1.5 Dynamic Patterns in Shallow Granular Layers
21
Fig. 1.11 Influence of the pulse frequency on the wavelength of surface patterns in shallow granular
layers of Geldart B glass beads. Experiments were conducted in a 3 mm deep shallow bed of a 14 cm
diameter. Gas superficial velocity U 0 /U mf = 0.6 + 0.8[1 + sin(2πft)]
where U a is the pulse amplitude, U t is the terminal velocity of particles, and φ is
the average solid fraction. The bulk dynamics are also addressed by a dimensionless
time scale that is a ratio of pulse frequency f over the system’s natural frequency f n .
Using p and f /f n , a universal instability curve was drawn to describe the onset of
pattern formation of Geldart B particles, as shown in Fig. 1.12, and distinguish two
flow regimes: a pattern arises when pulsed above the critical amplitude, otherwise
Fig. 1.12 Universal stability curve for pattern formation in shallow, cylindrical pulsed fluidised
beds of Geldart B particles under pulsed flows with superficial velocity U 0 = U 0,min + U a [1 +
sin(2πft)]. Particles include 130 μm glass beads with minmum gas velocity U 0,min = 3 or 4 cm/s
and height H = 2–7 mm (white symbols), 240 μm glass with U 0,min = 3 or 6 cm/s and H = 3–7 mm
(red symbols), and 600 μm polystyrene with minmum gas velocity U 0,min = 11.5 cm/s and height
H = 10 mm (stars). Reprinted with permission from [30]
21
Fig. 1.11 Influence of the pulse frequency on the wavelength of surface patterns in shallow granular
layers of Geldart B glass beads. Experiments were conducted in a 3 mm deep shallow bed of a 14 cm
diameter. Gas superficial velocity U 0 /U mf = 0.6 + 0.8[1 + sin(2πft)]
where U a is the pulse amplitude, U t is the terminal velocity of particles, and φ is
the average solid fraction. The bulk dynamics are also addressed by a dimensionless
time scale that is a ratio of pulse frequency f over the system’s natural frequency f n .
Using p and f /f n , a universal instability curve was drawn to describe the onset of
pattern formation of Geldart B particles, as shown in Fig. 1.12, and distinguish two
flow regimes: a pattern arises when pulsed above the critical amplitude, otherwise
Fig. 1.12 Universal stability curve for pattern formation in shallow, cylindrical pulsed fluidised
beds of Geldart B particles under pulsed flows with superficial velocity U 0 = U 0,min + U a [1 +
sin(2πft)]. Particles include 130 μm glass beads with minmum gas velocity U 0,min = 3 or 4 cm/s
and height H = 2–7 mm (white symbols), 240 μm glass with U 0,min = 3 or 6 cm/s and H = 3–7 mm
(red symbols), and 600 μm polystyrene with minmum gas velocity U 0,min = 11.5 cm/s and height
H = 10 mm (stars). Reprinted with permission from [30]