Powder Flow
EXECUTIVE SUMMARY
The main objective of the project is to study the mixing and elutriation of fines in a bed containing mostly coarse particles, eg. 40 /,um or 70 um fines in a bed of 480 um coarse particles.
In this year’s work programme, experiments were carried out to investigate the following:
- Qualitative study of the mechanisms of fines transport in the particulate phase of a two - dimensional bed.
- Measurement of gas flow through a two - dimensional bubble.
- Measurement of the axial and radial distributions of fines in a bubbling cylindrical bed.
Photographic evidence showed that there are two mechanisms mainly responsible for the upward transport of fines (i) fines carried up within the bubble void and (ii) fines moving with the wake of the bubble. Both mechanisms contribute to the ejection of fines from the bed surface; however, depending on the ratio of the fines terminal velocity to the minimum fluidisation velocity of the coarse particles, one of the mechanisms is more dominant than the other. If the ratio is much less than unity then mechanism (i) is dominant but if the ratio is greater than unity then mechanism (ii) is dominant. The presence of fines within the bubble void can make a significant contribution to the overall gas conversion in a fluidised bed reactor. Thus the presence of fines needs to be considered when designing fluidised bed reactors.
The concentration of fines within the bubble void is a function of the velocity of flow through the bubble which is proportional to the incipient fluidising velocity of the coarse material. The gas flow through a two - dimensional bubble was measured using a Laser Doppler Velocimeter, and the throughflow velocity was found to be about the same as the minimum fluidisation velocity.
The axial and radial distributions of 70 um fines in a bed of 480 um particles were measured in a 0.28 m diameter bed in batch and continuous modes of operation. In both cases it was found that the concentration of fines is higher at the top and lower at the bottom of the bed. The existence of such a profile indicates that the upward fines transport rate is primarily induced by bubbles; the bubbles are effective in transporting fines upwards as compared with the slow downwards movement of coarse particles over the whole cross section of the bed. As would be expected, the radial fines concentration gradient is much smaller than the axial concentration gradient.
It is postulated that there are three mechanisms by which fines mix in the bed (i) upwards mainly in the wake and void of the bubble (ii) downwards in the bulk circulation (iii) downwards by eddy diffusion. These mechanisms give rise to the observed concentration profile with high fines concentration at the top of the bed which promotes elutriation of fines from the bed surface.
For the future, attention will be focused on developing theoretical work based on the above mixing mechanisms in order to predict the fines concentration profile and the fines elutriation rate.
Theory arising from the above should be helpful in interpreting the effect of temperature on elutriation, to be measured at Bradford.
Background I
In the annual report for 1990 we described the experimental setup developed for characterizing group A powders at room temperature; results were reported on the influence which mean particle size and addition of fines fraction had on bed expansion, Umf, Umb, deaeration rates and times, and bubble sizes. It is generally assumed that if tests are conducted at high temperature, the powder behaviour will be predicted simply by using the appropriate physical properties of the gas, adjusted for temperature, in correlations based on data gathered at room temperature with different gases. However, it is our hypotheses that interparticle forces play a major role in the behaviour of group A powders, particularly these which are at the finer end of the group, and that temperature will alter these forces. Thus, the powder behaviour change at high temperature may not be predicted by hydrodynamics effects alone.
Temperature effects on incipient fluidization velocity Umf and bed voidage at incipient fluidization point and bubble sizes have been extensively studied on group B and group D powders. In this work, temperature effects on some fluidization characteristics of group A powders are reported: these are incipient fluidization velocity mf, and the voidage of loosely settled bed cS, incipient bubbling U velocity Umb, and bed expansion.
EXECUTIVE SUMMARY
This proposal originally addressed the issue of why stagnant zones, such as funnel flows in hoppers, appear in particle flows. To that end, we studied computer simulations of a Couette flow with gravity. In those simulations, gravity acted to force a stagnant zone of material to form, so that the conditions that led to the transition from fluid-like to solid-like behavior could be observed and studied. This work has been performed for both two-dimensional simulations of disc flows and three dimensional simulations of spheres. Large portions of this project involved the development of soft particle simulation models that can be applied to this, as well as other, studies.
The results indicate that this is a problem that runs the gamut of granular flow regimes, from the molecular like, rapid flow regime, to the slow quasistatic regime. As such, it covers the transition between the two limiting states, an area that has not been tackled theoretically. It was observed that, while a region demonstrating molecular-like behavior may exist, the transition to solid behavior is not, as was originally hoped, an analog to a phase change in real molecular systems. Instead, the first movement of the material occurs as a quasistatic yielding. The results are beginning to shed some light on the transition process. The main difference between macroscopic particles and molecules is that particles can sustain long duration contact with their neighbors (this is what makes quasistatic behavior possible) and this permits the material to push-through the phase change.
The scope of this project has been extended beyond its original proposal to include more general problems of the computer simulation of powder flows. At the Teaneck meeting in 1989, Gordon Butters asked me on behalf of the TC, to see if my work could shed some light on the fracture problem. On further consultation with Paul Isherwood, I learned that there was a general lack of information about the forces that are exerted by the flow induced particle collisions. While the simulations have been previously used to make stress tensor measurements and thus determined averaged forces applied to particles, these are generally irrelevant to the fracture problem as the most damage will be caused by the maximum and not the average force. Thus, I conducted a series of simulations to determine the maximum collisional impulses that the particles experience in a simple shear flow and their dependence on particle properties and solids concentration. The impulses are divided into their components normal and tangential to the particle surface as it was felt that the two might contribute to different attrition characteristics. The normal impulses - which might lead to large scale particle fracture - was always significantly larger than their tangential counterparts - which would tend to shear off the microroughness that lead to the interparticle surface friction. Along the way, histograms of the distribution of collision impulses as well as their geometric distribution over the surface of the particle were recorded.
Also at the Teaneck meeting, Hans Buggish, not on behalf of anybody but himself, suggested that I might be able to contribute to his IFPRI sponsored work on the flow induced mixing of particle in his granular shear cells. He had observed that the mixing might be modeled as a diffusion process, similar to that of molecule in a gas or liquid. The use of a computer simulation was particularly attractive in such a study as his experimental technique was limited to measuring the diffusion of particles in only the direction parallel to the velocity gradient, while the computer simulation could measure the diffusion in all directions. The results show that the particles do mix by diffusion except at the highest concentrations when the particles become tightly packed in a crystalline microstructure and unable to move relative to their neighbors. However, the diffusion in a shear flow is not isotropic and is only appropriately modeled as a tensor of diffusion coefficients. By far, the largest mixing occurring in the direction of flow. The components of the diffusion tear were measured both by particle tracking and by a statistical technique developed by Taylor (1922). Furthermore, it showed that the mixing in a granular flow was an example of Taylor diffusion by which the diffusion of particles in the direction of the velocity gradient greatly enhanced their mixing.
Summary
The object of this work is to develop methods for the quantitative prediction of all the major features of flow of a gas, together with solid particulate material, through a duct of arbitrary size and inclination. Flows of this sort are of great technical importance in pneumatic transport of particulate material, and in the circulation of particulate materials within chemical processes. Examples of the latter type include the riser reactors and standpipes which form components of the catalyst circulation 100~ in catalytic crackers, used in the refining of oil, and the long standpipes used in certain coal liquefaction plants. In all these systems the particles tend to distribute themselves over the cross section of the duct in a markedly non-uniform way, making it very difficult to predict the hold up of solid material and the pressure drop along the duct, or even to extrapolate these quantities from measurements made with the same materials in ducts of other sizes. In addition, the crowding of the particles into limited parts of the cross section can lead to undesirable effects, such as recirculation of the solid material against the direction of the main flow.
The key to making useful predictions for these systems is to understand and quantify the mechanism that determines the distribution of particle concentration over the cross section. This understanding must be based on equations of motion for the gas and the particles, so the object of the present work has been to propose such equations of motion and explore their solutions for flow through ducts. These solutions appear to simulate many of the characteristic observed properties of flows of this sort, including the undesirable recirculation patterns referred to above. However, they are unduly sensitive to the values of certain physical properties of the gas and the particles, indicating that turbulent flows must be considered to give a satisfactory account of the situation of greatest technical importance, where suspensions flow at high rates through large ducts. The modelling of turbulent flow of a suspension is difficult, but a start in this direction has been made.
Summary
The object of this work is to extend our earlier research on the flow of gas and particles through ducts to the situation in which the flow is turbulent. Such flows are of great technical importance in pneumatic transport of particulates and in the circulation of particulate materials within chemical processes. Examples of the latter type include the riser reactors and standpipes which form components of the catalyst circulation loop in catalytic crackers, used in the refining of oil, and the long standpipes used in certain coal liquefaction plants. In all these systems the particles are found to distribute themselves in a very non-uniform way over the width of the duct. Unless the nature of this distribution can be predicted, it is not possible to calculate the pressure drop along the duct or other quantities, such as the statistical distribution of particle residence times, which are needed in the design of these systems.
The key to making useful predictions is, therefore, to understand and quantify the mechanism responsible for the distribution of particle concentration over the cross section of the duct. In earlier work, sponsored by TFPRI, we have established that collisions among the particles can endow the assembly of particles with properties analogous to those of a molecular fluid, and that this can generate a distribution of the particles which is, in many ways, realistic. However, the behavior is found to be very sensitive to mechanical properties of the particles which affect the elasticity of collisions, and this is not at all realistic behavior for most systems of technical interest.
The present work examines the effect of turbulent flow on the cross sectional distribution of the particles, and indicates that there will be sharply enhanced concentration in the vicinity of the walls of the duct, as observed in practice. In contrast to the findings of our earlier work the predicted distribution of particle concentration appears to be rather insensitive to the properties of the particles or the parameters of the turbulence model used. It must be emphasized that these conclusions are tentative, since difficulties encountered in generating numerical solutions of the governing equations have not yet been entirely overcome, but the results obtained so far are encouraging.
Executive Summary
Bubble Control with electric fields in fluidized beds-Part I
New results are presented for both ac and dc electric field bubble control in gas fluidized beds tested to 125 “C. Modeling includes, (a) electrostatic forces at a bubble interface for dc fields, and (b) an ac theory for inter-particle capacitive forces. Correlations for bed expansion are presented that includes the electric field strength and superficial velocity based on an extension of two-phase fluidization theory. The experimental results reflect studies that were initiated last summer with the new Trek 10 kV high voltage power supply purchased with IFPRI funds. This supply has permitted us to undertake the study of charge relaxation, which is known to influence inter-particle forces, and also to study the effect of field strength and frequency on bubble control and bed expansion to greater extent than was possible before.
The experimental variables studied to date include bed temperature, electric field strength, and field frequency. Bubble control experiments were carried out on two sizes of glass microspheres, 44-77 urn and 77-144 pm., both glasses being Class A powders using Geldart’s quality of fluidization criteria. Significant effect was observed for bubble control with simultaneous bed expansion to 15% when optimized at a frequency of 3 Hz (compared to l-2% expansion for a field-free bed). An asymptotic drop-off in bed height with increasing frequency and improved bubble control with increasing temperature can be explained by ac modeling of inter-particle forces. The reason for the temperature dependence is not yet fully understood.
DC modeling for the mrtvimum electrostatic forces at the bubble interface follow an assumed spherical bubble shape, chosen to be consistent with the Davidson model used for the fluid dynamics. It is postulated that electrostatic forces must be of the same order of magnitude as particle-fluid forces for effective bubble control. Our dc model is successful in predicting the correct magnitude of electric field strength (E) required for the onset of bubble control showing that E - O(kV/cm) as observed experimentally. However, the model is deficient in that it does not show a dependence of bubble control on superficial velocity as observed experimentally with ac fields and to a lesser extend with dc fields.
Modeling of ac fields shows that inter-particle forces depend in addition (to dc force effects) on the frequency of the field, particle contact resistance, particle surface resistivity and the capacitance of adjacent particles. The ac model needs to be perfected to include the important effect of superficial velocity based on experimental evidence.
Future modeling will include non-spherical bubble shapes and the coupling between ac and dc particle forces with bed expansion (superficial velocity effect). Our numerical program K-Fix is still being developed by Forhad Hossain and is considered to be a long-range part of our modeling program for the electrostatics and hydrodynamics in fluidized beds. Future experiments will incorporate materials of industrially importance at elevated temperature using a quartz bed. These studies will also include particle diameter and relative humidity as variables.
Elutriation control with electric fields-Part II
Fines concentration reductions of up to 96% have been measured in the freeboard of a gas tluidized bed with ac and dc fields. Experimental studies were first reported at Harrogate for dc fields. An optical method employing a helium-neon laser was developed to measure real time particle concentration in the freeboard. A theory was then developed to interpret this data in terms of the elutriation constants (ki).
In the experiments, sand fines, 3.67 to 32 pm, were tested. with ac and dc fields in bulk sand having an average diameter of 300 pm. Elutriation constants were of the order of magnitude of ki = 0.02 set-l and varied with dc field strength depending on the temperature of the bed, whereas the elutriation constants remained relatively independent of tcmperaturc up to 500 “C. Additional data are needed to obtain correlations and to expand this research to include industrial materials of different kinds and shapes.
Modeling of electrostatic forces in the bed is needed to better understand the experimental results. Two approaches for modeling particle-surface forces arc suggested, (1) equilibrium and (2) stability analysis. A closed cell model will dctcrmine the macroscopic field in which fine particles are acted upon by electrostatic forces and surface currents.
The experimental aspect of our research, Parts I and II, is being carried out by J. S. Wang, a Ph.D. student in mechanical engineering
Electrostatic powder separation-Part Ill-a
This study concluded our first year IFPRI study of triboelectric charging in a circulating tluidized bed. It demonstrated that separation of the constituents in a powder mixture, in our case coal pyrite from the parent coal, is possible using selective triboelectric charging in a circulating lluidized bed. Analysis of data showed that the single most important parameter is the difference of charge received by individual constituents. The voltage difference in the precipitator and the superficial velocity were found to be of secondary importance.
Corona discharge-Part 111-b
Corona discharge will often accompany the application of high voltages, high temperatures, and surfaces exhibiting high curvature (e.g. fine particles). It is likely that corona breakdown takes place between particles in an electrofluidized bed under conditions of sufficiently high fields. In the presence of particles, the so called corona wind will literally blow particles toward walls.
Our first study in corona discharge was to investigate modeling of the corona wind and to measure its effect as drag on a glass plate in a low Reynolds number wind tunnel, Rex < 3.6x10^3 (x = length of glass plate ). Our model was successful in predicting the expected trend in drag phenomena over a flat plate using the Karman-Pohlhausen method. However, theoretical predictions of drag were two orders of magnitude too large compared to experiments with ac corona. The reason for the large discrepancy is thought to be that the model is essentially dc whereas the experiment was for an ac corona discharge, Also the effective ionic mobilities usad in the predictions were thought to be too large for the actual conditions.
There are no immediate plans to extend this work. However, corona discharge phenomena will likely need to be included or at least understood in our future modeling of high temperature fluidized beds as well as in the freeboard region if high voltage fields or highly charged particles present.
EXECUTIVE SUMMARY
The flow of coarse materials from hoppers is well correlated by the Beverloo correlation. However this over-predicts the flow rate of particles of size less than about 5:00 pm. The purpose of this work was to investigate the hypothesis that the retarded flow is caused by air drag resulting from the dilation of the material as it approaches the orifice.
The work was carried out in Cambridge by T.M.Verghese under the supervision of R.M.Nedderman. This report is a summary of the work presented in Verghese’s Ph.D. Dissertation.
Experimental work was carried out on kale seed and 6 closely-graded sands with mean sixes ranging from 2280 pm to 150 pm. Measurement of the flow rates confirmed the validity of the Beverloo correlation for coarse materials and the existence of related flow for finer materials. Direct measurement of the interstitial pressure profile showed that the immediate cause of retardation was the existence of adverse pressure gradients near the orifice. From this it can be inferred that dilation occurs and direct confirmation of this was obtained using gamma-ray tomography.
We conclude therefore that the work has confirmed the starting hypothesis and this has led to a correlation for the discharge rate of fine sands which shows good agreement with experiment.
A theoretical analysis for the discharge rate of coarse materials from bunkers and hoppers has been undertaken. This analysis differs from all previous analyses in that allowance has been made for the non-uniform velocity distribution in the hopper. For mass flow hoppers the predictions do not differ greatly from those of earlier work. However, the theory also predicts the discharge rate from core flow bunkers and to the best of our knowledge this is the first time that a theoretical prediction has been made for this situation.
Summary
During the past year the main object of our work has been to refine our model for fully developed turbulent flow in vertical tubes, improve the numerical algorithm for its solution, and explore its predictions over wide ranges of gas and particle fluxes.
For engineering purposes it is important
- (a) to be able to predict the relation between the gas pressure gradient and the fluxes of gas and particles, over wide ranges of these fluxes, and for tubes of widely varying diameters, and
- (b) to be able to predict the cross-sectional profiles of particle concentration, and the velocities of both particles and gas, and hence deduce quantities important for chemical reactions, such as residence time distributions.
In this Annual Report we demonstrate that the model meets both these requirements and test the agreement between its predictions and some limited experimental data. In order to establish confidence in its predictive capability it is now important to generate experimental data over as wide as possible a range of operating conditions. We hope that a suitable body of results will be generated by a related experimental exploration of riser flow, to be initiated by IFPRI.
Executive Summary
The goal of developing a unified field theory for bubble control in a fluidized bed is reviewed. Included in this unified theory is a single inter-particle force model that will handle the limiting cases of high as well vanishing field frequencies (ic. the ac and dc limits). The electrostatic bubble model utilizes a perturbation theory to relate force relationships at the particle level to the continuum equations of mass and momentum at the bulk bed level. An extension of the Davidson bubble model gives information on the local stresses induced around a bubble in terms of the far distant electric field strength.
For the first time in this IFPRI work we introduce a relationship between bubble control and elutriation control through an understanding of the various interparticle forces. Two mechanisms relating to electrostatics effects in elutriation are postulated by which the entrainment of fine particles can be diminished with electric fields:
- that bubble formation is inhibited with the application of electric fields, and
- that the bonding strength of fine particles to bulk bed particles is increased with electric fields.
To elaborate on these two mechanisms, various permanent and electrostatic interparticle forces are evaluated. For the electrical forces, current constriction is shown to be the dominating cohesion force that influences both bubble control and elutriation control, with the force of induction charging found to be less important. For the permanent forces, van der Walls and triboelectric particle forces contribute over different size ranges of fine particles depending on the surface roughness of the particle. Gravitational forces affect mainly bubble action through the larger bulk bed particles.
In a separate experiment it is now confirmed that elutriation control with electric fields is a consequence of field action within the bed and not simply a precipitator effect in the bed freeboard. The test was carried out on a specially designed fluidized bed in which the high voltage electrode entered through the bottom of the bed rather than from above so that the possibility of precipitator action was largely reduced or eliminated.
Our present correlations now include bed expansion, superficial velocity, particle diameter, and electric field strength for glass spheres. Previously, particle diameter had not been included in these correlations. The new results should be useful in helping to predict scale-up of beds as well as for predicting the delay of minimum bubbling conditions with fields.
The future plans for this research call for scale-up studies utilizing a larger bed experiment for bubble control and for developing a new high temperature facility. Numerical modeling studies will also be introduced. Our present facility has provided data up to 500 degrees C.