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Nonintrusive Monitoring and Control of
Metallurgical Processes by Acoustic Measurements
Hao-Ling Yu, Leili Tafaghodi Khajavi and Mansoor Barati
Version Post-print/Accepted Manuscript
Citation
(published version) Yu, HL., Khajavi, L.T. & Barati, M. Metall and Materi Trans B (2011) 42: 516. https://doi.org/10.1007/s11663-011-9496-3
Publisher’s statement This is a post-peer-review, pre-copyedit version of an article published in Metallurgical and Materials Transactions B. The final authenticated version is available online at: http://dx.doi.org/10.1007/s11663-011-9496-3
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1
Non– intrusive Monitoring and Control of Metallurgical Processes by Acoustic Measurements
Luke Yu, Leili Tafaghodi Khajavi, Mansoor Barati*
*) Corresponding author
Assistant professor
University of Toronto, Dept. of Materials Science and Engineering
140 – 184 College Street, Toronto, ON
Canada M5S 3E4
Tel: (416) 978 – 5637
Fax: (416) 978 – 4155
Email: [email protected]
The feasibility of developing a new on–line monitoring technique based on characteristic
acoustic response of gas bubbles in a liquid has been studied. The method is intended to
monitor the chemistry of the liquid through its relation to the bubble sound frequency. A
low temperature model consisting of water and alcohol mixtures was established and the
frequency of bubbles rising under varying concentrations of methanol was measured. It
has been shown that the frequency of the sound created by bubble pulsation is changed
by the percent of alcohol in water. The frequency drops sharply with the increase in
methanol content up to 20 wt%, after which the decreases is gradual. Surface tension
appears to be one of the critical liquid properties affecting the sound frequency through
its twofold effects on the bubble size and pulsation domain. The strong dependence
between the frequency and liquid composition suggests the feasibility of developing an
acoustic based technique for process control purposes.
I. INTRODUCTION
Today, gas injection into metallurgical baths is a standard practice, employed for thermal and/or chemical
homogenization of the liquid, as well as introduction of reactive gasses to promote the refining reactions. Of the critical
issues in metallurgical refining practices is controlling the chemistry of the melts to achieve desired composition, avoid
excessive use of the refining gases and fluxes, and maximize productivity by treating the melt for shortest time possible.
However, this has proved to be extremely difficult due to the continuous and rather rapid variations in the composition
and properties of the molten metal (or matte). Conventionally, the chemical composition of the melt is controlled by
off-line analysis of withdrawn samples, followed by corrective actions. This approach in monitoring is generally
inefficient because the feedback provided is not quick enough to allow precise and timely adjustments. Moreover, the
sampling practice can be costly and the results are affected by the sampling position and method. The evident
drawbacks of such control approach are: inconsistent analysis, loss in productivity, higher energy consumption, more
production rejects, and economic inefficiency. As a result, the tendency has shifted to online and preferably continuous
monitoring of the process.
It is well established that for many metallurgical melts, the physical properties of the liquid vary significantly
over the treatment process. For example, the sulfur removal or oxygen dissolution associated with the refining reactions
in steelmaking and converting of matte result in substantial variations in the surface tension of the liquid, as illustrated
in
2
Figure 1. Changes in the physicochemical properties of the melt with its chemistry may potentially be
employed to establish indirect monitoring and control of the process.
Figure 1: Variations in the surface tension of (a) Fe–S[1, 2] and (b) Cu–O[3] melts with the dissolved element content .
1E-4 1E-3 0.01 0.1
800
1000
1200
1400
1600
1800
2000
2200
Su
rfa
ce
Te
ns
ion
x1
03 (
N/m
)
Lee and Morita [1]
Keene et. al. [2]
Sulfur content (Mass %)
(a)
-13 -12 -11 -10 -9 -8 -7 -6 -5
800
900
1000
1100
1200
1300
1400
(b)
Su
rfa
ce
Te
ns
ion
x1
03 (
N/m
)
log (pO2
(atm))
1E-4 1E-3 0.01 0.1
800
1000
1200
1400
1600
1800
2000
2200
Su
rfa
ce
Te
ns
ion
x1
03 (
N/m
)
Lee and Morita [1]
Keene et. al. [2]
Sulfur content (Mass %)
(a)
-13 -12 -11 -10 -9 -8 -7 -6 -5
800
900
1000
1100
1200
1300
1400
(b)
Su
rfa
ce
Te
ns
ion
x1
03 (
N/m
)
log (pO2
(atm))
3
The application of acoustic–based techniques in process control is relatively new, with only a few reported
works in metallurgical industry [4-7]. The intended applications vary from controlling the desulfurization process in
ladle to monitoring the refractory lining in blast furnace or other reactors. Although the refractory monitoring attempts
have been successful to some extent, the control of melt chemistry through acoustic measurements is still very
immature and has not been studied in depth. The present study was undertaken to investigate the feasibility of relating
a liquid composition to the characteristics of the bubble sound, emitted during gas injection into the same liquid. Low
temperature system of water–methanol was selected as it allows easier measurements and more precise control of the
process conditions.
It is well established that the oscillation frequency of a bubble is related to the physical properties of the liquid
in which the bubble is formed, and the size of the rising bubble [8, 9]. The following equation was obtained by Lamb
[8] to express the frequency of a ball of one medium oscillating in another medium.
4𝜋𝑓2 = 𝑛(𝑛 − 1)(𝑛 + 1)(𝑛 + 2)𝜎
((𝑛 + 1)𝜌𝑙 − 𝑛𝜌𝑔) 𝑟3 (1)
where 𝑓 is the oscillation frequency, 𝑟 is the radius of the bubble, 𝜎 is the surface tension, 𝜌𝑔 and 𝜌𝑙 are
the densities of the gas and the surrounding liquid respectively, and n represents the type of bubble
oscillation. It is such dependency between bubble sound frequency and the physical properties of the
liquid that is used in the present work as a basis to correlate the bubble sound frequency to the liquid
composition.
II. EXPERIMENTAL WORK
The experiments were performed in a bottom blown rectangular Plexiglas container (10cmwidth , 20cm
length, 80-cm height). The tank was filled with 7 liters of methanol-water mixtures with varying methanol content and
compressed air was introduced from a 2 mm nozzle centred at the bottom. The bubble sound was recorded using two
ME66/K6 microphones (obtained from Sennheiser) placed on the top and side of the tank. The top microphone was
partially isolated from the ambient sound by mounting an antenna–like stainless steel shield around it. Raven Lite 1.0
software was used for recording the sound profile. The background noise was eliminated by comparing and contrasting
the noise profile before the experiment and the recorded sound track during the experiment. Eventually in order to
obtain the frequency peaks, the noise-free sound track was analyzed using Audacity sound editing program with Fast
Fourier Transform (FFT) method.
In addition to the sound recording apparatus, a CCD camera was used to record a video of the rising bubbles.
The video was later analyzed to measure the number of fully detached bubbles during a fixed time interval. Assuming
the bubbles to be spherical, the average bubble size can be calculated by dividing the flow rate to the number of released
bubbles within a specific timeframe. The schematic of the experimental set up is shown in Figure 2.
Figure 2: Schematic representation of the e xperimental setup
gas inlet
flowmeter
Camera
Microphones
4
In some preliminary experiments, the maximum gas flowrate and bath depth that give the highest contrast in
the recorded spectrum were determined. It was found that the bubble sound echo intensity increases with decreasing
the bath height, subsequently larger volumes of the solution would help to decrease the interference from the echo.
The optimum flow rate was determined according to the distinctness of the sound profile while the liquid
volume and methanol concentration were constant. The results of a primary experiment in seven litres of water solution
revealed that at higher flow rate (e.g. greater than 0.75 lpm) the background noise and bubble sounds interfere with
each other due to larger number of bubbles at higher flow rates. The flow rate was fixed at 0.6 lpm where it is easy to
distinguish the background noise and the bubble sound. The relatively small gas flow rate also facilitated detection and
counting of the bubbles in the recorded video. As Figure 3 shows, the frequency of bubble generation increase
substantially after the gas flowrate exceeds ~ 0.8 lpm.
Figure 3: Frequency of bubble generation as a function of gas flowrate.
In order to study the effect of liquid composition (and properties) on the acoustic response, numerous
experiments with different methanol concentrations (0–100 %) were performed at constant gas flow rate (0.6 lpm) and
bath height (35cm).
III. RESULTS AND DESCUSSION
A. Effect of solute content on liquid properties
The previously measured physical properties of water-methanol mixture [10-12] are available at specific
solute concentration. As presented in Appendix I, the values were fitted into equations that are used for evaluation of
the liquid properties in the current analysis.
B. Effect of additive content on bubble size
Bubble size and additive concentration
The average size of the bubbles generated in solutions with different methanol content is shown in Figure 4.
As seen, the bubble size goes through a sharp decrease for an increase in the methanol content up to 20 wt%. Further
increase in the methanol content results in only a slight decrease in the bubble size. It is well established that under the
conditions of fixed gas flowrate, pressure, and temperature, the size of the gas bubbles is predominantly decided by
the properties of the liquid and gas. According to several theoretical and experimental studies, the bubble size is directly
related to the interfacial tension and inversely proportional to the liquid density. More specifically, it has been shown
that the bubble size is a function of 𝜂 = (𝜎 𝜌⁄ )1/3[13-17]. The validity of this relationship was tested for the
experimental results of the present work by plotting bubble diameter against 𝜂 (Figure 5). As seen, in agreement with
0.0 0.2 0.4 0.6 0.8 1.0
0
20
40
60
80
100
120
140
Fre
qu
en
cy
of
bu
bb
le g
en
era
tio
n (
se
c-1)
Flowrate (LPM)
5
the previous findings, the bubble diameter follows a linear relationship with 𝜂 for the wide range of the compositions
examined in this study.
Figure 4: The effect of methanol content on bubble diameter
Figure 5: Bubble diameter as a function 𝜂 = (𝜎 𝜌⁄ )1/3
C. Effect of liquid composition on bubble acoustic frequency
Effect of solute concentration on frequency
The measured bubble sound frequency as a function of methanol concentration is shown in Figure 6. As seen,
the frequency gradually decreases as the solute concentration increases, but the variations are not strongly linked. This
is primarily because of the simultaneous variations in the physical properties of liquid and bubble size with methanol
content, both of which affect the bubble sound frequency. According to Minnaert equation provided below [9], at fixed
0 20 40 60 80 100
1.14
1.16
1.18
1.20
1.22
1.24
1.26
1.28
1.30
Bu
bb
le D
iam
ete
r (c
m)
Methanol Content (wt%)
3.0 3.2 3.4 3.6 3.8 4.0 4.2
1.14
1.16
1.18
1.20
1.22
1.24
1.26
1.28
1.30
Bu
bb
le D
iam
ete
r (c
m)
(
R2=0.8409
6
surface tension, the acoustic frequency of a single bubble in an infinity large container is inversely proportional to the
bubble radius and the square root of density.
𝑓 =1
2𝜋𝑟(
3𝛾𝑃𝐴
𝜌)
12 (2)
In this equation, f is the resonant frequency, r is the radius of the bubble, is the proportionality
coefficient, AP is the ambient pressure at place of bubble and is the density of the solution.
Since in metallurgical systems the density variation during refining is negligible (e.g. desulphurization), any
variations in the bubble sound frequency is chiefly originated from the changes in the surface tension and bubble size.
Therefore, in order to investigate the dependence of frequency on these parameters, the frequency is corrected by
eliminating the effect of the liquid density based on Eq. (2). After eliminating the density effect, the corrected frequency
values for methanol-water solutions are significantly lower than the measured frequency and the decrease with
methanol content is more pronounced (Figure 6).
Figure 6: The effect of methanol content on bubble sound frequency
Effect of liquid surface tension on frequency
Surface tension is one of the melt properties that is most affected during refining of metals/mattes (
0 20 40 60 80 100
400
420
440
460
480
500
520
540
560
Measured Frequency
Corrected Frequency
Fre
qu
en
cy
(H
z)
Methanol Content (wt%)
7
Figure 1). Also, surface tension is believed to affect the oscillation characteristics of a bubble through both its
direct effect on the bubble/liquid interface and also its effect on the bubble size (Figure 5), which in turn affects the
frequency through Eq. (2). Therefore, for an acoustic–based process monitoring technique in a system with negligible
variations in density and viscosity (such as liquid steel), strong dependence of the frequency to the surface tension is
warranted. As discussed earlier, the effect of density on bubble sound frequency was eliminated based on Minnaert
equation. In order to investigate the exclusive effect of surface tension on bubble sound frequency, the effect of
viscosity should be eliminated as well. The variations of surface tension and viscosity with methanol content are
provided in
Figure 7. As seen, with increase in methanol content, the viscosity first rises to a maximum at around 40 wt%
and then drops, while the surface tension decreases gradually. Several iso–viscosity compositions in this system can
be identified by drawing a horizontal line that intersects the viscosity profile, consequently two points with identical
values of viscosity can be obtained. The bubble sound frequencies associated with these pair of points are presented in
Table 1 for several iso–viscosity compositions.
1E-4 1E-3 0.01 0.1
800
1000
1200
1400
1600
1800
2000
2200
Su
rfa
ce
Te
ns
ion
x1
03 (
N/m
)
Lee and Morita [1]
Keene et. al. [2]
Sulfur content (Mass %)
(a)
-13 -12 -11 -10 -9 -8 -7 -6 -5
800
900
1000
1100
1200
1300
1400
(b)
Su
rfa
ce
Te
ns
ion
x1
03 (
N/m
)
log (pO2
(atm))
0 20 40 60 80 100
20
40
60
80
Methanol Content (wt%)
Su
rfa
ce
Te
ns
ion
at
25
°C
(m
N.m
-1)
0.0
0.4
0.8
1.2
1.6
2.0
Vis
co
sity
(mP
a.s
)
8
Figure 7: Surface tension and viscosity of methanol–water solutions
Table 1: Effect of surface tension of methanol - water mixture on bubble sound
µ (cS) σ1 (mN.m-1) σ2 (mN.m-1) σ1- σ2 f1 (Hz) f2 (Hz) f1-f2 (Hz)
1.0 71.9 23.3 48.6 540 461 79
1.2 54.0 24.0 30.0 532 472 60
1.3 48.8 24.4 24.4 525 483 42
1.4 45.1 24.8 20.3 524 488 36
1.5 42.7 25.2 17.4 522 493 29
1.6 37.6 26.2 11.4 517 502 15
1.8 33.3 28.0 5.3 517 512 5
It is evident from Table 1 that a decrease in the surface tension results in smaller frequencies. This is expected
according to Eq. (1) that suggests a direct relationship between f2 and surface tension. However, both equations (1)
and (2) show an inverse relationship between the frequency and the bubble size (although not entirely consistent in
degree of dependence), while the bubble size itself becomes smaller when the surface tension decreases. It may then
be discussed that the surface tension plays a twofold role on the sound frequency; on one hand, higher surface tension
favors faster pulsation of the bubble due to the smaller domain of oscillation. On the other hand it results in formation
of larger bubbles that are more resistant against pulsation and decrease the frequency. From the overall effect of surface
tension, it however is clear that the former, direct effect of surface tension, overcomes its secondary effect and increase
the bubble frequency.
0 20 40 60 80 100
20
40
60
80
Methanol Content (wt%)
Su
rfa
ce
Te
ns
ion
at
25
°C
(m
N.m
-1)
0.0
0.4
0.8
1.2
1.6
2.0V
isc
os
ity (m
Pa
.s)
9
Assuming negligible density of air compared to the liquid, frequency should be directly
proportional to 𝑆 = √𝜎 𝑑3⁄ , following Eq. (1).
Figure 8 presents the corrected frequency as a function of 𝑆, where each value of 𝑆 corresponds to a specific surface tension and the associated bubble diameter. The figure shows that as 𝑆 increases with decreasing methanol content, greater frequency values are obtained . A sharp
change in the slope of the graph can be seen at around 𝑆 = 4.2, which indicates slower increase in frequency after this point. According to the experimental results 𝑆 = 4.2 occurs at around 37wt% of methanol content at which the change in the surface tension prof ile of methanol-
water mixture becomes less steep. Moreover, as seen in
Figure 7, the increasing trend of viscosity with methanol content transforms to a decreasing trend at around
the same methanol content. The above changes in surface tension and viscosity of methanol-water mixture are the
possible reasons for the change of the slope in frequency vs. 𝑆 variations.
3.6 4.0 4.4 4.8 5.2 5.6 6.0
400
420
440
460
480
500
520
540
560
Co
rre
cte
d F
req
ue
nc
y (
Hz)
d3
Increasing
methanol content
0 20 40 60 80 100
20
40
60
80
Methanol Content (wt%)
Su
rfa
ce
Te
ns
ion
at
25
°C
(m
N.m
-1)
0.0
0.4
0.8
1.2
1.6
2.0
Vis
co
sity
(mP
a.s
)
10
Figure 8: The effect of the solution surface tension and bubble size on bubble sound frequency
The pulsation of bubble is a phenomenon that is primarily dominated by the resistance of the liquid against
bubble deformation. The liquid elasticity modulus (EM) that can be thought as the inverse of compressibility thus can
influence bubble sound frequency. Figure 9 shows EM for methanol-water mixtures vs. methanol concentration, from
a study by Blaudez et al.[18]. It is apparent that a sudden decrease in EM takes place at around the same methanol
content that the sharp change in frequency values occurred. By increasing the concentration above this specific point,
EM decreases continuously. The drop in EM indicates higher level of compressibility of the mixture, which leads to
easier pulsation of the bubbles or wider domain of pulsation, which in turn results in lower frequency values. After a
specific level, the increase in methanol content results in a sharp decrease in elasticity modulus which causes lower
bubble sound frequency. As the elasticity modulus starts decreasing rapidly with methanol content, the slope of the
graph of frequency vs. S becomes steeper (at around 37wt %).
3.6 4.0 4.4 4.8 5.2 5.6 6.0
400
420
440
460
480
500
520
540
560
Co
rre
cte
d F
req
ue
nc
y (
Hz)
d3
Increasing
methanol content
0 20 40 60 80 100
0.5
1.0
1.5
2.0
2.5
Ea
sti
cit
y M
od
ulu
s (
10
9 N
/m2)
Methanol Content (wt%)
11
Figure 9: Elasticity modulus of the water-methanol system vs. methanol concentration at room temperature[18].
Practical implications
The measurements in methanol–water system show that the dependence of the bubble sound frequency on
liquid composition is sensitive enough to enable prediction of the composition through non–intrusive acoustic
measurements. Therefore, in principle, the application of a technique based on bubble sound to monitor and control
metallurgical refining operations appears to be feasible, considering the substantial changes that take place in the
physical properties of the fluid. A purely theoretical or semi–empirical model that translates acoustic measurements
directly into process parameters (such as chemical composition or a physical property) may not be practically realized
because of the numerous parameters involved and the operation–specific response of the system. However, an
intelligent system that is calibrated over time can produce reliable results, and eventually become independent of
sampling.
IV. CONCLUSION
The sound frequency generated as result of bubble pulsation in water–methanol solutions was successfully
detected by using two microphones at the side and top of the container. The results obtained from the acoustic response
were found to be closely related to the physical properties of the liquid such as density, surface tension and viscosity.
The results from image analysis of the bubbles confirmed that at a constant gas flow rate and liquid volume the size of
the bubbles decreases with increasing methanol content. Moreover the bubble sound frequency decreases with
methanol content. The frequency increases with an increase in √𝜎 𝑑3⁄ while a substantial drop in the degree of
dependence is seen for mixtures containing over 37 wt% methanol. This composition corresponds well to a point where
the compressibility of the liquid becomes dependent and decreases with methanol content. Based on the findings of
this study, the application of an acoustic based technique for controlling the melt chemistry and/or quantifying physical
properties in metallurgical processes appears feasible.
REFERENCES
[1].J. Lee and K. Morita, ISIJ International, 2002, vol. 42, 6, pp. 588-594.
[2].B.J. Keene,K.C. Mills,J.W. Bryant and E.D. Hondros, Canadian Metallurgical Quarterly, 1981, vol.
21, 4, pp. 393-403.
[3].B. Gallois and C.H.P. Lupis, Metallurgical Transactions B (Process Metallurgy), 1981, vol. 12B, 3, pp.
549-57.
[4].A. Sadri,I. Gordon and A. Rampersad, Dnipropetrovsk, pp. 77-85.
[5].X.F. Zhang,A. McLean and I.D. Sommerville, Steelmaking Conference Proceedings, pp. 659-662.
[6].X.F. Zhang, A Study of Bubble Sound Emitted by Injecting Gas into Lquid through a downward
Facing Lance. 1990.
[7].Y. Kostetsky,D. Kukuy,I. Kvasov,V. Khodyachikh,I. Degtyarenko and O. A., METAL 2007, Hradec
nad Moravici, pp. 451-456.
[8].H. Lamb, Hydrodynamics. 1945, New York: Dover Publication, pp.
[9].M. Minnaert, On Musical Air-bubbles and the Sound of Running Water, in Philosophical Magazine.
1933. p. 235-248.
[10].A.V. Wolf, Aqueous Solutions and Body Fluids,. 1966, Hoeberpp.
[11].O. Söhnel and P. Novotny, Densities of Aqueous Solutions of Inorganic Substances. 1985,
Amsterdam: Elsevier, pp.
[12].G. Vhquez,E. Alvarez and J.M. Navaza, Surface Tension of Alcohol + Water from 20 to 50 °C, in
Journal of chemical engineering data. 1995. p. 611-614.
12
[13].M. Iguchi,H. Kawabata,Y. Ito,K. Nakajima and Z. Morita, Continuous Measurement of Bubble
Characteristics in a Molten lron Bath with Ar Gas Injection, in ISIJ International. 1994. p. 980-
985.
[14].J.F. Davidson,A.M.I. Mech and B.O.G. Shuler, Bubble Formation at an Orifice in an Inviscid Liquid,
in Transactions of the Institution of Chemical Engineers. 1960. p. 335-342.
[15].R.Q. Li and R. Harris, Bubble Formation from a Very Narrow Slot, in Canadian Metallurgical
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[16].A. Satyanarayan,R. Kumar and N.R. Kuloor, Studies in Bubble Formation—II Bubble Formation
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[17].A.V. Byakova,S.V. Gnyloskurenko,T. Nakamura and O.I. Raychenko, Influence of Wetting
Conditions on Bubble Formation at Orifice in an Inviscid Liquid Mechanism of Bubble
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[18].D. Blaudez,F. Mallamace,N. Micali,S. Trusso and C. Vasi, Il Nuovo Cimento D, 1994, vol. 16, 7, pp.
923-931.
APPENDIX I
The previously measured physicochemical properties of methanol–water solutions [10-12] were fitted into
the following equations and used in the evaluation of the solution properties where needed. In the equations below, 𝑋
is the methanol content in weight percent, 𝜌, 𝜎, and 𝜇 are density, surface tension, and viscosity of the liquid,
respectively.
𝜌 = 9.97 − 1.44 × 10−3𝑋 − 1.77 × 10−6𝑋2 − 4.47 × 10−8𝑋3 (𝑔. 𝑐𝑚–3)
𝜎 = 19.63 + 27.37 exp(− 𝑋 43.11⁄ ) + 25.17 exp(−𝑋 7.11⁄ ) (𝑚𝑁. 𝑚–1)
𝜇 = 9.86 + 3.80 × 10−3𝑋 − 2.34 × 10−4𝑋2 − 6.5 × 10−6𝑋3 + 4.65 × 10−8𝑋4 (𝑚𝑃𝑎. 𝑠)