XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3 2695
near an impeller due to the anisotropic and erratic nature of
the flow, as well as the presence of a highly turbulent mov-
ing jet generated by the impeller blades (Anandha Rao &
Brodkey, 1972 Lee &Yianneskis, 1998).
(ii) Turbulent Kinetic Energy Dissipation Rate (TKEDR)
For the second validation, the piezoelectric sensor measure-
ments in a 35L flotation tank were compared to TKE calcu-
lated from the kinetic energy dissipation rate. The TKEDR
was calculated by using the power consumption of the
motor when the cell was empty and loaded at particular
operating conditions. Measurements were conducted for
single- and two-phase cases at varying superficial gas veloci-
ties (0.8, 0.95, 1.1 cm/s) and tip speeds (5.0, 5.5, 6.0 m/s).
Power readings from the power meter were recorded in
triplicates and the arithmetic average was taken, denoted as
Ploaded and Pempty. The cell’s mean turbulent kinetic energy
dissipation rate (TKEDR) was calculated similar to that in
Amini et al. (2016), where Mcell is the total mass of the pulp
in the cell.
TKEDR M
P Pempty
cell
loaded =
-
(10)
The relationship between TKE and TKEDR based on
dimensional analysis relies on a length scale L, known as the
integral length scale. Experimentally, the integral length
scale represents the correlation distance of velocity compo-
nents in space and is calculated by integrating the velocity
correlation function that requires velocity measurements at
two different positions in space. For simplification, a wide
variation of L has been assumed previously (Wang et al.,
2021), however, Wu et al. (1989) proposed a revised form
of this relationship, by considering L to be equal to the
width of the fluid jet. The jet in a conventional flotation
cell comes from between the stator blades so it is assumed
that the width of the jet, and thus L, is equal to the distance
between the stator blades.
TKE a
TKEDR L 2 3 $=
f
`j (11)
where, a is a constant estimated by Wu and Patterson
(1989) to be 0.85. The two-phase comparison of the force
calculated by the piezosensor and the TKE calculated is
shown in Figure 3(b). The general trends between the two
graphs show good agreement, for instance, both TKE and
force measurements show a decrease in turbulence with
Figure 3. Comparison of the force signal from piezoelectric sensor with: (a) Single-phase TKE from PIV (b) Two-phase TKE
from empirical correlations, at different Jg and tip speeds
near an impeller due to the anisotropic and erratic nature of
the flow, as well as the presence of a highly turbulent mov-
ing jet generated by the impeller blades (Anandha Rao &
Brodkey, 1972 Lee &Yianneskis, 1998).
(ii) Turbulent Kinetic Energy Dissipation Rate (TKEDR)
For the second validation, the piezoelectric sensor measure-
ments in a 35L flotation tank were compared to TKE calcu-
lated from the kinetic energy dissipation rate. The TKEDR
was calculated by using the power consumption of the
motor when the cell was empty and loaded at particular
operating conditions. Measurements were conducted for
single- and two-phase cases at varying superficial gas veloci-
ties (0.8, 0.95, 1.1 cm/s) and tip speeds (5.0, 5.5, 6.0 m/s).
Power readings from the power meter were recorded in
triplicates and the arithmetic average was taken, denoted as
Ploaded and Pempty. The cell’s mean turbulent kinetic energy
dissipation rate (TKEDR) was calculated similar to that in
Amini et al. (2016), where Mcell is the total mass of the pulp
in the cell.
TKEDR M
P Pempty
cell
loaded =
-
(10)
The relationship between TKE and TKEDR based on
dimensional analysis relies on a length scale L, known as the
integral length scale. Experimentally, the integral length
scale represents the correlation distance of velocity compo-
nents in space and is calculated by integrating the velocity
correlation function that requires velocity measurements at
two different positions in space. For simplification, a wide
variation of L has been assumed previously (Wang et al.,
2021), however, Wu et al. (1989) proposed a revised form
of this relationship, by considering L to be equal to the
width of the fluid jet. The jet in a conventional flotation
cell comes from between the stator blades so it is assumed
that the width of the jet, and thus L, is equal to the distance
between the stator blades.
TKE a
TKEDR L 2 3 $=
f
`j (11)
where, a is a constant estimated by Wu and Patterson
(1989) to be 0.85. The two-phase comparison of the force
calculated by the piezosensor and the TKE calculated is
shown in Figure 3(b). The general trends between the two
graphs show good agreement, for instance, both TKE and
force measurements show a decrease in turbulence with
Figure 3. Comparison of the force signal from piezoelectric sensor with: (a) Single-phase TKE from PIV (b) Two-phase TKE
from empirical correlations, at different Jg and tip speeds