This study describes the development and validation of Computational Fluid Dynamics (CFD) methodology for the simulation of dispersed two-phase flows. A two-fluid (Euler-Euler) methodology previously developed at Imperial College is adapted to high phase fractions. It employs averaged mass and momentum conservation equations to describe the time-dependent motion of both phases and, due to the averaging process, requires additional models for the inter-phase momentum transfer and turbulence for closure. The continuous phase turbulence is represented using a two-equation k − ε−turbulence model which contains additional terms to account for the effects of the dispersed on the continuous phase turbulence. The Reynolds stresses of the dispersed phase are calculated by relating them to those of the continuous phase through a turbulence response function. The inter-phase momentum transfer is determined from the instantaneous forces acting on the dispersed phase, comprising drag, lift and virtual mass. These forces are phase fraction dependent and in this work revised modelling is put forward in order to capture the phase fraction dependency of drag and lift. Furthermore, a correlation for the effect of the phase fraction on the turbulence response function is proposed. The revised modelling is based on an extensive survey of the existing literature. The conservation equations are discretised using the finite-volume method and solved in a solution procedure, which is loosely based on the PISO algorithm, adapted to the solution of the two-fluid model. Special techniques are employed to ensure the stability of the procedure when the phase fraction is high or changing rapidely. Finally, assessment of the methodology is made with reference to experimental data for gas-liquid bubbly flow in a sudden enlargement of a circular pipe and in a plane mixing layer. Additionally, Direct Numerical Simulations (DNS) are performed using an interface-capturing methodology in order to gain insight into the dynamics of free rising bubbles, with a view towards use in the longer term as an aid in the development of inter-phase momentum transfer models for the two-fluid methodology. The direct numerical simulation employs the mass and momentum conservation equations in their unaveraged form and the topology of the interface between the two phases is determined as part of the solution. A novel solution procedure, similar to that used for the two-fluid model, is used for the interface-capturing methodology, which allows calculation of air bubbles in water. Two situations are investigated: bubbles rising in a stagnant liquid and in a shear flow. Again, experimental data are used to verify the computational results.

Computational fluid dynamics of dispersed two-phase flows at high phase fractions

Dr. R. Peter King covers the field of quantitative modeling of mineral processing equipment and the use of these models to simulate the actual behavior of ore dressing and coal washing as they are configured to work in industrial practice. The material is presented in a pedagogical style that is particularly suitable for readers who wish to learn the wide variety of modeling methods that have evolved in this field. The models vary widely from one unit type to another. As a result each model is described in some detail.Wherever possible model structure is related to the underlying physical processes that govern the behaviour of particulate material in the processing equipment. Predictive models are emphasised throughout so that, when combined, they can be used to simulate the operation of complex mineral processing flowsheets. The development of successful simulation techniques is a major objective of the work that is covered in the text.* Covers all aspects of modeling and simulation* Provides all necessary tools to put teh theory into practice* Free CD ROM includedAuthor: King, R. Peter Publisher: Butterworth-Heinemann Illustration: N Language: ENG Title: Modeling and Simulation of Mineral Processing Systems Pages: 00416 (Encrypted PDF) On Sale: 2001-11-27 SKU-13/ISBN: 9780750648844 Category: Technology & Engineering : Material Science Category: Technology & Engineering : Mechanical Category: Technology & Engineering : Metallurgy

http://www.dlfiles24.com/pdf42/109884105-modeling_and_simulation_of_mineral_processing_systems_r_peter_king.pdf

Modeling and simulation of mineral processing systems

Kinetics of iron complexation by dissolved natural organic matter in coastal waters

Formation of jarosite during Fe2+ oxidation by Acidithiobacillus ferrooxidans

The scenario of transition to chaos for a sphere falling or ascending under the action of gravity in a Newtonian fluid is investigated by numerical simulation. The mathematical formulation is parameterized using two non-dimensional parameters: the solid/fluid density ratio and the generalized Galileo number expressing the ratio between the gravity–buoyancy and viscosity effects. The study is carried out fully in this two-parameter space. The results show that for all density ratios the vertical fall or ascension becomes unstable via a regular axisymmetry breaking bifurcation. This bifurcation sets in slightly earlier for light spheres than for dense ones. A steady oblique fall or ascension follows before losing stability and giving way to an oscillating oblique movement. The secondary Hopf bifurcation is shown not to correspond to that of a fixed sphere wake for density ratios lower than 2.5, for which the oscillations have a significantly lower frequency. Trajectories of falling spheres become chaotic directly from the oblique oscillating regime. Ascending spheres present a specific behaviour before reaching a chaotic regime. The periodically oscillating oblique regime undergoes a subharmonic transition yielding a low-frequency oscillating ascension which is vertical in the mean (zigzagging regime). In all these stages of transition, the trajectories are planar with a plane selected randomly during the axisymmetry breaking. The chaotic regime appears to result from an interplay of a regular and of an additional Hopf bifurcation and the onset of the chaotic regime is accompanied by the loss of the remaining planar symmetry. The asymptotic chaotic states present an intermittent character, the relaminarization phases letting the subcritical plane and periodic trajectories reappear.

Instabilities and transition of a sphere falling or ascending freely in a Newtonian fluid

Rapid simultaneous quantitative determination of ferric and ferrous ions in drainage waters and similar solutions

The aim of the note is to determine the velocity and the drag coefficient of freely-rising light spheres, and to compare these data with that predicted for the case of free settling

Free rising spheres do not obey newton's law for free settling

The bed expansion characteristics of two-phase inverse fluidization were studied. Twelve different spheres with diameters from 1.31 to 7.24 mm and densities between 75 and 930 kg/m3 were fluidized with water. The experimental lne-lnU curves were parallel to those predicted by the model of Richardson and Zaki and therefore the exponents n were similar. However, Ui, the liquid velocity at e = 1 differed from that predicted from the standard drag curve for Ret > 130. This can be explained by the fact that the drag curve of a freely rising light sphere differs from that of a falling particle. The values of Ui calculated using this modified drag curve were in good agreement with the experimental results. The difference between experimental and calculated from the Ergun equation minimal fluidization velocities is explained by the difference in mechanical inertia of the light and heavy particles.

Bed expansion of liquid‐solid inverse fluidization

The inverse fluidization is a new multiphase gas-liquid or gas-liquid-solid system. The first studies of two phase (liquid-solid) inverse fluidization were originally published independently by Shimodaira et al. [6], Nikolov et al. [5] and Fan et al. [2]. The main difference between the classic and inverse fluidization is that the solid particle density in the inverse fluidized bed is less than the density of the continuous fluid and therefore the bed is fluidized by a downflow of the fluid. Schematic illustration of both classic and inverse fluidized beds is shown in Figure 1. One of the most important recent applications of fluidized beds is in the field of bioreactor engineering. It is well known that almost all types of microorganisms spontaneously attach themselves to any inert solid surface in contact with the liquid growth media. The microorganisms use exopolysaccharide {open_quotes}bridges{close_quotes} to attach themselves to the solid support and to each other. This structure of microorganisms and exopolysaccharides is known as biofilm. The fluidized bed bioreactors are used primarily for processes in which the fluidized particles are used as an inert solid support. There is a problem when the biofilm microorganisms multiply and the biofilm thickness increase. This limits diffusion ofmore » oxygen and/or the organic substrate to the deeper layers of the biofilm. Starvation of the microorganisms at the base of the biofilm causes pieces of the biofilm to detach (Figure 2) and leads to ineffective bioreactor operation. The maximal biofilm thickness at which no diffusional limitation is observed (phase 3 in Figure 2), is usually around 100 {mu}m. Therefore, to operate the bioreactor efficiently, the biofilm thickness should be approximately 100 {mu}m. The use of inverse fluidization can solve this problem. 6 refs., 10 figs.« less

L. Nikolov

Papers

Rapid simultaneous quantitative determination of ferric and ferrous ions in drainage waters and similar solutions

Free rising spheres do not obey newton's law for free settling

Bed expansion of liquid‐solid inverse fluidization

Application of inverse fluidization in wastewater treatment: from laboratory to full-scale bioreactors

The inverse fluidized bed biofilm reactor: a new laboratory scale apparatus for biofilm research.