Article

Terminal settling velocity for binary irregularly shaped particle mixture from fluidization study: experiment, empirical correlation, and GA-ANN modeling

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  • St. James' School, Kolkata
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Abstract

For precise prediction of the free settling velocities of the solid particle in the quiescent, the Newtonian fluid has been used for different liquid-particle systems, e.g., mineral processing, slurry pipelines, solid-liquid separation, and drilling. This study determined terminal settling velocity (TSV) from the fluidized bed experiments for binary particle mixture of the irregularly shaped particle and water as fluid. The influence of the particle diameter of the binary mixture on TSV was explored. Finally, a simple correlation was proposed to estimate the TSV for a binary mixture of irregular-shaped particles compared with the previously reported correlation in literature. TSV was also predicted with the help of a hybrid of genetic algorithm and artificial neural network (GAANN) model.

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... 19 The hybrid of GA and artificial neural network (ANN) was employed as an optimization technique over the past few years. 20,21 This work uses GA-ANN to speculate the percentage removal of Cu(II). ...
... A similar process was used by researchers in the past. 20,21,57,58 Variation of generation number with respect to the generation error was described in Figure 16. Table 8 gave the result of GA analysis. ...
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Graphical relations have been developed from data on the fall of spherical particles in Bingham fluids available in literature for predicting terminal settling velocity and drag coefficient. It has been found that the relations fit the data extremely well.
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The settling velocity of solids has been determined experimentally in a fluidizing column. The bed expansion characteristics of monodispersed (single component) systems have been noted using water as the fluid. The experimentally determined bed voidages have been plotted against particle Reynolds number, Rep on a log-log graph paper. The settling velocity, ut, has been obtained by extrapolating the resulting straight line to ϵ=1.0. Close-cut size fractions of coal, graphite, sand, limestone, chalcopyrite and magnetite have been used as different solids. Water has been used as the fluidizing fluid throughout the experiment.The experimental values of Ret have been empirically correlated with the relevant system properties, e.g., particle diameter, its shape, density of liquid and solid, liquid viscosity—all of these being represented by Archimedes number and shape factor, φs. The correlation proposed is: Ret=0.103(Ar0.804(φs)0.745 The standard deviation of the proposed correlation has been calculated to be ±15.2%. The ranges of Ar and φs are: 53≤Ar≤3761; 0.5000≤φs≤0.9740The present correlation has been compared with existing equations for monodispersed systems whereby a fair agreement is obtained. This is also found to be reasonably accurate for polydispersed systems when the calculated ut values, based on average bed properties, are compared with those calculated theoretically after being multiplied with the Pettyjohn-Christiansen sphericity correction factor.
Article
Sphere drag data from throughout the twentieth century are available in tabular form. However, much of the data arose from experiments in small diameter cylindrical vessels, where the results might have been influenced by the wall effect. Wall effect corrections developed by others were applied to 178 of the 480 data points collected. This corrected data set is believed to be free of the influence of wall effects. Existing drag and settling velocity correlations were compared to this data set. In addition, new correlations of the same forms were developed using the corrected data. Two new correlations of sphere terminal velocity are proposed, one applicable for all Reynolds numbers less than 2 X 10(5), and the other designed to predict settling velocities with exceptional accuracy for terminal Reynolds numbers less than 4,000, a region that contains almost all applications of interest in environmental engineering. The trial and error solution for settling velocity using the Fair and Geyer equation for drag should be retired in favor of the direct calculation available from these new correlations.
Article
The influence of non-Newtonian flow behavior on sedimentation velocity of particles is investigated using an approximate solution for the motion of an assemblage of solid spheres presented previously by the authors. It is theoretically predicted that the pseudoplasticity decreases the sedimentation velocity and its reduction is pronounced at large voidage. The present theory is discussed using the available empirical correlations. This work is pertinent to ore processing, ceramics manufacture, and sewage treatment.
Article
The published correlations for the drag force on a sphere moving in a fluid have been critically examined and their limitations have been identified. A series of new correlations has been proposed, each covering a wide range of particle Reynolds number Re(10< Re < 3 × 10) by choice of the appropriate form iterative calculations can be avoided.
Article
New correlations have been developed to estimate the steady-state free-fall conditions of isolated, nonspherical, isometric particles moving in Newtonian fluids. The proposed relationships cover the Stokes, the Newton, and the transitional flow regions. Their explicit forms enable the direct computation of the particle size corresponding to a chosen terminal velocity and the straightforward calculation of the terminal velocity of a given nonspherical particle. The terminal velocities of crushed particles of limestone and lime have been measured and compared to the values predicted by the proposed formulas.
Article
Bed expansion of liquid-solid fluidized beds has been correlated empirically in terms of particle Reynolds number and particle Galileo number. The proposed correlation is shown to be applicable from the onset of fluidization to the dilute phase fluidized bed with large voidage. The range of Galileo number covered is from 18 to 3 × 108.
Article
In der vorliegenden Arbeit werden Aufströmungseigenschaften und hydrodynamische Zustände mit Luft aufgewirbelter Partikelschichten untersucht. Anschliεßend wird eine Versuchsanordnung und Methode für Wärmeübergangs-Messungen in solchen Schichten im Vergleich zu ruhenden Schüttungen behandelt und eine Deutung der Versuchsergebnisse gegeben.
Article
The terminal settling velocity of several cylinders (of stainless steel, perspex and glass), needles (of steel) and rectangular prisms (of perspex) falling with their major axis parallel to the direction of motion has been measured in three Newtonian liquids. The measurements have been carried out in three to four fall tubes of different diameters to correct the measured terminal velocity for wall effects. The experimental results reported herein embrace the following ranges of conditions: particle to fall tube diameter ratio: 3.17 × 10−2 to 0.776; length to diameter ratio for cylinders and needles: 5 to 50; the sphericity of particles: 0.35 to 0.7 and particle Reynolds number: 0.095 to 400.Terminal velocity data (corrected for wall effects) have been correlated using two approaches, namely, the usual drag coefficient-Reynolds number relationship, and in terms of a dimensionless velocity factor denoting the departure from the behaviour of an equivalent sphere. Predictive expressions have been developed using both schemes. Finally, the paper is concluded by presenting detailed comparisons between the present results and the prior investigations available in the iterature.
Article
Prediction of the terminal velocity of solid spheres falling through stagnant pseudoplastic fluids is required in several applications like oil well drilling, geothermal drilling, transportation of non-Newtonian slurries and mineral processing. Prior attempts utilized various Newtonian correlations to predict the drag coefficient and from this the terminal velocity with varying degrees of success. We report here carefully derived experimental data for solid spheres falling through non-Newtonian liquids and present them together with measurements reported in the literature, for a total of 80 pairs of Re–CD, and show that the data fall along the same curve. Through nonlinear regression, an equation is derived, similar to the most accurate, simple, five-constant equation proposed for Newtonian liquids, which has not yet been tested for non-Newtonian liquids. The predictions compare favorably with the measurements both for the proposed equation and for the Newtonian equation. With a combination of non-Newtonian data with Newtonian data, from this work and work from other investigators, giving a database of 148 pairs, an improved equation is derived. Analysis of the predictions shows that the Newtonian equation describes extremely well the Newtonian data and furthermore it could be used with good engineering accuracy to predict the terminal velocity of solid spheres falling through stagnant non-Newtonian liquids.
Velocity voidage relationship in fluidizing and sedimenting beds
  • J Basu