Spatial distribution of acoustic pressure and cavitation activity zones in a fluid system: numerical modelling and experiment
DOI:
https://doi.org/10.7242/1999-6691/2025.18.1.6Keywords:
ultrasonic standing waves, acoustic cavitation, foil test technique, cavitation activity, acoustic pressure, numerical simulation, COMSOL Multiphysics softwareAbstract
One of the areas of study of physicochemical processes occurring in liquids under the influence of high-frequency sound vibrations (ultrasound) is the determination of the role of acoustic cavitation. This phenomenon occurs due to the uneven distribution of acoustic pressure generated by an ultrasound source (emitter) inside the working chamber. The objective of this article is to study numerically the three-dimensional stationary distribution of acoustic pressure in a working cavity filled with a liquid with constant physicochemical properties using the COMSOL Multiphysics software. In addition to numerical modeling, we also conduct an experimental study in which a foil test technique is applied to determine the location of the areas where cavitation takes place; the results of the test are estimated by their comparison with the calculated acoustic field structure inside the working chamber. Within the framework of the developed numerical model, for simplicity we consider standing ultrasonic waves. Two geometrical configurations of a computational domain are used: a circular cylinder and a rectangular parallelepiped. The stationary distribution of acoustic pressure over a circular radiator is analyzed. It is assumed that ultrasonic standing waves propagate in a compressible medium with sound energy dissipation due to viscous friction or the formation of vapor-gas bubbles in the liquid being neglected. We set zero pressure or an impedance condition at the upper and lateral boundaries of the working cavity. We investigate the distribution of acoustic pressure in standing ultrasonic waves at resonant and non-resonant operating frequencies of the emitter. The acoustic pressure distribution in the central section of the working cavity is compared with photographs of the aluminum foil surface obtained in a full-scale experiment using the foil test method.
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Ashokkumar M., Lee J., Kentish S., Grieser F. Bubbles in an acoustic field: An overview. Ultrasonics Sonochemistry. 2007b. Vol. 14, no. 4. P. 470–475. DOI: 10.1016/j.ultsonch.2006.09.016
Ashokkumar M. The characterization of acoustic cavitation bubbles — An overview. Ultrasonics Sonochemistry. 2011b. Vol. 18, no. 4. P. 864–872. DOI: 10.1016/j.ultsonch.2010.11.016
Butyugina E.V., Nasibullaeva E.S., Gumerov N.A., Akhatov I.S. Numerical simulations of gas microbubble dynamics in an acoustic field with the influence of rectified diffusion. Computational Continuum Mechanics. 2014. Vol. 7, no. 3. P. 234–244. DOI: 10.7242/1999-6691/2014.7.3.23
Konovalov V.V., Lyubimova T.P. Numerical study of the effect of vibrations on the interaction in an ensemble of gas bubbles and solid particles in a liquid. Computational Continuum Mechanics. 2019. Vol. 12, no. 1. P. 48–56. DOI: 10.7242/1999-6691/2019.12.1.5
Sboev I., Lyubimova T., Rybkin K., Kuchinskiy M. A Numerical Investigation of the Effect of Boundary Conditions on Acoustic Pressure Distribution in a Sonochemical Reactor Chamber. Fluid Dynamics & Materials Processing. 2024b. Vol. 20, no. 6. DOI: 10.32604/fdmp.2024.051341
Yasui K. Acoustic Cavitation and Bubble Dynamics. Cham: Springer International Publishing, 2018b. DOI: 10.1007/978-3-319-68237-2
Nguyen T.T., Asakura Y., Koda S., Yasuda K. Dependence of cavitation, chemical effect, and mechanical effect thresholds on ultrasonic frequency. Ultrasonics Sonochemistry. 2017b. Vol. 39. P. 301–306. DOI: 10.1016/j.ultsonch.2017.04.037
Arndt R.E. Recent Advances in Cavitation Research. Vol. 12. 1981b. P. 1–78. DOI: 10.1016/B978-0-12-021812-7.50006-7
Chatel G., Colmenares J.C. Sonochemistry: From Basic Principles to Innovative Applications. 2017b. Topics in Current Chemistry. DOI: 10.1007/978-3-319-54271-3
Kuchinskiy M., Lyubimova T., Rybkin K., Sadovnikova A., Galishevskiy V. Investigation of Cavitation in NaCl Solutions in a Sonochemical Reactor Using the Foil Test Method. Fluid Dynamics & Materials Processing. 2024b. Vol. 20, no. 5. DOI: 10.32604/fdmp.2024.050059
Leong T., Johansson L., Juliano P., McArthur S.L., Manasseh R. Ultrasonic Separation of Particulate Fluids in Small and Large Scale Systems: A Review. Industrial & Engineering Chemistry Research. 2013b. Vol. 52, no. 47. P. 16555–16576. DOI: 10.1021/ie402295r
Trujillo F.J., Juliano P., Barbosa-Cánovas G., Knoerzer K. Separation of suspensions and emulsions via ultrasonic standing waves -– A review. Ultrasonics Sonochemistry. 2014b. Vol. 21, no. 6. P. 2151–2164. DOI: 10.1016/j.ultsonch.2014.02.016
Luo X., Gong H., Yin H., He Z., He L. Optimization of acoustic parameters for ultrasonic separation of emulsions with different physical properties. Ultrasonics Sonochemistry. 2020b. Vol. 68. 105221. DOI: 10.1016/j.ultsonch.2020.105221
Chen Y., Truong V.N.T., Bu X., Xie G. A review of effects and applications of ultrasound in mineral flotation. Ultrasonics Sonochemistry. 2020b. Vol. 60. 104739. DOI: 10.1016/j.ultsonch.2019.104739
Mao Y., Xia W., Peng Y., Xie G. Ultrasonic-assisted flotation of fine coal: A review. Fuel Processing Technology. 2019b. Vol. 195. 106150. DOI: 10.1016/j.fuproc.2019.106150
Altun N.E., Hwang J.-Y., Hicyilmaz C. Enhancement of flotation performance of oil shale cleaning by ultrasonic treatment. International Journal of Mineral Processing. 2009b. Vol. 91, no. 1/2. P. 1–13. DOI: 10.1016/j.minpro.2008.10.003
Wang H., Yang W., Yan X., Wang L., Wang Y., Zhang H. Regulation of bubble size in flotation: A review. Journal of Environmental Chemical Engineering. 2020b. Vol. 8, no. 5. 104070. DOI: 10.1016/j.jece.2020.104070
Sutkar V.S., Gogate P.R., Csoka L. Theoretical prediction of cavitational activity distribution in sonochemical reactors. Chemical Engineering Journal. 2010b. Vol. 158, no. 2. P. 290–295. DOI: 10.1016/j.cej.2010.01.049
Advanced Experimental and Numerical Techniques for Cavitation Erosion Prediction. Vol. 106 / ed. by K. Kim, G. Chahine, J. Franc, A. Karimi. Springer Netherlands, 2014b. Fluid Mechanics and Its Applications. DOI: 10.1007/978-94-017-8539-6
Gogate P.R., Tatake P.A., Kanthale P.M., Pandit A.B. Mapping of sonochemical reactors: Review, analysis, and experimental verification. AIChE Journal. 2002b. Vol. 48, no. 7. P. 1542–1560. DOI: 10.1002/aic.690480717
Wei Z., Weavers L.K. Combining COMSOL modeling with acoustic pressure maps to design sono-reactors. Ultrasonics Sonochemistry. 2016b. Vol. 31. P. 490–498. DOI: 10.1016/j.ultsonch.2016.01.036
Klíma J., Frias-Ferrer A., González-García J., Ludvík J., Saez V., Iniesta J. Optimisation of 20 kHz sonoreactor geometry on the basis of numerical simulation of local ultrasonic intensity and qualitative comparison with experimental results. Ultrasonics Sonochemistry. 2007b. Vol. 14, no. 1. P. 19–28. DOI: 10.1016/j.ultsonch.2006.01.001
Krefting D., Mettin R., Lauterborn W. High-speed observation of acoustic cavitation erosion in multibubble systems. Ultrasonics Sonochemistry. 2004b. Vol. 11, no. 3/4. P. 119–123. DOI: 10.1016/j.ultsonch.2004.01.006
Rossing T.D. Springer Handbook of Acoustics. Springer New York, 2014b. DOI: 10.1007/978-1-4939-0755-7
Bampouli A., Goris Q., Van Olmen J., Solmaz S., Noorul Hussain M., Stefanidis G.D., Van Gerven T. Understanding the ultrasound field of high viscosity mixtures: Experimental and numerical investigation of a lab scale batch reactor. Ultrasonics Sonochemistry. 2023b. Vol. 97. 106444. DOI: 10.1016/j.ultsonch.2023.106444
Liu L., Wen J., Yang Y., Tan W. Ultrasound field distribution and ultrasonic oxidation desulfurization efficiency. Ultrasonics Sonochemistry. 2013b. Vol. 20, no. 2. P. 696–702. DOI: 10.1016/j.ultsonch.2012.10.009
Servant G., Laborde J.-L., Hita A., Caltagirone J.-P., Gérard A. Spatio-temporal dynamics of cavitation bubble clouds in a low frequency reactor: comparison between theoretical and experimental results. Ultrasonics Sonochemistry. 2001b. Vol. 8, no. 3. P. 163–174. DOI: 10.1016/S1350-4177(01)00074-8
Lyubimova T., Rybkin K., Fattalov O., Kuchinskiy M., Filippov L. Experimental study of temporal dynamics of cavitation bubbles selectively attached to the solid surfaces of different hydrophobicity under the action of ultrasound. Ultrasonics. 2021b. Vol. 117. 106516. DOI: 10.1016/j.ultras.2021.106516
Kaltenbacher M. Computational Acoustics. Cham: Springer International Publishing, 2018b. DOI: 10.1007/978-3-319-59038-7
Rashwan S.S., Mohany A., Dincer I. Development of efficient sonoreactor geometries for hydrogen production. International Journal of Hydrogen Energy. 2021b. Vol. 46, no. 29. P. 15219–15240. DOI: 10.1016/j.ijhydene.2021.02.113
Tudela I., Sáez V., Esclapez M.D., Díez-García M.I., Bonete P., González-García J. Simulation of the spatial distribution of the acoustic pressure in sonochemical reactors with numerical methods: A review. Ultrasonics Sonochemistry. 2014b. Vol. 21, no. 3. P. 909–919. DOI: 10.1016/j.ultsonch.2013.11.012
Laborde J.- L., Bouyer C., Caltagirone J.-P., Gérard A. Acoustic cavitation field prediction at low and high frequency ultrasounds. Ultrasonics. 1998b. Vol. 36, no. 1–5. P. 581–587. DOI: 10.1016/S0041-624X(97)00106-6
Tao T., Zhao J., Wang W. Study on the Characterization Method of Ultrasonic Cavitation Field based on the Numerical Simulation of the Amplitude of Sound Pressure. MATEC Web of Conferences. 2020b. Vol. 319. 02003. DOI: 10.1051/matecconf/202031902003
Wang Y.- C., Yao M.-C. Realization of cavitation fields based on the acoustic resonance modes in an immersion-type sonochemical reactor. Ultrasonics Sonochemistry. 2013b. Vol. 20, no. 1. P. 565–570. DOI: 10.1016/j.ultsonch.2012.07.026
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