Powder Flow
Introduction
Fine particles, especially smaller than one micrometer in diameter, are expected to be valuable materials for new ceramics such as jet engines or motor engines. Even the dust particles exhausted from steel industries may be changed to a useful powder from which chemical catalysts are made through grinding and classification.
This report covers the contract year 1985/86 and describes the work performed to investigate the flow of fine materials from conical hoppers. Six materials - Kale seed and five different grades of sand ranging in size from 2,28mm to 150pm - are used in the experiments, Mass flow rates and interstitial pressure profiles adjacent to the orifice are measured simultaneously. Results have been obtained for four orifice diameters on a cone of half angle 9.5’ and for six orifice diameters on a cone of half angle 15”.
Previous work in the field has been extensively reviewed. Experiments on the kale seed and the coarsest sand (d = 2.28mm) provide further evidence for the applicability of the Beverloo (196l)correlation in describing the flow of coarse granular materials. For conical hoppers, the form of the correction factor proposed by Hose and Tanaka has been verified but the value of the exponent is still in doubt. They proposed a value of -0.35 which compares with the value of n m -0.2 indicated by the results obtained in this work.
Experiments on the different size ranges indicate that for particles in the range 50 to 600pm the measured flow rates are less than those predicted by the Beverloo correlation. It is shown that this retarded flow is caused by self-generated interstitial pressure gradients which arise as the material dilates on approaching the orifice. The Crewdson equation (1977), originally developed for air-augmented flows is found to be adequate in describing these retarded flows. Below 50um cohesive arching becomes an important factor and it may even prevent flow.
Crewdson et al. investigated a theory of stress induced dilation but their efforts proved inconclusive because of the difficulty in obtaining an accurate voidage-stress relationship at the low stress levels prevailing near the orifice. This line of thought is revived as the commercially available consolidometer can be used to obtain a voidage- stress relationship for stresses less than 10kN/ms. However, experimentally determined voidage changes exceed those predicted from the theory by a factor of almost 100. This suggests that it is necessary to look elsewhere for a suitable mechanism to explain the cause of the dilation.
Possible avenues of further work, both experimental and theoretical, are presented. An important element in the future is to be the direct determination of the voidage profile, which will be attempted using the r-ray tomography method developed by Seville et al. (1986) at the University of Surrey.
It is hoped to be able to develop a correlation for the flow of fine powders in the near term using the fractional retardation W/Ws. Meanwhile in the absence of any suitable alternatives, Carleton’s (1972) correlation can be used to predict the flow of fine powders from orifices greater than 20mm. The results presented in this work suggest that an overprediction in the range 20% to 50% can be expected.
Work performed on agglomeration of particle systems in fluidized beds at both low temperatures (granulation) and high temperatures (sintering) is The research described in Part I and Part II of this report,. respectively. reported on was performed during the period December 1986 - November 1987. carried out from December 1987 to September 1988 is also included. A special section in Part I (7.2) contains Future work for both projects to be three years program starting in September 1988 for the low temperature granulation project only.
In Part I of this report, containing the description of theoretical and experimental work on granulation in fluidized beds, it is demonstrated that the viscosity of the binder (in addition to other properties such as surface tension, wetting, etc.) is a very important characteristic which in final analysis determines the morphology and strength of the formed granules. After a short review of theoretical and experimental procedures-relating to liquid bridge strength given in section 3, the newly developed "dynamic bridge apparatus" is described (see section 4) and its capabilities are shown. The effects of the Capillary number, viscosity, bridge volume, etc. on the' strength of an axially strained pendular bridge and comparison of theoretical and measured values are given. It was demonstrated that under conditions of low Reynolds and Capillary numbers, large bridge volumes and favorable wetting of the solid surface the theoretical and experimental data are in good agreement. It was also clearly shown (see section 5) that binders which show a high rate of strengthening with time as the solution becomes more concentrated, i.e., the viscosity increases, yield agglomerated granules as a final product from granulation while binders for which the strengthening rate is moderate or low, yield layered granules but no agregates. This result was also predicted from a simple experiment using the dynamic bridge apparatus. Additional experiments with different binders exhibiting a wide range of properties in both the dynamic bridge apparatus and in the fluidized bed granulator are given in the Appendix (see section 10).
In Part II of the report which contains work on agglomeration due to high temperature sintering, it is shown that there is a strong correlation between elongation-contraction behavior of a powder sample in the proposed future work for an additional dilatometer and the agglomeration of the same powder when fluidized. The minimum sintering temperature of m&y different materials as determined in the dilatometer was shown to correspond to the temperature at which the material will defluidize. It was also found however that, although the correlation mentioned above holds for'incipient sintering, there seems to be no direct relation between rates -of deformation in the dilatometer at temperatures beyond sintering and actual sintering rates in the fluid bed. It is therefore often necessary that both dilatometer and fluidized bed tests be performed on the same powder before a final conclusion can be drawn. A detailed description of both experimental methods mentioned above are given in sections 2 and 3 respectively, while results and discussion of different test materials are given in section 4.. This section also contains a case study of a powder undergoing a chemical reaction which induces agglomeration. It was found that if the product of the chemical reaction causes agglomeration the controlling factor in the process is the conversion rate; this type of agglomeration behavior can not be detected in the dilatometer.
Section 5 in Part II contains a critical review of existing models of agglomeration; this section also includes some directions for the development of a more realistic theoretical model. The need for some basic knowledge of the magnitude of the break-up forces in a fluidized bed is also discussed. Finally, the Appendix to Part II contains a copy of a paper on high temperature sintering presented at the annual AICHE meeting in November of 1987.
This report consists of an account of work done under IFPRI contract in Cambridge University during the year to December 1987. The principal achievements during that time are:
- Installing pressure transducers on the flow rig and developing the associated software so as to be able to measure the very low pressure differences occurring.
- The performance of a series of experiments on a hopper of half angle 15 degrees; the results confirming the observations tentatively reported in the last IFPRI report.
- The development of a possible theory to explain the observation.
Also included is the programme of work proposed for the rest of the contract.
This report covers research under the auspices cf IFPRI during the period January - December 1987 following the appointment of Hr. M.C. Turner to a Research Assistantship.
The foremost objective of the research is to elucidate the fundamental description and mechanisms of granular flow using both computer simulation and experimental methods. We aim to properly understand and formally describe the diversity of flax behaviour commonly observed in processes such as fluidisation of povters and flow from hoppers.
A generalised three-dimensional computer simulations program has Seen developed, ab initio, specifically designed to integrate the equations-of-motion of colloidal-like interacting spheres under gravitational flow on an inclined plane. The technique uses the general methodology of previous studies of dense suspensions under shear flow but incorporates numerous features essential to granular flow such as boundary friction and an interparticulate coefficier: of restitution to achieve steady-state conditions.
A novel feature of the simulations is the use of "gravitational units" whereby the gravitational constant g sets tie time and energy scales. With this approach we expect to gain s overview of the different regimes of behaviour (e.g. Geldart-types X, B, C, D, etc.) found for different powders on real laboratory of engineering time scales. The basic initial computer program is now 13 'production' and preliminary results are reported.
Laboratory experiments are being carried out alongside the simulations to investigate the flow behaviour of well-characterised (spherical, monodisperse) powders under gravitational: steady-shear flow. An experimental rig comprising a rotating bed, with the provision for a fluidisation flow field, has been constructed E d is operational. Preliminary experiments are reported, for larger particles (> 5~) and no gas field, to resemble the initial simulation conditions as closely as possible.
Both the simulations and the experimental studies are being extended to investigate the effects of a cohesive inter particle potential, which becomes important for fine powder when it is large compared to gmo, the gravitational energy, and t'L2 hydrodynamic flow field where aeration plays an important role.
SUMMARY
Characterisation and prediction of powder flow
D. Geldart, M. C. Turner and L. V. Woodcock
This report covers research under the auspices of IFPRI during the period January-December 1988. Mr. M. C. Turner has continued in the appointment of a Research Studentship for this second year of our IFPRI research.
Research is now advancing on the three interdependent fronts of experimental studies of well-characterised systems, computer simulations of powder rheology, and theoretical work in search of interparticle force models and scaling laws leading to computational fluid mechanics of powders.
The experimental studies have to date concentrated on a rotatine fluidised bed, which is being deployed to examine the behaviour of monodisperse shperical particulates and direct measurements of the coefficient of restitution. Results have been obtained for glass ballatini particles in the size range from 10^-4 m to 10^-3 m. It is planned to extend some of these experimental studies to perfect monodisperse particulates of polystyrene latices, presently under preparation in collaboration with the Polymer Research Unit at Bradford, down to a size range of 10^-6 m. These experimental measurements of the properties of "perfect powders" relate directly to the computer simulations and test the predictive ability and limitations of the early computer models at the particulate dynamics level.
The computer simulation work has developed along two distinct lines. The original approach, as reported previously, was to set up a computer simulation model with boundary conditions closely resembling the simple experimental geometry of chute flow. The early results, reported previously, are now being replaced by more advanced simulations which may include a more sophisticated coefficient of restitution and elementary aeration effects (i.e. Stokes's friction). "Gravitational units" are used in these simulations; the constant g sets the time-scale and hence the energy scale. This approach, once aeration and cohesive forces are incorporated, is expected to give an overview of the different commonly used powder classifications in real engineering time scales.
Since the beginning of 1988 we have embarked upon the determination of the constitutive rheology of the simplest ideal powder, monodisperse frictionless hard-spheres, by the methods of granular dynamics, using homogeneous-shear, non-equilibrium computer simulations. This essential simulation work will eventually lead, for the first-time, to the possibility of complete computational fluid mechanics for a well-defined model in a given geometry. These granular dynamic computations are being designed also to determine and test fundamental scaling laws for rapid granular flow from known thermal equilibrium behaviour.
On the theoretical side, scaling Laws for predicting the rate-of-strain deformation dependence of the pressure tensor in the region of rapid granular flow for slightly inelastic frictionless spheres have been derived. Results are reported for three cases of the form of the coefficient of restitution which may relate to experimental circumstances. Each case gives a quite distinct type of rheological behaviour even though the limiting behaviour in all cases is analytically predictable from the equation-of-state and viscosity data of the hard-sphere fluid at equilibrium. The stress and dilatancy of spheres with a constant (velocity-independent) coefficient of rastitutfon show discrepancies when compared with the kinetic theory predictions of Savage but generally compare favourably with experimental data.
Executive Summary
The majority of previous granulation research has been of a mechanistic nature examining the effect of operating variables such as ‘fluid-bed excess gas velocity or spray characteristics on granule growth rate and morphology. Various mechanisms of granule growth have been identified and a general population balance similarity theory of granulation has been developed. However, little 4 m knowledge of granulation phenomena is provided by the above disparate, essentially macroscopic approaches alone, One must instead turn to a microscale consideration of interparticle cohesive forces in relation to the energetics of disruptive particle motion.
A brief description of the fluid-bed granulation process is presented in Chapter 2 with the aim of clarifying various competing mechanisms as well as establishing their respective controlling material parameters. Specifically, the present work seeks to explain differences in observed granulation morphology and growth rates in terms of the strength of a dynamically strained pendular bridge and differences in the viscous history of the involved binders. An extensive review of growth mechanisms, the effect of operating and material parameters, and granulation modeling has been given previously (Ennis et al., 1986).
Research emphasizing the importance of dynamic pendular bridge strength is outlined in Chapter 3. Completed results concerned with the strength of an axially strained bridge are given in Ennis et al.(1988). These as well as further preliminary results dealing with relative sphere shearing motion, surface roughness, and imperfect wetting are summarized in Chapter 4. An ad hoc solution of dynamic bridge strength based on the superposition of lubrication theory and circular approximation is presented. For small gap distance with sufficient bridge volume and in the limit of small Reynolds’ number, good agteemgnt between the experimental and present theoretical axial force response is observed indicating the importance of a capillary number Ca in determining pendular bridge strength. The present theoretical analysis is zeroeth order in capillary number and gap distance and hence, is expected to break down with increasing local inertial effects. Such inertial effects are governed by a modified Bond number and, in the limit of low Ca, lead to an increase in bridge strength due to an added mass effect, whereas in the limit of high Ca, lead to a reduced, shifted force response due to an insufficient rate of vorticity propagation. Preliminary investigations indicate that the present theoretical analysis extends to the cases of arbitrary (nearly touching) particle motion, imperfect solid wetting, and particles with only small scale surface roughness.
Initial granulation results and binder bridge measurements supporting the influence of viscosity are presented in Chapter 5. Typical industrial binder solutions such as 2.5 weight percent aqueous carboxymethylcellulose exhibit an exponential increase in pendular bridge strength due to solvent evaporation and, therefore, display a full range of capillary number behavior from an initial weak surface tension response to an extensive viscous reponse with an equivalent viscosity of the order of fifty poise. Liquid bridge measurements of binder solutions appear to adequately predict fluid-bed granule morphology indicating that growth is controlled by a combination of a viscous strengthening time constant and a final solid bridge strength. Such a time constant and final bridge strength are, in turn, related to the effect of binder concentration on solution viscosity and the molecular weight of the binder, respectively.
Lastly, a preliminary analysis of the competing processes of fluid-bed coalescence and breakage as well as an attempt at incorporating knowledge of these phenomona into a population balance framework is presented in Chapter 6. Two unknown cctnqtants related to coalescence and breakage should bear a fundamental relationship to the properities of the binder - namely, the viscous strengthening time constant and solid bridge strength, respectively.