Accurate measurement of suspended particle concentration in pipelines is essential for analyzing the fluid mixing density and particle settlement. However, measuring concentration distributions along the flow path poses significant challenges due to the inherent complexity and variability of liquid–solid two-phase suspensions. In this study, we developed a sensor measurement system based on multi-frequency acoustic emission technology and a self-receiving single probe. The effects of suspended particle size, concentration, and ultrasonic transducer dimensions on acoustic wave propagation were analyzed using the COMSOL Multiphysics system. For multi-frequency echo signals, variational mode decomposition and the sparrow search algorithm were employed to decompose and optimize the signal, followed by reconstruction using the Pearson correlation coefficient. By combining the energy ratio method with the minimum concentration difference method, we propose a new approach for simultaneous measurement of particle size and concentration along the pipeline transmission path. Experimental results indicate that along the transmission path, the mean absolute percentage error is 18.74%, and 77.55% of the predicted results exhibit relative errors below 20%.
REFERENCES
1.
J.
Liu
,
P.
Zhang
,
Y.
Xiao
,
Z.
Wang
,
S.
Yuan
, and
H.
Tang
, “
Interaction between dual spherical particles during settling in fluid
,” Phys. Fluids
33
, 013312
(2021
).2.
C. B.
Fuller
,
J. S.
Bonner
,
M. S.
Islam
,
T.
Ojo
,
C. A.
Page
, and
W. D.
Kirkey
, “
Estimating colloidal concentration using acoustic backscatter
,” IEEE Sens. J.
13
, 4546
(2013
).3.
Z.
Xu
,
Y.
Jiang
,
B.
Wang
,
H.
Ji
,
Z.
Huang
, and
M.
Soleimani
, “
Void fraction measurement of gas–liquid two-phase flow with a 12-electrode contactless resistivity array sensor under different excitation patterns
,” Meas. Sci. Technol.
31
, 115103
(2020
).4.
X. B.
Li
,
X. Y.
Hao
,
H. N.
Zhang
,
W. H.
Zhang
, and
F. C.
Li
, “
Review on multi-parameter simultaneous measurement techniques for multiphase flow—Part A: Velocity and temperature/pressure
,” Measurement
223
, 113710
(2023
).5.
M.
Zhang
,
M.
Xu
, and
D. L. S.
Hung
, “
Simultaneous two-phase flow measurement of spray mixing process by means of high-speed two-color PIV
,” Meas. Sci. Technol.
25
, 095204
(2014
).6.
X.
Liu
,
Y.
Song
,
D.
Zhao
,
K.
Lan
,
K.
Zhai
,
M.
Wang
, and
L.
Fang
, “
Study on velocity profile of gas–liquid two-phase stratified flow in pipelines based on transfer component analysis-back propagation neural network
,” Phys. Fluids
36
, 063330
(2024
).7.
M.
Rastello
,
M. R.
Klema
,
A. B.
Carpenter
,
A.
Garanaik
,
S. K.
Venayagamoorthy
,
T. K.
Gates
, and
J. L.
Marié
, “
Velocity measurements in developing narrow open-channel flows with high free-stream turbulence: Acoustic Doppler velocimetry (ADV) vs laser Doppler anemometry (LDA)
,” Flow Meas. Instrum.
87
, 102206
(2022
).8.
T.
Virdung
and
A.
Rasmuson
, “
Measurements of continuous phase velocities in solid–liquid flow at elevated concentrations in a stirred vessel using LDV
,” Chem. Eng. Res. Des.
85
, 193
(2007
).9.
Z.
Xia
,
Z.
Cui
,
Y.
Chen
,
Y.
Hu
, and
H.
Wang
, “
Generative adversarial networks for dual-modality electrical tomography in multi-phase flow measurement
,” Measurement
173
, 108608
(2021
).10.
X.
Shi
,
C.
Tan
,
H.
Wu
, and
F.
Dong
, “
An electrical and ultrasonic Doppler system for industrial multiphase flow measurement
,” IEEE T. Instrum. Meas.
70
, 1
(2021
).11.
Y.
Zhao
,
S.
Yue
,
Y.
Zhang
, and
H.
Wang
, “
Flow velocity computation using a single ERT sensor
,” Flow Meas. Instrum.
93
, 102433
(2023
).12.
F.
Wang
,
Q.
Marashdeh
,
L.-S.
Fan
, and
R. A.
Williams
, “
Electrical capacitance, electrical resistance, and positron emission tomography techniques and their applications in multi-phase flow systems
,” in Advanced Experimental Methods in Multiphase Flow (Elsevier, 2009
), Chap. 5.13.
C.
Tan
,
Y.
Murai
,
W.
Liu
,
Y.
Tasaka
,
F.
Dong
, and
Y.
Takeda
, “
Ultrasonic Doppler technique for application to multiphase flows: A review
,” Int. J. Multiphas. Flow
144
, 103811
(2021
).14.
X.
Zhan
,
S.
Jiang
,
Y.
Yang
,
J.
Liang
,
T.
Shi
, and
X.
Li
, “
Ultrasonic spectrum for particle concentration measurement in multicomponent suspensions
,” Meas. Sci. Technol.
27
, 025501
(2016
).15.
F.
Hossein
,
M.
Materazzi
,
P.
Lettieri
, and
P.
Angeli
, “
Application of acoustic techniques to fluid-particle systems—A review
,” Chem. Eng. Res. Des.
176
, 180
(2021
).16.
J.
Sheng
and
A. E.
Hay
, “
An examination of the spherical scatterer approximation in aqueous suspensions of sand
,” J. Acoust. Soc. Am.
83
, 598
(1988
).17.
P. D.
Thorne
,
P. J.
Hardcastle
, and
R. L.
Soulsby
, “
Analysis of acoustic measurements of suspended sediments
,” J. Geophys. Res.: Oceans
98
, 899
, https://doi.org/10.1029/92JC01855 (1993
).18.
A. E.
Hay
, “
Sound scattering from a particle-laden, turbulent jet
,” J. Acoust. Soc. Am.
90
, 2055
(1991
).19.
C.
He
and
A. E.
Hay
, “
Broadband measurements of the acoustic backscatter cross section
,” J. Acoust. Soc. Am.
94
, 2247
(1993
).20.
A. S.
Schaafsma
and
A. E.
Hay
, “
Attenuation in suspensions of irregularly shaped sediment
,” J. Acoust. Soc. Am.
102
, 1485
(1997
).21.
H. P.
Rice
,
M.
Fairweather
,
J.
Peakall
,
T. N.
Hunter
,
B.
Mahmoud
, and
S. R.
Biggs
, “
Measurement of particle concentration in horizontal, multiphase pipe flow using acoustic methods: Limiting concentration and the effect of attenuation
,” Chem. Eng. Sci.
126
, 745
(2015
).22.
B. D.
Moate
and
P. D.
Thorne
, “
Measurements and inversion of acoustic scattering from suspensions having broad size distributions
,” J. Acoust. Soc. Am.
126
, 2905
(2009
).23.
E. D.
Thosteson
and
D. M.
Hanes
, “
A simplified method for determining sediment size and concentration from multiple frequency acoustic backscatter measurements
,” J. Acoust. Soc. Am.
104
, 820
(1998
).24.
A. M.
Crawford
and
A. E.
Hay
, “
Determining suspended sand size and concentration from multifrequency acoustic backscatter
,” J. Acoust. Soc. Am.
94
, 3312
(1993
).25.
J.
Schat
, “
Multifrequency acoustic measurement of concentration and grain size of suspended sand in water
,” J. Acoust. Soc. Am.
101
, 209
–217
(1997
).26.
J. J.
van der Werf
,
J. S.
Doucette
,
T.
O'Donoghue
, and
J. S.
Ribberink
, “
Detailed measurements of velocities and suspended sand concentrations over full‐scale ripples in regular oscillatory flow
,” J. Geophys. Res.: Earth Surf.
112
, 0148
, https://doi.org/10.1029/2006JF000614 (2007
).27.
A. E.
Hay
and
J.
Sheng
, “
Vertical profiles of suspended sand concentration and size from multifrequency acoustic backscatter
,” J. Geophys. Res.: Oceans
97
, 15661
, https://doi.org/10.1029/92JC01240 (1992
).28.
D.
Hurther
,
P. D.
Thorne
,
M.
Bricault
,
U.
Lemmin
, and
J. M.
Barnoud
, “
A multi-frequency acoustic concentration and velocity profiler (ACVP) for boundary layer measurements of fine-scale flow and sediment transport processes
,” Coast. Eng.
58
, 594
(2011
).29.
J. F.
Lynch
,
J. D.
Irish
,
C. R.
Sherwood
, and
Y. C.
Agrawal
, “
Determining suspended sediment particle size information from acoustical and optical backscatter measurements
,” Cont. Shelf. Res.
14
, 1139
(1994
).30.
G. W.
Wilson
and
A. E.
Hay
, “Acoustic backscatter inversion for suspended sediment concentration and size: A new approach using statistical inverse theory,” Cont. Shelf. Res.
106
, 130
–139
(2015
).31.
L. E.
Kinsler
,
A. R.
Frey
,
A. B.
Coppens
, and
J. V.
Sanders
, Fundamentals of Acoustics
, 3rd ed. (
John Wiley & Sons
, 1982
).32.
F. H.
Fisher
and
V. P.
Simmons
, “
Sound absorption in sea water
,” J. Acoust. Soc. Am.
62
, 558
(1977
).33.
S. D.
Richards
and
A. D.
Heathershaw
, “
The effect of suspended particulate matter on sound attenuation
,” J. Acoust. Soc. Am.
100
, 1447
(1996
).34.
B. D.
Moate
and
P. D.
Thorne
, “
Interpreting acoustic backscatter from suspended sediments of different and mixed mineralogical composition
,” Cont. Shelf. Res.
46
, 67
(2012
).35.
H. K.
Ha
,
W. Y.
Hsu
,
J. P. Y.
Maa
,
Y. Y.
Shao
, and
C. W.
Holland
, “
Using ADV backscatter strength for measuring suspended cohesive sediment concentration
,” Cont. Shelf. Res.
29
, 1310
(2009
).36.
W.
Li
,
S.
Yang
,
W.
Yang
,
Y.
Xiao
,
X.
Fu
, and
S.
Zhang
, “
Estimating instantaneous concentration of suspended sediment using acoustic backscatter from an ADV
,” Int. J. Sediment Res.
34
, 422
(2019
).37.
O.
Chmiel
,
I.
Baselt
, and
A.
Malcherek
, “
Applicability of acoustic concentration measurements in suspensions of artificial and natural sediments using an acoustic Doppler velocimeter
,” Acoust.
1
, 59
(2018
).38.
B. C.
Xavier
,
I. O.
Silva
,
L. G.
Guimarães
,
M. N.
Gallo
,
C. P.
Ribeiro
, and
A. G.
Figueiredo
, “
Estimation of suspended sediment concentration by acoustic scattering: An experimental and theoretical analysis for spherical particles
,” J. Soil Sediment.
14
, 1325
(2014
).39.
P. D.
Thorne
and
M. J.
Buckingham
, “
Measurements of scattering by suspensions of irregularly
,” J. Acoust. Soc. Am.
116
, 2876
(2004
).40.
Y.
Ban
,
T.
Chen
,
J.
Yan
, and
T.
Lei
, “
Accurate mass replacement method for the sediment concentration measurement with a constant volume container
,” Meas. Sci. Technol.
28
, 045906
(2017
).41.
J. J.
Sansalone
and
S. G.
Buchberger
, “
Characterization of solid and metal element distributions in urban highway stormwater
,” Water Sci. Technol.
36
, 155
–160
(1997
).42.
Z.
Zhao
,
B.
Wang
,
J.
Wang
,
L.
Fang
,
X.
Li
,
F.
Wang
, and
N.
Zhao
, “
Liquid film characteristics measurement based on NIR in gas–liquid vertical annular upward flow
,” Meas. Sci. Technol.
33
, 065014
(2022
).43.
J.
Xue
and
B.
Shen
, “
A novel swarm intelligence optimization approach: Sparrow search algorithm
,” Syst. Sci. Controlled Eng.
8
, 22
(2020
).44.
Y. C.
Sun
,
C. Y.
Ni
,
K. N.
Ying
,
A. H.
Xiong
,
T.
Shuai
, and
Z. H.
Shen
, “
Laser ultrasonic spatially resolved acoustic spectroscopy for grain size study based on improved variational mode decomposition (IVMD)
,” NDT&E Int.
144
, 103090
(2024
).45.
K.
Dragomiretskiy
and
D.
Zosso
, “
Variational mode decomposition
,” IEEE Trans. Signal Process.
62
, 531
–544
(2014
).46.
M.
Baak
,
R.
Koopman
,
H.
Snoek
, and
S.
Klous
, “
A new correlation coefficient between categorical, ordinal and interval variables with Pearson characteristics
,” Comput. Stat. Data An.
152
, 107043
(2020
).© 2024 Author(s). Published under an exclusive license by AIP Publishing.
2024
Author(s)
You do not currently have access to this content.
