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Near-surface dynamics of a gas bubble collapsing above a crevice

Published online by Cambridge University Press:  21 July 2020

Theresa Trummler Open the ORCID record for Theresa Trummler [Opens in a new window] ,
Spencer H. Bryngelson Open the ORCID record for Spencer H. Bryngelson [Opens in a new window] ,
Kevin Schmidmayer Open the ORCID record for Kevin Schmidmayer [Opens in a new window] ,
Steffen J. Schmidt Open the ORCID record for Steffen J. Schmidt [Opens in a new window] ,
Tim Colonius Open the ORCID record for Tim Colonius [Opens in a new window]  and
Nikolaus A. Adams Open the ORCID record for Nikolaus A. Adams [Opens in a new window]
Theresa Trummler*
Affiliation:
Chair of Aerodynamics and Fluid Mechanics, Technical University of Munich, Boltzmannstr. 15, 85748 Garching bei München, Germany
Spencer H. Bryngelson
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology, 1200 E. California Blvd., Pasadena, CA91125, USA
Kevin Schmidmayer
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology, 1200 E. California Blvd., Pasadena, CA91125, USA
Steffen J. Schmidt
Affiliation:
Chair of Aerodynamics and Fluid Mechanics, Technical University of Munich, Boltzmannstr. 15, 85748 Garching bei München, Germany
Tim Colonius
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology, 1200 E. California Blvd., Pasadena, CA91125, USA
Nikolaus A. Adams
Affiliation:
Chair of Aerodynamics and Fluid Mechanics, Technical University of Munich, Boltzmannstr. 15, 85748 Garching bei München, Germany
*
†Email address for correspondence: [email protected]
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Abstract

The impact of a collapsing gas bubble above rigid, notched walls is considered. Such surface crevices and imperfections often function as bubble nucleation sites, and thus have a direct relation to cavitation-induced erosion and damage structures. A generic configuration is investigated numerically using a second-order accurate compressible multi-component flow solver in a two-dimensional axisymmetric coordinate system. Results show that the crevice geometry has a significant effect on the collapse dynamics, jet formation, subsequent wave dynamics and interactions. The wall-pressure distribution associated with erosion potential is a direct consequence of development and intensity of these flow phenomena.

JFM classification

Drops and Bubbles: Bubble dynamics Drops and Bubbles: Cavitation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 899 , 25 September 2020 , A16
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

REFERENCES

Beig, S. A., Aboulhasanzadeh, B. & Johnsen, E. 2018 Temperatures produced by inertially collapsing bubbles near rigid surfaces. J. Fluid Mech. 852, 105–125.CrossRefGoogle Scholar
Benjamin, T. B., Ellis, A. T. & Bowden, F. P. 1966 The collapse of cavitation bubbles and the pressures thereby produced against solid boundaries. Phil. Trans. R. Soc. Lond. A 260 (1110), 221–240.Google Scholar
Besant, W. 1859 A Treatise on Hydrostatics and Hydrodynamics. Deighton.Google Scholar
Bohner, M., Fischer, R. & Gscheidle, R. 2001 Fachkunde Kraftfahrzeugtechnik. Verlag Europa-Lehrmittel.Google Scholar
Borkent, B. M., Gekle, S., Prosperetti, A. & Lohse, D. 2009 Nucleation threshold and deactivation mechanisms of nanoscopic cavitation nuclei. Phys. Fluids 21 (10), 102003.CrossRefGoogle Scholar
Brennen, C. E. 1995 Cavitation and Bubble Dynamics. Oxford University Press.Google Scholar
Dijkink, R. & Ohl, C.-D. 2008 Laser-induced cavitation based micropump. Lab on a Chip 8 (10), 1676–1681.CrossRefGoogle ScholarPubMed
Dorschner, B., Biasiori-Poulanges, L., Schmidmayer, K., El-Rabii, H. & Colonius, T. 2020 On the formation and recurrent shedding of ligaments in droplet aerobreakup. J. Fluid Mech. (submitted); see also https://arxiv.org/abs/2003.00048.Google Scholar
Hickling, R. & Plesset, M. S. 1964 Collapse and rebound of a spherical bubble in water. Phys. Fluids 7 (1), 7–14.CrossRefGoogle Scholar
Johnsen, E. 2007 Numerical simulations of non-spherical bubble collapse. PhD thesis, California Institute of Technology.Google Scholar
Johnsen, E. & Colonius, T. 2009 Numerical simulations of non-spherical bubble collapse. J. Fluid Mech. 629, 231–262.CrossRefGoogle ScholarPubMed
Kapila, A., Menikoff, R., Bdzil, J., Son, S. & Stewart, D. 2001 Two-phase modeling of deflagration-to-detonation transition in granular materials: reduced equations. Phys. Fluids 13 (10), 3002–3024.CrossRefGoogle Scholar
Lauer, E., Hu, X. Y., Hickel, S. & Adams, N. A. 2012 Numerical modelling and investigation of symmetric and asymmetric cavitation bubble dynamics. Comput. Fluids 69, 1–19.CrossRefGoogle Scholar
Le Métayer, O., Massoni, J., Saurel, R. 2005 Modelling evaporation fronts with reactive Riemann solvers. J. Comput. Phys. 205 (2), 567–610.CrossRefGoogle Scholar
Li, S., Zhang, A-M. & Han, R. 2018 Counter-jet formation of an expanding bubble near a curved elastic boundary. Phys. Fluids 30 (12), 121703.CrossRefGoogle Scholar
Lindau, O. & Lauterborn, W. 2003 Cinematographic observation of the collapse and rebound of a laser-produced cavitation bubble near a wall. J. Fluid Mech. 479, 327–348.CrossRefGoogle Scholar
Rayleigh, Lord 1917 VIII. On the pressure developed in a liquid during the collapse of a spherical cavity. London Edinburgh Dublin Philos. Mag. J. Sci. 34 (200), 94–98.CrossRefGoogle Scholar
Meng, J. C. & Colonius, T. 2018 Numerical simulation of the aerobreakup of a water droplet. J. Fluid Mech. 835, 1108–1135.CrossRefGoogle Scholar
Ohl, C.-D., Arora, M., Dijkink, R., Janve, V. & Lohse, D. 2006 Surface cleaning from laser-induced cavitation bubbles. Appl. Phys. Lett. 89 (7), 074102.CrossRefGoogle Scholar
Philipp, A. & Lauterborn, W. 1998 Cavitation erosion by single laser-produced bubbles. J. Fluid Mech. 361, 75–116.CrossRefGoogle Scholar
Pishchalnikov, Y. A., Behnke-Parks, W. M., Schmidmayer, K., Maeda, K., Colonius, T., Kenny, T. W. & Laser, D. J. 2019 High-speed video microscopy and numerical modeling of bubble dynamics near a surface of urinary stone. J. Acoust. Soc. Am. 146 (1), 516–531.CrossRefGoogle Scholar
Pishchalnikov, Y. A., Sapozhnikov, O. A., Bailey, M. R., Williams, J. C. Jr, Cleveland, R. O., Colonius, T., Crum, L. A., Evan, A. P. & McAteer, J. A. 2003 Cavitation bubble cluster activity in the breakage of kidney stones by lithotripter shockwaves. J. Endourol. 17 (7), 435–446.CrossRefGoogle ScholarPubMed
Plesset, M. S. & Chapman, R. B. 1971 Collapse of an initially spherical vapour cavity in the neighbourhood of a solid boundary. J. Fluid Mech. 47 (2), 283–290.CrossRefGoogle Scholar
Pöhl, F., Mottyll, S., Skoda, R. & Huth, S. 2015 Evaluation of cavitation-induced pressure loads applied to material surfaces by finite-element-assisted pit analysis and numerical investigation of the elasto-plastic deformation of metallic materials. Wear 330–331, 618–628.CrossRefGoogle Scholar
Quirk, J. J. & Karni, S. 1996 On the dynamics of a shock-bubble interaction. J. Fluid Mech. 318, 129–163.CrossRefGoogle Scholar
Rasthofer, U., Wermelinger, F., Karnakov, P., Šukys, J. & Koumoutsakos, P. 2019 Computational study of the collapse of a cloud with 12 500 gas bubbles in a liquid. Phys. Rev. Fluids 4 (6), 063602.CrossRefGoogle Scholar
Reuter, F., Gonzalez-Avila, S. R., Mettin, R. & Ohl, C.-D. 2017 Flow fields and vortex dynamics of bubbles collapsing near a solid boundary. Phys. Rev. Fluids 2 (6), 51–34.CrossRefGoogle Scholar
Saurel, R., Petitpas, F. & Berry, R. A. 2009 Simple and efficient relaxation methods for interfaces separating compressible fluids, cavitating flows and shocks in multiphase mixtures. J. Comput. Phys. 228 (5), 1678–1712.CrossRefGoogle Scholar
Schmidmayer, K. 2017 Simulation de l'atomisation d'une goutte par un écoulement à grande vitesse. PhD thesis, Aix-Marseille.Google Scholar
Schmidmayer, K., Bryngelson, S. H. & Colonius, T. 2020 An assessment of multicomponent flow models and interface capturing schemes for spherical bubble dynamics. J. Comput. Phys. 402, 109080.CrossRefGoogle Scholar
Schmidmayer, K., Petitpas, F. & Daniel, E. 2019 a Adaptive mesh refinement algorithm based on dual trees for cells and faces for multiphase compressible flows. J. Comput. Phys. 388, 252–278.CrossRefGoogle Scholar
Schmidmayer, K., Petitpas, F., Daniel, E., Favrie, N. & Gavrilyuk, S. L. 2017 A model and numerical method for compressible flows with capillary effects. J. Comput. Phys. 334, 468–496.CrossRefGoogle Scholar
Schmidmayer, K., Petitpas, F., Le Martelot, S. & Daniel, E. 2019 b ECOGEN: an open-source tool for multiphase, compressible, multiphysics flows. Comput. Phys. Commun. 251, 107093.CrossRefGoogle Scholar
Shima, A. & Nakajima, K. 1977 The collapse of a non-hemispherical bubble attached to a solid wall. J. Fluid Mech. 80 (02), 369–391.CrossRefGoogle Scholar
Shima, A., Takayama, K., Tomita, Y. & Ohsawa, N. 1983 Mechanism of impact pressure generation from spark-generated bubble collapse near a wall. AIAA J. 21 (1), 55–59.CrossRefGoogle Scholar
Shima, A., Tomita, Y. & Takahashi, K. 1984 The collapse of a gas bubble near a solid wall by a shock wave and the induced impulsive pressure. Proc. Inst. Mech. Engrs 198 (2), 81–86.Google Scholar
Supponen, O., Kobel, P., Obreschkow, D. & Farhat, M. 2015 The inner world of a collapsing bubble. Phys. Fluids 27 (9), 091113.CrossRefGoogle Scholar
Supponen, O., Obreschkow, D., Kobel, P., Tinguely, M., Dorsaz, N. & Farhat, M. 2017 Shock waves from nonspherical cavitation bubbles. Phys. Rev. Fluids 2 (9), 093601.CrossRefGoogle Scholar
Supponen, O., Obreschkow, D., Tinguely, M., Kobel, P., Dorsaz, N. & Farhat, M. 2016 Scaling laws for jets of single cavitation bubbles. J. Fluid Mech. 802, 263–293.CrossRefGoogle Scholar
Tiwari, A., Freund, J. B. & Pantano, C. 2013 A diffuse interface model with immiscibility preservation. J. Comput. Phys. 252, 290–309.CrossRefGoogle ScholarPubMed
Tiwari, A., Pantano, C. & Freund, J. B. 2015 Growth-and-collapse dynamics of small bubble clusters near a wall. J. Fluid Mech. 775, 1–23.CrossRefGoogle Scholar
Tomita, Y., Robinson, P. B., Tong, R. P. & Blake, J. R. 2002 Growth and collapse of cavitation bubbles near a curved rigid boundary. J. Fluid Mech. 466, 259–283.CrossRefGoogle Scholar
Tomita, Y. & Shima, A. 1986 Mechanisms of impulsive pressure generation and damage pit formation by bubble collapse. J. Fluid Mech. 169, 535–564.CrossRefGoogle Scholar
Toro, E. F. 1997 Riemann Solvers and Numerical Methods for Fluid Dynamics. Springer.CrossRefGoogle Scholar
Trummler, T., Freytag, L., Schmidt, S. J. & Adams, N. A. 2018 Large Eddy simulation of a collapsing vapor bubble containing non-condensable gas. In Proceedings of the 10th International Symposium on Cavitation CAV (ed. Katz, J.), pp. 656–659. ASME.CrossRefGoogle Scholar
Veilleux, J. C., Maeda, K. & Colonius, T. 2018 Transient cavitation in pre-filled syringes during autoinjector actuation. In Proceedings of the 10th International Symposium on Cavitation CAV (ed. Katz, J.), pp. 1068–1073. ASME.CrossRefGoogle Scholar
Zhang, Y., Li, S., Zhang, Y. & Zhang, Y. 2018 Dynamics of the bubble near a triangular prism array. In Proceedings of the 10th International Symposium on Cavitation CAV (ed. Katz, J.), pp. 312–317. ASME.CrossRefGoogle Scholar

Trummler et al. supplementary movie 1

Movie of an air bubble collapsing onto a wall showing numerical schlieren (left) and log-scale pressure field (right). Gas volume fraction $\alpha_g$ is shown as a shaded area of decreasing opacity with decreasing $\alpha_g$ (left), while the $\alpha_g = 0.5$ isoline is shown as a solid curve (right) representing a pseudo-phase-interface. Time and pressure correspond to a bubble with $R_0 = 400\,\mathrm{\mu m}$ exposed to a driving pressure of $p_\infty=10^7\,\mathrm{Pa}$. Note that the frame rate is ten times higher at the beginning of the movie. Movie 1 shows the configuration with a smooth wall (no crevice, $R_C= 0$) and an attached bubble with the stand-off distance $S/R_0 = 0.1 $.
Download Trummler et al. supplementary movie 1(Video)
Video 1.7 MB

Trummler et al. supplementary movie 2

Smooth wall (no crevice, $R_C= 0$), attached bubble $S/R_0 = 0.35$. See caption Movie 1.

Download Trummler et al. supplementary movie 2(Video)
Video 2.1 MB

Trummler et al. supplementary movie 3

Smooth wall (no crevice, $R_C= 0$), attached bubble $S/R_0 = 0.6 $. See caption Movie 1.

Download Trummler et al. supplementary movie 3(Video)
Video 2.1 MB

Trummler et al. supplementary movie 4

Smooth wall (no crevice, $R_C= 0$), detached bubble $S/R_0 = 1.1 $. See caption Movie 1.

Download Trummler et al. supplementary movie 4(Video)
Video 2.6 MB

Trummler et al. supplementary movie 5

Small crevice ($R_C/R_0= 0.15$), attached bubble $S/R_0 = 0.1 $. See caption Movie 1.

Download Trummler et al. supplementary movie 5(Video)
Video 1.7 MB

Trummler et al. supplementary movie 6

Small crevice ($R_C/R_0= 0.15$), attached bubble $S/R_0 = 0.35$. See caption Movie 1.

Download Trummler et al. supplementary movie 6(Video)
Video 1.7 MB

Trummler et al. supplementary movie 7

Small crevice ($R_C/R_0= 0.15$), attached bubble $S/R_0 = 0.6 $. See caption Movie 1.

Download Trummler et al. supplementary movie 7(Video)
Video 1.9 MB

Trummler et al. supplementary movie 8

Small crevice ($R_C/R_0= 0.15$), detached bubble $S/R_0 = 1.1 $. See caption Movie 1.

Download Trummler et al. supplementary movie 8(Video)
Video 2.7 MB

Trummler et al. supplementary movie 9

Large crevice ($R_C/R_0= 0.75$), attached bubble $S/R_0 = 0.1 $. See caption Movie 1.

Download Trummler et al. supplementary movie 9(Video)
Video 3.3 MB

Trummler et al. supplementary movie 10

Large crevice ($R_C/R_0= 0.75$), attached bubble $S/R_0 = 0.35$. See caption Movie 1.

Download Trummler et al. supplementary movie 10(Video)
Video 3.1 MB

Trummler et al. supplementary movie 11

Large crevice ($R_C/R_0= 0.75$), attached bubble $S/R_0 = 0.6 $. See caption Movie 1.

Download Trummler et al. supplementary movie 11(Video)
Video 4.4 MB

Trummler et al. supplementary movie 12

Large crevice ($R_C/R_0= 0.75$), detached bubble $S/R_0 = 1.1 $. See caption Movie 1.

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Video 3.1 MB
Supplementary material: PDF

Trummler et al. supplementary material

Supplementary captions for movies 1-12

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PDF 78 KB