established that the...

On constitutive functions for hindered settling velocity in 1-D settler models: Selection of appropriate model structure

Advanced 1-D models for Secondary Settling Tanks (SSTs) explicitly account for several phenomena that influence the settling process (such as hindered settling and compression settling). For each of these phenomena a valid mathematical expression needs to be selected and its parameters calibrated to obtain a model that can be used for operation and control. This is, however, a challenging task as these phenomena may occur simultaneously. Therefore, the presented work evaluates several available expressions for hindered settling based on long-term batch settling data. Specific attention is paid to the behaviour of these hindered settling functions in the compression region in order to evaluate how the modelling of sludge compression is influenced by the choice of a certain hindered settling function. The analysis shows that the exponential hindered settling forms, which are most commonly used in traditional SST models, not only account for hindered settling but partly lump other phenomena (compression) as well. This makes them unsuitable for advanced 1-D models that explicitly include each phenomenon in a modular way. A power-law function is shown to be more appropriate to describe the hindered settling velocity in advanced 1-D SST models.

Practical identifiability and uncertainty analysis of the one-dimensional hindered-compression continuous settling model

The practical application of the one-dimension hindered-compression settling models remains a challenge, since the model calibration strongly depends on experimental observations with limited information. In this study, the identifiability of parameter subsets of the hindered-compression models is evaluated for various experimental layouts. Global sensitivity analysis is used to preliminarily select the influential parameters which can be reasonably estimated, while the identifiability analysis of parameter subsets is conducted based on the local sensitivity functions and collinearity measures. The batch settling curve observations are informative for calibrating hindered parameters, and to determine the compression parameters, the concentration profile observations may need to be collected. For different experimental layouts, at least three parameters are identifiable, and the number of identifiable parameters can potentially increase to five, if both batch settling curve and concentration observations are available. The parameter subset identifiability is sensitive to the choice of initial parameter values, and determining the initial values of hindered parameters and gel concentration by measuring the hindered settling velocities and the top concentration of the static sediment respectively allows efficient reduction of the sensitivity. Parameter subset estimates are sensitive to the values of fixed parameters, and reliable estimation of identifiable parameter subsets is possible to significantly decrease model prediction uncertainties.

Limit of stokesian settling concentration characterizes sludge settling velocity

Flocculent settling (stokesian) is predominant within ideally operating clarifiers, and the shift to ‘slower’ hindered settling (non-stokesian) causes both failure and poor effluent quality. Therefore, a new metric for settling characteristics was developed and classified as Limit of Stokesian Settling (LOSS). The technique consisted of determining the total suspended solids (TSS) concentration at which mixed liquor settling characteristics transition from stokesian to non-stokesian settling. An image analytical technique was developed with the aid of MATLAB® to identify this transition. The MATLAB tool analyzed RGB images from video, and identified the presence of an interface by a dramatic shift in the Red indices. LOSS data for Secondary activated-sludge systems were analyzed for a period of 60 days at the Blue Plains Advanced Wastewater Treatment Plant. LOSS for secondary systems typically occurred between 600 and 700 mg TSS/L but reached 1000 mg TSS/L for a good settling secondary sludge and 500 mg TSS/L for a poor settling secondary sludge, settling quality was based on hindered settling rates. In addition, LOSS was collected for granular systems seeded with cyclone underflow from Strass Wastewater Treatment Plant, it was observed that LOSS was higher for granular systems ranging from 1600 to 5500 mg TSS/L for low and high levels of granulation, respectively. The monovalent to divalent cation ratio (M/D) was increased with the addition of sodium ions to deteriorate settling properties. Samples adjusted with higher M/D consistently had 100 mg TSS/L (15%) decrease in LOSS from the control. LOSS numbers collected experimentally were validated with the Takacs et al. (1991) settling model. When compared to flux curves with small changes in sludge matrix, LOSS was proven to be faster at characterizing hindered settling velocity and was less erratic. This is the first time a measurement method has been developed to characterize the transition from stokesian to non-stokesian settling. Additionally, this is the first step in developing new metrics to predict clarifier failure, and determine effluent quality through the development of flocculent settling metrics.

Studies of a Water-Only Cyclone with a Three-Stage Cone for Fine Coal Beneficiation

ABSTRACTSeparation tests on a high-sulfur-coal sample were carried out using a water-only cyclone (WOC) with a three-stage cone (also named a tri-cone water-only cyclone). The lower size limits of deashing and desulfurization were determined to be 0.098 mm and 0.045 mm, respectively. According to a float-and-sink analysis of various size fractions in the overflow and underflow, the Ecart probable (Ep) value as well as the separation density increased as the lower size fractions decreased. According to dynamic analysis, terminal hindered-settling velocities of spherical particles in the radial direction were obtained and an equation to estimate the lower removal size limits of heavy minerals was developed. With the help of numerical simulations of water–air two-phase flow fields in a tri-cone water-only cyclone (TWOC) and a conventional hydrocyclone, the role of the three-stage cone in the separation process was analyzed.

Microthrix parvicella abundance associates with activated sludge settling velocity and rheology – Quantifying and modelling filamentous bulking

The objective of this work is to identify relevant settling velocity and rheology model parameters and to assess the underlying filamentous microbial community characteristics that can influence the solids mixing and transport in secondary settling tanks. Parameter values for hindered, transient and compression settling velocity functions were estimated by carrying out biweekly batch settling tests using a novel column setup through a four-month long measurement campaign. To estimate viscosity model parameters, rheological experiments were carried out on the same sludge sample using a rotational viscometer. Quantitative fluorescence in-situ hybridisation (qFISH) analysis, targeting Microthrix parvicella and phylum Chloroflexi, was used. This study finds that M. parvicella – predominantly residing inside the microbial flocs in our samples – can significantly influence secondary settling through altering the hindered settling velocity and yield stress parameter. Strikingly, this is not the case for Chloroflexi, occurring in more than double the abundance of M. parvicella, and forming filaments primarily protruding from the flocs. The transient and compression settling parameters show a comparably high variability, and no significant association with filamentous abundance. A two-dimensional, axi-symmetrical computational fluid dynamics (CFD) model was used to assess calibration scenarios to model filamentous bulking. Our results suggest that model predictions can significantly benefit from explicitly accounting for filamentous bulking by calibrating the hindered settling velocity function. Furthermore, accounting for the transient and compression settling velocity in the computational domain is crucial to improve model accuracy when modelling filamentous bulking. However, the case-specific calibration of transient and compression settling parameters as well as yield stress is not necessary, and an average parameter set – obtained under bulking and good settling conditions – can be used.

Analysis of the Effect of High‐Pressure Homogenization (HPH) on the Settling Velocity of Particles in an Alcoholic Rice Beverage Using Video Recording, Turbidity and Computational Fluid Dynamic Simulation

AbstractHigh‐pressure homogenization (HPH) was applied to an alcoholic rice beverage (ARB). The effects of pressure (48–172 MPa) and the number of passes (1–3) on the fluid properties of the ARB, such as particle size, viscosity, turbidity and settling velocity, were investigated. Mean diameters continuously decreased with increasing homogenization pressure (P) and pass number (PN) until it reached a saturated condition (172 MPa with PN = 2). The viscosity and volume fraction of ARBs proportionally increased with increasing P and PN. The turbidity of HPH‐treated samples had stable characteristic until approximately 40 min. The settling velocities estimated by three different methods, including video recording, computational fluid dynamics simulation and analytic solutions (free and hindered flow). The free and hindered settling velocity of nonhomogenized and HPH‐treated samples were in the range of 1.2 × 10−4 to 1.7 × 10−4 and 0.3 × 10−7 to 4.3 × 10−7 m/s, respectively.Practical ApplicationFor alcoholic rice beverages (ARB), the unique translucent milky color differentiates ARB from distilled alcoholic beverage. The translucency is mainly due to the solid particles in the ARB, which could not be completely separated by the coarse filtration. Settling of solid particles caused a phase separation of ARB during storage or even serving in the glass. Our study showed that the high‐pressure homogenization (HPH) dramatically reduced the particle size of the ARB. Consequently, the settling velocity of HPH‐treated samples were significantly lower than that of nonhomogenized (NH) sample. The phase separation of ARB was delayed significantly after HPH.

Hindered Settling Velocity & Structure Formation during Particle Settling by Direct Numerical Simulation

Direct numerical simulation is used to study the dynamics of particle settling for Reynolds number from 0.1 to 50 and solid volume fraction from single particle to 0.4. The principle investigations are the effects of Reynolds number and solid volume fraction on average settling velocity, velocity fluctuations and particles structuring during settling. It is observed that average settling velocity deviates from the well-known power law for dilute suspension and moderate range of Reynolds number. Moreover, the increase of velocity fluctuations with domain size saturates and becomes about constant for moderate range of Reynolds numbers in contrast to low Reynolds number in which the fluctuations keep increasing. These behaviors are due to the separated particle pairs which are formed due to inter-particle wake interactions. As the solid volume fraction increases, the smaller inter-particle distances diminish the wake effects and corresponding particle structures.

EULER-LAGRANGE SIMULATIONS OF SEDIMENT TRANSPORT IN OSCILLATORY BOUNDARY LAYERS WITH BEDFORMS

Accurate prediction of sediment transport in the presence of bedforms such as sand ripples requires an advanced understanding of how dynamic sediment beds interact with turbulent oscillatory flows. In this paper we propose a new approach for simulating these interactions, based on a fixed grid multiphase Euler-Lagrange simulation, that fully couples dynamic bed evolution to the motion of a sub-grid scale Lagrangian sediment phase. The sediment phase is evolved by computing hydrodynamic and inter-particle forces and torques acting on individual particles, and is coupled to the fluid phase through the volume-filtered Navier-Stokes equations. We validate the approach for sediment transport applications using hindered settling velocity tests, and show very good agreement with the experimental data of Baldock et al. (2004). We then apply the approach to simulate sediment transport and ripple bed morphology in oscillatory flow conditions corresponding to the experimental studies of Van der Werf et al. (2007). During the simulation, particles near ripple surface are isolated from immobile ones below allowing the computation to devote resources only to particles that may be become mobilized. Although preliminary in nature, the simulation results demonstrate that that the model can correctly capture the near bed velocities, suspended sediment concentrations, and pick-up of sediment by key vortical structures.

Toward numerical modeling of fine particle suspension using a two-way coupled Euler–Euler model. Part 1: Theoretical formulation and implications

This paper presents a two-way coupled Euler–Euler model to simulate the dilute suspension of fine particles. The goal is to develop a three-dimensional numerical model that is capable of replicating detailed features of particle-laden turbulent flow. In addition to the terms found in typical two-phase Euler–Euler models, the present formulation also accounts for the effects of added mass and pressure, which are crucial to solid–liquid systems in which densities for each phase are of the same order. This study derives various approximations with which to assess existing model formulations, namely solid–gas equations, equilibrium-state approximation, simplified Euler models, and hindered settling velocity. We then emphasize the deviation of the present simulation results from the equilibrium state, which is simulated by the single-phase approach. We investigate simple examples of the Rayleigh–Taylor instability induced by the suspension of fine particles, the results of which reveals the distribution of non-equilibrium particle inertia. We then examine its influence on the carrier flow. A comparison between the present two-phase model and single-phase approximation demonstrates the importance of the coupled pressure on the evolution of a single bubble induced by the particle-driven Rayleigh Taylor instability.

Towards Improved 1-D Settler Modelling: Calibration of the Bürger Model and Case Study

Recently, Burger et al. (2011) developed a new 1-D SST model which allows for more realistic predictions of the sludge settling behaviour than traditional 1-D models used to date. However, the addition of a compression function in this new 1-D model complicates the model calibration. This study aims to report advances in the calibration of this novel 1-D model. Data of the evolution of the sludge blanket height during batch settling experiments were collected at different initial solids concentrations. Based on the linear slopes of the batch settling curves the hindered settling velocity functions by Vesilind (1968) and Takacs et al. (1991) were calibrated. Although both settling velocity functions gave a good fit to the experimental data, very large confidence intervals were found for the parameters of the settling velocity by Takacs. Global sensitivity analysis showed that it is not possible to find a unique set of parameter values for the settling function by Takacs based on experimental data of the hindered settling velocity. Subsequently, the calibrated Vesilind settling velocity was implemented in the 1-D model by Burger et al. (2011) and the parameters of the additional compression function were calibrated by fitting the model by Burger et al. (2011) to the batch settling curves. Simulation results showed that while the 1-D model by Takacs et al. (1991) underpredicted the experimental data of sludge blanket heights, the model by Burger et al. (2011) was able to predict the experimental data far more accurately. However, a global sensitivity analysis showed that no unique optimum for the combined set of hindered and compression parameters could be found. (Less)

Numerical simulation of bidisperse hard spheres settling in a fluid

Average settling velocity of non-uniform hard spheres in a viscous fluid is determined by using a large-scale numerical simulation that is carried out for over 103 spheres in a periodic unit cell which extends infinitely. An efficient calculation scheme is used for reducing the computation cost which steeply increases with the number of the spheres. The calculation scheme is based on a fast summation method for far-field hydrodynamic interaction among spheres. It is applied in the computation of hindered settling velocity of hard spheres with bidisperse size distribution in a viscous fluid. The simulation results are compared with the theoretical predictions by Batchelor [8] and Davis and Gecol [9]. It is found that the prediction by Davis and Gecol reasonably agrees with the numerical results.

Model for Mixture Theory Simulation of Vortex Sand Ripple Dynamics

The complex coupled interactions between fluid and sandy sediment on the seafloor are simulated with a three-dimensional bottom boundary layer model (SedMix3D) developed from mixture theory. SedMix3D solves the unfiltered Navier-Stokes equations for a fluid-sediment mixture treated as a single continuum with effective properties that parameterize the fluid-sediment and sediment-sediment interactions including a variable mixture viscosity, a bulk hindered settling velocity, and a shear-induced, empirically calibrated, mixture diffusion term. A sediment flux equation models the concentration of sediment by describing the balance of sediment flux by advection, gravity, and shear-induced diffusion. The grid spacing is on the order of a sediment grain diameter, and simulated flows had maximum free-stream velocities between 20 and 120 cm/s and periods between 2 and 4 s. Modeled ripple geometries ranged from a single ripple to multiple ripples with varying heights, lengths, and steepness. Only noncohesive sedim...

Estimation of hindered settling velocity of suspensions

Four effective-medium models (EM-I, II, III, IV) are utilized and compared for determining hindered settling velocity of equi-sized particles in a viscous fluid. Among the models, EM-IV model is found to accurately predict the effective viscosity and the hindered settling velocity of monodisperse suspensions. In EM-IV model which was developed for determining the diffusivity of proteins in a biological membrane by Dodd et al. [T.L. Dodd, D. A. Hammer, A.S. Sangani, D.L. Koch, J. Fluid Mech. 293 (1995) 147], the effective-medium region begins at the distance R = a[(1 − S( 0))/ ϕ] 1/3 from the origin where the center of the test particle is located, where a is the radius of the particle, ϕ is the volume fraction of the particles in the suspension, and S( 0) is the zero wavenumber limit of the structure factor. The estimations by EM-IV model agree very well with the exact calculations and the experimental observations. The hindered settling velocity U of the particles is given, in Richardson–Zaki form, by U/ U 0 = (1 − ϕ) 5.5, where U 0 is the settling velocity for an isolated particle.

Hindered settling velocity of cohesive/non-cohesive sediment mixtures

New methods are proposed for predicting the hindered settling conditions encountered by concentrated suspensions containing mixtures of sand particles and mud flocs. These methods, based on two-fraction formulations, are developed by consideration of the settling characteristics of monodisperse and polydisperse solid particle suspensions applied to cohesive/non-cohesive mixtures of mud flocs and sand particles. The behaviour of these predictive methods is evaluated over a wide range of mixture conditions and compared with existing formulations, with their parametric dependence on the relative volumetric concentrations and floc/particle sizes for the mud and sand constituents established. The results indicate that consideration of the full return flow effects generated by both fractions provides the best modelling framework for predicting the hindered settling conditions over a wide range of sand–mud mixtures.

Calculation of the settling velocity of particles for the hindered sedimentation of polydisperse mixtures of arbitrarily shaped solid particles in a Newtonian liquid

The method developed earlier for calculating the hindered settling velocity of arbitrarily shaped particles is generalized for polydisperse particle-size distributions. The calculated results are in satisfactory agreement with the experimental data on the sedimentation of bi-and trimodal mixtures of spherical glass particles.

Hindered settling velocity and microstructure in suspensions of solid spheres with moderate Reynolds numbers

Lattice-Boltzmann simulations are employed to determine the mean settling velocity and pair distribution function for spheres settling in a liquid. The Reynolds number based on the terminal velocity ranges from 1 to 20, the solid-to-fluid density ratio is ρp∕ρf=2.0, and the solid volume fraction is varied from 0.005 to 0.40. At volume fractions larger than about 0.05, the ratio of the mean settling velocity to the terminal velocity u* can be fit by a power-law expression u*=k(1−ϕ)n, where k and n are functions of the Reynolds number based on the terminal velocity. The constant k is typically about 0.86–0.92 and u* deviates from the power-law behavior in dilute suspensions. The extent of this deviation increases with increasing Reynolds number. We show that the hindered settling velocity follows a power law when the particle microstructure is similar to that in a hard-sphere suspension. The deviation from the power-law behavior can be correlated with an anisotropic microstructure resulting from wake interactions among the spheres. This microstructure, which occurs in dilute suspensions and is most pronounced at the higher Reynolds numbers explored in our study, consists of a decreased pair distribution function for pairs with vertical separation vectors and a peak in the pair distribution function for horizontal separations corresponding to about two particle diameters.

Solids characterisation in an anaerobic migrating bed reactor (AMBR) sewage treatment system

The aim of this work was to characterise the solids in an anaerobic sewage treatment process. Hindered settling velocity, particle size distributions (PSD), influent and effluent COD P/SS and discrete settling velocity distributions were all measured. The anaerobic migrating bed reactor (AMBR) solids were mainly flocculent and had a settling rate equivalent to a good settling activated sludge (∼SSVI=60 mL/g). The PSD of the anaerobic solids were very different to PSD for activated sludge flocs, with the anaerobic solids having a modal size an order of magnitude smaller than activated sludge, but a range of particle sizes being two orders of magnitude larger. There was a far greater range in size and structure in the anaerobic solids. The anaerobic process solids were primarily feed solids undergoing VSS destruction (hydrolysis). The biological mass was small. The solids seemed to retain their size as the volatiles were degraded and the density decreased (‘skeletons’ of the influent particulates). The small fraction of slowly settling solids, which have been identified to have a similar modal size but lower density than the mixed solids in the reactor, pose a solids retention time (SRT) control problem when relying on settling alone for solids retention.

Calculation of the hindered settling velocity of a bimodal mixture of solid particles of arbitrary shape in a Newtonian fluid

A method for calculating the settling velocity of a bimodal mixture of particles of arbitrary shape is proposed. The method uses the concept of effective particle diameter, which characterizes the particle shape, volume, and midsection area. The method takes into account the contact interaction between particles of different sizes due to their collisions. The calculation results are compared with experimental data on settling of bimodal mixtures of limestone particles of arbitrary shape.

Hindered settling velocity of a bimodal mixture of spherical solid particles in a Newtonian fluid

Works describing methods for calculating the settling velocity of a biomodal mixture of solid particles are analyzed. A method for calculating the settling velocity of a bimodal mixture of spherical particles is proposed that takes into account the contact interaction between particles of different sizes due to their collisions. The calculation results are in satisfactory agreement with experimental data on settling of a bimodal mixture of spherical solid particles.