2692 XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3
(TKEDR) also denoted as 𝜀, are often estimated from local
velocity fluctuations. Experimental techniques such as par-
ticle image velocimetry (PIV), Laser Doppler Anemometry
(LDA), and constant temperature anemometry (CTA)
have been discussed in literature to measure local velocities.
Particle Image Velocimetry (PIV) is a non-intrusive opti-
cal measurement technique that captures velocity vectors
within large flow fields (A. Schröder &Willert, 2008). It
relies on the recording of particle positions in a section of
the flow at a given instant in time, allowing for spatially
resolved velocity measurements (Buchhave, 1994). More
recent advances in particle tracking to determine particle-
bubble probabilities of collision and attachment have also
been developed for applications in flotation (Sommer et
al., 2018). LDA is a similar laser-based technique in that
it measures the single point velocities in a transparent or
semitransparent fluid using Doppler Shift principle of laser
beams which are reflected by the seeded particles (Tropea,
2010). Despite being non-intrusive and providing pre-
cise velocity vectors, the applicability of PIV and LDA in
froth flotation as a real-time measurement technique is
limited. CTA is based on measuring the heat loss of the
wire which is heated by electrical current. Measurements of
the TKEDR using hot wires has been previously discussed
(Antonia, 2003 J W Elsner &W Elsner, 1996), and a main
drawback is that once an anemometer has been calibrated
in a constant temperature flow, it must be operated in a
flow of identical temperature else unintentional tempera-
ture fluctuations may be misinterpreted as a velocity change
(Benjamin &Roberts, 2002). Computationally, Direct
Numerical Simulation (DNS) can resolve turbulence to the
smallest scales and has been a versatile tool for studying the
properties of energy dissipation (M. Schröder et al., 2024).
However, due to high computational cost of DNS, research-
ers have turned to larger scale models such as Large Eddy
Simulation (LES) and Reynolds-Averaged Navier Stokes
(RANS), with the limitation being that Kolmogorov scale
eddies, which are responsible for energy dissipation, are not
resolved (Wang et al., 2021). The estimation of the global
kinetic energy turbulent dissipation rate via dimensional
analysis has been used by several studies (Balachandar &
Eaton, 2009 Baldi &Yianneskis, 2004 Kresta &Wood,
1991 Nguyen et al., 2016 Wang et al., 2014 Wu et al.,
1989), where the TKEDR is a function of velocity fluctua-
tions and an integral length scale (𝐿) that has been defined
as a fraction of the diameter of the stirred tank (Wang et
al., 2021). Turbulence is nevertheless primarily an aniso-
tropic and inhomogeneous process, meaning that the
global TKEDR is not equivalent to local energy dissipation
(Kuzzay et al., 2015).
This overview of turbulence in multiphase flows and
measurement techniques sets a preface to the need of an
adaptable, robust sensor that can measure turbulence in flo-
tation cells. An approach based on a Piezoelectric Vibration
Sensor (PVS) has been developed as a tool for turbulence
measurements in industrial flotation environments, show-
ing a correlation between intensity of kinetic energy fluc-
tuation and turbulent kinetic energy (TKE) (Meng et
al., 2014). A piezoelectric vibration sensor consists of a
piezoelectric material that generates electrical energy when
subjected to mechanical deformations. The sensor detects
vibrations, and the resulting electrical signals can be mea-
sured and analyzed via a suitable data acquisition device
(DAQ) (Meng et al., 2016). The aim of this work is to
present an improved workflow of PVS measurements and
provide initial validations through PIV and by calculating
TKEDR. The spatial distribution of turbulence is further
shown by measuring the PVS signals at different radial and
axial positions in a cylindrical flotation cell.
METHODS
A transparent (acrylic) 35L mechanical flotation cell (next-
STEP ™ rotor/stator-system by FLSmidth &Co. A/S) with
forced-air injection was used a basis for the bench-scale flo-
tation tests. The tank has an inner diameter ID =35.5cm
and is 45cm in height with four vertical baffles at the outer
walls. Single-phase (liquid) and two-phase (liquid-gas)
experiments were performed at three different tip speeds
(5.0, 5.5, and 6.0 m/s) and at three different air flow rates
(0.8, 0.95, 1.1 cm/s) for the two-phase case. MIBC (methyl
isobutyl carbinol) was used as the frother with a constant
concentration of 20ppm. Table 1 lists the measurement
positions and the varying operating parameters.
Table 1. Sensor position and measurement parameters for
testing in a 35L flotation cell
Variable Range
Radial positions R 9 cm, 15 cm
Axial positions H
(above cell floor)
8 cm, 16 cm, 25 cm
Airflow 0, 0.8 cm/s, 0.95 cm/s, 1.1 cm/s
Tip speed 5 m/s, 5.5 m/s, 6 m/s
Frother (MIBC) 20 ppm
The magnitude of force using the piezoelectric sensor
was measured at different radial (R) and axial (H) positions
of the 35L flotation cell as shown in Figure 1(a). The piezo-
sensor along with its casing in two-phase flow is shown in
Figure 1(b).
The piezoelectric sensor (MEAS LDT1-028 K) was
housed in a 3D-printed (ABS) casing (L =45 mm, W
(TKEDR) also denoted as 𝜀, are often estimated from local
velocity fluctuations. Experimental techniques such as par-
ticle image velocimetry (PIV), Laser Doppler Anemometry
(LDA), and constant temperature anemometry (CTA)
have been discussed in literature to measure local velocities.
Particle Image Velocimetry (PIV) is a non-intrusive opti-
cal measurement technique that captures velocity vectors
within large flow fields (A. Schröder &Willert, 2008). It
relies on the recording of particle positions in a section of
the flow at a given instant in time, allowing for spatially
resolved velocity measurements (Buchhave, 1994). More
recent advances in particle tracking to determine particle-
bubble probabilities of collision and attachment have also
been developed for applications in flotation (Sommer et
al., 2018). LDA is a similar laser-based technique in that
it measures the single point velocities in a transparent or
semitransparent fluid using Doppler Shift principle of laser
beams which are reflected by the seeded particles (Tropea,
2010). Despite being non-intrusive and providing pre-
cise velocity vectors, the applicability of PIV and LDA in
froth flotation as a real-time measurement technique is
limited. CTA is based on measuring the heat loss of the
wire which is heated by electrical current. Measurements of
the TKEDR using hot wires has been previously discussed
(Antonia, 2003 J W Elsner &W Elsner, 1996), and a main
drawback is that once an anemometer has been calibrated
in a constant temperature flow, it must be operated in a
flow of identical temperature else unintentional tempera-
ture fluctuations may be misinterpreted as a velocity change
(Benjamin &Roberts, 2002). Computationally, Direct
Numerical Simulation (DNS) can resolve turbulence to the
smallest scales and has been a versatile tool for studying the
properties of energy dissipation (M. Schröder et al., 2024).
However, due to high computational cost of DNS, research-
ers have turned to larger scale models such as Large Eddy
Simulation (LES) and Reynolds-Averaged Navier Stokes
(RANS), with the limitation being that Kolmogorov scale
eddies, which are responsible for energy dissipation, are not
resolved (Wang et al., 2021). The estimation of the global
kinetic energy turbulent dissipation rate via dimensional
analysis has been used by several studies (Balachandar &
Eaton, 2009 Baldi &Yianneskis, 2004 Kresta &Wood,
1991 Nguyen et al., 2016 Wang et al., 2014 Wu et al.,
1989), where the TKEDR is a function of velocity fluctua-
tions and an integral length scale (𝐿) that has been defined
as a fraction of the diameter of the stirred tank (Wang et
al., 2021). Turbulence is nevertheless primarily an aniso-
tropic and inhomogeneous process, meaning that the
global TKEDR is not equivalent to local energy dissipation
(Kuzzay et al., 2015).
This overview of turbulence in multiphase flows and
measurement techniques sets a preface to the need of an
adaptable, robust sensor that can measure turbulence in flo-
tation cells. An approach based on a Piezoelectric Vibration
Sensor (PVS) has been developed as a tool for turbulence
measurements in industrial flotation environments, show-
ing a correlation between intensity of kinetic energy fluc-
tuation and turbulent kinetic energy (TKE) (Meng et
al., 2014). A piezoelectric vibration sensor consists of a
piezoelectric material that generates electrical energy when
subjected to mechanical deformations. The sensor detects
vibrations, and the resulting electrical signals can be mea-
sured and analyzed via a suitable data acquisition device
(DAQ) (Meng et al., 2016). The aim of this work is to
present an improved workflow of PVS measurements and
provide initial validations through PIV and by calculating
TKEDR. The spatial distribution of turbulence is further
shown by measuring the PVS signals at different radial and
axial positions in a cylindrical flotation cell.
METHODS
A transparent (acrylic) 35L mechanical flotation cell (next-
STEP ™ rotor/stator-system by FLSmidth &Co. A/S) with
forced-air injection was used a basis for the bench-scale flo-
tation tests. The tank has an inner diameter ID =35.5cm
and is 45cm in height with four vertical baffles at the outer
walls. Single-phase (liquid) and two-phase (liquid-gas)
experiments were performed at three different tip speeds
(5.0, 5.5, and 6.0 m/s) and at three different air flow rates
(0.8, 0.95, 1.1 cm/s) for the two-phase case. MIBC (methyl
isobutyl carbinol) was used as the frother with a constant
concentration of 20ppm. Table 1 lists the measurement
positions and the varying operating parameters.
Table 1. Sensor position and measurement parameters for
testing in a 35L flotation cell
Variable Range
Radial positions R 9 cm, 15 cm
Axial positions H
(above cell floor)
8 cm, 16 cm, 25 cm
Airflow 0, 0.8 cm/s, 0.95 cm/s, 1.1 cm/s
Tip speed 5 m/s, 5.5 m/s, 6 m/s
Frother (MIBC) 20 ppm
The magnitude of force using the piezoelectric sensor
was measured at different radial (R) and axial (H) positions
of the 35L flotation cell as shown in Figure 1(a). The piezo-
sensor along with its casing in two-phase flow is shown in
Figure 1(b).
The piezoelectric sensor (MEAS LDT1-028 K) was
housed in a 3D-printed (ABS) casing (L =45 mm, W