Abstract: Mixing is intrinsically a Lagrangian process and, whilst Eulerian data are very important, Lagrangian information is necessary for its complete description. Lagrangian data can, in principle, be generated by employing numerical simulations or experimental techniques based on Lagrangian tracking to provide the trajectories of fluid elements or particles. We present a set of theoretical and computational tools specifically developed for the analysis and validation of single- and multi-phase Lagrangian flow data obtained from tracer trajectories in mechanically agitated vessels. The implementation and power of these tools are demonstrated by analysing a wide range of measurements acquired using the technique of positron emission particle tracking during mixing of Newtonian and non-Newtonian fluids, as well as mixing of concentrated solid-liquid suspensions. Finally, the accuracy of the raw Lagrangian data treatment developed here is illustrated by comparing with a Eulerian technique and showing very precise mass continuity for an agitated solid-liquid system.
Abstract: The three-component flow field and spatial phase distribution of binary mixtures of glass particles suspended in water in a stirred vessel have been resolved using positron emission particle tracking (PEPT). The Lagrangian flow data provided by the technique have been converted to give a detailed Eulerian description of each of the three phase components of the flow generated by a pitched blade turbine. For the first time, it has been possible to determine the full 3D velocity and concentration fields of the liquid phase and both the solid components within opaque dense slurries of this type containing up to 40 wt % solids. Spatial distributions of local time-averaged slip velocity have also been obtained for each solid component showing wide variations. The detailed PEPT measurements have enabled the solids mass balance and the mass continuity of the three phase components to be accurately verified throughout the vessel.
Abstract: If 100 dice cannot be cast simultaneously, one single die can be cast 100 times. On the basis of this simple principle, the experimental technique of positron emission particle tracking has been used to develop and implement a new methodology for quantifying the local and global mixing characteristics within a mechanically agitated fluid batch system. This Lagrangian technique uses a single positron-emitting particle as flow follower. Using a high data acquisition rate, such a tracer is continuously tracked in 3D space and time to accurately determine its trajectory over a considerable period of time. By partitioning its long trajectory, the single particle tracer can be regarded as thousands of simultaneously tracked particles which are instantaneously, locally and non-invasively injected in the mixing system at varying feed positions. A large amount of PEPT data were collected for impeller rotational speeds ranging from 100 to 500Â rpm which allowed new statistical tools derived from information theory, such as Shannon entropy and uncertainty, to be implemented in the data analysis. Thus, measurements of entropy mixing indices were obtained as a function of position, time and impeller speed. The method also allowed the determination of characteristic time parameters including the macroscale mixing time which agreed very well with correlations of the dimensionless mixing time available in the mixing literature. Detailed local information is provided on minimum mixing time positions for feed and withdrawal of material, which can be used to optimise the design or operation of stirred batch mixing systems.
Abstract: Two-dimensional particle image velocimetry (PIV) is usually used to determine the complex flow field in mechanically agitated vessels on the basis of measurements taken in a single vertical plane, thus, assuming axial symmetry. In this paper, we use 2D PIV to investigate the effects of the azimuthal position of the measurement plane in a fully baffled vessel agitated by a pitched blade turbine. Seventeen planes located at 5 degree intervals between two adjacent baffles are analysed. To maintain a high spatial resolution of ~1Â mm when examining each plane, a two-block approach is employed combining data from two fields of view to reconstruct the whole flow field. Time-averaged velocity and turbulent kinetic energy fields are obtained under fully turbulent conditions as a function of the azimuthal position of the laser plane. It is shown that the assumption of axial symmetry for such Eulerian fields is not fully justified within a fully baffled vessel, as there are considerable differences between planes. The results also show for the type and size of impeller used here, the importance of including both the axial and radial discharge contributions for an accurate evaluation of the flow number, otherwise it can be underestimated by up to 60%. The three-dimensional nature of the PIV measurements has also enabled the mass continuity to be accurately verified throughout the vessel.
Abstract: The technique of positron emission particle tracking (PEPT) has been used to determine the two-phase flow field and spatial phase distribution in a stirred vessel containing coarse glass particles suspended in water. The Lagrangian flow data provided by PEPT have been converted to give a detailed Eulerian description of the two-phase flow generated by a pitched blade turbine (PBT) operating in up-pumping or down-pumping mode. For the first time, it has been possible to determine the full 3D velocity and concentration fields of both the liquid and the solid phase within an opaque dense slurry of this type containing up to 40Â wt% solids. The detailed PEPT measurements have also enabled the solids mass balance and the mass continuity of the two phases to be accurately verified throughout the vessel. The data show that the pumping effectiveness of the PBT is unaffected at moderate solid fractions, but is considerably reduced at high fractions and even more so in the up-pumping mode. A uniformity index based on the variance of the local solids concentration in the vessel shows that, overall, a down-pumping PBT achieves a significantly better homogeneity than an up-pumping PBT.
Abstract: The technique of positron emission particle tracking (PEPT) is a unique non-intrusive Lagrangian flow visualisation technique which allows probing of opaque fluids and within opaque apparatus. It uses a single positron-emitting particle as flow tracer which is tracked in 3D space and time to reveal its full Lagrangian trajectory. PEPT was used to study the mixing of a concentrated suspension of coarse glass particles, containing up to 10.6Â wt% solids, in a vessel agitated by a pitched blade turbine operating in both up-pumping and down-pumping modes. The Lagrangian information obtained was used to obtain a detailed Eulerian description of the two-phase flow inside the vessel. For the first time, it has been possible to determine the full 3D velocity and concentration fields of both the liquid and the solid phase within an opaque flow of this type.
Abstract: Mixing is intrinsically a Lagrangian process. Lagrangian data can be generated by employing numerical simulations or experimental techniques based on Lagrangian tracking to provide the trajectories of fluid elements or particles. We present a set of theoretical and computational tools specifically developed for the analysis and validation of single- and multi-phase Lagrangian flow data obtained in stirred vessels.
Abstract: In the UK, monitoring and inspection is required by the regulators to ensure continued safe storage, retrievability and disposability of packages of radioactive waste in interim storage. Monitoring and inspection requirements may also be determined by any requirements for transport, further storage or disposal when the store is emptied. This paper presents an approach to establishing a monitoring and inspection strategy for stored intermediate level waste (ILW) packages that was developed under the UK Nuclear Decommissioning Authority’s Direct Research Portfolio programme.
The key aspects to be considered when developing a package monitoring and inspection strategy are identified and used to develop a generic multi-stage process that will enable store operators to identify a justifiable monitoring and inspection strategy for ILW packages in long-term interim storage. Two spreadsheet tools have also been developed to facilitate use of the multi-stage process by store operators (IMPS – Inspection and Monitoring of Packages in Stores and CBAT – Cost / Benefit Analysis Tool).
A statistically based methodology has been used to identify the number of waste packages to be inspected and an appropriate frequency of inspection, and aspects such as cost, risk and operational feasibility are taken into account.
Abstract: The technique of Positron Emission Particle Tracking (PEPT) is a unique non-intrusive Lagrangian flow visualisation technique which allows probing of opaque fluids and within opaque apparatus. It uses a single positron-emitting particle as flow tracer which is tracked in 3D space and time to reveal its full Lagrangian trajectory. PEPT was used to study the mixing of a concentrated suspension of coarse glass particles in a vessel agitated by a pitched blade turbine operating in both up-pumping and down-pumping modes. The Lagrangian information obtained was used to obtain a detailed Eulerian description of the two-phase flow inside the vessel. For the first time, it has been possible to determine the full 3D velocity and concentration fields of both the liquid and the solid phase within an opaque flow of this type.
Abstract: Positron Emission Particle Tracking (PEPT) is unique in flow visualisation terms, being able to examine flow phenomena quantitatively in three dimensions in systems that cannot be studied by techniques such as PIV and LDA because they do not allow the passage of laser light. Slurries are a typical case. They are found in many industries including minerals, food processing, household and personal care products. Indeed, some 80% of products in the chemical industry, for example, are of this type. The suspension of solids in low viscosity fluids is one common example and is critical for promoting chemical reaction between the two phases, or for enhancing crystal growth. In the latter, a wide size range is found and establishing their spatial distribution as function of size has proved difficult though it is important. PEPT is able to do this and also determine the velocity of each of the two phases. In many other cases, especially in food processing, household and personal care products, slurries exhibit non-Newtonian, paste-like behaviour. Little work has been done to understand how to mix them effectively. The reason for this is their opaque nature. Therefore, it has been assumed that knowing the rheology of the slurry enables the prediction of its behaviour, based on studies on transparent polymer solutions with similar rheological properties. Again, PEPT can tackle such issues, giving a full flow field, viz., the three velocity vectors throughout the vessel. Such work has been carried out on paper pulp (a yield stress fluid), a personal care product (yield stress and viscoelastic) and on a china clay slurry (shear thickening}. All this work will be summarized, along with a critique of the technique and a study to establish its accuracy, based on a comparison with the extensive literature on Rushton turbines in water.
Abstract: Positron Emission Particle Tracking (PEPT), is a non-intrusive flow visualisation technique which allows probing of opaque fluids and within opaque apparatus. It uses a single positron-emitting particle as flow tracer which is tracked in 3D space and time to reveal its full Lagrangian trajectory. PEPT was used to study the mixing of a polydispersed suspension of glass particles at concentrations up to 40 wt%, in a vessel agitated by a pitched blade turbine. For the first time, it has been possible to determine the full 3D velocity and concentration fields of the liquid phase and of each particle size fraction within the suspension.
Abstract: When a positron is subjected to annihilation with an electron, a pair of almost back-to-back collinear 511 KeV γ-quanta is emitted. If two such γ-rays are detected in coincidence, it may be assumed that the annihilation has occurred on the line joining the two detection points, the photon-trajectory. The Birmingham positron camera comprises two gamma camera-heads working in coincidence, mounted on a motorised gantry which allows their rotation about a horizontal axis. Each head contains a single sodium iodide crystal optically coupled to an array of photomultiplier tubes. When a positron annihilation occurs, the γ-rays emitted produce scintillations in the crystals, the related photomultipliers generate positional signals and the two centroids are then obtained using a dedicated software. With a small number of annihilation events (theoretically only two), the position of a single positron-emitting particle can be located at the intersection of the photon-trajectories. The technique of Positron Emission Particle Tracking (PEPT), developed on the basis of these concepts, was used to study the mixing of a concentrated suspension of glass particles in a stirred vessel. For the first time, it has been possible to determine the full 3D velocity and concentration fields of the liquid and the solid phase within an opaque multi-phase flow of this type.
Abstract: Positron Emission Particle Tracking (PEPT) is unique in flow visualisation terms, being able to examine flow phenomena in three dimensions that could not be observed as effectively by using other techniques. PEPT was used to determine the 3D velocity field as well as solids distribution developed during mixing of a polydisperse slurry consisting of glass particles from 1 to 3.30 mm, at mass concentrations varying from 5 to 40%, in a vessel agitated by a pitched blade turbine. For the first time, it has been possible to determine the local velocity as well as concentration distributions of each individual particle size fraction. The flow fields were determined for both up-pumping and down-pumping operation of the turbine. The accuracy of PEPT was independently ascertained by comparison with 2D PIV measurements in water, and via mass continuity calculations.
Abstract: The formation of caverns around the impeller during mixing of an opaque industrial slurry having a Herschel- Bulkley type rheology, was studied using Positron Emission Particle Tracking (PEPT). Fluid motion is totally confined within the cavern boundary, and is dominated by the tangential component, vϑ. The flow field inside the cavern is characterized by complex toroidal fluid motion. Results show that a cavern boundary drawn through the locus point corresponding to sqrt(vr^2+vz^2) = 0.01vtip is more in line with the experimentally observed boundary than the usual assumption of vϑ = 0.01vtip.
