Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-26T15:27:24.189Z Has data issue: false hasContentIssue false
  • English
  • Français

Impingement of high-speed cylindrical droplets embedded with an air/vapour cavity on a rigid wall: numerical analysis

Published online by Cambridge University Press:  15 February 2019

Wangxia Wu Open the ORCID record for Wangxia Wu [Opens in a new window] ,
Bing Wang Open the ORCID record for Bing Wang [Opens in a new window]  and
Gaoming Xiang Open the ORCID record for Gaoming Xiang [Opens in a new window]
Wangxia Wu
Affiliation:
School of Aerospace Engineering, Tsinghua University, Beijing100084, China
Bing Wang*
Affiliation:
School of Aerospace Engineering, Tsinghua University, Beijing100084, China
Gaoming Xiang
Affiliation:
School of Aerospace Engineering, Tsinghua University, Beijing100084, China
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The high-speed impingement of hollow droplets embedded with a cavity has fundamental applications in various scenarios, such as in spray coating and biomedical engineering. The impingement dynamics is modulated by the wrapping medium, different from that of denser solid droplets. With air and vapour cavities, the impingement of two kinds of hollow cylindrical droplets is simulated in the present study to investigate the morphology and physical mechanisms regarding droplet and cavity dynamics. The compressible two-phase Eulerian model is used to couple with the phase transition procedure. The results detail the evolution of droplets and collapsing dynamics of the two kinds of cavities. Processes are captured in which the impinging water-hammer shock wave interacts with the cavity, and vertical liquid jets are induced to impact the embedded cavity. For the case of the air cavity, a transmitted shock wave is formed and propagates inside the cavity. The air cavities are compressively deformed and broken into a series of small cavities. Subsequently, a range of intermittent collapsing compression wavelets are generated due to the interface collapse driven by local jets. As for the vapour cavity in the saturated state, initially, once it is impacted by the impinging shock wave, it gradually shrinks accompanied by local condensation but without generation of transmitted waves. Following the first interaction between the lower and upper surfaces of the cavity, the vapour cavity undergoes continuous condensation and collapse with repeated interface fusion. The vapour cavity finally turns into liquid water blended into the surroundings, and the strong collapsing shock waves are expanded inside the droplet. The radius ratios and initial impinging speeds are chosen to analyse the variation of the collapsing time, maximum collapsing pressure and mean pressure on the rigid wall. The pressure withstood by the wall due to the collapsing cavity increases with the initial size of the cavity and initial impinging speed. The maximum local pressures in the entire fluids and the mean pressure on the wall during the collapsing of the vapour cavities are higher than those for the air cavities.

JFM classification

Drops and Bubbles: Cavitation Drops and Bubbles: Drops Multiphase and Particle-laden Flows: Gas/liquid flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 864 , 10 April 2019 , pp. 1058 - 1087
Check for updates
Copyright
© 2019 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ball, G. J., Howell, B. P., Leighton, T. G. & Schofield, M. J. 2000 Shock-induced collapse of a cylindrical air cavity in water: a free-Lagrange simulation. Shock Waves 10 (4), 265–276.Google Scholar
Betney, M. R., Tully, B., Hawker, N. A. & Ventikos, Y. 2015 Computational modelling of the interaction of shock waves with multiple gas-filled bubbles in a liquid. Phys. Fluids 27 (3), 036101.Google Scholar
Bourne, N. K. & Field, J. E. 1992 Shock-induced collapse of single cavities in liquids. J. Fluid Mech. 244, 225–240.Google Scholar
Brennen, C. E. 2013 Cavitation and Bubble Dynamics. Cambridge University Press.Google Scholar
Camus, J. J.1971 High speed flow in impact and its effect on solid surfaces. PhD thesis, University of Cambridge.Google Scholar
Chizhov, A. V. & Schmidt, A. A. 2000 Impact of a high-velocity drop on an obstacle. Tech. Phys. 45 (12), 1529–1537.Google Scholar
Cleveland, R. O. & McAteer, J. A. 2012 The physics of shock wave lithotripsy. In Smith’s Textbook on Endourology, 3rd edn. Wiley-Blackwell.Google Scholar
Cook, S. S. 1928 Erosion by water-hammer. Proc. R. Soc. Lond. A 119 (783), 481–488.Google Scholar
Coralic, V. & Colonius, T. 2014 Finite-volume WENO scheme for viscous compressible multicomponent flows. J. Comput. Phys. 274, 95–121.Google Scholar
Field, J. E., Dear, J. P. & Ogren, J. E. 1989 The effects of target compliance on liquid drop impact. J. Appl. Phys. 65 (2), 533–540.Google Scholar
Field, J. E., Lesser, M. B. & Dear, J. P. 1985 Studies of two-dimensional liquid-wedge impact and their relevance to liquid-drop impact problems. Proc. R. Soc. Lond. A 401, 225–249.Google Scholar
Franc, J. P. & Michel, J. M. 2006 Fundamentals of Cavitation, vol. 76. Springer Science & Business Media.Google Scholar
Gottlieb, S. & Shu, C. W. 1998 Total variation diminishing Runge–Kutta schemes. Math. Comput. Am. Math. Soc. 67 (221), 73–85.Google Scholar
Gulyaev, I. 2015 Experience in plasma production of hollow ceramic microspheres with required wall thickness. Ceram. Int. 41 (1), 101–107.Google Scholar
Gulyaev, I. P. & Solonenko, O. P. 2013 Hollow droplets impacting onto a solid surface. Exp. Fluids 54 (1), 1–12.Google Scholar
Gulyaev, I. P., Solonenko, O. P., Gulyaev, P. Y. & Smirnov, A. V. 2009 Hydrodynamic features of the impact of a hollow spherical drop on a flat surface. Tech. Phys. Lett. 35 (10), 885–888.Google Scholar
Haller, K. K., Poulikakos, D., Ventikos, Y. & Monkewitz, P. 2003 Shock wave formation in droplet impact on a rigid surface: lateral liquid motion and multiple wave structure in the contact line region. J. Fluid Mech. 490, 1–14.Google Scholar
Haller, K. K., Ventikos, Y., Poulikakos, D. & Monkewitz, P. 2002 Computational study of high-speed liquid droplet impact. J. Appl. Phys. 92 (5), 2821–2828.Google Scholar
Han, E., Hantke, M. & Müller, S. 2017 Efficient and robust relaxation procedures for multi-component mixtures including phase transition. J. Comput. Phys. 338, 217–239.Google Scholar
Hawker, N. A. & Ventikos, Y. 2012 Interaction of a strong shockwave with a gas bubble in a liquid medium: a numerical study. J. Fluid Mech. 701, 59–97.Google Scholar
Heymann, F. J. 1969 High-speed impact between a liquid drop and a solid surface. J. Appl. Phys. 40 (13), 5113–5122.Google Scholar
Ilinskii, Y. A., Zabolotskaya, E. A., Hay, T. A. & Hamilton, M. F. 2012 Models of cylindrical bubble pulsation. J. Acoust. Soc. Am. 132 (3), 1346–1357.Google Scholar
Jamaluddin, A. R., Ball, G. J., Turangan, C. K. & Leighton, T. G. 2011 The collapse of single bubbles and approximation of the far-field acoustic emissions for cavitation induced by shock wave lithotripsy. J. Fluid Mech. 677, 305–341.Google Scholar
Johnsen, E. & Colonius, T. 2006 Implementation of WENO schemes in compressible multicomponent flow problems. J. Comput. Phys. 219 (2), 715–732.Google Scholar
Johnsen, E. & Colonius, T. 2009 Numerical simulations of non-spherical bubble collapse. J. Fluid Mech. 629, 231–262.Google Scholar
Klinkov, S. V., Kosarev, V. F. & Rein, M. 2005 Cold spray deposition: significance of particle impact phenomena. Aerosp. Sci. Technol. 9 (7), 582–591.Google Scholar
Kondo, T. & Ando, K. 2016 One-way-coupling simulation of cavitation accompanied by high-speed droplet impact. Phys. Fluids 28 (3), 033303.Google Scholar
Kumar, A., Gu, S. & Kamnis, S. 2012 Simulation of impact of a hollow droplet on a flat surface. Appl. Phys. A 109 (1), 101–109.Google Scholar
Kumar, A., Gu, S., Tabbara, H. & Kamnis, S. 2013 Study of impingement of hollow ZrO2 droplets onto a substrate. Surf. Coat. Technol. 220, 164–169.Google Scholar
Lauer, E., Hu, X. Y., Hickel, S. & Adams, N. A. 2012 Numerical investigation of collapsing cavity arrays. Phys. Fluids 24 (5), 052104.Google Scholar
Lesser, M. B. 1981 Analytic solutions of liquid-drop impact problems. Proc. R. Soc. Lond. A 377, 289–308.Google Scholar
Li, W. Y., Liao, H., Li, C. J., Li, G., Coddet, C. & Wang, X. 2006 On high velocity impact of micro-sized metallic particles in cold spraying. Appl. Surf. Sci. 253 (5), 2852–2862.Google Scholar
Lohse, D., Bergmann, R., Mikkelsen, R., Zeilstra, C., van der Meer, D., Versluis, M., van der Weele, K., van der Hoef, M. & Kuipers, H. 2004 Impact on soft sand: void collapse and jet formation. Phys. Rev. Lett. 93 (19), 198003.Google Scholar
Magaletti, F., Gallo, M., Marino, L. & Casciola, C. M. 2016 Shock-induced collapse of a vapor nanobubble near solid boundaries. Intl J. Multiphase Flow 84, 34–45.Google Scholar
Mandre, S., Mani, M. & Brenner, M. P. 2009 Precursors to splashing of liquid droplets on a solid surface. Rev. Mod. Phys. 102 (13), 134502.Google Scholar
Menikoff, R. & Plohr, B. J. 1989 The Riemann problem for fluid flow of real materials. Rev. Mod. Phys. 61 (1), 75–130.Google Scholar
Mountford, P. A., Thomas, A. N. & Borden, M. A. 2015 Thermal activation of superheated lipid-coated perfluorocarbon drops. Langmuir 31 (16), 4627–4634.Google Scholar
Niu, Y. Y. & Wang, H. W. 2016 Simulations of the shock waves and cavitation bubbles during a three-dimensional high-speed droplet impingement based on a two-fluid model. Comput. Fluids 134, 196–214.Google Scholar
Obreschkow, D., Dorsaz, N., Kobel, P., de Bosset, A., Tinguely, M., Field, J. & Farhat, M. 2011 Confined shocks inside isolated liquid volumes: a new path of erosion?. Phys. Fluids 23 (10), 101702.Google Scholar
Ohl, C. D., Arora, M., Ikink, R., De Jong, N., Versluis, M., Delius, M. & Lohse, D. 2006 Sonoporation from jetting cavitation bubbles. Biophys. J. 91 (11), 4285–4295.Google Scholar
Quinto-Su, P. A., Lim, K. Y. & Ohl, C. D. 2009 Cavitation bubble dynamics in microfluidic gaps of variable height. Phys. Rev. E 80 (4), 047301.Google Scholar
Quinto-Su, P. A. & Ohl, C. D. 2009 Interaction between two laser-induced cavitation bubbles in a quasi-two-dimensional geometry. J. Fluid Mech. 633, 425–435.Google Scholar
Rapoport, N. 2016 Drug-loaded perfluorocarbon nanodroplets for ultrasound-mediated drug delivery. In Therapeutic Ultrasound, pp. 221–241. Springer.Google Scholar
Rayleigh, L. 1917 On the pressure developed in a liquid during the collapse of a spherical cavity. Phil. Mag. Ser. 6 34, 94–98.Google Scholar
Rein, M. 1993 Phenomena of liquid drop impact on solid and liquid surfaces. Fluid Dyn. Res. 12 (2), 61–93.Google Scholar
Rioboo, R., Marengo, M. & Tropea, C. 2002 Time evolution of liquid drop impact onto solid, dry surfaces. Exp. Fluids 33 (1), 112–124.Google Scholar
Rousseau, F., Fourmond, C., Prima, F., Serif, M. H. V., Lavigne, O., Morvan, D. & Chereau, P. 2011 Deposition of thick and 50 % porous YpSZ layer by spraying nitrate solution in a low pressure plasma reactor. Surf. Coat. Technol. 206 (7), 1621–1627.Google Scholar
Sanada, T., Ando, K. & Colonius, T. 2011 A computational study of high-speed droplet impact. Fluid Dyn. Mater. Process. 7 (4), 329–340.Google Scholar
Sanada, T., Watanabe, M., Shirota, M., Yamase, M. & Saito, T. 2008 Impact of high-speed steam-droplet spray on solid surface. Fluid Dyn. Res. 40 (7), 627–636.Google Scholar
Sankin, G. N., Simmons, W. N., Zhu, S. L. & Zhong, P. 2005 Shock wave interaction with laser-generated single bubbles. Phys. Rev. Lett. 95 (3), 034501.Google Scholar
Saurel, R. & Abgrall, R. 1999 A multiphase Godunov method for compressible multifluid and multiphase flows. J. Comput. Phys. 150 (2), 425–467.Google Scholar
Saurel, R., Petitpas, F. & Abgrall, R. 2008 Modelling phase transition in metastable liquids: application to cavitating and flashing flows. J. Fluid Mech. 607, 313–350.Google Scholar
Sheeran, P. S., Daghighi, Y., Yoo, K., Williams, R., Cherin, E., Foster, F. S. & Burns, P. N. 2016 Image-guided ultrasound characterization of volatile sub-micron phase-shift droplets in the 20–40 MHz frequency range. Ultrasound Med. Biol. 42 (3), 795–807.Google Scholar
Sheeran, P. S., Luois, S., Dayton, P. A. & Matsunaga, T. O. 2011 Formulation and acoustic studies of a new phase-shift agent for diagnostic and therapeutic ultrasound. Langmuir 27 (17), 10412–10420.Google 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.Google 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 C 198 (2), 81–86.Google Scholar
Solonenko, O. P., Gulyaev, I. P. & Smirnov, A. V. 2008 Plasma processing and deposition of powdered metal oxides consisting of hollow spherical particles. Tech. Phys. Lett. 34 (12), 1050–1052.Google Scholar
Solonenko, O. P., Nishiyama, H., Smirnov, A. V., Takana, H. & Jang, J. 2015 Visualization of arc and plasma flow patterns for advanced material processing. J. Vis. 18 (1), 1–15.Google Scholar
Stewart, M. P., Langer, R. & Jensen, K. F. 2018 Intracellular delivery by membrane disruption: mechanisms, strategies, and concepts. Chem. Rev. 118 (16), 7409–7531.Google Scholar
Thompson, P. A. 1988 Compressible-fluid Dynamics. Maple Press Company.Google Scholar
Toro, E. F. 2013 Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction. Springer Science & Business Media.Google Scholar
Turangan, C. K., Jamaluddin, A. R., Ball, G. J. & Leighton, T. G. 2008 Free-Lagrange simulations of the expansion and jetting collapse of air bubbles in water. J. Fluid Mech. 598, 1–25.Google Scholar
Wang, B., Xiang, G. M. & Hu, X. Y. 2018 An incremental-stencil WENO reconstruction for simulation of compressible two-phase flows. Intl J. Multiphase Flow 104, 20–31.Google Scholar
Wang, C. H., Kang, S. T., Lee, Y. H., Luo, Y. L., Huang, Y. F. & Yeh, C. K. 2012 Aptamer-conjugated and drug-loaded acoustic droplets for ultrasound theranosis. Biomaterials 33 (6), 1939–1947.Google Scholar
Wu, W. X., Xiang, G. M. & Wang, B. 2018 On high-speed impingement of cylindrical droplets upon solid wall considering cavitation effects. J. Fluid Mech. 857, 851–877.Google Scholar
Xiong, J., Koshizuka, S. & Sakai, M. 2010 Numerical analysis of droplet impingement using the moving particle semi-implicit method. J. Nucl. Sci. Technol. 47 (3), 314–321.Google Scholar
Xiong, J., Koshizuka, S. & Sakai, M. 2011 Investigation of droplet impingement onto wet walls based on simulation using particle method. J. Nucl. Sci. Technol. 48 (1), 145–153.Google Scholar
Xiong, J., Koshizuka, S., Sakai, M. & Ohshima, H. 2012 Investigation on droplet impingement erosion during steam generator tube failure accident. Nucl. Engng Des. 249, 132–139.Google Scholar
Yarin, A. L. 2006 Drop impact dynamics: splashing, spreading, receding, bouncing. Annu. Rev. Fluid Mech. 38, 159–192.Google Scholar
Zein, A., Hantke, M. & Warnecke, G. 2010 Modeling phase transition for compressible two-phase flows applied to metastable liquids. J. Comput. Phys. 229 (8), 2964–2998.Google Scholar
Zein, A., Hantke, M. & Warnecke, G. 2013 On the modeling and simulation of a laser-induced cavitation bubble. Intl J. Numer. Methods Fluids 73 (2), 172–203.Google Scholar