XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3 2693
=20 mm, H =10 mm) and attached to a hollow stain-
less-steel rod of 10 mm in diameter. When subjected to
unsteady flow conditions, the piezosensor film moves back
and forth, generating an alternating current that was read
by the data acquisition device (LabJack ™ U3-HV) and
was processed via a suitable signal processing software
(SigView ®). At each measurement position, a signal of 30s
at 8kHz was taken with triplicates. The resulting signal was
passed through an in-house developed Python workflow,
that performs a Fast Fourier Transform (FFT), calculates
the force applied on the sensor, and computes the averages,
which are plotted against measurement distances. The over-
all workflow is depicted in Figure 2 and detailed in the fol-
lowing paragraphs.
The piezoelectric sensor technique has been discussed
by Meng et al. (2014) previously, however, a corrected
workflow is proposed to ensure dimensionality in the
equations is preserved as well as their physical meaning. The
revised calculation overview is shown below. When the
piezofilm is excited with a sinusoidal movement at a fre-
quency f, the time-derivative of the measured voltage V
L
o is:
V VS C R 1 2rif^C
2rjfC0RL
L
L 0
=++
o o
h (1)
j is the imaginary unit, C is the capacity introduced by wires
and the measurement circuit, and VS is the input resistance.
The sensor behaves as a voltage source (VS) with an inner
capacitance (C0 =500pF).
V g33tS
S f =o (2)
The piezoelectric voltage coefficient (g33) is also called volt-
age output constant, which is defined as the ratio of the
electric field produced to the mechanical stress applied. Sf is
the normal stress (N/m2) applied with a frequency f and t is
the film thickness (m). Introducing d =g33t, the measured
voltage is
VL
R C C0h2
dS C R f
1
L
f L
2 2
0
~
=
++^
(3)
The characteristic, or eigen-frequency of the measurement
circuit is given by:
f C C 2rR
1
L
0
0
=+^h (4)
Substituting Eq. (4) into (3) gives:
VL f f
C R f
1
2rdS
f L
0
0
2 =+_i
(5)
Rearranging (5) to get Sf gives:
S
V f f
f
1
2rdC0R f
L
L
0
2
=
+_i
(6)
Figure 1. (a) Schematic of 35L cell with different measurement positions (b) PVS film in two-phase flow
=20 mm, H =10 mm) and attached to a hollow stain-
less-steel rod of 10 mm in diameter. When subjected to
unsteady flow conditions, the piezosensor film moves back
and forth, generating an alternating current that was read
by the data acquisition device (LabJack ™ U3-HV) and
was processed via a suitable signal processing software
(SigView ®). At each measurement position, a signal of 30s
at 8kHz was taken with triplicates. The resulting signal was
passed through an in-house developed Python workflow,
that performs a Fast Fourier Transform (FFT), calculates
the force applied on the sensor, and computes the averages,
which are plotted against measurement distances. The over-
all workflow is depicted in Figure 2 and detailed in the fol-
lowing paragraphs.
The piezoelectric sensor technique has been discussed
by Meng et al. (2014) previously, however, a corrected
workflow is proposed to ensure dimensionality in the
equations is preserved as well as their physical meaning. The
revised calculation overview is shown below. When the
piezofilm is excited with a sinusoidal movement at a fre-
quency f, the time-derivative of the measured voltage V
L
o is:
V VS C R 1 2rif^C
2rjfC0RL
L
L 0
=++
o o
h (1)
j is the imaginary unit, C is the capacity introduced by wires
and the measurement circuit, and VS is the input resistance.
The sensor behaves as a voltage source (VS) with an inner
capacitance (C0 =500pF).
V g33tS
S f =o (2)
The piezoelectric voltage coefficient (g33) is also called volt-
age output constant, which is defined as the ratio of the
electric field produced to the mechanical stress applied. Sf is
the normal stress (N/m2) applied with a frequency f and t is
the film thickness (m). Introducing d =g33t, the measured
voltage is
VL
R C C0h2
dS C R f
1
L
f L
2 2
0
~
=
++^
(3)
The characteristic, or eigen-frequency of the measurement
circuit is given by:
f C C 2rR
1
L
0
0
=+^h (4)
Substituting Eq. (4) into (3) gives:
VL f f
C R f
1
2rdS
f L
0
0
2 =+_i
(5)
Rearranging (5) to get Sf gives:
S
V f f
f
1
2rdC0R f
L
L
0
2
=
+_i
(6)
Figure 1. (a) Schematic of 35L cell with different measurement positions (b) PVS film in two-phase flow