Positron Emission Particle Tracking Research Articles

Numerical and Experimental Investigations of Horizontal Turbulent Particle-Liquid Pipe Flow.

A Eulerian–Eulerian computational fluid dynamics approach is used in conjunction with appropriate auxiliary models for turbulence and solid dynamic properties to study the complex turbulent flow of particle–liquid suspensions in a horizontal pipe. Numerical simulations of the detailed flow field are fully and successfully validated using a unique experimental technique of positron emission particle tracking. The study includes nearly neutrally buoyant as well as dense particles, ranging from small to large at low to high concentrations, conveyed by a Newtonian liquid. Results are analyzed in terms of radial particle and liquid velocity profiles as well as particle distribution in the pipe. The approach provides predictions with a high degree of accuracy. Particle behavior can be classified into three categories depending on their size and particle–liquid density ratio. An analysis of the forces governing the two-phase flow is used to interpret the phenomena observed.

Eulerian-Lagrangian Modelling of Turbulent Two-Phase Particle-Liquid Flow in a Stirred Vessel: CFD and Experiments Compared

A 3D Eulerian-Lagrangian CFD model is set up to simulate the turbulent flow and mixing of coarse dense particles in a standard batch vessel, mechanically agitated by a down-pumping pitched-blade turbine. Flow is investigated in the just-suspended regime and regimes much above. All simulations are fully and successfully validated by experimental Lagrangian measurements provided by positron emission particle tracking. Predicted distributions of the local 3D phase-velocity components, local particle slip velocities and local particle concentration show very good agreement with experiment. Lagrangian particle trajectories are exploited to infer detailed accurate information on particle circulation time and local residence time. The predicted two-phase flow number is in excellent agreement with experimental values under all flow regimes. Being accurate and robust, the numerical model can be extended to study even more complex particle-liquid suspensions of industrial relevance, and to provide much needed Lagrangian data to other data-driven modelling techniques.

Performance Evaluation of the Current Birmingham PEPT Cameras

Positron emission particle tracking (PEPT), a powerful technique for studying fluid and granular flows, has been developed at Birmingham over the last 30 years. In PEPT, a “positron camera” is used to detect the pairs of back-to-back photons emitted from positron annihilation. Accurate high-speed tracking of small tracer particles requires a positron camera with high sensitivity and data rate. In this paper, we compare the sensitivity and data rates obtained from the three principal cameras currently used at Birmingham. The recently constructed SuperPEPT and MicroPEPT systems have much higher sensitivity than the longstanding ADAC Forte and can generate data at much higher rates, greatly extending the potential for PEPT studies.

Multiscale wavelet analysis of 3D Lagrangian trajectories in a mechanically agitated vessel

Flow turbulence properties are of utmost importance for the optimization of mixing in stirred vessels. A new experimental-theoretical framework is developed to study such turbulence properties. A discrete wavelet transform is used to decompose Lagrangian flow trajectories measured by positron emission particle tracking into their mean and stochastic components representing different scales. The mean component represents low frequency scale motion or non-diffusive/background motion, while the stochastic component accounts for high frequency scale motion or diffusive motion of small eddies. Decomposed Lagrangian trajectories are used to construct maps of local mean and fluctuation flow velocity, turbulent kinetic energy and its dissipation rate, and, for the first time, turbulent diffusion coefficients. Particle image velocimetry measurements are utilised to independently validate results and tune the input parameters of the analysis. Such detailed information on local mixing scales is invaluable to aid equipment design and operation and facilitate heat/mass transfer and enhance reaction kinetics.

Hydrodynamics in a three-phase flotation system – Fluid following with a new hydrogel tracer for Positron Emission Particle Tracking (PEPT)

Understanding the hydrodynamics of three-phase stirred tanks, such as froth flotation cells, is paramount for the characterisation of turbulence, stability and performance. Although positron emission particle tracking (PEPT) is known for its effectiveness in measuring the hydrodynamics of particles in opaque, high solid content systems, it has not been widely used for characterising the liquid phase. This work presents a new, neutrally buoyant, alginate hydrogel tracer, designed to emulate the density of the liquid phase, which is suitable for high-speed tracking with PEPT.PEPT experiments were conducted in a bench-scale flotation cell, comparing the new tracer to ion-exchange resin tracers previously used in this system. Results showed statistically significant differences in pathlines, residence time and velocity distribution among the tracers. Moreover, the hydrodynamics of the new tracer agree with existing CFD predictions for the liquid phase. This methodology enables the comprehensive study of relative flow behaviour in complex multiphase systems.

Effects of operation parameters on particle mixing performance in a horizontal high shear mixer

Abstract Particle mixing is an important unit operation in many industry processes. This work employed the discrete element method (DEM) to characterize the mixing performance of iron ore particles in a horizontal high shear mixer. The simulation results were first compared with the positron emission particle tracking (PEPT) data reported by Forrest et al. to validate the DEM model. Then the effects of key operation factors such as impeller rotation speed, number of impellers and filling ratio on the mixing efficiency were discussed. The Lacey mixing index was employed to evaluate the mixing performance. The results show that the mixing efficiency of particles increased with increasing the number of impellers and their rotation speeds. On the other hand, the filling ratio was negatively related to the particles velocity and the mixing efficiency. This was because the effective space left for free movement of particles decreased as the filling ratio increased, and the mixing of particles was therefore restricted. In addition, the mixing rate of particles in the axial direction of the high shear mixer was much slower than that in the radial direction.

Computation of Lagrangian coherent structures from experimental fluid trajectory measurements in a mechanically agitated vessel

• Lagrangian coherent structures are computed from 3D particle tracking measurements. • LCSs characterise the hidden complex topology of turbulent flow in a stirred vessel. • Results show that LCSs are related to mixer configuration and macroscale mixing. In mechanically agitated vessels, bulk flow circulation which plays a leading role in macroscale mixing is controlled by hidden Lagrangian coherent structures (LCSs). We use a numerical finite-time Lyapunov exponent (FTLE) approach, for the first time, to resolve such LCSs. Experimental 3D Lagrangian trajectories obtained from a unique positron emission particle tracking (PEPT) technique are used to drive the FTLE model. By computing forward and backward FTLE fields and extracting repelling and attracting FTLE ridges in various azimuthal planes of the flow, a highly complex flow topology is unravelled which varies significantly with azimuthal position. We demonstrate how LCSs organise and quantify the chaotic behaviour of fluid particle paths that underpin mixing through the exchange of fluid between zones of different kinematics. This new Lagrangian approach driven by unique PEPT data is able to unfold some of the complexities of turbulent flow that are beyond the capability of traditional methods.

Characterisation of solid hydrodynamics in a three-phase stirred tank reactor with positron emission particle tracking (PEPT)

It is challenging to measure the hydrodynamics of stirred tank reactors when they contain multiphase flows comprising liquid, gas bubbles and particles. Radioactive particle tracking techniques such as positron emission particle tracking (PEPT) are the only established techniques to determine internal flow behaviour due to the inherent opacity and density of fluid and the vessel walls. The profiles of solids flow are an important tool for robust reactor design and optimisation and offer insight into underlying transport processes and particle–fluid–bubble interactions for applications such as froth flotation. In this work, measurements with PEPT were performed with two tracer particles differing in surface hydrophobicity to characterise the solids hydrodynamics in a baffled vessel agitated with a Rushton turbine. The location data from PEPT were averaged with time to estimate the probability density function (PDF) of particle velocity in individual voxels. The peaks of these voxel distributions were used to produce profiles of solids flow in different azimuthal and horizontal slices. Bimodal vertical velocity distributions were observed in the impeller radial jet which suggest the particles experienced trajectory crossing effects due to inertia. Statistical tests were performed to compare the velocity distributions of the hydrophilic and hydrophobic tracer particles, which indicated similar average flow behaviour in the liquid or pulp phase of the vessel and differences near the air inlet, in the impeller discharge stream and pulp–froth interface. With tracers designed to represent gangue and valuable mineral species, the differences in velocity reveal interactions such as bubble–particle attachment and entrainment. • Positron emission particle tracking (PEPT) measurements of multiphase flow. • Solid hydrodynamics in a three-phase stirred tank reactor of gas, liquid and solids. • Comparison of hydrophilic and hydrophobic particle flow behaviour. • Observations of particle interaction with the gas bubble flow field.

Experimental validation of DEM in rotating drums using Positron Emission Particle Tracking

Despite the widespread use of the Discrete Element Method (DEM) to simulate industrial rotating drum flows, comparatively little work has been done to evaluate its accuracy. To bridge this gap, Positron Emission Particle Tracking (PEPT) was employed to benchmark tuned DEM simulations. Two granular mixtures of mono-sized glass beads (31% filling), run at 60 and 75% of critical speed, were used. To ensure an equitable comparison, both DEM and PEPT data were coarse grained. The comparisons include the free surface (average RMS error = 2.6 mm), equilibrium surface (average RMS error = 3.3 mm), bin-by-bin comparisons of the solids fraction (15% relative error) and velocity (10% relative error), and equivalent comparisons along slices drawn orthogonal to the free surface that produced complete statistical agreement between PEPT and DEM. The results suggest a strong statistical agreement between the tuned DEM and coarse grained PEPT data.

DEM2GATE: Combining discrete element method simulation with virtual positron emission particle tracking experiments

Positron Emission Particle Tracking (PEPT) is a Lagrangian particle tracking technique useful for imaging flow in opaque granular media. The scientific and industrial systems studied using PEPT and the PEPT technique can also be simulated: Discrete Element Method (DEM) for granular systems and Monte Carlo for PEPT. Using the open-source DEM2GATE library, we quantify the reconstruction of particle trajectories and overall system behaviour by integrating particle trajectories from a rotating drum simulation with a PEPT detector simulation. The results show the main drivers of PEPT spatial error are particle acceleration and gamma-ray scattering. The accuracy of reconstructed flow fields increases logarithmically with measurement time. Measurements of higher-order, derived quantities require more time to reach a desired level of accuracy. Surprisingly, our results imply PEPT measurements relying on fluctuating velocity deviate substantially from the system's true behaviour. However, using DEM2GATE, these errors are predictable and can be corrected.

Standard method for performing positron emission particle tracking (PEPT) measurements of froth flotation at PEPT Cape Town

Positron emission particle tracking (PEPT) is a technique for measuring the motion of tracer particles in systems of flow such as mineral froth flotation. An advantage of PEPT is that tracer particles with different physical properties can be tracked in the same experimental system, which allows detailed studies of the relative behaviour of different particle classes in flotation. This work describes the standard operating protocol developed for PEPT experiments in a flotation vessel at PEPT Cape Town in South Africa. A continuously overflowing vessel with constant air recovery enables several hours of data acquisition at steady state flow and consistent flotation conditions. Tracer particles are fabricated with different coatings to mimic mineral surface hydrophobicity and size, and a data treatment derived from a rotating disk study is utilized to produce high frequency (1 kHz) location data relative to the tracer activity. Time averaging methods are used to represent the Eulerian flow field and occupancy of the tracer behaviour based on voxel schemes in different co-ordinate systems. The average velocity of the flow in each voxel is calculated as the peak of the probability density function to represent the peak of asymmetrical or multimodal distributions.•A continuously overflowing flotation vessel was developed for extended data acquisition at steady state flow.•The data treatment enabled the direct comparison of different particle classes in the flotation vessel.•The solids flow fields was described by the probability density function of tracer particle velocity measured in different voxel schemes.

SuperPEPT: A new tool for positron emission particle tracking; first results

Positron emission particle tracking (PEPT) is a powerful technique for studying flow inside engineering systems by tracking radioactively-labelled particles. A positron camera is used to record coincidence data arising from positron annihilation; since the precision of PEPT depends on the recorded data rate, the camera sensitivity is crucial. We report first results from a new positron camera, SuperPEPT, which has been constructed using components from CTI/Siemens ECAT EXACT 31, ART, and EXACT HR+ scanners and has a versatile geometry with a large field-of-view (FOV). These results were obtained using just two of the three detector sections but already show sensitivity and data rates much higher than achievable with previous positron cameras.

Noninvasive interrogation of local flow phenomena in twisted tape swirled flow via positron emission particle tracking (PEPT)

Twisted tape inserts are often used to enhance the performance of heat exchangers. Previous simulations suggest the existence of secondary vortices and modified axial velocity profiles in these swirled flows, with only limited experimental evidence for these predictions. In this work, positron emission particle tracking (PEPT) is used to interrogate turbulent twisted tape swirl flow in a pipe. PEPT is a noninvasive, radiotracer based flow measurement technique that does not require optical access, making it suitable for measurements in a number of engineering flow systems. The existence of the modified velocity profile and secondary flows is confirmed using PEPT, and flow is seen to still be developing 20 diameters downstream of the twisted channel entrance. Secondary vortices are further confirmed by the presence of increased vorticity in these regions, and turbulent fluctuations are seen to increase in magnitude near these flow structures. These results are in line with predictions and point to possible regions of reduced heat transfer and hot spots in twisted tape based heat exchangers. Suggestions are made for future experiments to investigate heated flows, utilizing the ability of PEPT to image flows in opaque systems for validating simulation of flows in engineering equipment, such as nuclear heat transport equipment.

Coffee bean particle motion in a spouted bed measured using Positron Emission Particle Tracking (PEPT)

Coffee roasting is a heat treatment process that transforms green coffee into a product that can subsequently be ground and brewed. Understanding roasting is critical in developing new downstream processes and formulations, as well as in optimising existing ones. Positron Emission Particle Tracking (PEPT) allows tracking of particles in process equipment and has been used here to characterise particle dynamics of coffee beans within a spouted bed roaster subject to varying air-to-bean ratios without roasting. Occupancy profiles associated with each air-to-bean ratio have been determined and two distinct regions identified: (i) a dense bean bed of high occupancy (ii) a dilute freeboard of lower occupancy. Results also revealed the effect of coffee density on particle dynamics within the roaster. Overall, this work demonstrates that PEPT can be a useful tool to generate data regarding granular flow patterns in roasters that might be used to improve existing heat and mass transfer models for roasting.

Hydrodynamic characterisation of flotation impeller designs using Positron Emission Particle Tracking (PEPT)

Impellers play a key role in flotation cells, as the turbulence generated through agitation aids particle suspension, air dispersion and particle–bubble collision. Therefore, it is important to understand the effect that different impeller designs have on flotation hydrodynamics, as small variations could enhance flotation performance. The study of flotation hydrodynamics is, however, a complex task due to the nature of flotation systems, which are opaque, multiphase, and polydisperse. In this paper, the impact of impeller design modifications on the hydrodynamics of a flotation cell was quantified for the first time in a three-phase system. Two different impeller designs, with and without a stator, were assessed using positron emission particle tracking (PEPT), a technique that allows the position and velocity of radioactive particle tracers within an opaque vessel to be determined. A novel PEPT data analysis strategy, as well as a statistical analysis on the basis of the Jensen–Shannon distance, were used. This statistical analysis, applied for the first time to PEPT data, facilitated the comparison of the different designs, by generating a robust quantification of their hydrodynamic differences. The experimental results showed that the stator significantly modified the hydrodynamics within the flotation cell, distorting the lower mixing loop that is characteristic of radial impellers. The use of a stator also resulted in the reduction of particle velocity and swirling outside of the impeller–stator region, both at the level of the impeller and, notably, at the pulp–froth interface. These findings have important implications for impeller–stator design, evidencing that the impeller has a direct effect on the hydrodynamics of the pulp and froth.

An expectation-maximization algorithm for positron emission particle tracking.

We develop a new algorithm for the tracking of radioactive particles using Positron Emission Particle Tracking (PEPT). The algorithm relies on the maximization of the likelihood of a simple Gaussian mixture model of the lines of response associated with positron annihilation. The model includes a component that accounts for spurious lines caused by scattering and random coincidence, and it treats the relative activity of particles as well as their positions as parameters to be inferred. Values of these parameters that approximately maximize the likelihood are computed by the application of an expectation-maximization algorithm. A generalization of the model that includes the particle velocities and accelerations as additional parameters takes advantage of the information contained in the exact timing of positron annihilations to reconstruct pieces of trajectories rather than fixed positions, with clear benefits. We test the algorithm on both simulated and experimental data. The results show the algorithm to be highly effective for the simultaneous tracking of many particles (up to 80 in one test). It provides estimates of particle positions that are easily mapped to entire trajectories and handles a variable number of particles in the field of view. The ability to track a large number of particles robustly offers the possibility of a dramatic expansion of the scope of PEPT.

Dynamics of fabric and dryer sheet motion in domestic clothes dryers

Positron emission particle tracking (PEPT) has been used to investigate the motion of radioactively labeled tracer particles attached to fabrics and solid fabric enhancer (SFE) delivery articles, such as dryer sheets, in the domestic clothes dryer. This work examines the dynamics of motion within the dryer across a range of operating conditions. Six regions within the dryer drum are identified, demonstrating the range of movements experienced by items during tumbling. These show clear correlation with existing flow regimes describing behavior of granular media in rotating drums. Fabric motion is primarily cataracting to maximize the surface area of fabric available to interact with drying air in the falling region, with some conditions moving toward centrifuging or cascading flows. Movement in the axial direction was significantly slower than the primary radial flow. Dryer sheets were more prone to centrifuging than fabrics, with significant time spent in contact with the drum wall. Conversely, a wool dryer ball was more likely to cascade, spending time mixed into the top of a fabric bed which forms in the impact and lifting regions. Behavior in this bed is primarily determined by frictional interactions with the drum wall, which subsequently affects behavior in the 5 remaining regions. The most significant changes to this behavior were observed when changing fabric moisture content and volumetric fill ratio, with wet fabrics and smaller load sizes both exhibiting faster falling speeds and spending more time in the fabric bed. The changes were most significant in the lifting, falling and detachment regions, with varying acceleration and shearing likely to influence both fabric wear and SFE delivery.

Monte Carlo model validation of a detector system used for Positron Emission Particle Tracking

The spatiotemporal resolution of Lagrangian particle trajectories captured using Positron Emission Particle Tracking (PEPT) is difficult to predict prior to experimentation, since this relies on the detector systems, source activity distribution, and experimental apparatus. However, understanding the limitations of an experiment is crucial to quantifying error and ensuring that the captured trajectories reveal phenomena of interest in enough detail for meaningful analysis. These factors are especially important in PEPT experiments since this technique is applied to image opaque systems lacking optical access for complementary measurement techniques, such as Particle Image Velocimetry. Using the Monte Carlo simulator Geant4 Application for Tomographic Emission (GATE), a computational model of the ADAC/Phillips Forte, a detector system used at the Positron Imaging Centre (PIC) for PEPT studies, is created and validated against experiments testing the spatial resolution, sensitivity, scatter fraction, and count-rates following National Electronic Manufactures Association standards. In this work, fluorine-18 sources and experimental geometries are recreated, generating synthetic data analogous to experimentally acquired data. Over all experiments and activities tested, this GATE model reports agreement to within 1%–10% of experiments. In the future, this model is expected to be used by the PIC to conduct feasibility studies of potential experiments. Further, optimization of experiments can now be conducted without expending the considerable time and resources required for physical experimentation, representing a major improvement of the PIC’s PEPT modeling capabilities.

A data-driven respiratory motion estimation approach for PET based on time-of-flight weighted positron emission particle tracking.

PurposeRespiratory motion of patients during positron emission tomography (PET)/computed tomography (CT) imaging affects both image quality and quantitative accuracy. Hardware‐based motion estimation, which is the current clinical standard, requires initial setup, maintenance, and calibration of the equipment, and can be associated with patient discomfort. Data‐driven techniques are an active area of research with limited exploration into lesion‐specific motion estimation. This paper introduces a time‐of‐flight (TOF)‐weighted positron emission particle tracking (PEPT) algorithm that facilitates lesion‐specific respiratory motion estimation from raw listmode PET data.MethodsThe TOF‐PEPT algorithm was implemented and investigated under different scenarios: (a) a phantom study with a point source and an Anzai band for respiratory motion tracking; (b) a phantom study with a point source only, no Anzai band; (c) two clinical studies with point sources and the Anzai band; (d) two clinical studies with point sources only, no Anzai band; and (e) two clinical studies using lesions/internal regions instead of point sources and no Anzai band. For studies with radioactive point sources, they were placed on patients during PET/CT imaging. The motion tracking was performed using a preselected region of interest (ROI), manually drawn around point sources or lesions on reconstructed images. The extracted motion signals were compared with the Anzai band when applicable. For the purposes of additional comparison, a center‐of‐mass (COM) algorithm was implemented both with and without the use of TOF information. Using the motion estimate from each method, amplitude‐based gating was applied, and gated images were reconstructed.ResultsThe TOF‐PEPT algorithm is shown to successfully determine the respiratory motion for both phantom and clinical studies. The derived motion signals correlated well with the Anzai band; correlation coefficients of 0.99 and 0.94‐0.97 were obtained for the phantom study and the clinical studies, respectively. TOF‐PEPT was found to be 13–38% better correlated with the Anzai results than the COM methods. Maximum Standardized Uptake Values (SUVs) were used to quantitatively compare the reconstructed‐gated images. In comparison with the ungated image, a 14–39% increase in the max SUV across several lesion areas and an 8.7% increase in the max SUV on the tracked lesion area were observed in the gated images based on TOF‐PEPT. The distinct presence of lesions with reduced blurring effect and generally sharper images were readily apparent in all clinical studies. In addition, max SUVs were found to be 4–10% higher in the TOF‐PEPT‐based gated images than in those based on Anzai and COM methods.ConclusionA PEPT‐ based algorithm has been presented for determining movement due to respiratory motion during PET/CT imaging. Gating based on the motion estimate is shown to quantifiably improve the image quality in both a controlled point source phantom study and in clinical data patient studies. The algorithm has the potential to facilitate true motion correction where the reconstruction algorithm can use all data available.

Ensuring adequate statistics in particle tracking experiments

Particle tracking techniques such as magnetic particle tracking, radioactive particle tracking and positron emission particle tracking are widely used in academia and industry to image the dynamics of particulate and multiphase systems. These techniques can provide detailed data concerning a range of important, whole-field quantities based only on the time-averaged dynamics of a small number of tracer particles. However, in order for this data to be reliable, the duration over which these time-averages are taken must be suitably long. Further, the ‘minimum averaging time’ required to produce good statistics depends sensitively on the system in question and, at present, cannot be determined a priori in advance of an experiment. In this paper, we take a step toward resolving this issue, using discrete element method simulations of a simple vibrofluidised granular bed to develop a series of scaling laws relating said minimum averaging time to a variety of key system variables. The scaling laws developed may be used by future experimentalists to predict the required averaging time for each given system during an experimental campaign, thus improving both the efficiency with which particle tracking techniques may be applied, and the reliability of the data produced thereby.