Development of positron emission particle tracking for studying laminar mixing in Kenics static mixer

Positron emission particle tracking (PEPT) is a flow visualisation technique that has found application in a wide range of processes. In this work, PEPT has been used to study laminar flow of a high viscosity Newtonian and non-Newtonian fluid in a Kenics static mixer (KM). Through analysis of the trajectories of many hundreds of passes of the tracer particle through the mixer, it is possible to compute the overall flow field and to visualise how the fluid twists and folds as it passes along the mixer. Eulerian velocity maps plotted for the Newtonian and non-Newtonian fluids showed that the length required for the flow to develop is shorter for the non-Newtonian fluid than the Newtonian. The stretching and folding mechanism of mixing was observed by grouping the trajectories into clusters according to whether the trajectory passes to the left or right of the blade at the transition between elements. Those trajectories making the same L–R–L decision tended to remain in the same striation through two or three elements until that striation became stretched and folded back on itself, sandwiching other layers. It is clear that the PEPT data is rich and powerful. We are hopeful that the techniques we develop for the flow and mixing in the Kenics mixer will be applicable to studying more complex laminar flows.     

Particle flow in a hydrocyclone investigated by positron emission particle tracking

The flow of a particle through a hydrocyclone acting on water has been studied by positron emission particle tracking (PEPT). The positron-emitting radioactive tracer was ¹⁸F. It was found that the activity on an ion-exchange resin particle labeled with ¹⁸F did not leach out into the water during the duration of an experiment. In the state-of-the-art PET camera it is shown to be possible to locate the centroid of the tracer particle with a standard deviation of only about 0.2 mm once per ms, making both the temporal and spatial resolution high enough to trace the particle in its very fast motion through the hydrocyclone. The design of the hydrocyclone was a modified Stairmand high-efficiency geometry with a long cone. The results are, among other things, shown as spatial tracks of the tracer particle as it moves through the hydrocyclone. Several interesting features were seen. The particle path, although the particle was much larger than the cut size of the cyclone, exhibited excursions into the inner, upwardly directed, part of the vortex giving rise to recirculatory loops. Moreover, at a particular position low in the cyclone, the particle exhibited a complicated flowpattern moving up and down repeatedly across this position. Careful analysis of the motion is presented, particularly of the motion low in the hydrocyclone, on basis of which it is made likely that this position represents the end of the vortex in the hydrocyclone.     

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.     

Particle motion in L-valve as observed by positron emission particle tracking

L-valves are widely used in circulating fluidized beds (CFB) to control the solid circulation rate. Positron emission particle tracking (PEPT) is used to view and study the real-time particle motion in the L-valve. The paper presents experimental results of the solid motion and solid flux in the L-valve, G_s, as a function of the superficial injection air velocity, U. Results are compared with earlier work. The size of the L-valve is 4.5 cm I.D. Two different experimental configurations (L-valve discharge in a CFB riser and free discharge) were used. The L-valve flow regime is stable until approximately 6 U / U_mf, with proportionality between solid flux and U / U_mf. At a higher U / U_mf, unsteady fluctuations in the solid flow gradually increase due to cavity formation around the L-valve elbow. Increasing the air flow even further, a maximum flow is reached, corresponding to the maximum discharge rate through the cyclone or hopper apex. PEPT has also confirmed the existence of a dune flow. For the first time, it gives quantitative data of the velocity profile of the dune flow which is governed by two important factors. The first factor is the distance of solids from the base of the L-valve, with solid velocity increasing away from the base. The second factor is the location of solids with respect to the dune, i.e. solid velocity is minimum at the base of the dunes and maximum at the top of the dunes. The average voidage in the L-valve is approximately constant and independent of U.     

Testing of a new dynamic Ergun equation for transport with positron emission particle tracking

The issue of formulating an Ergun‐like equation that applies to dynamic beds previously considered in Tupper et al. (2013) is revisited. Using new high quality positron emission particle tracking data, the volume and time averaged kinematic distributions of the granular (glass beads) and slurry (silica sand and water) mixture are computed. Incorporating these measured ingredients into the model then reveals that turbulence is not described by the usual effective viscosity, but nonetheless is negligible such that the new “Inertial Cell Equation” is first order in spatial derivatives. © 2015 American Institute of Chemical Engineers AIChE J, 62: 939–946, 2016     

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.     

Restoration of particle size distributions from fiber-optical in-line measurements in fluidized bed processes

An in-line probe for the measurement of chord length distributions was employed in fluidized bed granulation processes to investigate the growth behavior and the influence of process parameters. The application of a transformation approach of chord lengths into particles sizes enabled the real-time detection of the evolving particle size distribution, which is a presupposition for the integration into process control systems. Due to the ill-conditioned nature of the transformation algorithm several concepts for noise reduction and stability preservation were investigated and revealed significant synergetic effects for the combination of filtering techniques with discretization parameters. In order to meet the fluctuating, process dependent SNR-levels of the chord length distribution measured by the probe the filtering approaches were required to be self-regulating. Featuring a dynamic noise reduction the power spectral density aided sliding discrete Fourier transform produced the most adequate filtering results.     

A volume-based multi-dimensional population balance approach for modelling high shear granulation

A volume-based multi-dimensional population balance model based on the approach used by Verkoeijen et al. [2002. Population balances for particulate processes—a volume approach. Chemical Engineering Science 57, 2287-2303], is further developed and applied to a wet granulation process of pharmaceutically relevant material, performed in a high shear mixer. The model is improved by a generalization that accounts for initial non-uniformly distributed liquid and air among the different particle size classes. Only the wet massing period of the granulation process has been modelled and it is experimentally found that the pores in the granules are fully saturated by liquid, i.e., no air is present in the granules during this period. Hence, an alternative model formulation is used as no model for the air in the granules is needed. Particle volume distribution, liquid saturation, liquid-to-solid ratio and porosity of the granules can all be modelled, as these properties can all be expressed as combinations of three model parameters, i.e., the volume fraction of solid material, total liquid fraction and the liquid fraction inside the granules. The model is also improved by introducing a new coalescence kernel and by increasing the number of size classes used. The simulated results are compared to measurements from a series of five designed experiments where impeller speed and water content are varied. It is found that the evolution of the volume, liquid saturation and porosity distributions could all be explained by fitting the compaction and coalescence rate constants.     

Numerical and experimental study on multiple-spout fluidized beds

In this paper we study the effect of multiple spouts on the bed dynamics in a pseudo-2D triple-spout fluidized bed, employing the discrete particle model (DPM) and non-intrusive measurement techniques such as particle image velocimetry (PIV) and positron emission particle tracking (PEPT). A flow regime map was constructed, revealing new regimes that were not reported so far. The multiple-interacting-spouts regime (C) has been studied in detail for a double- and triple-spout fluidized bed, where the corresponding fluidization regime for a single-spout fluidized bed has been studied as a reference case. The experimental results obtained with PIV and PEPT agree very well for all the three cases, showing the good performance of these techniques. The DPM simulation results slightly deviate from the experiments which is attributed to particle–wall effects that are more dominant in pseudo-2D beds than in 3D systems. The investigated multiple-interacting-spouts regime is a fully new flow regime that does not appear in single-spout fluidized beds. Two flow patterns have been observed, viz. particle circulation in between the spouts near the bottom of the bed, and an apparent single-spout fluidization motion at a higher location upwards in the bed. These findings show that the presence of multiple spouts in a spout fluidized bed highly affect the flow behaviour, which cannot be distinguished by solely investigating single-spout fluidized beds.     

A multiple radioactive particle tracking technique to investigate particulate flows

Radioactive particle tracking is a nonintrusive technique that has been successfully used to study the flow dynamics in a wide range of reactors and blenders. However, it is still limited to the tracking of only one tracer at a time. A multiple radioactive particle tracking (MRPT) technique that can determine the trajectory of two free or restricted (attached to the same particle) moving tracers in a system is introduced. The accuracy (<5 mm) and precision (<5 mm) of the proposed technique is evaluated by tracking two stationary tracers and two moving tracers. The results confirm the reliability and validity of the MRPT technique when the two tracers have the same isotope and the distance between them is not too small (>2 cm). The tracking of two sticking tracers at the two ends of a cylindrical particle in a rotating drum is also considered to illustrate the potential of this characterization method. © 2014 American Institute of Chemical Engineers AIChE J, 61: 384–394, 2015     

A study of solid behavior in spouted beds using 3-D particle tracking

A non-invasive γ-ray emission system, employing eight NaI detectors, has been developed to follow the motion of a single radioactive particle in a three-dimensional spouted bed reactor. The count-rates measured simultaneously by the detectors are converted into tracer coordinates (x, y, z) using a pre-established calibration model which accounts for every physical and geometrical aspects involved in the spouting facility. Typically four hundred thousands successive coordinates, obtained over 3.5 hours of particle tracking, are used for determining the average particle velocity field and other hydrodynamic quantities such as the cycle time distribution, the spout shape and the solid exchange distribution at the spout boundary, which could not be evaluated accurately using any available techniques.     

Using the discrete element method to predict collision-scale behavior: A sensitivity analysis

Discrete element method (DEM) simulations have recently been used to investigate collision-scale measurements such as collision frequency and impact velocity distributions. These simulations are typically validated against particle velocity fields using experimental techniques such as particle image velocimetry or positron emission particle tracking. An important question that has not been addressed is whether validation of a macroscopic velocity field or solid fraction field also implies a validation of collision-scale measurements such as collision frequency. In this study, DEM measurements of solid fraction, shear rate, collision frequency, and impact velocity are made in a small region just beneath the free surface in a rotating drum. The effects of periodic drum length, particle stiffness, coefficient of restitution, and particle size are investigated. The solid fraction and shear rate do not vary with particle stiffness or coefficient of restitution over the range of values studied. However, the collision rate increases with increasing particle stiffness and coefficient of restitution. In addition, the average collision speed decreases as particles become stiffer or less elastic. The shear rate varies with particle size, but the average collision velocity remains constant. These findings indicate that validation against particle velocity and solid fraction fields does not necessarily imply validation of collision frequency and impact velocity. Indeed, the velocity and solid fraction fields were found to be relatively insensitive to a range of DEM contact stiffnesses and coefficients of restitution while the collision distributions were sensitive.