Ultrasonic Simulation Research of Two-Dimensional Distribution in Gas-Solid Two-Phase Flow by Backscattering Method
Abstract
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 methodReferences
1. Anderson V.C. (1950), Sound scattering from a fluid sphere, The Journal of the Acoustical Society of America, 22(4): 426–431, https://doi.org/10.1121/1.1906621
2. 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, https://doi.org/10.1016/j.foodres.2012.05.004
3. Boonkhao B., Wang X.Z. (2012), Ultrasonic attenuation spectroscopy for multivariate statistical process control in nanomaterial processing, Particuology, 10(2): 196–202, https://doi.org/10.1016/j.partic.2011.11.009
4. 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, https://doi.org/10.1016/j.flowmeasinst.2005.03.011
5. 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, https://doi.org/10.1088/0034-4885/68/7/R01
6. 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, https://doi.org/10.3788/irla202049.0403005
7. 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, https://doi.org/10.1016/j.ultras.2020.106117
8. 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, https://doi.org/10.1016/S0927-7757(01)00730-0
9. Dukhin A.S., Goetz P.J. (1996), Acoustic spectroscopy for concentrated polydisperse colloids with high density contrast, American Chemical Society, 12(21): 4987–4997, https://doi.org/10.1021/la951085y
10. 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, https://doi.org/10.1016/S0927-7757(00)00593-8
11. 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, https://doi.org/10.1016/j.ultras.2015.08.009
12. 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, https://doi.org/10.1121/1.1907107
13. Faran Jr. J.J. (1951), Sound scattering by solid cylinders and spheres, The Journal of the Acoustical Society of America, 23(4): 405–418, https://doi.org/10.1121/1.1906780
14. 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, https://doi.org/10.1121/1.381780
15. 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, https://doi.org/10.1016/j.powtec.2011.09.044
16. 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, https://doi.org/10.1016/j.apacoust.2018.03.034
17. 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, https://doi.org/10.1016/j.expthermflusci.2015.11.008
18. 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, https://doi.org/10.1080/0020718508961200
19. 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, https://doi.org/10.1121/1.4996127
20. 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, https://doi.org/10.1016/j.energy.2010.11.025
21. 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, https://doi.org/10.1016/j.jmmm.2010.11.035
22. Lax M. (1951), Multiple scattering of waves, Reviews of Modern Physics, 23(4): 287–310, https://doi.org/10.1103/RevModPhys.23.287
23. 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, https://doi.org/10.1016/j.ultsonch.2011.06.007
24. 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, https://doi.org/10.1364/AO.414041
25. Mathieu J., Schweitzer P. (2004), Measurement of liquid density by ultrasound backscattering analysis, Measurement Science and Technology, 15(5): 869–876, https://doi.org/10.1088/0957-0233/15/5/012
26. McClements D.J. (1991), Ultrasonic characterisation of emulsions and suspensions, Advances in Colloid and Intetface Science, 37: 33–72, https://doi.org/10.1016/0001-8686(91)80038-L
27. 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, https://doi.org/10.1016/j.flowmeasinst.2010.02.006
28. Percus J.K., Yevick G.J. (1958), Analysis of classical statistical mechanics by means of collective coordinates, Physical Review, 110(1): 1–13, https://doi.org/10.1103/PhysRev.110.1
29. 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, https://doi.org/10.1016/j.jsv.2020.115373
30. 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, https://doi.org/10.1364/josa.39.000762
31. 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, https://doi.org/10.1063/1.4732819
32. Shaffer F.D., Bajura R.A. (1990), Analysis of Venturi performance for gas-particle flows, Journal of Fluids Engineering, 112(1): 121–127, https://doi.org/10.1115/1.2909359
33. 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, https://doi.org/10.13232/j.cnki.jnju.2013.01.017
34. 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, https://doi.org/10.1016/j.ultras.2019.105974
35. 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, https://doi.org/10.1364/JOSA.65.000524
36. 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.
37. 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, https://doi.org/10.1049/cje.2017.12.005
38. 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, https://doi.org/10.2991/amee-17.2017.12
39. Weser R., Wöckel S., Wessely B., Hempel U. (2013), Particle characterisation in highly concentrated dispersions using ultrasonic backscattering method, Ultrasonics, 53(3): 706–716, https://doi.org/10.1016/j.ultras.2012.10.013
40. 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, https://doi.org/10.1016/j.powtec.2014.08.026
41. 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, https://doi.org/10.1109/jsen.2017.2682929
2. 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, https://doi.org/10.1016/j.foodres.2012.05.004
3. Boonkhao B., Wang X.Z. (2012), Ultrasonic attenuation spectroscopy for multivariate statistical process control in nanomaterial processing, Particuology, 10(2): 196–202, https://doi.org/10.1016/j.partic.2011.11.009
4. 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, https://doi.org/10.1016/j.flowmeasinst.2005.03.011
5. 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, https://doi.org/10.1088/0034-4885/68/7/R01
6. 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, https://doi.org/10.3788/irla202049.0403005
7. 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, https://doi.org/10.1016/j.ultras.2020.106117
8. 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, https://doi.org/10.1016/S0927-7757(01)00730-0
9. Dukhin A.S., Goetz P.J. (1996), Acoustic spectroscopy for concentrated polydisperse colloids with high density contrast, American Chemical Society, 12(21): 4987–4997, https://doi.org/10.1021/la951085y
10. 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, https://doi.org/10.1016/S0927-7757(00)00593-8
11. 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, https://doi.org/10.1016/j.ultras.2015.08.009
12. 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, https://doi.org/10.1121/1.1907107
13. Faran Jr. J.J. (1951), Sound scattering by solid cylinders and spheres, The Journal of the Acoustical Society of America, 23(4): 405–418, https://doi.org/10.1121/1.1906780
14. 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, https://doi.org/10.1121/1.381780
15. 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, https://doi.org/10.1016/j.powtec.2011.09.044
16. 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, https://doi.org/10.1016/j.apacoust.2018.03.034
17. 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, https://doi.org/10.1016/j.expthermflusci.2015.11.008
18. 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, https://doi.org/10.1080/0020718508961200
19. 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, https://doi.org/10.1121/1.4996127
20. 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, https://doi.org/10.1016/j.energy.2010.11.025
21. 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, https://doi.org/10.1016/j.jmmm.2010.11.035
22. Lax M. (1951), Multiple scattering of waves, Reviews of Modern Physics, 23(4): 287–310, https://doi.org/10.1103/RevModPhys.23.287
23. 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, https://doi.org/10.1016/j.ultsonch.2011.06.007
24. 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, https://doi.org/10.1364/AO.414041
25. Mathieu J., Schweitzer P. (2004), Measurement of liquid density by ultrasound backscattering analysis, Measurement Science and Technology, 15(5): 869–876, https://doi.org/10.1088/0957-0233/15/5/012
26. McClements D.J. (1991), Ultrasonic characterisation of emulsions and suspensions, Advances in Colloid and Intetface Science, 37: 33–72, https://doi.org/10.1016/0001-8686(91)80038-L
27. 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, https://doi.org/10.1016/j.flowmeasinst.2010.02.006
28. Percus J.K., Yevick G.J. (1958), Analysis of classical statistical mechanics by means of collective coordinates, Physical Review, 110(1): 1–13, https://doi.org/10.1103/PhysRev.110.1
29. 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, https://doi.org/10.1016/j.jsv.2020.115373
30. 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, https://doi.org/10.1364/josa.39.000762
31. 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, https://doi.org/10.1063/1.4732819
32. Shaffer F.D., Bajura R.A. (1990), Analysis of Venturi performance for gas-particle flows, Journal of Fluids Engineering, 112(1): 121–127, https://doi.org/10.1115/1.2909359
33. 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, https://doi.org/10.13232/j.cnki.jnju.2013.01.017
34. 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, https://doi.org/10.1016/j.ultras.2019.105974
35. 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, https://doi.org/10.1364/JOSA.65.000524
36. 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.
37. 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, https://doi.org/10.1049/cje.2017.12.005
38. 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, https://doi.org/10.2991/amee-17.2017.12
39. Weser R., Wöckel S., Wessely B., Hempel U. (2013), Particle characterisation in highly concentrated dispersions using ultrasonic backscattering method, Ultrasonics, 53(3): 706–716, https://doi.org/10.1016/j.ultras.2012.10.013
40. 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, https://doi.org/10.1016/j.powtec.2014.08.026
41. 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, https://doi.org/10.1109/jsen.2017.2682929
