Abstract
This paper reviews the various modeling strategies adopted in the literature to capture the response of bubble clusters to pressure changes. The first part is focused on the strategies adopted to model and simulate the response of individual bubbles to external pressure variations discussing the relevance of the various mechanisms triggered by the appearance and later collapse of bubbles. In the second part we review available models proposed for large scale bubbly flows used in different contexts including hydrodynamic cavitation, sound propagation, ultrasonic devices and shockwave induced cavitation processes. Finally we discuss the main challenges of cavitation models.
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References
Abgrall, R.: How to prevent pressure oscillations in multicomponent flow calculations: a quasi conservative approach. J. Comput. Phys. 125(1), 150–160 (1996)
Abgrall, R., Karni, S.: Computations of compressible multifluids. J. Comput. Phys. 169(2), 594–623 (2001)
Abu-Al-Saud, M.O., Popinet, S., Tchelepi, H.A.: A conservative and well-balanced surface tension model. J. Comput. Phys. 371, 896–913 (2018)
Ahuja, V., Hosangadi, A., Arunajatesan, S.: Simulations of cavitating flows using hybrid unstructured meshes. J. Fluids Eng. 123(2), 331–340 (2001)
Ainslie, M.A., Leighton, T.G.: Review of scattering and extinction cross-sections, damping factors, and resonance frequencies of a spherical gas bubble. J. Acoust. Soc. Am. 130(5), 3184–3208 (2011)
Akbar, R., Kaneshige, M., Schultz, E., Sheperd, J.: Detonations in H2-N2OCH4-NH3-O2-N2 mixtures. Final report 1, California Institute of Technology, Pasadena, CA 91125 (January 2000)
An, Y., Ying, C.: Model of single bubble sonoluminiscence. Phys. Rev. E 71 (036308), 1–12 (2005)
Ando, K.: Effects of polydispersity in bubbly flows. PhD Thesis, California Institute of Technology. See also URL http://thesis.library.caltech.edu/5859/ (2010)
Ando, K., Colonius, T., Brennen, C.E.: Numerical simulation of shock propagation in a polydisperse bubbly liquid. Int. J. Mult Flow 37, 596–608 (2011)
Andriotis, A., Gavaises, M., Arcoumanis, C.: Vortex flow and cavitation in diesel injector nozzles. J. Fluid Mech. 610, 195–215 (2008)
Apfel, R.E.: The role of impurities in cavitation-threshold determination. J. Acoust. Soc. Am. 48(5B), 1179–1186 (1970)
Atchley, A.A., Prosperetti, A.: The crevice model of bubble nucleation. J. Acoust. Soc. Am. 86, 1065 (1989)
Azouzi, M.M., Ramboz, C., Lenain, J.-F., Caupin, F.: A coherent picture of water at extreme negative pressure. Nat. Phys. 9(1), 38 (2013)
Baer, M.R., Nunziato, J.W.: A two-phase mixture theory for the deflagration-to-detonation transition (ddt) in reactive granular materials. Int. J. Multiphase Flow 12(6), 861–889 (1986)
Bailey, M.R., McAteer, J.A., Pishchalnikov, Y.A., Hamilton, M.F., Colonius, T.: Progress in lithotripsy research. Acoust. Today 2, 18–29 (2006)
Baldwin, B., Lomax, H.: Thin-layer approximation and algebraic model for separated turbulentflows. In: 16Th Aerospace Sciences Meeting, p. 257 (1978)
Bensow, R.E., Bark, G.: Implicit les predictions of the cavitating flow on a propeller. J. Fluids Eng. 132(4), 041302 (2010)
Bergamasco, L., Fuster, D.: Oscillation regimes of gas/vapor bubbles. Int. J. Heat Mass Transfer 112, 72–80 (2017)
Blake, J.R., Gibson, D.C.: Growth and collapse of a vapour cavity near a free surface. J. Fluid Mech. 111, 123–140 (1981)
Blake, J.R., Gibson, D.C.: Cavitation bubbles near boundaries. Annu. Rev. Fluid Mech. 19(1), 99–123 (1987)
Brackbill, J.U., Kothe, D.B., Zemach, C.: A continuum method for modeling surface tension. J Comput. Phys. 100, 335–354 (1992)
Brandner, P.A., Walker, G.J., Niekamp, P.N., Anderson, B.: An experimental investigation of cloud cavitation about a sphere. J. Fluid Mech. 656, 147–176 (2010)
Bremond, N., Arora, M., Dammer, S.M., Lohse, D.: Interaction of cavitation bubbles on a wall. Phys Fluids 121505, 18 (2006)
Bremond, N., Arora, M., Ohl, C.D., Lohse, D.: Controlled multibubble surface cavitation. Phys. Rev. Let. 96(22), 224501 (2006)
Bremond, N., Arora, M., Ohl, C.-D., Lohse, D.: Cavitation on surfaces. J. Phys. Condens. Matter 17(45), S3603 (2005)
Brennen, C.: The dynamic behavior and compliance of a stream of cavitating bubbles. J. Fluids Eng. 95(4), 533–541 (1973)
Brennen, C.: Cavitation and Bubble Dynamics, p 254. Oxford University Press, New York (1995). ISBN 0195094093
Brennen, C.E.: Cavitation in Medicine. Interface focus 5(5), 20150022 (2015)
Brøns, M., Thompson, M.C., Leweke, T., Hourigan, K.: Vorticity generation and conservation for two-dimensional interfaces and boundaries. J. Fluid Mech. 758, 63–93 (2014)
Caflisch, R.E., Miksis, M.J., Papanicolaou, G.C., Ting, L.: Effective equations for wave propagation in bubbly liquids. J. Fluid Mech. 153, 259–273 (1985)
Campbell, I.J., Pitcher, A.S.: Shock waves in a liquid containing gas bubbles. Proc. R. Soc. Lond A 243(1235), 534–545 (1958)
Caupin, F., Herbert, E.: Cavitation in water: a review. Comptes Rendus Physique 7(9-10), 1000–1017 (2006)
Chahine, G.L.: The final stage of the collapse of a cavitation bubble near a rigid wall. J. Fluid Mech. 1(257), 147–181 (1993)
Chahine, G.L., Kapahi, A., Choi, J.K., Hsiao, C.T.: Modeling of surface cleaning by cavitation bubble dynamics and collapse. Ultrason. Sonochem. 29, 528–549 (2016)
Chiapolino, A., Saurel, R., Nkonga, B.: Sharpening diffuse interfaces with compressible fluids on unstructured meshes. J. Comput. Phys. 340, 389–417 (2017)
Colombet, D., Goncalvès, E., Fortes-Patella, R.: On numerical simulation of cavitating flows under thermal regime. Int. J. Heat Mass Transfer 105, 411–428 (2017)
Colonius, T., Fuster, D.: Investigation of a New Model for Bubbly Cavitating Flow. In: Proceedings 8Th Int. Symp. Cav. (2012)
Commander, K.W., Prosperetti, A.: Linear pressure waves in bubbly liquids Comparison between theory and experiments. J. Acoust. Soc. Am. 85, 732 (1989)
Coralic, V., Colonius, T.: Finite-volume weno scheme for viscous compressible multicomponent flows. J. Comput. Phys. 274, 95–121 (2014)
Coste, C., Laroche, C.: S. Fauve. Sound propagation in a liquid with vapour bubbles. EPL (Europhys. Lett.) 11(4), 343–347 (1990)
Coutier-Delgosha, O., Reboud, J.L., Delannoy, Y.: Numerical simulation of the unsteady behaviour of cavitating flows. Int. J. Numer. Methods Fluids 42(5), 527–548 (2003)
Crespo, A.: Sound and shock waves in liquids containing bubbles. Phys. Fluids 12(11), 2274–2282 (1969)
Crum, L.A.: Acoustic cavitation thresholds in water. In: Cavitation and Inhomogeneities in Underwater Acousticspp. pp. 84–89. Springer (1980)
d’Agostino, L., Brennen, C.E.: On the acoustical dynamics of bubble clouds (1983)
d’Agostino, L., Brennen, C.E.: Linearized dynamics of spherical bubble clouds. J. Fluid Mech. 199, 155–176 (1989)
De Lorenzo, M., Lafon, P.H., Di Matteo, M., Pelanti, M., Seynhaeve, J.M., Bartosiewicz, Y.: Homogeneous two-phase flow models and accurate steam-water table look-up method for fast transient simulations. Int. J. Multiphase Flow 95, 199–219 (2017)
De Lorenzo, M., Pelanti, M., Lafon, P.: Hllc-type and path-conservative schemes for a single-velocity six-equation two-phase flow model: a comparative study. Appl. Math. Comput. 333, 95–117 (2018)
Dean, R.B.: The formation of bubbles. J. Appl. Phys. 15(5), 446–451 (1944)
Debenedetti, P.G.: Metastable Liquids: Concepts and Principles. Princeton University Press, Princeton (1996)
Degani, D., Schifft, L.B.: Computation of turbulent supersonic flows around pointed bodies having crossflow separation. J. Comput. Phys. 66(1), 173–196 (1986)
Delale, C.F., Nas, S., Tryggvason, G.: Direct numerical simulations of shock propagation in bubbly liquids. Phys. Fluids 17(12), 121705 (2005)
Delale, C.F., Tryggvason, G.: Shock structure in bubbly liquids: comparison of direct numerical simulations and model equations. Shock Waves 17(6), 433–440 (2008)
Dellanoy, Y., Kueny, J.L.: Two phase flow approach in unsteady cavitation modeling. In: Cavitation and Multiphase Flow Forum, vol. 98, pp 153–158 (1990)
Denner, F., Xiao, C.N., van Wachem, B.G.M.: Pressure-based algorithm for compressible interfacial flows with acoustically-conservative interface discretisation. J. Comput. Phys. 367, 192–234 (2018)
Didenko, Y.T., McNamara III, W.B., Suslick, K.S.: Effect of noble gases on sonoluminescence temperatures during multibubble cavitation. Phys. Rev. Lett. 84 (4), 777 (2000)
Dijkink, R., Ohl, C.D.: Measurement of cavitation induced wall shear stress. Appl. Phys. Lett. 93(25), 254107 (2008)
Doc, J.B., Conoir, J.M., Marchiano, R., Fuster, D.: Nonlinear acoustic propagation in bubbly liquids multiple scattering, softening and hardening phenomena. J. Acoust. Soc. Am. 139(4), 1703–1712 (2016)
Dopazo, C.: On conditioned averages for intermittent turbulent flows. J. Fluid Mech. 81(3), 433–438 (1977)
Dopazo, C., O’Brien, E.: Intermittency in free turbulent shear flows. In: Turbulent Shear Flows I, pp 6–23. Springer (1979)
Dular, M., Coutier-Delgosha, O.: Thermodynamic effects during growth and collapse of a single cavitation bubble. J. Fluid Mech. 736, 44–66 (2013)
Dular, M., Stoffel, B., Širok B.: Development of a cavitation erosion model. Wear 261(5–6), 642–655 (2006)
Epstein, P.S., Plesset, M.S.: On the stability of gas bubbles in liquid-gas solutions. J. Chem. Phys. 18, 1505 (1950)
Esche, R.: Untersuchung der schwingungskavitation in flüssigkeiten. Acta Acustica united with Acustica 2(6), 208–218 (1952)
Franc, J.P., Riondet, M., Karimi, A., Chahine, G.L.: Material and velocity effects on cavitation erosion pitting. Wear 274, 248–259 (2012)
Freund, J., Colonius, T., Evan, A.P.: A cumulative shear mechanism for tissue damage initiation in shock-wave lithotripsy. Ultrasound Med. Biol. 33(9), 1495–1503 (2007)
Fureby, C., Grinstein, F.F.: Monotonically integrated large eddy simulation of free shear flows. AIAA Journal 37(5), 544–556 (1999)
Fureby, C., Grinstein, F.F.: Large eddy simulation of high-reynolds-number free and wall-bounded flows. J. Comput. Phys. 181(1), 68–97 (2002)
Fuster, D.: An energy preserving formulation for the simulation of multiphase turbulent flows. J. Comput. Phys. 235, 114–128 (2013)
Fuster, D., Colonius, T.: Modeling bubble clusters in compressible liquids. J. Fluid Mech. 688, 253–289 (2011)
Fuster, D., Conoir, J.M., Colonius, T.: Effect of direct bubble-bubble interactions on linear-wave propagation in bubbly liquids. Phys. Rev. E 90(6), 063010 (2014)
Fuster, D., Dopazo, C., Hauke, G.: Liquid compressibility effects during the collapse of a single cavitating bubble. J. Acoust. Soc. Am. 129(1), 122–131 (2011)
Fuster, D., Hauke, G., Dopazo, C.: Parametric analysis for a single collapsing bubble. Journal of Flow, Turbulence and Combustion 82, 25–46 (2008)
Fuster, D., Hauke, G., Dopazo, C.: Influence of accommodation coefficient on nonlinear bubble oscillations. J. Acoust. Soc Am. 128, 5–10 (2010)
Fuster, D., Montel, F.: Mass transfer effects on linear wave propagation in diluted bubbly liquids. J. Fluid Mech. 779, 598–621 (2015)
Fuster, D., Pham, K., Zaleski, S.: Stability of bubbly liquids and its connection to the process of cavitation inception. Phys. Fluids 26, 042002 (2014)
Fuster, D., Popinet, S.: An all-mach method for the simulation of bubble dynamics problems in the presence of surface tension. J. Comput. Phys. 374, 752–768 (2018)
Gaitan, F., Crum, L.A., Church, C., Roy, R.: Sonoluminiscence and bubble dynamics for a single, stable, cavitation bubble. J. Acoust. Soc. Am. 91(063166), 3166–3183 (1992)
Ganesh, H., Mäkiharju, S.A., Ceccio, S.L.: Bubbly shock propagation as a mechanism for sheet-to-cloud transition of partial cavities. J. Fluid Mech. 802, 37–78 (2016)
Garrick, D.P., Owkes, M., Regele, J.D.: A finite-volume hllc-based scheme for compressible interfacial flows with surface tension. J. Comput. Phys. 339, 46–67 (2017)
Giannadakis, E., Gavaises, M., Arcoumanis, C.: Modelling of cavitation in diesel injector nozzles. J. Fluid Mech. 616, 153–193 (2008)
Gilmore, F.R.: The growth or collapse of a spherical bubble in a viscous compressible liquid (1952)
Gnanaskandan, A., Mahesh, K.: A numerical method to simulate turbulent cavitating flows. Int. J. Multiphase Flow 70, 22–34 (2015)
Gnanaskandan, A., Mahesh, K.: Large eddy simulation of the transition from sheet to cloud cavitation over a wedge. Int. J. Multiphase Flow 83, 86–102 (2016)
Gnanaskandan, A., Mahesh, K.: Numerical investigation of near-wake characteristics of cavitating flow over a circular cylinder. J. Fluid Mech. 790, 453–491 (2016)
Goncalves, E.: Modeling for non isothermal cavitation using 4-equation models. Int. J. Heat Mass Transfer 76, 247–262 (2014)
Goncalves, E., Patella, R.F.: Numerical simulation of cavitating flows with homogeneous models. Comput. Fluids 38(9), 1682–1696 (2009)
Gopalan, S., Katz, J.: Flow structure and modeling issues in the closure region of attached cavitation. Phys. Fluids 12(4), 895–911 (2000)
Grab, M., Quintal, B., Caspari, E., Deuber, C., Maurer, H., Greenhalgh, S.: The effect of boiling on seismic properties of water-saturated fractured rock. J. Geophys. Res. Solid Earth 122(11), 9228–9252 (2017)
Grandjean, H., Jacques, N., Zaleski, S.: Shock propagation in liquids containing bubbly clusters: a continuum approach. J. Fluid Mech. 701, 304–332 (2012)
Groß, T.F., Pelz, P.F.: Diffusion-driven nucleation from surface nuclei in hydrodynamic cavitation. J. Fluid Mech. 830, 138–164 (2017)
Gumerov, N.A.: Dynamics of vapor bubbles with nonequilibrium phase transitions in isotropic acoustic fields. Phys. Fluids 12(1), 71–88 (2000)
Gumerov, N.A., Hsiao, C.T., Goumilevski, A.G.: Determination of the accomodation coefficient using vapor/gas bubble dynamics in an acoustic field. Technical Report 1, California Institute of Technology, DYNAFLOW, Inc., Fulton, Maryland, January 2001. See also URL http://gltrs.grc.nasa.gov/GLTRS (date last viewed 09/05)
Gumerov, N.A.: Weakly non-linear oscillations of the radius of a vapour bubble in an acoustic field. J. Appl. Math. Mech 55, 205 (1991)
Hao, Y., Prosperetti, A.: The dynamics of vapor bubbles in acoustic pressure fields. Phys. Fluids 11(8), 2008–2019 (1999)
Harkin, A., Kaper, T.J., Nadim, A.: Coupled pulsation and translation of two gas bubbles in a liquid. J. Fluid Mech. 445, 377–411 (2001)
Harlow, F.H., Welch, J.E.: Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. The Phys. Fluids 8(12), 2182–2189 (1965)
Newton Harvey, E., Barnes, D.K., McElroy, W m D, Whiteley, A.H., Pease, D.C., Cooper, K.W.: Bubble formation in animals. i. physical factors. J. Cell. Physiol. 24(1), 1–22 (1944)
Newton Harvey, E., Whiteley, A.H., McElroy, W.D., Pease, D.C., Barnes, D.K.: Bubble formation in animals. ii. gas nuclei and their distribution in blood and tissues. J. Cell. Physiol. 24(1), 23–34 (1944)
Hauke, G., Fuster, D., Dopazo, C.: Dynamics of a single cavitating and reacting bubble. Phys. Rev. E. 75(066310), 1–14 (2007)
Hawker, N.A., Ventikos, Y.: Interaction of a strong shockwave with a gas bubble in a liquid medium: a numerical study. J. Fluid Mech. 701, 59–97 (2012)
Hertz, H.: ÜBer die Verdunstug der flüssigkeiten, Inbesondere des Quecksilbers im lufteren räume (on the evaporation of fluids, especially of mercury, in vacuum spaces). Ann. Phys. 17, 177 (1982)
Hidalgo, V., Luo, X., Escaler Puigoriol, F.X., Ji, B., Aguinaga, A.: Implicit large eddy simulation of unsteady cloud cavitation around a plane-convex hydrofoil. J. Hydrodyn. 27(6), 815–823 (2015)
Ilinskii, Y.A., Hamilton, M.F., Zabolotskaya, E.A.: Bubble interaction dynamics in Lagrangian and Hamiltonian mechanics. J. Acoust. Soc. Am. 121, 786 (2007)
Jemison, M., Sussman, M., Arienti, M.: Compressible, multiphase semi-implicit method with moment of fluid interface representation. J. Comput. Phys. 279, 182–217 (2014)
Ji, B., Luo, X., Wu, Y., Peng, X., Duan, Y.: Numerical analysis of unsteady cavitating turbulent flow and shedding horse-shoe vortex structure around a twisted hydrofoil. Int. J. Multiphase Flow 51, 33–43 (2013)
Ji, B., Luo, X.W., Arndt, R.E.A., Peng, X., Wu, Y.: Large eddy simulation and theoretical investigations of the transient cavitating vortical flow structure around a naca66 hydrofoil. Int. J. Multiphase Flow 68, 121–134 (2015)
Johansen, S.T., Wu, J., Shyy, W.: Filter-based unsteady rans computations. Int. J. Heat Fluid Flow 25(1), 10–21 (2004)
Johnsen, E., Colonius, T.: Implementation of weno schemes in compressible multicomponent flow problems. J. Comput. Phys. 219(2), 715–732 (2006)
Johnsen, E., Colonius, T.: Implementation of WENO schemes in compressible multicomponent flow problems. J. Comput. Phys. 219(2), 715–732 (2006)
Johnsen, E., Colonius, T.: Shock-induced collapse of a gas bubble in shockwave lithotripsy. J. Acoust. Soc. Am. 124, 2008 (2011)
Johnsen, E., Colonius, T.: Numerical simulations of non-spherical bubble collapse. J. Fluid Mech. 629, 231–262 (2009)
Jones, S.F., Evans, G.M., Galvin, K.P.: Bubble nucleation from gas cavities: a review. Adv. Colloid Interface Sci. 80(1), 27–50 (1999)
Jones, W.P., Launder, B.E.: The prediction of laminarization with a two-equation model of turbulence. Int. J. Heat Mass Transfer 15(2), 301–314 (1972)
Kapila, A.K., Menikoff, R., Bdzil, J.B., Son, S.F., Stewart, D.S.: Two-phase modeling of deflagration-to-detonation transition in granular materials reduced equations. Phys. Fluids 13(10), 3002–3024 (2001)
Keller, J., Miksis, M.: Bubble oscillations of large amplitude. J. Acoust. Soc Am. 68(2), 628–633 (1980)
Khabeev, N.S.: Heat transfer and phase transition effects in the oscillation of vapor bubbles. Sov. Phys. Acoust. 21, 501 (1976)
Khabeev, N.S.: Diffusion effects in the oscillation of vapor–gas bubbles in a sound field. Int. J. Heat Mass Transfer 50(17–18), 3556–3560 (2007)
Kim, J., Lee, J.S.: Numerical study of cloud cavitation effects on hydrophobic hydrofoils. Int. J. Heat Mass Transfer 83, 591–603 (2015)
Klaseboer, E., Fong, S.W., Turangan, C.K., Khoo, B.C., Szeri, A.J., Calvisi, M.L., Sankin, G.N., Zhong, P.: Interaction of lithotripter shockwaves with single inertial cavitation bubbles. J. Fluid Mech. 593, 33–56 (2007)
Knudsen, M.: Maximum rate of vaporization of mercury. Ann. Phys. 47, 697 (1915)
Koch, M., Lechner, C., Reuter, F., Köhler, K., Mettin, R., Lauterborn, W.: Numerical modeling of laser generated cavitation bubbles with the finite volume and volume of fluid method, using openfoam. Comput. Fluids 126, 71–90 (2016)
Koukouvinis, P., Gavaises, M., Supponen, O., Farhat, M.: Numerical simulation of a collapsing bubble subject to gravity. Phys. Fluids 28(3), 032110 (2016)
Kubota, A., Kato, H., Yamaguchi, H.: A new modelling of cavitating flows: a numerical study of unsteady cavitation on a hydrofoil section. J. Fluid Mech. 240, 59–96 (1992)
Kunz, R.F., Boger, D.A., Chyczewski, T.S., Stinebring, D., Gibeling, H., Govindan, T.R.: Multi-phase cfd analysis of natural and ventilated cavitation about submerged bodies. In: 3rd ASME/JSME Joint Fluids Engineering Conference, vol. 1823. San Francisco (1999)
Kunz, R.F., Boger, D.A., Stinebring, D.R., Chyczewski, T.S., Lindau, J.W., Gibeling, H.J., Venkateswaran, S., Govindan, T.R.: A preconditioned navier–stokes method for two-phase flows with application to cavitation prediction. Comput. Fluids 29(8), 849–875 (2000)
Landau, L.D., Lifshitz, E.M.: Fluid mechanics. Pergamon Press, Oxford (1987)
Lauterborn, W., Bolle, H.: Experimental investigations of cavitation-bubble collapse in the neighbourhood of a solid boundary. J. Fluid Mech. 72(02), 391–399 (1975)
Legendre, D., Borée, J., Magnaudet, J.: Thermal and dynamic evolution of a spherical bubble moving steadily in a superheated or subcooled liquid. Phys. Fluids 10(6), 1256–1272 (1998)
Leroy, V., Strybulevych, A., Scanlon, M.G., Page, J.H.: Transmission of ultrasound through a single layer of bubbles. Eur. Phys. J. E 29(1), 123–130 (2009)
Lezzi, A., Prosperetti, A.: Bubble dynamics in a compressible liquid. Part 2. Second-order theory. J. Fluid Mech. 185, 289–321 (1987)
Lin, H., Storey, B.D., Szeri, A.J.: Inertially driven inhomogeneities in violently collapsing bubbles: the validity of the rayleigh-plesset equation. J. Fluid Mech. 452, 145–162 (2002)
Lohse, D., Zhang, X.: Surface nanobubbles and nanodroplets. Rev. Mod. Phys. 87(3), 981 (2015)
Louisnard, O.: A simple model of ultrasound propagation in a cavitating liquid. Part I: Theory, nonlinear attenuation and traveling wave generation. Ultrason. Sonochem. 19(1), 56–65 (2012)
Louisnard, O.: A simple model of ultrasound propagation in a cavitating liquid. Part II: Primary bjerknes force and bubble structures. Ultrason. Sonochem. 19(1), 66–76 (2012)
Louisnard, O., Gonzalez-Garcia, J., Tudela, I., Klima, J., Saez, V., Vargas-Hernandez, Y.: Fem simulation of a sono-reactor accounting for vibrations of the boundaries. Ultrason. Sonochem. 16(2), 250–259 (2009)
Lundgren, T., Koumoutsakos, P.: On the generation of vorticity at a free surface. J. Fluid Mech. 382, 351–366 (1999)
Luo, X., Bin, J., Tsujimoto, Y.: A review of cavitation in hydraulic machinery. J. Hydrodyn. Ser. B 28(3), 335–358 (2016)
Ma, J., Chahine, G.L., Hsiao, C.T.: Spherical bubble dynamics in a bubbly medium using an euler–lagrange model. Chem. Eng. Sci. 128, 64–81 (2015)
Maeda, K., Colonius, T., Kreider, W., Maxwell, A., Bailey, M.: Modeling and experimental analysis of acoustic cavitation bubble clouds for burst-wave lithotripsy. J. Acoust. Soc. Am. 140(4), 3307–3307 (2016)
Maeda, K., Colonius, T., Kreider, W., Maxwell, A.D., Bailey, M.: Quantification of the shielding of kidney stones by bubble clouds during burst wave lithotripsy. J. Acoust. Soc. Am. 141(5), 3673–3673 (2017)
Mallock, A.: The damping of sound by frothy liquids. Proc. R. Soc. London, Ser. A 84(572), 391–395 (1910)
Menter, F.R.: Two-equation eddy-viscosity turbulence models for engineering applications. AIAA Journal 32(8), 1598–1605 (1994)
Menzl, G., Gonzalez, M., Geiger, P., Caupin, F., Abascal, J., Valeriani, C., Dellago, C.: Molecular mechanism for cavitation in water under tension. Proc. Natl. Acad. Sci. 113(48), 13582–13587 (2016)
Merkle, C.L.: Computational modelling of the dynamics of sheet cavitation. In: Proceedings of the 3rd Int. Symp. on Cavitation, p 1998. Grenoble, France (1998)
Miller, S.T., Jasak, H., Boger, D.A., Paterson, E.G., Nedungadi, A.: A pressure-based, compressible, two-phase flow finite volume method for underwater explosions. Comput. Fluids 87, 132–143 (2013)
Minnaert, M.: On musical air-bubbles and the sounds of running water. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 16(104), 235–248 (1933)
Mørch, K.A.: Cavitation inception from bubble nuclei. Interface Focus 5(5), 20150006 (2015)
Nagrath, S., Jansen, K., Lahey Jr, R.T., Akhatov, I.: Hydrodynamic simulation of air bubble implosion using a level set approach. J. Comput. Phys. 215 (1), 98–132 (2006)
Nigmatulin, R.I., Khabeev, N.S., Nagiev, F.B.: Dynamics, heat and mass transfer of vapour-gas bubbles in a liquid. Int. J. Heat Mass Transfer 24(6), 1033–1044 (1981)
Obreschkow, D., Tinguely, M., Dorsaz, N., Kobel, P., De Bosset, A., Farhat, M.: Universal scaling law for jets of collapsing bubbles. Phys. Rev. Lett. 107(20), 204501 (2011)
Olsson, E., Kreiss, G.: A conservative level set method for two phase flow. J. Comput. Phys. 210(1), 225–246 (2005)
Omta, R.: Oscillations of a cloud of bubbles of small and not so small amplitude. J. Acoust. Soc. Am. 82(3), 1018–1033 (1987)
Passandideh-Fard, M., Roohi, E.: Transient simulations of cavitating flows using a modified volume-of-fluid (vof) technique. International Journal of Computational Fluid Dynamics 22(1–2), 97–114 (2008)
Pelanti, M., Shyue, K.M.: A mixture-energy-consistent six-equation two-phase numerical model for fluids with interfaces, cavitation and evaporation waves. J. Comput. Phys. 259, 331–357 (2014)
Pendar, M.R., Roohi, E.: Cavitation characteristics around a sphere: an les investigation. Int. J. Multiphase Flow 98, 1–23 (2018)
Petitpas, F., Massoni, J., Saurel, R., Lapebie, E., Munier, L.: Diffuse interface model for high speed cavitating underwater systems. Int. J. Multiphase Flow 35(8), 747–759 (2009)
Plesset, M.S.: The dynamics of cavitation bubbles. J. Appl. Mech. 16, 277–282 (1949)
Plesset, M.S., Chapman, R.B.: Collapse of an initially spherical vapour cavity in the neighbourhood of a solid boundary. J. Fluid Mech. 47(2), 283–290 (1971)
Plesset, M.S., Zwick, S.A.: The growth of vapor bubbles in superheated liquids. J. App. Phys. 25(4), 493–500 (1954)
Popinet, S., Zaleski, S.: Bubble collapse near a solid boundary: a numerical study of the influence of viscosity. J. Fluid Mech. 464, 137–163 (2002)
Preston, A.T., Colonius, T., Brennen, C.E.: A numerical investigation of unsteady bubbly cavitating nozzle flows. Phys. Fluids 14, 300 (2002)
Preston, A.T., Colonius, T., Brennen, C.E.: A reduced order model of diffusive effects on the dynamics of bubbles. Phys. Fluids 19(123302), 1–19 (2007)
Prosperetti, A.: A generalization of the Rayleigh-Plesset equation of bubble dynamics. Phys. Fluids 25(3), 409–410 (1982)
Prosperetti, A.: The speed of sound in a gas-vapour bubbly liquid. Interface Focus, 5(5) (2015)
Prosperetti, A., Lezzi, A.: Bubble dynamics in a compressible liquid. Part 1. First-order theory. J. Fluid Mech. 168, 457–478 (1986)
Rayleigh, L.: On the pressure developed in a liquid during the collapse of a spherical cavity. Phil. Mag. 34, 94 (1917)
Richards, W., Lomis, A.: J. Am. Chem. Soc. 49, 3086 (1927)
Rodríguez-Rodríguez, J., Casado-Chacón, A., Fuster, D.: Physics of beer tapping. Phys. Rev. Lett. 113(21), 214501 (2014)
Roohi, E., Pendar, M.R., Rahimi, A.: Simulation of three-dimensional cavitation behind a disk using various turbulence and mass transfer models. Appl. Math. Model. 40(1), 542–564 (2016)
Roohi, E., Zahiri, A.P., Passandideh-Fard, M.: Numerical simulation of cavitation around a two-dimensional hydrofoil using vof method and les turbulence model. Appl. Math. Model. 37(9), 6469–6488 (2013)
Rossinelli, D., Hejazialhosseini, B., Hadjidoukas, P., Bekas, C., Curioni, A., Bertsch, A., Futral, S., Schmidt, S., Adams, N., Koumoutsakos, P.: 11 pflop/S simulations of cloud cavitation collapse. In: 2013 International Conference for High Performance Computing, Networking, Storage and Analysis (SC), pp 1–13. IEEE (2013)
Saito, Y., Takami, R., Nakamori, I., Ikohagi, T.: Numerical analysis of unsteady behavior of cloud cavitation around a naca0015 foil. Comput. Mech. 40(1), 85 (2007)
Saurel, R., Abgrall, R.: A multiphase godunov method for compressible multifluid and multiphase flows. J. Comput. Phys. 150(2), 425–467 (1999)
Saurel, R., Lemetayer, O.: A multiphase model for compressible flows with interfaces, shocks, detonation waves and cavitation. J. Fluid Mech. 431, 239–271 (2001)
Saurel, R., Pantano, C.: Diffuse-interface capturing methods for compressible two-phase flows. Annu. Rev. Fluid Mech. 50(1), 105–130 (2018)
Saurel, R., Petitpas, F., Berry, R.A.: Simple and efficient relaxation methods for interfaces separating compressible fluids, cavitating flows and shocks in multiphase mixtures. J. Comput. Phys. 228(5), 1678–1712 (2009)
Schmidmayer, K., Petitpas, F., Daniel, E., Favrie, N., Gavrilyuk, S.: A model and numerical method for compressible flows with capillary effects. J. Comput. Phys. 334, 468–496 (2017)
Schnerr, G.H., Sauer, J.: Physical and numerical modeling of unsteady cavitation dynamics. In: Fourth International Conference on Multiphase Flow, New Orleans, USA, vol. 1 (2001)
Schnerr, G.H., Sezal, I.H., Schmidt, S.J.: Numerical investigation of three-dimensional cloud cavitation with special emphasis on collapse induced shock dynamics. Phys. Fluids 20(4), 040703 (2008)
Senocak, I., Shyy, W.: A pressure-based method for turbulent cavitating flow computations. J. Comput. Phys. 176(2), 363–383 (2002)
Shyue, K.M., Xiao, F.: An eulerian interface sharpening algorithm for compressible two-phase flow: the algebraic thinc approach. J. Comput. Phys. 268, 326–354 (2014)
Shyy, W., Thakur, S.S., Ouyang, H., Liu, J., Blosch, E.: Computational Techniques for Complex Transport Phenomena. Cambridge University Press, Cambridge (2005)
Singhal, A., Athavale, M.M., Li, H., Jiang, Y.: Mathematical basis and validation of the full cavitation model. J. Fluids Eng. 124(3), 617–624 (2002)
Singhal, A.K.: Multi-dimensional simulation of cavitating flows using a pdf model of phase change. In: Proceedings ASME FED Meeting, Vancouver, Canada, 1997 (1997)
Smeulders, D.M.J., Van Dongen, M.E.H.: Wave propagation in porous media containing a dilute gas–liquid mixture: theory and experiments. J. Fluid Mech. 343 (-1), 351–373 (1997)
Smith, W.R., Wang, Q.X.: Radiative decay of the nonlinear oscillations of an adiabatic spherical bubble at small mach number. J. Fluid Mech. 837, 1–18 (2018)
Sparks, R., Stephen, J.: The dynamics of bubble formation and growth in magmas: a review and analysis. J. Volcanol. Geotherm. Res. 3(1-2), 1–37 (1978)
Storey, B.D., Szeri, A.J.: Water vapour, sonoluminiscence and sonochemistry. Proc. R. Soc. Lond. A 456, 1685–1709 (2000)
Supponen, O., Obreschkow, D., Tinguely, M., Kobel, P., Dorsaz, N., Farhat, M.: Scaling laws for jets of single cavitation bubbles. J. Fluid Mech. 802, 263–293 (2016)
Tiwari, A., Freund, J.B., Pantano, C.: A diffuse interface model with immiscibility preservation. J. Comput. Phys. 252, 290–309 (2013)
Tiwari, A., Pantano, C., Freund, J.B.: Growth-and-collapse dynamics of small bubble clusters near a wall. J. Fluid Mech. 775, 1–23 (2015)
Tomar, G., Fuster, D., Zaleski, S., Popinet, S.: Multiscale simulations of primary atomization using gerris. Comp. and Fluids 39(4), 1864–1874 (2010)
Tomita, Y., Shima, A.: On the behavior of a spherical bubble and the impulse pressure in a viscous compressible liquid. JSME Bulletin 20, 1453–1460 (1977)
Tseng, C.C., Shyy, W.: Modeling for isothermal and cryogenic cavitation. Int. J. Heat Mass Transfer 53(1-3), 513–525 (2010)
Van Wijngaarden, L.: On the collective collapse of a large number of gas bubbles in water. In: Applied Mechanics, pp. 854–861. Springer (1966)
Van Wijngaarden, L.: On the equations of motion for mixtures of liquid and gas bubbles. J. Fluid Mech. 33(3), 465–474 (1968)
Venkateswaran, S., Lindau, J.W., Kunz, R.F., Merkle, C.L.: Computation of multiphase mixture flows with compressibility effects. J. Comput. Phys. 180(1), 54–77 (2002)
Vogelaar, B., Smeulders, D., Harris, J.: Exact expression for the effective acoustics of patchy-saturated rocks. Geophysics 75(4), N87 (2010)
Wang, G., Ostoja-Starzewski, M.: Large eddy simulation of a sheet/cloud cavitation on a naca0015 hydrofoil. Appl. Math. Model. 31(3), 417–447 (2007)
Wang, G., Senocak, I., Shyy, W., Ikohagi, T., Cao, S.: Dynamics of attached turbulent cavitating flows. Prog. Aerosp. Sci. 37(6), 551–581 (2001)
Wang, Q.X., Blake, R.: Non-spherical bubble dynamics in a compressible liquid. part 1. travelling acoustic wave. J. Fluid Mech. 659, 191–224 (2010)
Wang, Q.X.: Non-spherical bubble dynamics of underwater explosions in a compressible fluid. Phys. Fluids 25(7), 072104 (2013)
Wang, Q.X., Blake, J.R.: Non-spherical bubble dynamics in a compressible liquid. part 2. acoustic standing wave. J. Fluid Mech. 679, 559–581 (2011)
Watanabe, S., Hidaka, T., Horiguchi, H., Furukawa, A., Tsujimoto, Y.: Steady analysis of the thermodynamic effect of partial cavitation using the singularity method. J. Fluids Eng. 129(2), 121–127 (2007)
Wood, A.B.: Textbook of Sound. G. Bell, London (1946)
Wood, R.W., Loomis, A.L.: Xxxviii. the physical and biological effects of high-frequency sound-waves of great intensity. The London Edinburgh, and Dublin Philosophical Magazine And Journal Of Science 4(22), 417–436 (1927)
Xiao, F., Akoh, R., Ii, S.: Unified formulation for compressible and incompressible flows by using multi-integrated moments II: Multi-dimensional version for compressible and incompressible flows. J. Comput. Phys. 213(1), 31–56 (2006)
Xu, N., Apfel, R.E., Khong, A., Hu, X., Wang, L.: Water vapor diffusion effects on gas dynamics in a sonoluminescing bubble. Phys. Rev. Lett. E 68(016309), 1–7 (2003)
Yang, Y.X., Wang, Q.X., Keat, T.S.: Dynamic features of a laser-induced cavitation bubble near a solid boundary. Ultrason. Sonochem. 20(4), 1098–1103 (2013)
Yao, Z., Xian-Wu, L., Shu-Hong, L., Yu-Lin, W., Hong-Yuan, X.: A thermodynamic cavitation model for cavitating flow simulation in a wide range of water temperatures. Chin. Phys. Lett. 27(1), 016401 (2010)
Yasui, K., Tuziuti, T., Sivakumar, M., Iida, Y.: Theoretical study of single-bubble sonochemistry. J. Chem Phys. 122(224706), 1–12 (2005)
Yavas, O., Leiderer, P., Park, H.K., Grigoropoulos, C.P., Poon, C.C., Tam, A.C.: Enhanced acoustic cavitation following laser-induced bubble formation: Long-term memory effect. Phys. Rev. Lett. 72(13), 2021 (1994)
Yu, P.W., Ceccio, S.L., Tryggvason, G.: The collapse of a cavitation bubble in shear flows: a numerical study. Phys. Fluids 7(11), 2608–2616 (1995)
Zeng, Q., Gonzalez-Avila, S.R., Dijkink, R., Koukouvinis, P., Gavaises, M., Ohl, C.D.: Wall shear stress from jetting cavitation bubbles. J. Fluid Mech. 846, 341–355 (2018)
Zeravcic, Z., Lohse, D., Van Saarloos, W.: Collective oscillations in bubble clouds. J. Fluid Mech. 680, 114–149 (2011)
Zhang, D.Z., Prosperetti, A.: Averaged equations for inviscid disperse two-phase flow. J. Fluid Mech. 267, 185–219 (1994)
Zhang, D.Z., Prosperetti, A.: Ensemble phase-averaged equations for bubbly flows. Phys. Fluids 6, 2956–2970 (1994)
Zhang, Y.: A criterion for the fragmentation of bubbly magma based on brittle failure theory. Nature 402(6762), 648 (1999)
Zheng, Q., Durben, D.J., Wolf, G.H., Angell, C.A.: Liquids at large negative pressures: water at the homogeneous nucleation limit. Science 254(5033), 829 (1991)
Zhu, J., Chen, Y., Zhao, D., Zhang, X.: Extension of the Schnerr–Sauer model for cryogenic cavitation. Eur. J. Mech. B. Fluids 52, 1–10 (2015)
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The author would like to acknowledge the exchanges and support of Professor Cesar Dopazo and the useful discussions with Maurice Rossi.
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Fuster, D. A Review of Models for Bubble Clusters in Cavitating Flows. Flow Turbulence Combust 102, 497–536 (2019). https://doi.org/10.1007/s10494-018-9993-4
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DOI: https://doi.org/10.1007/s10494-018-9993-4