2.2 Experimental Implementation and Analysis Methodology
41
to be 0.4 cm in order to remove spurious voids, which are too small to be strictly
recognised as bubbles.
D b =
4 A b
π
0.5
(2.2)
where A b is the measured area of bubbles.
Bubble rising velocity is measured as the axial component of bubble velocity that
is the reciprocal of bubble residence time. After identifying bubbles, the velocity of
individuals is measured by cross-correlating bubbles in consecutive frames. As the
time step t for consecutive frames is 0.01 s, bubbles can be considered correlated
if the displacement r t < D b and size evolution |D b | ≤ 0.3D b . The measurement
is validated and sufficiently robust. The calculation of rising velocity is expressed in
Eq. (2.3).
V b =
r y,t
t
=
r y,t 2 − r y,t 1
t 2 − t 1
(2.3)
where r is the position vector, and t is the flow time.
In addition, bubbles in structured flows rise and form triangular lattices, separated
horizontally by a constant distance λ. The neighbouring bubbles are determined
by pairing individuals that locate within a given relative position angle. This cutoff angle is set to be 20°, and the tests show that the measured wavelengths only
vary by up to 5% if one offsets the cut-off angle by 10°. It is noteworthy that λ
is considered as the wavelength only in structured flows, whereas it stands for the
separation between immediate neighbouring bubbles in chaotic flows. Therefore, the
expression for bubble separation is expressed in Eq. (2.4):
λ = |r x | = |r x1 − r x2 |
for − 20
◦
≤ tan
−1
((r y
r x ) ≤ 20
◦
(2.4)
2.3 Results and Discussion
2.3.1 Validation of Gas Distribution
To ensure a decent distribution of the inlet gas, the sintered metal distributor is examined firstly by analysing the spatial distribution of bubbles. For this reason, the cell
loaded of 20 cm deep G2 glass beads is fluidised with three different constant superficial velocities that are 6 cm/s (1.30U mf ), 8 cm/s (1.74U mf ) and 10 cm/s (2.17U mf ),
respectively. The created flows of bubbles are recorded continuously for 30 s under
steady flow fluidisation. The domain is divided evenly into three compartments for
the purpose of comparison.
41
to be 0.4 cm in order to remove spurious voids, which are too small to be strictly
recognised as bubbles.
D b =
4 A b
π
0.5
(2.2)
where A b is the measured area of bubbles.
Bubble rising velocity is measured as the axial component of bubble velocity that
is the reciprocal of bubble residence time. After identifying bubbles, the velocity of
individuals is measured by cross-correlating bubbles in consecutive frames. As the
time step t for consecutive frames is 0.01 s, bubbles can be considered correlated
if the displacement r t < D b and size evolution |D b | ≤ 0.3D b . The measurement
is validated and sufficiently robust. The calculation of rising velocity is expressed in
Eq. (2.3).
V b =
r y,t
t
=
r y,t 2 − r y,t 1
t 2 − t 1
(2.3)
where r is the position vector, and t is the flow time.
In addition, bubbles in structured flows rise and form triangular lattices, separated
horizontally by a constant distance λ. The neighbouring bubbles are determined
by pairing individuals that locate within a given relative position angle. This cutoff angle is set to be 20°, and the tests show that the measured wavelengths only
vary by up to 5% if one offsets the cut-off angle by 10°. It is noteworthy that λ
is considered as the wavelength only in structured flows, whereas it stands for the
separation between immediate neighbouring bubbles in chaotic flows. Therefore, the
expression for bubble separation is expressed in Eq. (2.4):
λ = |r x | = |r x1 − r x2 |
for − 20
◦
≤ tan
−1
((r y
r x ) ≤ 20
◦
(2.4)
2.3 Results and Discussion
2.3.1 Validation of Gas Distribution
To ensure a decent distribution of the inlet gas, the sintered metal distributor is examined firstly by analysing the spatial distribution of bubbles. For this reason, the cell
loaded of 20 cm deep G2 glass beads is fluidised with three different constant superficial velocities that are 6 cm/s (1.30U mf ), 8 cm/s (1.74U mf ) and 10 cm/s (2.17U mf ),
respectively. The created flows of bubbles are recorded continuously for 30 s under
steady flow fluidisation. The domain is divided evenly into three compartments for
the purpose of comparison.