Archives of Acoustics, 47, 3, pp. 373–382, 2022

Ultrasonic Simulation Research of Two-Dimensional Distribution in Gas-Solid Two-Phase Flow by Backscattering Method

Jinhui FAN
Zhejiang University

Zhejiang University

The two-dimensional distribution of gas-solid flow parameters is a great research significance to reflect the actual situation in industry. The commonly used method is the ultrasonic tomography method, in which multiple probes are arranged at various angles, or the measurement device is rotated as that in medicine, but in most industrial situations, it is impossible to install probes at all angles or rotate the measured pipe. The backscattering method, however, uses only one transducer to both transmit and receive signals, and the two-dimensional information is obtained by only rotating the transducer. Ultrasound attenuates greatly in the air, and the attenuation changes with frequency. Therefore, Comsol is used to study the reflection of particles with different radii in the air to ultrasound with various frequencies. It is found that the backscattering equivalent voltage is the largest when the product of ultrasonic frequency and particle radius is about 27.78 Hz·m, and the particle concentration of 30% causes the strongest backscattering. The simulated results are in good agreement with the Faran backscattering model, which can provide references for selecting the appropriate frequency and obtaining the concentration when measuring gas-solid two-phase flow with the ultrasonic backscattering method.
Keywords: gas-solid two-phase flow; COMSOL simulation; ultrasonic backscattering method
Full Text: PDF
Copyright © The Author(s). This is an open-access article distributed under the terms of the Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA 4.0).


Anderson V.C. (1950), Sound scattering from a fluid sphere, The Journal of the Acoustical Society of America, 22(4): 426–431,

Awad T.S., Moharram H.A., Shaltout O.E., Asker D., Youssef M.M. (2012), Applications of ultrasound in analysis, processing and quality control of food: A review, Food Research International, 48(2): 410–427,

Boonkhao B., Wang X.Z. (2012), Ultrasonic attenuation spectroscopy for multivariate statistical process control in nanomaterial processing, Particuology, 10(2): 196–202,

Cai X., Li J., Ouyang X., Zhao Z., Su M. (2005), In-line measurement of pneumatically conveyed particles by a light transmission fluctuation method, Flow Measurement and Instrumentation, 16(5): 315–320,

Challis R.E., Povey M., Mather M.L., Holmes A.K. (2005), Ultrasound techniques for characterizing colloidal dispersions, Reports on Progress in Physics, 68(7): 1541–1637,

Chen H. et al. (2020), Study on backscattering characteristics of pulsed laser fuze in smoke [in Chinese], Infrared and Laser Engineering, 49(4): 403005–403005,

Dong T., Norisuye T., Nakanishi H., Tran-Cong-Miyata Q. (2020), Particle size distribution analysis of oil-in-water emulsions using static and dynamic ultrasound scattering techniques, Ultrasonics, 108: 106–117,

Dukhin A.S., Goetz P.J. (2001), New developments in acoustic and electroacoustic spectroscopy for characterizing concentrated dispersions, Colloids and Surfaces A: Physicochemical and Engineering Aspects, 192: 267–306,

Dukhin A.S., Goetz P.J. (1996), Acoustic spectroscopy for concentrated polydisperse colloids with high density contrast, American Chemical Society, 12(21): 4987–4997,

Dukhin A.S., Goetz P.J., Wines T.H., Somasundaran P. (2000), Acoustic and electroacoustic spectroscopy, Colloids and Surfaces A: Physicochemical and Engineering Aspects, 173(1–3): 127–158,

Elvira L., Vera P., Canadas F.J., Shukla S.K., Montero F. (2016), Concentration measurement of yeast suspensions using high frequency ultrasound backscattering, Ultrasonics, 64: 151–161,

Epstein P.S., Carhart R.R. (1953), The absorption of sound in suspensions and emulsion. I. Water fog in air, The Journal of the Acoustical Society of America, 25(3): 553–565,

Faran Jr. J.J. (1951), Sound scattering by solid cylinders and spheres, The Journal of the Acoustical Society of America, 23(4): 405–418,

Flax L., Dragonette L.R., Überall H. (1978), Theory of elastic resonance excitation by sound scattering, The Journal of the Acoustoical Society of America, 63(3): 723–731,

Furlan J.M., Mundla V., Kadambi J., Hoyt N., Visintainer R., Addie G. (2012), Development of A-scan ultrasound technique for measuring local particle concentration in slurry flows, Powder Technology, 215–216: 174–184,

Gu J., Su M., Cai X. (2018), In-line measurement of pulverized coal concentration and size in pneumatic pipelines using dual-frequency ultrasound, Applied Acoustics, 138: 163–170,

Han Y.F., Zhao A., Zhang H.X., Ren Y.Y., Liu W.X., Jin N.D. (2016), Differential pressure method for measuring water holdup of oil–water two-phase flow with low velocity and high water-cut, Experimental Thermal and Fluid Science, 72: 197–209,

Hwang C., Chen M.-Y. (2007), Analysis and optimal control of time-varying linear systems via shifted Legendre polynomials, International Journal of Control, 41(5): 1317–1330,

Jia H., Li X., Meng X. (2017), Rigid and elastic acoustic scattering signal separation for underwater target, The Journal of the Acoustical Society of America, 142(2): 653,

Jing J., Li Z., Zhu Q., Chen Z., Ren F. (2011), Influence of primary air ratio on flow and combustion characteristics and NOx emissions of a new swirl coal burner, Energy, 36(2): 1206–1213,

Khushrushahi S., Zahn M. (2011), Ultrasound velocimetry of ferrofluid spin-up flow measurements using a spherical coil assembly to impose a uniform rotating magnetic field, Journal of Magnetism and Magnetic Materials, 323(10): 1302–1308,

Lax M. (1951), Multiple scattering of waves, Reviews of Modern Physics, 23(4): 287–310,

Louisnard O. (2012), A simple model of ultrasound propagation in a cavitating liquid, Part I: Theory, nonlinear attenuation and traveling wave generation, Ultrasonics Sonochemistry, 19(1): 56–65,

Ma Y. et al. (2021), Influence of probe geometry on the characteristics of optical fiber gas-liquid two-phase flow measurement signals, Applied Optics, 60(6): 1660–1666,

Mathieu J., Schweitzer P. (2004), Measurement of liquid density by ultrasound backscattering analysis, Measurement Science and Technology, 15(5): 869–876,

McClements D.J. (1991), Ultrasonic characterisation of emulsions and suspensions, Advances in Colloid and Intetface Science, 37: 33–72,

Meng Z., Huang Z., Wang B., Ji H., Li H., Yan Y. (2010), Air–water two-phase flow measurement using a Venturi meter and an electrical resistance tomography sensor, Flow Measurement and Instrumentation, 21(3): 268–276,

Percus J.K., Yevick G.J. (1958), Analysis of classical statistical mechanics by means of collective coordinates, Physical Review, 110(1): 1–13,

Pessôa M.A.S., Neves A.A.R. (2020), Acoustic scattering and forces on an arbitrarily sized fluid sphere by a general acoustic field, Journal of Sound and Vibration, 479: 115373,

Rank D.H., McKelvey J.P. (1949), A Study of the Mechanism of Modified Rayleigh Scattering, Journal of the Optical Society of America B, 39(9): 762–765,

Sakamoto A., Saito T. (2012), Computational analysis of responses of a wedge-shaped-tip optical fiber probe in bubble measurement, Review of Scientific Instruments, 83(7): 075107,

Shaffer F.D., Bajura R.A. (1990), Analysis of Venturi performance for gas-particle flows, Journal of Fluids Engineering, 112(1): 121–127,

Tian C., Su M., Chen X., Cai X. (2013), An investigation on ultrasonic process tomography system for particle two-phase flow measurement [in Chinese], Journal of NanJing University (Natural Sciences), 49(1): 20–26,

Tsuji K., Norisuye T., Nakanishi H., Tran-Cong-Miyata Q. (2019), Simultaneous measurements of ultrasound attenuation, phase velocity, thickness, and density spectra of polymeric sheets, Ultrasonics, 99: 105974,

Twerskyt V. (1975), Transparency of pair-correlated, random distributions of small scatterers, with applications to the cornea, Journal of the Optical Society of America, 65(5): 524–530,

Wang Y. et al. (2016), The simulation analysis of effect with particles in different sizes on ultrasonic measurement of gas-solid two phase flow, [in:] Proceedings of 2016 International Conference on Wireless Communication and Network Engineering (WCNE 2016), pp. 307–310.

Wang Y., Lyu X., Li W., Yao G., Bai J., Bao A. (2018), Investigation on measurement of size and concentration of solid phase particles in gas-solid two phase flow, Chinese Journal of Electronics, 27(2): 381–385,

Wang Y., Yao G., Zhang Y., Liu M., Ge P. (2017), Ultrasonic radial simulation research of solid particle distribution of segregation flow in gas-solid two phase flow, [in:] Proceedings of the 2017 2nd International Conference on Automation, Mechanical and Electrical Engineering (AMEE 2017), Advances in Engineering, 87: 61–64,

Weser R., Wöckel S., Wessely B., Hempel U. (2013), Particle characterisation in highly concentrated dispersions using ultrasonic backscattering method, Ultrasonics, 53(3): 706–716,

Weser R., Woeckel S., Wessely B., Steinmann U., Babick F., Stintz M. (2014), Ultrasonic backscattering method for in-situ characterisation of concentrated dispersions, Powder Technology, 268: 177–190,

Yao J., Takei M. (2017), Application of process tomography to multiphase flow measurement in industrial and biomedical fields: a review, IEEE Sensors Journal, 17(24): 8196–8205,

DOI: 10.24425/aoa.2022.142011