Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-07T20:16:54.388Z Has data issue: false hasContentIssue false

On aerodynamic droplet breakup

Published online by Cambridge University Press:  26 February 2021

Isaac M. Jackiw
Affiliation:
Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, ONM5S 3G8, Canada
Nasser Ashgriz*
Affiliation:
Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, ONM5S 3G8, Canada
*
Email address for correspondence: [email protected]

Abstract

The breakup of droplets in a high-speed air stream is investigated experimentally and theoretically. This study is based on experiments conducted by exposing pendant droplets to a high-speed air jet, which allowed for imaging of the droplets at high temporal and spatial resolutions while maintaining a large field of view to capture the breakup process. Two factors of primary importance in droplet breakup are the breakup morphology and the resulting child droplet sizes. However, benchmark models have erroneous assumptions that impede the prediction of both morphology and breakup size and give non-physical geometries. The present theoretical work focuses on the ‘internal flow’ hypothesis, which suggests that the droplet's internal flow governs its breakup. The breakup process is subdivided into four stages: droplet deformation, rim formation, rim expansion and rim breakup. The internal flow mechanism is used to mathematically model the first two stages. The rim expansion is related to the growth of bags, while its breakup is shown to be due to Rayleigh–Plateau capillary instability. It is found that the breakup morphology is related to the division of the droplet into a disk that forms on the windward face and the undeformed droplet core. The amount of the droplet volume contained in the undeformed core decides the breakup morphology. Using this framework, it is shown that a three-step calculation can give an improved prediction of child drop sizes and morphology.

Type
JFM Papers
Copyright
© The Author(s), 2021. Published by 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

REFERENCES

Aliseda, A., Hopfinger, E.J., Lasheras, J.C., Kremer, D.M., Berchielli, A. & Connolly, E.K. 2008 Atomization of viscous and non-newtonian liquids by a coaxial, high-speed gas jet. Experiments and droplet size modeling. Intl J. Multiphase Flow 34 (2), 161175.CrossRefGoogle Scholar
ANSYS Inc. 2011 ANSYS FLUENT User's Guide Release 14.0. Canonsburg, PA.Google Scholar
Ashgriz, N. 2011 Handbook of Atomization and Sprays: Theory and Applications. Springer.CrossRefGoogle Scholar
Bremond, N. & Villermaux, E. 2005 Bursting thin liquid films. J. Fluid Mech. 524, 121130.CrossRefGoogle Scholar
Chou, W.H. & Faeth, G.M. 1998 Temporal properties of secondary drop breakup in the bag breakup regime. Intl J. Multiphase Flow 24 (6), 889912.CrossRefGoogle Scholar
Dai, Z. & Faeth, G.M. 2001 Temporal properties of secondary drop breakup in the multimode breakup regime. Intl J. Multiphase Flow 27, 217236.CrossRefGoogle Scholar
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. 904, A20.CrossRefGoogle Scholar
Flock, A.K., Guildenbecher, D.R., Chen, J., Sojka, P.E. & Bauer, H.-J. 2012 Experimental statistics of droplet trajectory and air flow during aerodynamic fragmentation of liquid drops. Intl J. Multiphase Flow 47, 3749.CrossRefGoogle Scholar
Guildenbecher, D.R., López-Rivera, C. & Sojka, P.E. 2009 Secondary atomization. Exp. Fluids 46 (3), 371402.CrossRefGoogle Scholar
Hanson, A.R., Domich, E.G. & Adams, H.S. 1963 Shock tube investigation of the breakup of drops by air blasts. Phys. Fluids 6 (8), 10701080.CrossRefGoogle Scholar
Harper, E.Y., Grube, G.W. & Chang, I.-D. 1972 On the breakup of accelerating liquid drops. J. Fluid Mech. 52 (3), 565591.CrossRefGoogle Scholar
Hinze, J.O. 1955 Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes. AIChE J. 1 (3), 289295.CrossRefGoogle Scholar
Hsiang, L.P. & Faeth, G.M. 1992 Near-limit drop deformation and secondary breakup. Intl J. Multiphase Flow 18 (5), 635652.CrossRefGoogle Scholar
Ibrahim, E.A., Yang, H.Q. & Przekwas, A.J. 1993 Modeling of spray droplets deformation and breakup. J. Propul. Power 9 (4), 651654.CrossRefGoogle Scholar
Jain, M., Prakash, R.S., Tomar, G. & Ravikrishna, R.V. 2015 Secondary breakup of a drop at moderate Weber numbers. Proc. R. Soc. Lond. A 471, 20140930.Google Scholar
Jain, S.S., Tyagi, N., Prakash, R.S., Ravikrishna, R.V. & Tomar, G. 2018 Secondary breakup of drops at moderate Weber numbers: effect of Density ratio and Reynolds number. Intl J. Multiphase Flow 117, 2541.CrossRefGoogle Scholar
Jalaal, M. & Mehravaran, K. 2014 Transient growth of droplet instabilities in a stream. Phys. Fluids 26, 012101.CrossRefGoogle Scholar
Joseph, D.D., Beavers, G.S. & Funada, T. 2002 Rayleigh–Taylor instability of viscoelastic drops at high Weber numbers. J. Fluid Mech. 453, 109132.CrossRefGoogle Scholar
Keller, J.B. & Kolodner, I. 1954 Instability of liquid surfaces and the formation of drops. J. Appl. Phys. 25 (7), 918921.CrossRefGoogle Scholar
Krzeczkowski, S.A. 1980 Measurement of liquid droplet disintegration mechanisms. Intl J. Multiphase Flow 6 (3), 227239.CrossRefGoogle Scholar
Kulkarni, V. & Sojka, P.E. 2014 Bag breakup of low viscosity drops in the presence of a continuous air jet. Phys. Fluids 26, 072103.CrossRefGoogle Scholar
Lane, W.R. 1951 Shatter of drops in streams of air. Ind. Engng Chem. 43 (6), 13121317.CrossRefGoogle Scholar
Lee, M.W., Park, J.J., Farid, M.M. & Yoon, S.S. 2012 Comparison and correction of the drop breakup models for stochastic dilute spray flow. Appl. Math. Model. 36 (9), 45124520.CrossRefGoogle Scholar
Lhuissier, H. & Villermaux, E. 2012 Bursting bubble aerosols. J. Fluid Mech. 696, 544.CrossRefGoogle Scholar
Liu, A.B., Mather, D. & Reitz, R.D. 1993 Modeling the effects of drop drag and breakup on fuel sprays. SAE Tech. Paper Series 930072.CrossRefGoogle Scholar
Mashayek, A. & Ashgriz, N. 2009 Model for deformation of drops and liquid jets in gaseous crossflows. AIAA J. 47 (2), 303313.CrossRefGoogle Scholar
Meng, J.C. & Colonius, T. 2018 Numerical simulation of the aerobreakup of a water droplet. J. Fluid Mech. 835, 11081135.CrossRefGoogle Scholar
O'Rourke, P.J. & Amsden, A.A. 1987 The tab method for numerical calculation of spray droplet breakup. SAE Tech. Paper Series 872089.CrossRefGoogle Scholar
Park, J.-H., Yoon, Y. & Hwang, S.-S. 2002 Improved tab model for prediction of spray droplet deformation and breakup. Atomiz. Sprays 12, 387401.CrossRefGoogle Scholar
Pilch, M. & Erdman, C.A. 1987 Use of breakup time data and velocity history data to predict the maximum size of stable fragments for acceleration-induced breakup of a liquid drop. Intl J. Multiphase Flow 13 (6), 741757.CrossRefGoogle Scholar
Poulain, S., Villermaux, E. & Bourouiba, L. 2018 Ageing and burst of surface bubbles. J. Fluid Mech. 851, 636671.CrossRefGoogle Scholar
Pritchard, P.J. & Leylegian, J.C. 2011 Introduction to Fluid Mechanics. John Wiley and Sons.Google Scholar
Rimbert, N., Castrillon Escobar, S., Meignen, R., Hadj-Achour, M. & Gradeck, M. 2020 Spheroidal droplet deformation, oscillation and breakup in uniform outer flow. J. Fluid Mech. 904, A15.CrossRefGoogle Scholar
Schlichting, H. & Gersten, K. 2017 Boundary-Layer Theory, Springer.CrossRefGoogle Scholar
Stefanitsis, D., Strotos, G., Nikolopoulos, N., Kakaras, E. & Gavaises, M. 2019 Improved droplet breakup models for spray applications. Intl J. Heat Fluid Flow 76, 274286.CrossRefGoogle Scholar
Strotos, G., Malgarinos, I., Nikolopoulos, N. & Gavaises, M. 2016 Predicting droplet deformation and breakup for moderate Weber numbers. Intl J. Multiphase Flow 85, 96109.CrossRefGoogle Scholar
Tanner, F.X. 1997 Liquid jet atomization and droplet breakup modeling of non-evaporating diesel fuel sprays. SAE Tech. Papers 970050.CrossRefGoogle Scholar
Theofanous, T.G., Li, G.J. & Dinh, T.N. 2004 Aerobreakup in rarefied supersonic gas flows. Trans. ASME: J. Fluids Engng 126 (4), 516527.Google Scholar
Theofanous, T.G., Mitkin, V.V., Ng, C.L., Chang, C.-H., Deng, X. & Sushchikh, S. 2012 The physics of aerobreakup. II. Viscous liquids. Phys. Fluids 24, 022104.CrossRefGoogle Scholar
Varga, C.M., Lasheras, J.C. & Hopfinger, E.J. 2003 Initial breakup of a small-diameter liquid jet by a high-speed gas stream. J. Fluid Mech. 497 (497), 405434.CrossRefGoogle Scholar
Villermaux, E. & Bossa, B. 2009 Single-drop fragmentation determines size distribution of raindrops. Nat. Phys. 5 (9), 697702.CrossRefGoogle Scholar
Vledouts, A., Quinard, J., Vandenberghe, N. & Villermaux, E. 2016 Explosive fragmentation of liquid shells. J. Fluid Mech. 788, 246273.CrossRefGoogle Scholar
Xiao, F., Dianat, M. & McGuirk, J.J. 2016 A robust interface method for drop formation and breakup simulation at high density ratio using an extrapolated liquid velocity. Comput. Fluids 136, 402420.CrossRefGoogle Scholar
Yang, W., Jia, M., Che, Z., Sun, K. & Wang, T. 2017 Transitions of deformation to bag breakup and bag to bag-stamen breakup for droplets subjected to a continuous gas flow. Intl J. Heat Mass Transfer 111, 884894.CrossRefGoogle Scholar
Zhao, H., Liu, H.-F., Cao, X.-K., Li, W.-F. & Xu, J.-L. 2011 a Breakup characteristics of liquid drops in bag regime by a continuous and uniform air jet flow. Intl J. Multiphase Flow 37 (5), 530534.CrossRefGoogle Scholar
Zhao, H., Liu, H.-F., Li, W.-F. & Xu, J.-L. 2010 Morphological classification of low viscosity drop bag breakup in a continuous air jet stream. Phys. Fluids 22, 114103.CrossRefGoogle Scholar
Zhao, H., Liu, H.-F., Xu, J.-L. & Li, W.-F. 2011 b Experimental study of drop size distribution in the bag breakup regime. Ind. Engng Chem. Res. 50 (16), 97679773.CrossRefGoogle Scholar
Zhao, H., Liu, H.-F., Xu, J.-L., Li, W.-F. & Lin, K.-F. 2013 Temporal properties of secondary drop breakup in the bag-stamen breakup regime. Phys. Fluids 25, 054102.CrossRefGoogle Scholar

Jackiw and Ashgriz supplementary movie 1

Side-view of Bag breakup morphology. Experiment conditions are annotated with the elapsed non-dimensional time. In parentheses is the dimensional time in ms. Playback speed is 15 FPS.

Download Jackiw and Ashgriz supplementary movie 1(Video)
Video 1.1 MB

Jackiw and Ashgriz supplementary movie 2

End-on view of Bag breakup morphology. Experiment conditions are annotated with the elapsed non-dimensional time. In parentheses is the dimensional time in ms. Playback speed is 15 FPS.

Download Jackiw and Ashgriz supplementary movie 2(Video)
Video 895.4 KB

Jackiw and Ashgriz supplementary movie 3

Side-view of Bag & Stamen breakup morphology. Experiment conditions are annotated with the elapsed non-dimensional time. In parentheses is the dimensional time in ms. Playback speed is 15 FPS.

Download Jackiw and Ashgriz supplementary movie 3(Video)
Video 810.2 KB

Jackiw and Ashgriz supplementary movie 4

End-on view of Bag & Stamen breakup morphology. Experiment conditions are annotated with the elapsed non-dimensional time. In parentheses is the dimensional time in ms. Playback speed is 15 FPS.

Download Jackiw and Ashgriz supplementary movie 4(Video)
Video 1.1 MB

Jackiw and Ashgriz supplementary movie 5

Side-view of Multibag breakup morphology where core breaks as single bag. Experiment conditions are annotated with the elapsed non-dimensional time. In parentheses is the dimensional time in ms. Playback speed is 15 FPS.

Download Jackiw and Ashgriz supplementary movie 5(Video)
Video 755.6 KB

Jackiw and Ashgriz supplementary movie 6

End-on view of Multibag breakup morphology where core breaks as single bag. Experiment conditions are annotated with the elapsed non-dimensional time. In parentheses is the dimensional time in ms. Playback speed is 15 FPS.

Download Jackiw and Ashgriz supplementary movie 6(Video)
Video 913 KB

Jackiw and Ashgriz supplementary movie 7

Side-view of Multibag breakup morphology where core breaks as multiple bags. Experiment conditions are annotated with the elapsed non-dimensional time. In parentheses is the dimensional time in ms. Playback speed is 15 FPS.

Download Jackiw and Ashgriz supplementary movie 7(Video)
Video 665.3 KB

Jackiw and Ashgriz supplementary movie 8

End-on view of Multibag breakup morphology where core breaks as multiple bags. Experiment conditions are annotated with the elapsed non-dimensional time. In parentheses is the dimensional time in ms. Playback speed is 15 FPS.

Download Jackiw and Ashgriz supplementary movie 8(Video)
Video 1 MB

Jackiw and Ashgriz supplementary movie 9

Side-view of Sheet-Thinning breakup morphology. Experiment conditions are annotated with the elapsed non-dimensional time. In parentheses is the dimensional time in ms. Playback speed is 15 FPS.

Download Jackiw and Ashgriz supplementary movie 9(Video)
Video 371.7 KB

Jackiw and Ashgriz supplementary movie 10

End-on view of Sheet-Thinning breakup morphology. Experiment conditions are annotated with the elapsed non-dimensional time. In parentheses is the dimensional time in ms. Playback speed is 15 FPS.

Download Jackiw and Ashgriz supplementary movie 10(Video)
Video 931.4 KB
Supplementary material: File

Jackiw and Ashgriz supplementary material

Supplementary data
Download Jackiw and Ashgriz supplementary material(File)
File 40.2 KB