Journal articles: 'Hindered settling function'

1

Stricker, A. E., I. Takács, and A. Marquot. "Hindered and compression settling: parameter measurement and modelling." Water Science and Technology 56, no. 12 (December 1, 2007): 101–10. http://dx.doi.org/10.2166/wst.2007.786.

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The Vesilind settling velocity function forms the basis of flux theory used both in state point analysis (for design and capacity rating) and one-dimensional dynamic models (for dynamic process modelling). This paper proposes new methods to address known shortcomings of these methods, based on an extensive set of batch settling tests conducted at different scales. The experimental method to determine the Vesilind parameters from a series of bench scale settling tests is reviewed. It is confirmed that settling cylinders must be slowly stirred in order to represent settling performance of full scale plants for the whole range of solids concentrations. Two new methods to extract the Vesilind parameters from settling test series are proposed and tested against the traditional manual method. Finally, the same data set is used to propose an extension to one-dimensional (1-D) dynamic settler models to account for compression settling. Using the modified empirical function, the model is able to describe the batch settling interface independently of the number of layers.

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Davis, Robert H., and Hatice Gecol. "Hindered settling function with no empirical parameters for polydisperse suspensions." AIChE Journal 40, no. 3 (March 1994): 570–75. http://dx.doi.org/10.1002/aic.690400317.

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Zhu, Zhongfan, Hongrui Wang, Dingzhi Peng, and Jie Dou. "Modelling the Hindered Settling Velocity of a Falling Particle in a Particle-Fluid Mixture by the Tsallis Entropy Theory." Entropy 21, no. 1 (January 11, 2019): 55. http://dx.doi.org/10.3390/e21010055.

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The settling velocity of a sediment particle is an important parameter needed for modelling the vertical flux in rivers, estuaries, deltas and the marine environment. It has been observed that a particle settles more slowly in the presence of other particles in the fluid than in a clear fluid, and this phenomenon has been termed ‘hindered settling’. The Richardson and Zaki equation has been a widely used expression for relating the hindered settling velocity of a particle with that in a clear fluid in terms of a concentration function and the power of the concentration function, and the power index is known as the exponent of reduction of the settling velocity. This study attempts to formulate the model for the exponent of reduction of the settling velocity by using the probability method based on the Tsallis entropy theory. The derived expression is a function of the volumetric concentration of the suspended particle, the relative mass density of the particle and the particle’s Reynolds number. This model is tested against experimental data collected from the literature and against five existing deterministic models, and this model shows good agreement with the experimental data and gives better prediction accuracy than the other deterministic models. The derived Tsallis entropy-based model is also compared with the existing Shannon entropy-based model for experimental data, and the Tsallis entropy-based model is comparable to the Shannon entropy-based model for predicting the hindered settling velocity of a falling particle in a particle-fluid mixture. This study shows the potential of using the Tsallis entropy together with the principle of maximum entropy to predict the hindered settling velocity of a falling particle in a particle-fluid mixture.

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Mazzolani, G., F. Pirozzi, and G. d'Antonoi. "A generalized settling approach in the numerical modeling of sedimentation tanks." Water Science and Technology 38, no. 3 (August 1, 1998): 95–102. http://dx.doi.org/10.2166/wst.1998.0184.

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Numerical models for the prediction of turbulent flow field and suspended solid distribution in sedimentation tanks are characterized by refined modeling of hydrodynamics, but apparently weak modeling of settling properties of suspensions. It is known that sedimentation tanks typically treat highly heterodisperse suspensions, whose concentrations range from relatively high to low values. However, settling is modeled either by considering one or more particle classes of different settling velocity, without accounting for hindered settling conditions, or by treating the suspension as monodisperse, even in regions of low concentration. A new generalized settling model is proposed to account for both discrete settling conditions in low concentration regions of the tanks and hindered settling conditions in high concentration regions. Settling velocities of heterodisperse suspensions are then determined as a function of particle velocities in isolation and their total concentration. The settling model is used in the framework of a transport model for the simulation of hydrodynamics and solid distribution in a rectangular sedimentation tank. Results show that solid distribution is mainly affected by particle interactions in the inlet region and by settling properties of individual particles in the outlet region. Comparison of the proposed settling model with other settling models suggests that a generalized approach of the modeling of settling properties of suspensions is a primary concern to obtain reliable predictions of the removal rate.

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Usher, Shane P., and Peter J. Scales. "Steady state thickener modelling from the compressive yield stress and hindered settling function." Chemical Engineering Journal 111, no. 2-3 (August 2005): 253–61. http://dx.doi.org/10.1016/j.cej.2005.02.015.

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Bürger, Raimund, Julio Careaga, Stefan Diehl, Ryan Merckel, and Jesús Zambrano. "Estimating the hindered-settling flux function from a batch test in a cone." Chemical Engineering Science 192 (December 2018): 244–53. http://dx.doi.org/10.1016/j.ces.2018.07.029.

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Bürger, Raimund, Stefan Diehl, Sebastian Farås, Ingmar Nopens, and Elena Torfs. "A consistent modelling methodology for secondary settling tanks: a reliable numerical method." Water Science and Technology 68, no. 1 (July 1, 2013): 192–208. http://dx.doi.org/10.2166/wst.2013.239.

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The consistent modelling methodology for secondary settling tanks (SSTs) leads to a partial differential equation (PDE) of nonlinear convection–diffusion type as a one-dimensional model for the solids concentration as a function of depth and time. This PDE includes a flux that depends discontinuously on spatial position modelling hindered settling and bulk flows, a singular source term describing the feed mechanism, a degenerating term accounting for sediment compressibility, and a dispersion term for turbulence. In addition, the solution itself is discontinuous. A consistent, reliable and robust numerical method that properly handles these difficulties is presented. Many constitutive relations for hindered settling, compression and dispersion can be used within the model, allowing the user to switch on and off effects of interest depending on the modelling goal as well as investigate the suitability of certain constitutive expressions. Simulations show the effect of the dispersion term on effluent suspended solids and total sludge mass in the SST. The focus is on correct implementation whereas calibration and validation are not pursued.

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Rzayev, A. H., R. Sh Asadova, and V. M. Haqverdiyev. "CONTROL OF THE PROCESSES OF DYNAMIC SETTLING OF OIL EMULSION." ASJ. 2, no. 40 (September 9, 2020): 36–42. http://dx.doi.org/10.31618/asj.2707-9864.2020.2.40.22.

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A systematic analysis of the state of the art in the methods for enhancing processes of thermochemical treatment of oil is carried out. A new method and a new system for controlling the process of dynamic settling of oil emulsion (OE) is developed, which allows increasing the efficiency of managing the process of dynamic settling by more accurately measuring the degree of phase separation, while avoiding the process of “flooding”. The mechanism of formation of an electrical double layer around emulsified water droplets (EWD) and the interaction energy of these droplets as a distance function is shown. An adequate mathematical model of hindered settling of EWD is proposed. It is shown that OE and intermediate emulsion layer (IEL) can be broken down by using microwave radiation. By virtue of this, the authors develop a new method, algorithm and system for automatic measurement of the water cushion level and the thickness of the İEL in settlers based on measuring the optical density of oil.

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Bürger, R., J. Careaga, and S. Diehl. "A review of flux identification methods for models of sedimentation." Water Science and Technology 81, no. 8 (March 11, 2020): 1715–22. http://dx.doi.org/10.2166/wst.2020.113.

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Abstract Most models of sedimentation contain the nonlinear hindered-settling flux function. If one assumes ideal conditions and no compression, then there exist several theoretically possible ways of identifying a large portion of the flux function from only one experiment by means of formulas derived from the theory of solutions of partial differential equations. Previously used identification methods and recently published such, which are based on utilizing conical vessels or centrifuges, are reviewed and compared with synthetic data (simulated experiments). This means that the identification methods are evaluated from a theoretical viewpoint without experimental errors or difficulties. The main contribution of the recent methods reviewed is that they, in theory, can identify a large portion of the flux function from a single experiment, in contrast to the traditional method that provides one point on the flux curve from each test. The new methods lay the foundation of rapid flux identification; however, experimental procedures need to be elaborated.

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Cunha, F. R., G. C. Abade, A. J. Sousa, and E. J. Hinch. "Modeling and Direct Simulation of Velocity Fluctuations and Particle-Velocity Correlations in Sedimentation." Journal of Fluids Engineering 124, no. 4 (December 1, 2002): 957–68. http://dx.doi.org/10.1115/1.1502665.

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In this paper we present direct numerical simulations of monodisperse and polydisperse suspensions of non-Brownian particles sedimenting at low Reynolds number. We describe a scheme to generate ergodic ensembles of random particulate systems and a numerical procedure for computing interactions among spherical particles based on Ewald summation technique for hydrodynamic mobility tensors. From the generation process truly random both monodisperse and multimodal size distributions of particles were obtained for dilute and moderate densities based on a minimum energy criterion. Concerned with computations of the Ewald sums our numerical procedure drastically reduces the CPU simulation time providing results of the hindered settling function in good agreement with available experimental data and asymptotic results for ordered and random periodic arrays of particles. We show new computer simulations with no flux boundary perpendicular to gravity and periodic boundary conditions in horizontal direction. The simulations reproduce the experimental correlation-time and anisotropy of the velocity fluctuations, but have the magnitude of these fluctuations increasing proportional to the size of the system.

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Lester, Daniel R., Shane P. Usher, and Peter J. Scales. "Estimation of the hindered settling functionR(?) from batch-settling tests." AIChE Journal 51, no. 4 (2005): 1158–68. http://dx.doi.org/10.1002/aic.10333.

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12

Bruneau, D., R. Anthore, F. Feuillebois, X. Auvray, and C. Petipas. "Measurement of the average velocity of sedimentation in a dilute polydisperse suspension of spheres." Journal of Fluid Mechanics 221 (December 1990): 577–96. http://dx.doi.org/10.1017/s0022112090003688.

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An X-ray attenuation technique is used to obtain the local concentration of spherical particles in a polydisperse suspension as a function of vertical position and time. From these experimental data, the average velocity of sedimentation in the homogeneous part of the suspension is derived by considering the variation with time of the total volume of particles located above a given fixed horizontal plane. Measurements have been performed in suspensions of particles which differ from each other in size with a total volume concentration in particles between 0.13% and 2.5%, and also in suspensions of particles which differ from each other both in size and in density, the total volume concentration being 2%. For the first kind of suspension, the experimental hindered settling factor is plotted versus the concentration and a linear regression analysis provides the slope with its 90% confidence limits: Se = −5.3 ± 1.1. This experimental average coefficient of sedimentation is in good agreement with the theoretical average coefficient St = −5.60 obtained from the results of Batchelor & Wen (1982). The second kind of suspension, for which permanent doublets of spheres may theoretically exist, is not in the range of validity of Batchelor & Wen's results. The experimental average coefficient of sedimentation for this case is found to be much larger than the prediction obtained by extrapolating Batchelor & Wen's results out of their range of validity. This increased velocity may be experimental evidence of the existence of permanent doublets.

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Plósz, Benedek G., Javier Climent, Christopher T. Griffin, Sergio Chiva, Rani Mukherjee, Elena Penkarski-Rodon, Matthew Clarke, and Borja Valverde-Pérez. "Hindered and compression solid settling functions – Sensor data collection, practical model identification and validation." Water Research 184 (October 2020): 116129. http://dx.doi.org/10.1016/j.watres.2020.116129.

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14

Torfs, Elena, Sophie Balemans, Florent Locatelli, Stefan Diehl, Raimund Bürger, Julien Laurent, Pierre François, and Ingmar Nopens. "On constitutive functions for hindered settling velocity in 1-D settler models: Selection of appropriate model structure." Water Research 110 (March 2017): 38–47. http://dx.doi.org/10.1016/j.watres.2016.11.067.

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15

Vowinckel, B., J. Withers, Paolo Luzzatto-Fegiz, and E. Meiburg. "Settling of cohesive sediment: particle-resolved simulations." Journal of Fluid Mechanics 858 (October 31, 2018): 5–44. http://dx.doi.org/10.1017/jfm.2018.757.

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We develop a physical and computational model for performing fully coupled, grain-resolved direct numerical simulations of cohesive sediment, based on the immersed boundary method. The model distributes the cohesive forces over a thin shell surrounding each particle, thereby allowing for the spatial and temporal resolution of the cohesive forces during particle–particle interactions. The influence of the cohesive forces is captured by a single dimensionless parameter in the form of a cohesion number, which represents the ratio of cohesive and gravitational forces acting on a particle. We test and validate the cohesive force model for binary particle interactions in the drafting–kissing–tumbling (DKT) configuration. Cohesive sediment grains can remain attached to each other during the tumbling phase following the initial collision, thereby giving rise to the formation of flocs. The DKT simulations demonstrate that cohesive particle pairs settle in a preferred orientation, with particles of very different sizes preferentially aligning themselves in the vertical direction, so that the smaller particle is drafted in the wake of the larger one. This preferred orientation of cohesive particle pairs is found to remain influential for systems of higher complexity. To this end, we perform large simulations of 1261 polydisperse settling particles starting from rest. These simulations reproduce several earlier experimental observations by other authors, such as the accelerated settling of sand and silt particles due to particle bonding, the stratification of cohesive sediment deposits, and the consolidation process of the deposit. They identify three characteristic phases of the polydisperse settling process, viz. (i) initial stir-up phase with limited flocculation, (ii) enhanced settling phase characterized by increased flocculation, and (iii) consolidation phase. The simulations demonstrate that cohesive forces accelerate the overall settling process primarily because smaller grains attach to larger ones and settle in their wakes. For the present cohesive number values, we observe that settling can be accelerated by up to 29 %. We propose physically based parametrization of classical hindered settling functions introduced by earlier authors, in order to account for cohesive forces. An investigation of the energy budget shows that, even though the work of the collision forces is much smaller than that of the hydrodynamic drag forces, it can substantially modify the relevant energy conversion processes.

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Rajan, T. P. D., and B. C. Pai. "Processing of Functionally Graded Aluminium Matrix Composites by Centrifugal Casting Technique." Materials Science Forum 690 (June 2011): 157–61. http://dx.doi.org/10.4028/www.scientific.net/msf.690.157.

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Functionally graded materials (FGM) possess a gradual transition in the composition or microstructure within a component inducing gradual changes in the functions and properties of the material with varying location. The present investigation is to form functionally graded aluminum composites with varying microstructural features and properties gradation using centrifugal casting by varying the material and process parameters. The ex-situ Al-SiC FGM has shown graded distribution of SiC towards the outer periphery and Al-SiC-Graphite has shown both particle gradations of SiC and Graphite towards inner periphery due to hindered settling phenomena. In in-situ Al-Si and Al-Si-Mg2Si system the particles are distributed towards the inner periphery of the casting. The paper also emphasizes on selected engineering components and tailoring their graded structures and properties by utilization of suitable reinforcement combinations and process parameters are discussed.

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Apostolopoulos, Sotiris, Marion Leibold, and Martin Buss. "Transitioning Between Underactuated Periodic Orbits: An Optimal Control Approach for Settling Time Reduction." International Journal of Humanoid Robotics 15, no. 06 (December 2018): 1850027. http://dx.doi.org/10.1142/s0219843618500275.

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In underactuated systems, a transition between two periodic orbits is generally characterized by slow convergence. This is due to the fact that the unactuated degree of freedom (DoF) hinders the state of the system to enter the domain of attraction of the target orbit close to the fixed point of the Poincaré Map. In this paper, we introduce an optimal control algorithm to reduce the settling time of transitions between periodic orbits of underactuated walking robots. This is achieved by utilizing the hybrid zero dynamics (HZD) framework to express the feasibility condition of the transition which can be imposed as an inequality constraint in the proposed optimal control problem. In addition, the cost function penalizes deviations from the fixed point of the target periodic orbit in the zero dynamics manifold while at the same time all dynamic and kinematic assumptions are treated as constraints. Furthermore, high magnitude torques are also penalized. The numerical results show that the proposed methodology can indeed improve the settling time compared to the transition methodology usually found in the bibliography and at the same time provide a feasible and smooth motion.

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Brzinski, T. A., and D. J. Durian. "Observation of two branches in the hindered settling function at low Reynolds number." Physical Review Fluids 3, no. 12 (December 10, 2018). http://dx.doi.org/10.1103/physrevfluids.3.124303.

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Journal articles on the topic 'Hindered settling function'

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