Dynamics of Particulate Systems

Measurement Techniques Electrical Capacitance Tomography (ECT) Velocity (Twin Plane) Concentration Particle Image Velocimetry (PIV) Velocity Phase Doppler Particle Analyzer (PDPA) Number density

Single Plane ECT System Components Capacitance Measurement Data Acquisition Unit Multiplexing Circuit Capacitance To Voltage Transfer A/D Converter Insulating Pipe Control Signals Electrode Data Post Processing Image Reconstruction Algorithm

Single Plane ECT System Mechanism Measures capacitance of 12 electrodes Obtains 66 capacitance values Utilizes distribution of permeability to obtain porosity Solves for solid concentration

Twin Plane ECT System ( D ) U = L /D Plane 1 Plane 2 V Signal Delay Cross Correlation Signal Delay ( D ) U = L /D Plane 1 Plane 2 V

Twin Plane ECT System Mechanism Measures particulate concentration profiles at two axially-separated locations Obtains velocity profile via correlation techniques Obtains overall flow rate via integration of product of both concentration and velocity profiles Obtains the volumetric flow of the particulates via second integration over a period of time

PIV System (1) Synchronizer (2) Computer (3) Laser generator (4) CCD camera (5) Vessel (6) Vibrator (7) Function generator (8) Power amplifier

PIV System Mechanism Measures instantaneous global velocity in a flowing fluid CCD camera takes pictures Displacement/Time = Velocity

Stability Analysis

Perturbation Form Perturbations: Where: And:

Ωr is > 0 (positive): amplitude of disturbance increases with time Ωr is < 0 (negative): amplitude of disturbance decays with time Ωr is positive: unstable mode If you introduce a small disturbance, integrate forward with time, the variable will move away from steady state Ωr is negative: stable mode

Stability Diagram (+ve Eigen value) (-ve Eigen value)

Electrostatic Characterization 5: MPCT / ECT 6: Induced current measurement 7: Faraday Cage

Types of flow Disperse flow (highest u) Half Ring flow Ring flow (lowest u)

Summary Air flow rate - lower air flow rate, higher induced current and particle charge density Time – Charge accumulation for pipewall and individual particle increases with time for all types of flow. Leads to clustering of particles even in case of disperse flow. Composition – Antistatic agent, Lacrostat 519 powder can reduce electrostatic effect. Tribroelectrification – strong force effect created on walls when particles slide on pipe wall.

Discrete element method (DEM) A numerical method for computing the motion and effect of a large number of small particles in a pipe by using computational fluid dynamics. Outline of the method A DEM-simulation is started selecting a model and setting an initial gas velocity. The forces which act on each particle are computed from the initial data, relevant physical laws and contact models. The change in the position and the velocity of each particle during a certain time step can be computed from Newton's laws of motion.

Models Force Displacement Model Fluid Drag Force Model

Types of flows Vertical pneumatic conveying Dispersed flow Plug flow Horizontal pneumatic conveying Stratified Flow Moving dunes Slug Flow Homogeneous Flow For different types of flow and gas velocity, the solid flow rate profile and the solid concentration profile can be determined from the data and graph.

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