©2002 Regents of University of Minnesota Fluidization of 1204 Spheres 1 Direct Numerical Simulation (DLM) of 1204 Spheres in a Slit Bed zSphere Diameter 0.25” yCompare computed bed expansion with the observed in. 8 in in. Pan, Sarin, Joseph, Glowinski & Bai 1999

©2002 Regents of University of Minnesota Fluidization of 1204 Spheres 2 Crystal configuration 1204 Particles SimulationExperiment

©2002 Regents of University of Minnesota Fluidization of 1204 Spheres 3 V = 2.0 : Particle position at t = The maximal particle Reynolds number is The maximal averaged particle Reynolds number is Particles Experiment Simulation

©2002 Regents of University of Minnesota Fluidization of 1204 Spheres 4 V = 3.0 : Particle position at t = 20 The maximal particle Reynolds number is The maximal averaged particle Reynolds number is Particles Experiment Simulation

©2002 Regents of University of Minnesota Fluidization of 1204 Spheres 5 V = 3.5 : Particle position at t = The maximal particle Reynolds number is The maximal averaged particle Reynolds number is Particles Experiment Simulation

©2002 Regents of University of Minnesota Fluidization of 1204 Spheres 6 V = 4.0 : Particle position at t = 32 The maximal particle Reynolds number is The maximal averaged particle Reynolds number is Particles Simulation Experiment

©2002 Regents of University of Minnesota Fluidization of 1204 Spheres 7 V = 4.5 : Particle position at t = 31 The maximal particle Reynolds number is The maximal averaged particle Reynolds number is Particles Experiment Simulation

©2002 Regents of University of Minnesota Fluidization of 1204 Spheres 8 Bed Expansion Richardson-Zaki V(  ) A d = 1/4” Superficial Inlet Velocity

©2002 Regents of University of Minnesota Fluidization of 1204 Spheres 9 Blow Out Velocity

©2002 Regents of University of Minnesota Fluidization of 1204 Spheres 10 Bed Height vs. Fluidizing Velocity for Both Experiment and Simulation zFor the monodispersed case studied in simulation (d = 0.635cm) H s = 4.564/(1-  ) zThe mean sphere size for the polydisperse case studied in the experiments is slightly larger (d = cm) and H e = 4.636/(1-  )

©2002 Regents of University of Minnesota Fluidization of 1204 Spheres 11 Data from Previous Slide Plotted in a log-log Plot and D is the tube radius. In our experiments and simulations Re is confined to the range for which n =  The slopes of the straight line are given by the Richardson- Zaki n = The blow-out velocities V s (0) and V e (0) are defined as the intercepts at  = 1. zThe Richardson-Zaki correlation is given by V(  ) = V(0)  n(Re) where V(0) is V when  = 1  V s (  ) =  2.39 cm/s and  V e (  ) = 10.8  2.39 cm/s.

©2002 Regents of University of Minnesota Fluidization of 1204 Spheres 12 Bed Height vs. Fluidizing Velocity After Shifting by the Ratio of Blow-out Velocities zd 1 = 0.635cm simulation zd 2 = cm (average d for experiments) zWalls will increase the drag more in the experiments than in the simulations. Wall correction of Francis [1933] zThe value is very close to the shift ratio

©2002 Regents of University of Minnesota Fluidization of 1204 Spheres 13 Slip Velocity is Computed on Data Strings at Nodes U2U2 U1U1 U3U3 The slip velocity for U 1 - U 2 is zero + noise

©2002 Regents of University of Minnesota Fluidization of 1204 Spheres 14 Transitions Between Power Laws Logistic dose curve This curve is fitted to data and is convenient to use with a spread sheet

©2002 Regents of University of Minnesota Fluidization of 1204 Spheres 15 Transitions Between Power Laws Example: Richardson-Zaki Correlation Power law Transition Power law