- Title
- Dispersion behaviour in binary solid-liquid fluidised beds
- Creator
- Khan, Md. Shakhaoath
- Relation
- University of Newcastle Research Higher Degree Thesis
- Resource Type
- thesis
- Date
- 2017
- Description
- Research Doctorate - Doctor of Philosophy (PhD)
- Description
- Solid-liquid fluidised beds (SLFB) are often encountered in mineral processing applications which include particle classification and mineral ore leaching/washing. Due to complex phase interactions, the fluidised bed shows some interesting characteristics such as phase segregation and mixing, depending on the variation in particle diameter, density and superficial fluid velocity. In the design of such multiphase fluidised beds, it is important to understand the bed expansion behaviour, the spatial distribution of phase volume fractions, and the segregation and intermixing of the solid phases involved for successful performance of the equipment.A widely used hypothetical notion in binary SLFB systems is that total bed height is additive, i.e. bed height equals to the sum of heights of the two individual components bed fluidised at the same liquid superficial velocity, However, a significant negative deviation was reported in another study. Consequently, the hypothesis that combined bed heights are additive requires further investigation. SLFB system involves complex hydrodynamics exhibiting complete segregation to complex mixing due to coupled phase interactions. Literature review indicates that segregation hydrodynamics in binary SLFB system such as complete segregation, partial segregation and no segregation mainly occur due to both unequal diameter and density ratio. While the effect of unequal density for the observed segregation behaviour is more intuitive, effect of particle diameter ratio for constant particle density system needs further attention. Literature review also indicates that individual solid mass for the binary SLFB was not reported in most of the cases which is a critical requirement to justify solid mass conservation of the system for any related modelling work. Effect of solid mass ratio, therefore, on the bed pattern for constant density particles system remains rather unexplored. It is also of interest to understand the dynamics in the mixing zone specifically the effect of superficial velocity and mass ratio which provides an insight to the dispersion behaviour in SLFB system. It is also noted that this aspect has not been addressed even in the previously reported Computational Fluid Dynamics (CFD) based studies. The present study investigated the bed expansion behaviour of a mono and binary particle (spherical glass beads of diameter 3, 5 and 8 mm of equal density, 2,230 kg m-3) filled solid-liquid fluidised bed (SLFB) using water as a fluidising medium. Experiments were carried out using different particle mass ratios ranging from 0.17 to 6.0. In the expanded bed, both the segregated and intermixed zones were observed with the different particle diameter combinations. In a completely segregated SLFB, the bottom mono-sized layer exhibited a negative deviation ~ 23 % whereas a positive deviation ~ 25 % was found in the top mono-sized layer, when compared with the corresponding counterpart of mono-sized system. A small mixing zone was observed even in a completely segregated SLFB for the higher diameter ratio case which decreased slightly due to the increase in the liquid superficial velocity. For relatively lower diameter ratio cases, a relatively larger mixing zone was observed which increased in size, with an increase in the liquid superficial velocity. The bed expansion ratio was observed to decrease with an increase in the solid mass ratio of the binary system, however it increased with an increase in the fluidising velocity ratio, following a reasonable power law trend. The final bed height of the binary mixture was not a simple addition of its constituent mono-component bed heights and both positive and negative deviations were noted when compared with the individual expansions of the mono-sized SLFB system. Numerically, a two-dimensional (2-D) Eulerian-Eulerian (E-E) model incorporating the Kinetic Theory of Granular Flow (KTGF) was developed, which reasonably predicted the bed expansion behaviour within ± 4% deviation from the experimental measurements. The effect of solid loading method on the final bed expansion behaviour was found to be insignificant in binary SLFB experiments; however, CFD simulation times for different loading conditions were shown to differ by ~ 40 %. Finally, the CFD model was used to predict the spatial distribution of solid-liquid phase volume fractions and which also provided reasonably good agreement with the experimental data (± 6% deviation) in terms of the predicted heights of the segregated and intermixed zones. The overall pressure drop and bed volume fraction behaviour of a solid-liquid fluidised bed containing mono and binary particles of different sizes were also studied. Though the pressure and bed volume fraction characteristics of SLFB have been thoroughly experimentally investigated, there is a lack of knowledge in mathematical and numerical modelling. An Energy Balance Pressure Model (EBPM) was developed based on balancing the energy input and output rate of the mono and binary segregated SLFB. The bed volume fraction and pressure drop predictions of the EBPM were compared with those of the Richardson-Zaki and Ergun models and verified against the experimental data. The EPBM predicted data were in fairly good agreement (within 7% of positive deviation) in both the mono and binary SLFB (partially and completely segregated) systems. However, as high as a ~ 30% deviation was noted in the completely mixed binary SLFB because of the fact that the approach was based on the binary segregated SLFB. A two-dimensional (2D) CFD model (ANSYS FLUENT) was carried out to determine the absolute pressure distribution along the axial direction of the binary SLFB. The axial pressure distribution predictions of EBPM agreed well with the CFD model for both the mono SLFB, as well as the completely and partially segregated binary SLFBs. In addition, different available averaging approaches, namely serial model, packing model, property-averaging model, and volume fraction-averaging model on bed volume fraction predictions were compared with the present experiments and the limitations discussed. CFD predicted bed volume fraction was also validated against the experimental data which showed a deviation of around 6%. An important parameter used to describe the hydrodynamics of the SLFB system is dispersion coefficient which indicates the quality of mixing hence the spread of one particular component in a mixture. Literature review indicates that the dispersion coefficient depends on the system parameters such as fluid phase properties (density, viscosity, superficial velocity and liquid voidage) and solid phase properties (diameters, densities, terminal settling velocities, minimum fluidisation velocity and volume fraction). Drawing analogy with diffusion, dispersion coefficient can also be expressed as a product of mean free path (average distance between two successive collision) and the fluctuating velocity component of particles. To quantify the mean free path and velocity fluctuations, single particle tracking technique was utilised using high speed imaging. The trajectory of a coloured tracer particle was tracked in time and particle velocity was computed in vertical (y) and horizontal directions (x) from the particle centroid data. At the same time, the z-velocity data were obtained by measuring the change in particle diameter with its movement either towards or away from the camera focal plane. The particle velocity was found to follow a normal distribution pattern only in the direction of flow. From the velocity data, the particle acceleration (-26 to 28 m s-2) was computed which revealed numerous peaks due to the contact force resulting from collisions with the neighbouring particles and the column walls. The average distance between the two successive peaks was then computed to determine the mean free path (MFP) which was estimated to be 3 x 10-4m and this was comparable with the theoretical estimations (within an order of magnitude). Finally, the solid dispersion coefficient was determined as the product of MFP and the fluctuating velocity component in each direction (Di ~ λVi/) which was obtained in the range from 10-5 to 10-9 m2 s-1.The above-mentioned expression provides a scaling for the dispersion coefficient and requires a proportionality constant which was obtained through regression of the available experimental results covering a wide range of particle diameters (0.39 to 23 mm), the liquid superficial velocity (0.0009 to 0.6 m s-1) and Reynolds number (4 – 2820). An additional term (VS∞/Vmf) was multiplied with the model which is an empirical correction factor to account for the particle velocity which provided better fit to the experimental data. The developed model was observed to be generalised and improved than the other empirical models reported in the literature. Also, quantified was the effect of specific energy dissipation rate on the dispersion coefficient. Energy dissipation rate was estimated using a simple energy balance over the fluidised bed and used as a measure of existing turbulence. It was observed that the dispersion coefficients of the binary solid phases increase with an increase in the energy dissipation rate of the system. Dispersion coefficients varied in the range of ~ 5 x 10-5 to 5 x 10-4 m2 s-1 when energy dissipation rate increased from ~ 0.005 – 0.01 m2 s-3 (w kg-1). The present study further focused on the applications of dispersion coefficient to describe the mixing and segregation behaviour in a binary solid-liquid fluidised bed. A one-dimensional convection-diffusion modelling approach was utilised. The analytical approach of Galvin et al. (2006) was modified by the incorporation of present dispersion coefficient correlation; and the experimental data of Galvin et al. (2006) was then used to validate the modified approach. The one-dimensional (1D) numerical approach was found to be capable of capturing the mixing-segregation behaviour appropriately without requiring any fitting parameter. In the numerical modelling framework, the use of the dispersion sub-model developed in the present study provided good agreement with the experimentally measured axial concentration profile when compared with the other empirical models. Also, the previously developed CFD model was used to predict axial variation of the binary solids concentration which showed good agreement (~8 - 15% deviation) with the published experimental data.
- Subject
- particle dispersion coefficient; solid-liquid fluidisation; binary particle system; CFD; mixing; segregation; bed expansion
- Identifier
- http://hdl.handle.net/1959.13/1353412
- Identifier
- uon:31095
- Rights
- Copyright 2017 Md. Shakhaoath Khan
- Language
- eng
- Full Text
- Hits: 1067
- Visitors: 1683
- Downloads: 758
| Thumbnail | File | Description | Size | Format | |||
|---|---|---|---|---|---|---|---|
| View Details Download | ATTACHMENT01 | Thesis | 11 MB | Adobe Acrobat PDF | View Details Download | ||
| View Details Download | ATTACHMENT02 | Abstract | 312 KB | Adobe Acrobat PDF | View Details Download |