3.2 Experimental Implementation and Analysis Methodology
69
is determined as the pattern wavelength λ, whereas it is less meaningful for chaotic
flows. In this chapter, a slightly different algorithm is employed, as λ is measured in
conjunction with pattern recognition. By assembling the extracted bubbles in a single
frame, as shown in Fig. 3.3, a radial distribution function of bubbles (RDF bub ) can
be calculated by looking only at bubbles within a range of polar angles −20° < θ <
20°. The wavelength is then determined as the most frequent separation measured, at
which RDF bub peaks. Such adaption in procedures does not affect the measurement
for patterned flows but chaotic flows, as long-range bubble separations are considered
and multiple modes emerge in RDF bub .
Besides, the concept of the span is employed to represents the dimensionless
broadness of the distribution. The span δ is determined by the following expression,
using a subscripted d for bubble size, V for rising velocity and λ for bubble separation,
respectively:
δ =
X 90 − X 10
X 50
(3.2)
where X 90 , X 10 and X 50 stand for the value in a distribution that is greater than 90%,
10% and 50% of the samples, respectively.
3.3 Results and Discussion
The experiments are carried out in a quasi-2D bed to identify the conditions leading
to structured flows and evaluate their impacts on pattern regularity and bubble
properties. The conditions used are shown in Table 3.2.
3.3.1 Impact of Flow Conditions on Pattern Intensity
The impacts of pulse conditions, such as A, B and f , on the degree of structuring
is quantified with the computed pattern intensity. Figure 3.8 illustrates the intensities measured with G2 type particle in a 10 cm deep pulsed bed. The intensity, as
Table 3.2 Pulsed gas flow
U 0 = A·U mf + B·[1 +
sin(2πft)] and static bed
height H investigated
Symbol
Parameter
Value
H
Static bed depth (cm)
5, 10, 15, 20
A
Pulse offset/U mf (–)
0.5, 0.75, 1, 1.25
B
Pulse amplitude (cm/s)
5, 7, 9, 11
f
Pulse frequency (Hz)
3, 4, 5, 6, 7, 8, 9, 10
69
is determined as the pattern wavelength λ, whereas it is less meaningful for chaotic
flows. In this chapter, a slightly different algorithm is employed, as λ is measured in
conjunction with pattern recognition. By assembling the extracted bubbles in a single
frame, as shown in Fig. 3.3, a radial distribution function of bubbles (RDF bub ) can
be calculated by looking only at bubbles within a range of polar angles −20° < θ <
20°. The wavelength is then determined as the most frequent separation measured, at
which RDF bub peaks. Such adaption in procedures does not affect the measurement
for patterned flows but chaotic flows, as long-range bubble separations are considered
and multiple modes emerge in RDF bub .
Besides, the concept of the span is employed to represents the dimensionless
broadness of the distribution. The span δ is determined by the following expression,
using a subscripted d for bubble size, V for rising velocity and λ for bubble separation,
respectively:
δ =
X 90 − X 10
X 50
(3.2)
where X 90 , X 10 and X 50 stand for the value in a distribution that is greater than 90%,
10% and 50% of the samples, respectively.
3.3 Results and Discussion
The experiments are carried out in a quasi-2D bed to identify the conditions leading
to structured flows and evaluate their impacts on pattern regularity and bubble
properties. The conditions used are shown in Table 3.2.
3.3.1 Impact of Flow Conditions on Pattern Intensity
The impacts of pulse conditions, such as A, B and f , on the degree of structuring
is quantified with the computed pattern intensity. Figure 3.8 illustrates the intensities measured with G2 type particle in a 10 cm deep pulsed bed. The intensity, as
Table 3.2 Pulsed gas flow
U 0 = A·U mf + B·[1 +
sin(2πft)] and static bed
height H investigated
Symbol
Parameter
Value
H
Static bed depth (cm)
5, 10, 15, 20
A
Pulse offset/U mf (–)
0.5, 0.75, 1, 1.25
B
Pulse amplitude (cm/s)
5, 7, 9, 11
f
Pulse frequency (Hz)
3, 4, 5, 6, 7, 8, 9, 10