Week 8 Dynamics of Particulate systems – (1) Electrohydrodynamic atomization fabrication of pharmaceutical particles, (2) bubble motion in Taylor vortex, (3) vibrated granular bed system, (4) pneumatic transport of granular material. –Measurement techniques used in the study of such systems include Electrical Capacitance Tomography (ECT), Particle Image Velocimetry (PIV) and Phase Doppler Particle Analyzer (PDPA). Bubble Motion in Taylor Vortex Camera Mineral Oil: (25C) ρ=0.86g/cm3 η=29.67cp Synchronizer Outer cylinder Laser Generator Inner cylinder Computer Bubble Motion in Taylor Vortex 1 8 5 9 6 2 3 Radius ratio (η=ri/ro) : 0.613 Aspect ratio (Γ=L/d): 5.17 Clearance ratio (c=d/ri): 0.63 Air bubble: (25C) ρ=0.0012g/cm3 η=0.0185cp 4 Reynolds number: 7 10 Re Ri d 65 ~ 520 Taylor number: Figure 1 Schematic diagram of experimental apparatus (1) motor (2) outer cylinder (3) working liquid (4) inner cylinder (5) needle (6) lamp (7) camera (8) computer for viscosimeter (9) syringe pump (10) computer for high-speed video camera Ta 2 Ri d 3 2 1.1e4 ~ 6.8e5 Core bubble: ring structure Ω =300rpm, Side View 68 Bubbles 110 Bubbles R.S. Deng, C.H. Wang, and K. A. Smith, “Bubble behavior in a Taylor vortex”, Physical Review E, 73, 036306 (2006). Flow pattern in pure liquid system Ri Ro 20.0 rpm Ri Ro 90.1 rpm Ri Ro 107.8 rpm Ri Ro 155.3 rpm Ri Ro 179.9 rpm Ri Ro Ri Ro Ri Ro Ri Ro Ri Ro Ri Ro Ri Ro 200.1 rpm 300.0 rpm 352.4 rpm 387.6 rpm 500.0 rpm 600.0 rpm 800.4 rpm Ω One-dimensional flow turns into Taylor vortex flow at about 95rpm, and no wavy vortex is observed below 800rpm in the present system. Two types of bubbles R.S. Deng, C.H. Wang, and K. A. Smith, “Bubble behavior in a Taylor vortex”, P hysical Review E, 73, 036306 (2006). P3 P1 P4 P2 Ri Core Bubble Wall Bubble Ro Pressure distribution calculated from CFD (Fluent 6.1) Application of Particle Image Velocimetry (PIV) for Pattern Characterization in a Vertically Vibrated Granular Layer High-speed video camera, 1,000fps Discrete Element Simulation Experimental apparatus 1 5 3 A, f 4 2 6 7 8 (1) Synchronizer (2) Computer (3) Laser generator (4) CCD camera (5) Vessel (6) Vibrator (7) Function generator (8) Power amplifier Image captured by PIV camera Peak Peak Y O X Free Space Valley Granular Layer Detachment Bottom Plate Typical stages in a vibrating cycle (First Half) (First Half) Impact Contact R.S. Deng and C.H. Wang, "Particle Image Velocimetry Study on the Pattern Formation in a Vertically Vibrated Granular Bed", Phys. Fluids, 15(12) 3718-3729 (2003). Free-flight (Second Half) Flow Stability Analysis H Taking average over one period Granular Layer M t A, f X A sin(t ) Vibrator Example VY H t Granular Layer M t VY=0 Qt Governing Equations Continuity Momentum Energy ( u) 0 t Du g Dt 3 DT q : u J 2 Dt Stability Analysis Perturbation Form Perturbations: Where: u u0 u 0 0 T T0 T u ue (Y ) exp( ) exp(iK x X ) e (Y ) exp( ) exp(iK x X ) e (Y ) exp( ) exp(iK x X ) T Te (Y ) exp( ) exp(iK x X ) And r ii Stability Analysis Stability Diagram L-C margin Unstable Qt S-C margin Stationary Mode r B Layer Mode Stable A Mt R.S. Deng and C.H. Wang, "Instabilities of Granular Materials under Vertical Vibrations", J. Fluid Mechanics, 492, 381-410 (2003). Surface Patterns (I) Stripe R.S. Deng and C.H. Wang, "Instabilities of Granular Materials under Vertical Vibrations", J. Fluid Mechanics, 492, 381-410 (2003). (a) (b) (c) X z/D Z x/D 1-Perturbation Simulation (This work) Experiment (Umbanhowar, Nature, 389, 1997) Surface Patterns (II) Square R.S. Deng and C.H. Wang, "Instabilities of Granular Materials under Vertical Vibrations", J. Fluid Mechanics, 492, 381-410 (2003). (a) (b) (c) X z/D Z x/D 2-Perturbations Simulation (This work) Experiment (Umbanhowar, Nature, 389, 1997) Chem. Eng. Sci., 53(22), 3803-3819 (1998) J. Fluid Mech., 435, 217-246 (2001). J. Fluid Mech., 435, 217-246 (2001). Components Capacitance Measurement Data Acquisition Unit C2 C1 Multiplexing Capacitance A/D Circuit to Voltage Converter Transfer Insulating Pipe Control Signals Data Electrode Post-processing Image Reconstruction Algorithm Schematic Diagram of ECT System Plane 1 L Plane 2 V Twin plane ECT system (Velocity measurement) S.M. Rao, K. Zhu, C.H. Wang, and S. Sundaresan, “Electrical Capacitance Tomography Measurements on the Pneumatic Conveying of Solids”, Ind. Eng. Chem. Res. 40(20) 4216-4226 (2001). (a) (a) (b) (b) t t X Y Homogeneous flow (a) typical flow pattern (b) time averaged particle concentration profile (c) particle concentration contours. X Y Moving Dunes (a) typical flow pattern (b) time averaged particle concentration profile (c) particle concentration contours. (a) (a) (b) (b) t t X Y Flow over settled layer (a) typical flow pattern (b) time averaged particle concentration profile (c) particle concentration contours. X Y Plug Flow (a) typical flow pattern (b) time averaged particle concentration profile (c) particle concentration contours. S.M. Rao, K. Zhu, C.H. Wang, and S. Sundaresan, “Electrical Capacitance Tomography Measurements on the Pneumatic Conveying of Solids”, Ind. Eng. Chem. Res. 40(20) 4216-4226 (2001). S.M. Rao, K. Zhu, C.H. Wang, and S. Sundaresan, “Electrical Capacitance Tomography Measurements on the Pneumatic Conveying of Solids”, Ind. Eng. Chem. Res. 40(20) 4216-4226 (2001). Homogeneous s Moving dunes 0.015 0.01 0.005 S s 0 -6 x0 10 6 4 2 0 0 1 2 Sec 3 4 5 2 4 6 8 10 Hz 0.08 0.06 0.04 0.02 0 0 -5 x 10 8 6 S 4 2 0 0 Eroding dunes s 0.2 0.15 0.1 0.05 0 0 -4 x 10 4 3 S 2 1 0 0 1 2 Sec 3 4 5 2 4 6 8 10 Hz Plug flow 0.8 0.6 0.4 0.2 s 1 2Sec 3 4 5 1 2 Hz 3 4 5 1 0 10 -2 2 x 10 15 20 Sec 25 1 S 0 0 1 2 Hz 3 4 Polypropylene particles ( - average solid concentration, S – power spectrum density) Power spectra of solid concentration fluctuations from single plane data can characterize various flow regimes of pneumatic conveying. 5 Distribution of polypropylene particles in a vertical riser flow –dispersed flow Ug = 15.6 m/s (a) (b) Gs = 31.4 kg/(m2.s). K. Zhu, S.M. Rao , C.H. Wang, and S. Sundaresan “Electrical Capacitance Tomography Measurements on the Vertical and Inclined Pneumatic Conveying of Granular Solids“, Chem. N N Eng. Sci. 58(18) 4225-4245 (2003). (d) (c) Left: z = 0.47 m W E W E Right: z = 2.05 m S S Distribution of polypropylene particles in a vertical riser flow – slugging flow 0.1 0 (b) (a) Slugging flow Ug = 14.3 m/s Gs = 21.7 kg/(m2.s) t Z = 2.05 m K. Zhu, S.M. Rao , C.H. Wang, and S. Sundaresan “Electrical Capacitance Tomography Measurements on the Vertical and Inclined Pneumatic Conveying of Granular Solids“, Chem. Eng. Sci. 58(18) 4225-4245 (2003). (c) Distribution of polypropylene particles in a vertical riser flow – annular capsule flow N (a) W E (b) (c ) S Slugging flow Ug = 13.0 m/s Gs = 7.0 kg/(m2.s) Z = 2.05 m K. Zhu, S.M. Rao , C.H. Wang, and S. Sundaresan “Electrical Capacitance Tomography Measurements on the Vertical and Inclined Pneumatic Conveying of Granular Solids“, Chem. Eng. Sci. 58(18) 4225-4245 (2003). t (d) Summary for Horizontal & Vertical Conveying Using single plane data - time averaged particle concentration. Using twin plane cross correlation – pattern velocity. Single plane particle concentration data vs time data – (a) Homogeneous is not homogeneous. – (b) Moving dunes and eroding dunes with multiple characteristic peaks in the lower frequency region. – (c ) Plug flow with a single largest peak at near zero frequency. Cross sectional variation of time averaged density distribution in different flow regimes. Electrostatic Characterization J. Yao, Y. Zhang, C.H. Wang, S. Matsusaka, H. Masuda, “Electrostatics of the Granular Flow in a Pneumatic Conveying System“, Ind. Eng. Chem. Res., 43, 7181-7199 (2004). Disperse flow – pattern observed in the vertical pipe Initial condition The clusters were located fairly high up in the pipe and traveled along a curved path by the pipe wall. These clusters appeared and disappeared intermittently in an unpredictable manner. Two hours later J. Yao, Y. Zhang, C.H. Wang, S. Matsusaka, H. Masuda, “Electrostatics of the Granular Flow in a Pneumatic Conveying System“, Ind. Eng. Chem. Res., 43, 7181-7199 (2004). Ring flow - vertical granular pattern Initial condition Particles were observed to travel in a spiral fashion up the vertical pipe along the pipe wall. This resulted in a ring or annulus structure with high particle concentrations adjacent to the wall and a relatively empty core region Fifteen minutes later J. Yao, Y. Zhang, C.H. Wang, S. Matsusaka, H. Masuda, “Electrostatics of the Granular Flow in a Pneumatic Conveying System“, Ind. Eng. Chem. Res., 43, 7181-7199 (2004). Induced current measurement Polymer film Sections A & C Pipe wall Test station B Aluminum foil electrometer K. Zhu, S.M. Rao , Q.H. Huang, C.H. Wang, S Matsusaka, and H. Masuda, “On the Electrostatics of Pneumatic Conveying of Granular Materials Using Electrical Capacitance Tomography“, Chem. Eng. Sci., 59(15) 3201-3213 (2004). 80 (a) (a) MPCT measurement 60 (b) ECT Measurement i, microA 40 20 0 -20 U = 14.3 m/s, Gs = 0.08 kg/s -40 0 10 15 20 t, sec 1.0 Moving capsule flow (b) plane1 plane 2 0.8 0.6 s K. Zhu, S.M. Rao , Q.H. Huang, C.H. Wang, S Matsusaka, and H. Masuda, “On the Electrostatics of Pneumatic Conveying of Granular Materials Using Electrical Capacitance Tomography“, Chem. Eng. Sci., 59(15) 3201-3213 (2004). 5 0.4 0.2 0.0 0 5 10 time, sec 15 20 2.5E-07 Disperse flow Half-ring flow Ring flow vertical pipe Charge Q (C) I(A) Induced current – Negative 2E-07 Disperse flow Half-ring flow Ring flow 8E-05 Negative 6E-05 1.5E-07 4E-05 1E-07 5E-08 2E-05 0 0 2000 4000 6000 8000 0 2000 4000 Time(second) 6000 Time(second) (a) Comparison of the current value (negative) for the three flows. (b) Comparison of the charge accumulation for the three flows. J. Yao, Y. Zhang, C.H. Wang, S. Matsusaka, H. Masuda, “Electrostatics of the Granular Flow in a Pneumatic Conveying System“, Ind. Eng. Chem. Res., 43, 7181-7199 (2004). Summary: Electrostatics in Pneumatic Conveying Air flow rate is a key factor determining the electrostatic behavior of granular flow. The lower the air flow rate, the higher the induced current and particle charge density. These in turn lead to particle clustering and the formation of such structures as half-ring and ring in the vertical conveying pipe. Electrostatic effects increase with time. The charge accumulated at the pipe wall increases with time and the rate of increase seems constant for each of the three types of flow. Particle charge density also increases with time and this may account for clustering behavior occurring at the vertical pipe wall even when a high air flow rate is used and the dominant flow regime is that of disperse flow. Pipe wall material has an obvious effect on the electrostatics of the granular flow. Electrostatic effects depend on composition for particle mixture. The commercially available anti-static agent, Larostat-519 powder, was found to reduce electrostatic effects within the system effectively. The mechanism of electrostatic charge generation for the granular flow in the pneumatic conveying system mainly depends on tribroelectrification due to strong force effect on the surface when the particles slide on the pipe wall. DEM Simulation • Newton’s Laws of Motion N dv i mi f c,ij f d ,ij m i g f f ,i dt j1 N dω i Ii Tij dt j1 g • Force-displacement Model f cn,ij n ,i δ n ,ij f ct,ij t ,i δ t ,ij f dn ,ij n,i v r ni ni f dt ,ij t ,i v r t i t i ωi R i ω j R j Reversed flow in pneumatic conveying in an inclined pipe DEM Simulation • Fluid Drag Force Model f f ,i f f 0,i i1 f f 0,i 0.5cd0,i f R i2 i2 ui v i ui v i 1.5 log10 Re p ,i 2 3.7 0.65exp 2 2 4.8 cd 0,i 0.63 0.5 Re p,i 2 f R i i u i v i Re p,i f Fluidized bed simulation using DEM Di Felice, R. The voidage function for fluid-particle interaction systems. Int. J. Multiph. Flow 1994, 20, 153. DEM Simulation • Computational Fluid Dynamics u 0 t f u f uu P f u f g F t 0.04 0.035 0.03 0.025 0.02 0.015 0.01 0.005 0 0 0.25 0.5 0.75 1 0.75 1 0.75 1 V2 0.04 0.035 0.03 0.025 0.02 0.015 0.01 0.005 0 0 0.25 0.5 V2 0.04 0.035 0.03 0.025 0.02 0.015 0.01 0.005 0 0 0.25 0.5 V2 Pneumatic Conveying simulations using DEM Simulation Conditions Material Properties and System Parameters Shape of particles Type of particles Number of particles Particle diameter, d Particle density, p Spring constant in force model, Viscous contact damping coefficient, Coefficient of friction Gas density, f Gas viscosity, f Pipe diameter Pipe length Computational cell size Simulation time step, t Spherical Polypropylene 500, 1000, 1500, 2000 2.8 10-3 m 1123 kg m-3 5.0 103 N m-1 0.35 0.3 1.205 kg m-3 1.8 10-5 N s m-2 0.04 m 1.0 m 4 mm 4 mm 10-7 s Rao, S. M.; Zhu, K.; Wang, C. H.; Sundaresan, S. Electrical capacitance tomography measurements on the pneumatic conveying of solids. Ind. Eng. Chem. Res. 2001, 40, 4216. Simulation Conditions • Particles first allowed to settle under gravity for 0.5 s before gas flow was initiated • Periodic boundary conditions applied to the solid phase to simulate an open flow system • Solid concentration, , defined as overall volume fraction of particles divided by volume fraction of particles at maximum packing (0.64) Results and Discussion Dispersed Flow = 0.08 Gas velocity 14 m s-1 Plug Flow = 0.32 Gas velocity 14 m s-1 W.C. Lim, C.H. Wang, and A.B. Yu, “Discrete Element Simulation for Pneumatic Conveying of Granular Material” AIChE Journal, 52, 496-509 (2006). Results and Discussion Stratified Flow = 0.08, Gas velocity 10 m s-1 Moving dunes = 0.16, Gas velocity 10 m s-1 Slug Flow = 0.32, Gas velocity 10 m s-1 Homogeneous Flow = 0.16, Gas velocity 30 m s-1 W.C. Lim, C.H. Wang, and A.B. Yu, “Discrete Element Simulation for Pneumatic Conveying of Granular Material” AIChE Journal, 52, 496-509 (2006). Results and Discussion 1.6 -1 Solid flow rate (kg s ) 1.4 1.2 = 0.32 = 0.24 = 0.16 = 0.08 1.0 0.8 Plug Flow 0.6 Dispersed Flow 0.4 0.2 0.0 12 14 16 18 20 22 Gas velocity (m s-1) 24 26 • The different flow regimes in vertical pneumatic conveying are represented in the form of phase diagrams • Dashed lines separate regions representing different flow regimes while dashed circles enclose regions where transition between two adjacent flow regimes might be taking place • In vertical pneumatic conveying, the dispersed flow regime is dominant at high gas velocities and low solid concentrations while the plug flow regime is dominant otherwise W.C. Lim, C.H. Wang, and A.B. Yu, “Discrete Element Simulation for Pneumatic Conveying of Granular Material” AIChE Journal, 52, 496-509 (2006). Results and Discussion 1.8 -1 Solid flow rate (kg s ) 1.6 1.4 1.2 = 0.32 = 0.24 = 0.16 = 0.08 Slug Flow 1.0 0.8 Homogeneous Flow 0.6 0.4 MD/H Moving dunes 0.2 S/H 0.0 8 12 16 20 24 Gas velocity (m s-1) 28 32 • Similarly, the homogeneous flow regime is dominant at high gas velocities and low solid concentrations while the slug flow regime is dominant otherwise in horizontal conveying • At low gas velocities and solid concentrations, effects of gravitational settling result in the formation of the moving dunes and stratified flow regimes • Intermediate values of gas velocities involve transitions between moving dunes and homogeneous flow and between stratified and homogeneous flow W.C. Lim, C.H. Wang, and A.B. Yu, “Discrete Element Simulation for Pneumatic Conveying of Granular Material” AIChE Journal, 52, 496-509 (2006). Results and Discussion Solid concentration 0.18 • The solid concentration profile for dispersed flow in vertical pneumatic conveying shows that solid concentrations are higher near the walls than in the center of the pipe • This trend is similar for all gas velocities simulated Gas velocity 0.16 14 m s-1 0.14 16 m s-1 18 m s-1 0.12 20 m s-1 0.10 24 m s-1 0.08 0.06 0.04 0.02 0.00 0.00 0.01 0.02 0.03 0.04 Radial position (m) W.C. Lim, C.H. Wang, and A.B. Yu, “Discrete Element Simulation for Pneumatic Conveying of Granular Material” AIChE Journal, 52, 496-509 (2006). Results and Discussion 0.04 • The solid concentration profiles in horizontal pneumatic conveying show quantitatively the effects of gravitational settling which results in higher solid concentrations along the bottom wall of the pipe • As before, the solid concentration profiles are quantitatively similar for different gas velocities used Gas velocity 14 m s-1 Radial position (m) 18 m s-1 0.03 22 m s-1 26 m s-1 30 m s-1 0.02 0.01 0.00 0.00 0.10 0.20 0.30 0.40 0.50 Solid concentration W.C. Lim, C.H. Wang, and A.B. Yu, “Discrete Element Simulation for Pneumatic Conveying of Granular Material” AIChE Journal, 52, 496-509 (2006).