LDA measurements of near wall powder velocities in a high shear mixer

In this study, a new method has been developed to measure particle velocity distributions in the near wall region of a high shear mixer by using Laser Doppler Anemometry (LDA). The velocities along the side of the granulator have been measured at different impeller speeds and it has been found that it is possible to obtain tangential and axial velocity data in the dense powder flow up to 4 mm in depth. Moreover, it has been found that the tangential velocity component increases slightly with distance from the wall in the near wall region, indicating a partial slip boundary condition for the solid phase at the vessel wall. It is also shown that the tangential velocity decreases with increased vertical distance to the impeller. The velocity fluctuations, represented by root mean square (rms) velocities, also decrease with increased vertical distance to the impeller and the tangential and axial rms components are found to be of the same order of magnitude.     

Surface velocity measurement in a high shear mixer

Particle velocity measurement in high shear granulation systems has been an area of interest in recent years. This paper gives an insight into the systemic variation of the bulk motion in a high shear mixer (HSM) equipped with a three-blade impeller. The velocities are measured using a high speed camera and particle image velocimetry (PIV) software. Fourier analysis of the velocity data shows a very regular pattern of velocity variation largely dependent on the impeller frequency. The effect of binder viscosity on the bulk flow is investigated as well. From these experiments it was possible to characterize, quantitatively, both the mean surface flow, and the fluctuations in this motion.     

CFD simulation of the high shear mixing process using kinetic theory of granular flow and frictional stress models

In order to enhance process understanding and to develop predictive process models in high shear granulation, there is an ongoing search for simulation tools and experimental methods to model and measure the velocity and shear fields in the mixer. In this study, the Eulerian-Eulerian approach to model multiphase flows has been used to simulate the mixer flow. Experimental velocity profiles for the solid phase at the wall in the mixer have been obtained using a high speed camera following the experimental procedure as described by Darelius et al. [2007a. Measurement of the velocity field and frictional properties of wet masses in a high shear mixer. Chemical Engineering Science, 62, 2366-2374]. The governing equations for modelling the dense mixer flow have been closed by using closure relations from the kinetic theory of granular flow (KTGF) combined with frictional stress models. The free slip and partial slip boundary conditions for the solid phase velocity at the vessel wall have been utilized. The partial slip model originally developed for dilute flows by Tu and Fletcher [1995. Numerical computation of turbulent gas-solid particle flow in a 90^° bend. A.I.Ch.E. Journal, 41, 2187-2197] has been employed. It was found that the bed height could be well predicted by implementing the partial slip model, whereas the free slip model could not capture the experimentally found bed height satisfactorily. In the simulation, the swirling motion of the rotating torus formed was over-predicted and the tangential wall velocity was under-predicted, probably due to the fact that the frictional stress model needs to be further developed, e.g. to tackle cohesive particles in dense flow. The advantage of using the Eulerian-Eulerian approach compared to discrete element methods is that there is no computational limitation on the number of particles being modelled, and thus manufacturing scale granulators can be modelled as well.     

Measurement of velocity and density profiles in discharging conical hoppers by NMR imaging

Nuclear magnetic resonance (NMR) imaging was used to measure velocity and density profiles in 3-D conical hoppers fed from an open vertical silo. Discharge of a 200 μm-diameter powder in both mass and plug flow was studied with hoppers of different half angles, of 10° and 80°, respectively. An analytical solution for compressible (variable density) mass flow in the 3-D axi-symmetric geometry was also developed following the procedure outlined in Tardos (1997) and Tardos and Mort (2005). The density variation and velocity profiles obtained experimentally were compared to predictions of this theory for dense, compressible granular flows. We found, from both theory and experiment, that the powder has to exhibit significant dilation (compressibility) as it is accelerated through the constriction in the hopper. The degree of compressibility was found, experimentally, to be lower than that predicted by the mass flow hopper theory. The powder unexpectedly exhibited a boundary layer with a fully-rough boundary condition in the mass flow hopper. In the funnel-flow hopper, the expected “dead zone” was found around the orifice and extended about one diameter length into the silo. The centerline velocity increased according to an exponential function.     

Modelling of dense and complex granular flow in high shear mixer granulator—A CFD approach

In the aspect of granulation process control, the numerical simulations appear to be a cost-effective and flexible tool to investigate the flow structure of granular materials in mixer granulators of various configurations and operating conditions. Computational fluid dynamics (CFD) is used in this study to model the granular flow in a vertical high shear mixer granulator. The simulation is based on the continuum model of dense-gas kinetic theory [Gidaspow, D., Bezburuah, R., Ding, J., 1992. Hydrodynamics of circulating fluidized beds, kinetic theory approach. In: Fluidization, vol. VII, Proceedings of the 7th Engineering Foundation Conference on Fluidization, Brisbane, Australia, pp. 75-82] with consideration of inter-particle friction force at dense condition [Schaeffer, D.G., 1987. Instability in the evolution equations describing incompressible granular flow. Journal of Differential Equations 66 (1), 19-50]. This study aims to verify this numerical method in modelling dense and complex granular flows, where the solids motion obtained from the simulation is validated against the experimental results of positron emission particle tracking (PEPT) technique [Ng, B.H., Kwan, C.C., Ding, Y.L., Ghadiri, M., Fan, X.F., 2007. Solids motion of calcium carbonate particles in a high shear mixer granulator: a comparison between dry and wet conditions. Powder Technology 177 (1), 1-11]. In general, the Eulerian based continuum model captures the main features of solids motion in high shear mixer granulator including the bed height and dominating flow direction (the tangential velocity). However, the continuum based kinetic-frictional model is not capable of capturing the complex vertical swirl pattern. Quantitative comparison shows over-predictions in the tangential velocity and stiff drops of the tangential velocity at the wall region. These results demonstrate the deficiency in transmitting forces in the bed of granular materials which indicate the necessity to improve the constitutive relations of dense granular materials as a continuum.     

Solids motion of calcium carbonate particles in a high shear mixer granulator: A comparison between dry and wet conditions

An experimental study has been carried out on the solids motion in a conical frustum-shaped vertical high shear mixer granulator by using the positron emission particle tracking (PEPT) technique. The mixer granulator has a vertical shaft, to which four sets of impellers are attached at different elevations. The shaft is operated at 3.9 Hz, 4.9 Hz and 5.8 Hz, which corresponded to the top impeller tip speed of 2.8, 3.5 and 4.1 m/s. The motion of calcium carbonate particles with and without a liquid binder is evaluated. Particles are observed to circulate in both the horizontal and vertical directions. The macroscopic solids circulation in the vertical direction reduces after adding the binder. There is a dominant solids motion in the tangential direction under both the dry and wet conditions with the maximum tangential velocity of 2.2 to 12.6 times that of the maximum axial and radial velocities. No obvious change is observed in the average axial and radial velocities when the impeller speed is changed under both dry and wet conditions, while the ratio of the maximum tangential velocity to the tip speed decreases with increasing impeller speed, suggesting a velocity-dependent behaviour. The three velocity components decrease in the magnitude after adding the binder at all tested agitation speeds except for the tangential velocity at a shaft speed of 3.9 Hz. The main difference between the dry and wet operations is that the decrease of tangential velocity in the near-wall zone under the dry condition is not observed under the wet condition.     

Solids motion in a conical frustum-shaped high shear mixer granulator

An experimental study has been carried out on the solids motion in a conical frustum-shaped vertical high shear mixer granulator by using the positron emission particle tracking (PEPT) technique. The mixer granulator has a vertical shaft attached to which are 4 sets of impellers at different elevations. The shaft is operated at 3, 6 and 12 Hz, which correspond to the top impeller tip speed of 2.1, 4.1 and 8.3 m/s. Particles are observed to circulate in both the horizontal and vertical directions. The period of horizontal circulation is short and is in the order of seconds, whereas that of the vertical circulation takes tens of seconds and often consists of lots of higher frequency fluctuations. There is a dominant solids motion in the tangential direction at all impeller speeds with the maximum tangential velocity 2.2-5.3 times that of the maximum axial and radial velocities. The maximum values of the three velocity components increase with increasing impeller speed, but the ratios of the maximum velocity to the tip speed decreases with increasing impeller speed, suggesting a rate-dependent behaviour. The particle flow pattern shows the presence of swirling flows at a position depending on the impeller speed. The results also suggest the existence of an optimal impeller speed that gives the best macroscopic mixing characterised by the vertical solids circulation.     

Granular flow and segregation in a four-bladed mixer

In this study, we experimentally examine flow and segregation of granular material in a cylindrical mixer geometry agitated by four 45 pitched blades, which is representative of equipment such as high-shear granulators and filter-dryers. We observe that the free surface of the granular bed deforms, rising where the blades are present and falling between blades passes. Using particle image velocimetry (PIV), we measure the instantaneous, average, and fluctuating velocity fields at exposed surfaces (top surface and near the wall), for both near-monodisperse and polydisperse granular materials. The radial and axial point-velocity profiles indicate three-dimensional recirculation patterns indicative of avalanching and bed penetration. For polydisperse mixtures, we find that depending on the shear rate, different segregation mechanisms can take place. Under low shear, complex lobe and striation segregation patterns occur through stretching and folding due to surface avalanching. This leads to enhanced initial mixing rates in a manner consistent with spontaneous chaotic granular mixing. At high-shear rates, segregation is controlled by the rotation of the blades. As a result, coarse particles have a tendency to migrate both to the free surface and the outer wall independently of initial bed loading conditions.     

A density based segmentation method to determine the coordination number of a particulate system

The coordination number is an important parameter for understanding the particulate systems, especially when agglomerated particles are present. However, experimental determination of the coordination number is not trivial. In this study, we describe a 3D classification method, which is based on the revised DBSCAN (Density-Based Spatial Clustering of Applications with Noise) and its application to X-ray micro-tomographic (XMT) images to determine the coordination number distribution. Pellets of micro-crystalline cellulose were used as model particles. The validity of the segmentation was checked by comparing the particle size distribution (PSD) obtained by XMT-DBSCAN with PSD obtained by optical microscopy. The results were found to be in good agreement, demonstrating the suitability of the DBSCAN method. The means and standard deviations of coordination numbers were (8.2±1.7, n=994 particles), (8.1±1.5, n=904) and (6.2±1.2, n=159) for pellets with length based mean sizes of 157, 307 and 437 μm, respectively. The coordination number distribution was in line with previous finding in mono-sized acrylic beads.     

Slow and intermediate flow of a frictional bulk powder in the Couette geometry

Most current research in the field of dry, non-aerated powder flows is directed toward rapid granular flows of large particles. Slow, frictional, dense flows of powders in the so-called quasi-static regime were also studied extensively using Soil Mechanics principles. The present paper describes the rheological behavior of powders in the “intermediate” regime lying between the slow and rapid flow regimes. Flows in this regime have direct industrial relevance. Such flows occur when powders move relative to solid walls in hoppers, bins and around inserts or are mixed in high and low shear mixers using moving paddles. A simple geometry that of a Couette device is used as a benchmark of more complicated flows.The constitutive equations derived by Schaeffer [J. Differ. Equ. 66 (1987) 19] for slow, incompressible powder flows were used in a new approach proposed by Savage [J. Fluid Mech. 377 (1998) 1] to describe flows in the intermediate regime. The theory is based on the assumption that both stress and strain-rate fluctuations are present in the powder. Using Savage's approach, we derive an expression for the average stress that reduces to the quasi-static flow limit when fluctuations go to zero while, in the limit of large fluctuations, a “liquid-like”, “viscous” character is manifested by the bulk powder.An analytical solution of the averaged equations for the specific geometry of the Couette device is presented. We calculate both the velocity profile in the powder and the shear stress in the sheared layer and compare these results to experimental data. We show that normal stresses in the sheared layer depend linearly on depth (somewhat like in a fluid) and that the shear stress in the powder is shear rate dependent. We also find that the velocity of the powder in the vicinity of a rough, moving boundary, decays exponentially so that the flow is restricted to a small area adjacent to the wall. The width of this area is of the order of 10-13 particle diameters. In the limit of very small particles, this is tantamount to a shear band-type behavior near the wall.     

Structure of powder flow in a planetary mixer during wet-mass granulation

Wet massing granulation, a widely used industrial process, is difficult to monitor and control and the structure of the flow is poorly understood. Flow patterns in a planetary mixer were investigated using positron emission particle tracking. Both dry and wet powders of a model pharmaceutical formulation were studied to develop understanding of the influence of moisture content on the flow structure during granulation. The flow structure was characterised using the distributions of the velocity components in different cross-sections of the mixer. Fourier analysis showed that the dry system is essentially dissipative and disordered whereas the wet system, being more inertial, shows signs of being more ordered with a periodic recirculation within the bowl. In both systems, radial and axial displacements are strongly correlated. For the dry system, within a central radial core region, the behaviour of the particle was determined by the rapid movement of the agitator, forming a single toroidal recycling cell. The radial and axial velocities of the tracer were up to two orders of magnitude lower than the tangential component. However, in the regions close to the wall, the particle was found to exhibit small movements dictated by the planetary rotation. For wet systems these two main regions were again observed. However, velocity field and velocity distribution showed the presence of two toroidal circulation loops, one above the other. In the wall region, the small movements governed by the planetary motion were again found, but with the amplitude of the displacements reduced by an order of magnitude.     

Mixing characteristics of wet granular matter in a bladed mixer

We performed numerical simulations of dry and wet granular flow inside a four-bladed mixer using the discrete element method (DEM). A capillary force model was incorporated to mimic the complex effects of pendular liquid bridges on particle flow. The simulations are able to capture the main features of granular flow, which is substantiated by the comparison of our results with experimental data.It was found that mean and fluctuating velocity fields for wet and dry particles differ significantly from each other. Our results indicate a strong increase in heap formation for wet particles and hence velocity fluctuations in the vertical direction become more pronounced. We observe that mixing in bladed mixers is strongly heterogeneous for wet granular matter due to the formation of different flow regimes within the mixer. The analysis of mixing quality shows that the spatial distribution of mixing intensity is influenced by the moisture content. This can lead to locally and even globally higher mixing rates for wet particles compared to dry granular matter.     

Direct measurement of surface granular temperature in a high shear granulator

High speed images of the bulk motion in a flat disc high shear granulator have been analysed using particle image velocimetry (PIV) to obtain surface velocity fields. The fluctuations in the temporal surface velocity field are found to exhibit a Gaussian distribution, allowing direct measurement of the granular temperature from the velocity field. The spatial correlation of fluctuations is examined, indicating a high level of correlation at the length scale of granule diameter, which then decreases rapidly with increasing distance. This spatial correlation profile is shown to be consistent with the expected profile for uncorrelated motion, confirming that individual granules exhibit random fluctuations during bulk motion.     

Effects of an electrostatic field in pneumatic conveying of granular materials through inclined and vertical pipes

The pneumatic transport of granular materials through an inclined and vertical pipe in the presence of an electrostatic field was studied numerically using the discrete element method (DEM) coupled with computational fluid dynamics (CFD) and a simple electrostatic field model. The simulation outputs corresponded well with previously reported experimental observations and measurements carried out using electrical capacitance tomography and high-speed camera techniques in the present study. The eroding dunes and annular flow regimes, observed experimentally by previous research workers in inclined and vertical pneumatic conveying, respectively, were reproduced computationally by incorporating a simplified electrostatic field model into the CFD-DEM method. The flow behaviours of solid particles in these regimes obtained from the simulations were validated quantitatively by experimental observations and measurements. In the presence of a mild electrostatic field, reversed flow of particles was seen in a dense region close to the bottom wall of the inclined conveying pipe and forward flow in a more dilute region in the space above. At sufficiently high field strengths, complete backflow of solids in the inclined pipe may be observed and a higher inlet gas velocity would be required to sustain a net positive flow along the pipe. However, this may be at the expense of a larger pressure drop over the entire conveying line. In addition, the time required for a steady state to be attained whereby the solids flow rate remains substantially constant with respect to time was also dependent on the amount of electrostatic effects present within the system. The transient period was observed to be longer when the electrostatic field strength was higher. Finally, a flow map or phase diagram was proposed in the present study as a useful reference for designers of inclined pneumatic conveying systems and a means for a better understanding of such systems.     

The influence of DEM simulation parameters on the particle behaviour in a V-mixer

Results are described of simulations based on the discrete element method (DEM) using a code developed by Tsuji, Kawaguchi, and Tanaka (Discrete particles simulation of 2-dimensional fluidized bed. Powder Technology 77 (1993) 79-87). The mechanical interactions between particles and also between particles and the walls in granular flows are modelled by linear springs, dash-pots and friction sliders. The simulation parameters are the restitution coefficient, normal stiffness, friction coefficient between particles and between particles and the walls, and two ratios which relate the normal and tangential stiffness and damping coefficients. Their influence on particle motion in a V-mixer has been evaluated and compared with radioactive tracer measurements of particle motion. A number of quantitative methods for comparing DEM and experimental data were developed. Given the simplified nature of the modelled interactions, the agreement between the predicted and measured data is remarkably close for restitution coefficient values of 0.7 and 0.9, internal friction coefficient values of 0.3 and 0.6 and wall friction coefficient values of 0 and 0.3. The internal and wall friction coefficients are important in determining the initiation of particle movement, while the value of the restitution coefficient has a larger influence on particles in a dynamic state. The simulation of the fully elastic case (coefficient of restitution =1.0) with zero internal and wall friction, gives results that are very different from the experiment data.     

Modeling of heat transfer in granular flow in rotating vessels

Heat transfer in particulate materials affects a wide variety of applications ranging from multi-phase reactors to kilns and calciners. In catalyst manufacturing, heat transfer through granular media (catalyst) occurs in the impregnation and calcinations stages. We use the discrete element model to simulate flow, mixing, and heat transport in granular flow systems in rotary calciners and impregnators. Granular flow and heat transport properties are taken into account in order to develop a fundamental understanding of their effect on dryer and calcination performance. Simulations have shown that as rotation speed decreases, both heat transfer and temperature uniformity of the granular bed for both calciner and impregnator increase. Depending on baffle size, baffles can either increase or decrease heat transfer in double cone impregnators. Granular cohesion does not affect heat transfer in the range of values examined.     

Effects of process parameters on granules properties produced in a high shear granulator

Results of a study on the influence of process parameters such as impeller speed, granulation time and binder viscosity on granule strength and properties are reported. A high shear granulator (Cyclomix manufactured by Hosokawa Micron B.V., The Netherlands) has been used to produce granules. Calcium carbonate (Durcal) was used as feed powder and aqueous polyethylene glycol (PEG) as the binder. The dried granules have been analysed for their strength, density and size distribution. The results show that increasing the granulation time has a great affect on granules strength, until an optimum time has been reached. The underlying cause is an increase in granule density. Granules are consolidated more at higher impeller speeds. Moreover, the granule size distribution seems not to be affected significantly by an increase in impeller speed. Granules produced with high binder viscosity have a considerably lower strength, wide strength distribution due to poor dispersion of binder on the powder bed. Binder addition methods have showed no considerable effect on granule strength or on granule size distribution.     

Investigating mixing in a multi-dimensional rotary mixer: Experiments and simulations

Mixing is an important but poorly understood aspect in petrochemical, food, ceramics, fertilizer and pharmaceutical processing and manufacturing. Segregation and mixing phenomenon occur in most systems of powdered or granular solids and have a significant influence on their behavior. Deliberate mixing of granular solids is an essential operation in the production of industrial powder products usually constituted from different ingredients. The knowledge of particle flow and mixing in a blender is critical to optimize the design and operation. Since performance of the product depends on blend homogeneity, the consequence of variability can be detrimental. A common approach to powder mixing is to use a tumbling blender, which is essentially a hollow vessel horizontally attached to a rotating shaft. This single axis rotary blender is one of the most common batch mixers among in industry, and finds use in myriad of application as dryers, kilns, coaters, mills and granulators. In most of the rotary mixers, the radial convection is faster than axial dispersion transport. This slow dispersive process hinders mixing performance in many blending, drying and coating applications. A double cone mixer is designed and fabricated which rotates around two axes, causing axial mixing competitive to its radial counterpart. Discrete Element Method (DEM) based numerical model is developed to simulate the granular flow within the mixer. Digitally recorded mixing states from experiments are used to fine-tune the numerical model. Discrete pocket samplers are also used in the experiments to quantify the characteristics of mixing. A parametric study of the effect of initial loading, particle size, fill ratio, vessel speeds, on the granular mixing is investigated by experiments and numerical simulation. Incorporation of dual axis rotation enhances axial mixing by 60 to 90% in comparison to single axis rotation. Mixing is achieved faster with front-back initial loading than with side-side loading. Particle size and fill level are found to have no significant effect on mixing characteristics.     

Study of the rheological behaviour of monomodal quartz particle beds under stress. A model for the shear yield functions of powders

A model is proposed that describes the yield locus of powders. The model is based on the adhesive contact of elastic spheres theory developed by Johnson, Kendall, and Roberts (JKR model). The proposed model improves the results by applying the Warren Spring Laboratory (WSL) equation and the Coulomb model. Only two parameters are needed in the present model to describe the yield locus of a powder: powder cohesion (C) and the coefficient of friction (μ) of the powder bed. The study verifies the validity of the new equation to describe the yield locus of different powders.The proposed model was used to calculate the cohesion and coefficient of friction of monomodal quartz particle beds with different average particle sizes. The study examines the influence of average particle size (d_s) and bed compactness (?) on these parameters. Cohesion was observed to increase by the sixth power of compactness and inverse of the particle Sauter diameter. The bed coefficient of friction increased asymptotically with bed compactness, this relationship depending on particle size.     

Characterization of the granular-to-fluid state process during mixing by power evolution in a planetary concrete mixer

Adding product into the mixer exerts a strong and rapid impact during concrete mixing. Experimental data obtained from a planetary mixer in a full-scale concrete plant under laboratory conditions show that the state of mixture progress with mixing time is well described by the mixing power evolution. More specifically, a reliable method for detecting the time corresponding to the transformation of a mixture from a cohesive granular material into a granular paste (i.e. the so-called “transition time”), through use of a mixing power measurement, will be presented herein. Moreover, once this transition has been achieved, mixing power consumption will be related to mixture rheology and then to mixer geometry by means of a simplified hypothesis. This equation can also be obtained via a dimensionless analysis. Lastly, it will be shown that mixture behavior beyond the transition point is well fitted by a hyperbolic equation. The corresponding mixing power evolution can then be predicted by the level of power at this transition time. These results are suitable for application to online process monitoring.