Hostname: page-component-7479d7b7d-m9pkr Total loading time: 0 Render date: 2024-07-14T12:06:12.316Z Has data issue: false hasContentIssue false

Size distribution of a drop undergoing breakup at moderate Weber numbers

Published online by Cambridge University Press:  24 March 2023

Someshwar Sanjay Ade
Affiliation:
Center for Interdisciplinary Program, Indian Institute of Technology Hyderabad, Kandi, 502 284 Sangareddy, Telangana, India
Lakshmana Dora Chandrala*
Affiliation:
Department of Mechanical and Aerospace Engineering, Indian Institute of Technology Hyderabad, Kandi, 502 284 Sangareddy, Telangana, India
Kirti Chandra Sahu*
Affiliation:
Department of Chemical Engineering, Indian Institute of Technology Hyderabad, Kandi, 502 284 Sangareddy, Telangana, India
*
Email addresses for correspondence: lchandrala@mae.iith.ac.in, ksahu@che.iith.ac.in
Email addresses for correspondence: lchandrala@mae.iith.ac.in, ksahu@che.iith.ac.in

Abstract

The size distribution of child droplets resulting from a dual-bag fragmentation of a water drop is investigated using shadowgraphy and digital in-line holography techniques. It is observed that parent drop fragmentation contributes to the atomisation of tiny child droplets, whereas core drop disintegration predominantly results in larger fragments. Despite the complexity associated with dual-bag fragmentation, we demonstrate that it exhibits a bi-modal size distribution. In contrast, the single-bag breakup undergoes a tri-modal size distribution. We employ the analytical model developed by Jackiw & Ashgriz (J. Fluid Mech., vol. 940, 2022, A17) for dual-bag fragmentation that convincingly predicts the experimentally observed droplet volume probability density. We also estimate the temporal evolution of child droplet production in order to quantitatively illustrate the decomposition into initial and core breakups. Furthermore, we confirm that the analytical model adequately predicts the droplet size distribution for a range of Weber numbers.

Type
JFM Papers
Copyright
© Indian Institute of Technology Hyderabad, India, 2023. 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

Ade, S.S., Kirar, P.K., Chandrala, L.D. & Sahu, K.C. 2023 Droplet size distribution in a swirl airstream using in-line holography technique. J. Fluid Mech. 954, A39.CrossRefGoogle Scholar
Boggavarapu, P., Ramesh, S.P., Avulapati, M.M. & Ravikrishna, R.V. 2021 Secondary breakup of water and surrogate fuels: breakup modes and resultant droplet sizes. Intl J. Multiphase Flow 145, 103816.CrossRefGoogle Scholar
Cao, X.K., Sun, Z.G., Li, W.F., Liu, H.F. & Yu, Z.H. 2007 A new breakup regime of liquid drops identified in a continuous and uniform air jet flow. Phys. Fluids 19 (5), 057103.CrossRefGoogle Scholar
Essaïdi, Z., Lauret, P., Heymes, F., Aprin, L. & Slangen, P. 2021 Aerodynamic fragmentation of water, ethanol and polyethylene glycol droplets investigated by high-speed in-line digital holography. Opt. Mater. 122, 111747.CrossRefGoogle Scholar
Gao, J., Guildenbecher, D.R., Reu, P.L., Kulkarni, V., Sojka, P.E. & Chen, J. 2013 Quantitative, three-dimensional diagnostics of multiphase drop fragmentation via digital in-line holography. Opt. Lett. 38 (11), 18931895.CrossRefGoogle ScholarPubMed
Guildenbecher, D.R., Cooper, M.A. & Sojka, P.E. 2016 High-speed (20 kHz) digital in-line holography for transient particle tracking and sizing in multiphase flows. Appl. Opt. 55 (11), 28922903.CrossRefGoogle ScholarPubMed
Guildenbecher, D.R., Gao, J., Chen, J. & Sojka, P.E. 2017 Characterization of drop aerodynamic fragmentation in the bag and sheet-thinning regimes by crossed-beam, two-view, digital in-line holography. Intl J. Multiphase Flow 94, 107122.CrossRefGoogle Scholar
Guildenbecher, D.R., López-Rivera, C. & Sojka, P.E. 2009 Secondary atomization. Exp. Fluids 46 (3), 371402.CrossRefGoogle Scholar
Jackiw, I.M. & Ashgriz, N. 2021 On aerodynamic droplet breakup. J. Fluid Mech. 913, A33.CrossRefGoogle Scholar
Jackiw, I.M. & Ashgriz, N. 2022 Prediction of the droplet size distribution in aerodynamic droplet breakup. J. Fluid Mech. 940, A17.CrossRefGoogle Scholar
Keshavarz, B., Houze, E.C., Moore, J.R., Koerner, M.R. & McKinley, G.H. 2020 Rotary atomization of Newtonian and viscoelastic liquids. Phys. Rev. Fluids 5 (3), 033601.CrossRefGoogle Scholar
Kirar, P.K., Soni, S.K., Kolhe, P.S. & Sahu, K.C. 2022 An experimental investigation of droplet morphology in swirl flow. J. Fluid Mech. 938, A6.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 (7), 072103.CrossRefGoogle Scholar
Li, J., Shen, S., Liu, J., Zhao, Y., Li, S. & Tang, C. 2022 Secondary droplet size distribution upon breakup of a sub-milimeter droplet in high speed cross flow. Intl J. Multiphase Flow 148, 103943.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
Radhakrishna, V., Shang, W., Yao, L., Chen, J. & Sojka, P.E. 2021 Experimental characterization of secondary atomization at high Ohnesorge numbers. Intl J. Multiphase Flow 138, 103591.CrossRefGoogle Scholar
Raut, B.A., Konwar, M., Murugavel, P., Kadge, D., Gurnule, D., Sayyed, I., Todekar, K., Malap, N., Bankar, S. & Prabhakaran, T. 2021 Microphysical origin of raindrop size distributions during the Indian monsoon. Geophys. Res. Lett. 48 (16), e2021GL093581.CrossRefGoogle Scholar
Shao, S., Mallery, K., Kumar, S.S. & Hong, J. 2020 Machine learning holography for 3D particle field imaging. Opt. Express 28 (3), 29872999.CrossRefGoogle ScholarPubMed
Soni, S.K., Kirar, P.K., Kolhe, P. & Sahu, K.C. 2020 Deformation and breakup of droplets in an oblique continuous air stream. Intl J. Multiphase Flow 122, 103141.CrossRefGoogle Scholar
Suryaprakash, R. & Tomar, G. 2019 Secondary breakup of drops. J. Indian Inst. Sci. 99 (1), 7791.CrossRefGoogle Scholar
Taylor, G.I. 1963 The shape and acceleration of a drop in a high speed air stream. In The Scientific Papers of G. I. Taylor (ed. G.K. Batchelor), vol. 3, pp. 457–464. Cambridge University Press.Google Scholar
Villermaux, E. 2007 Fragmentation. Annu. Rev. Fluid Mech. 39, 419446.CrossRefGoogle Scholar
Villermaux, E. & Bossa, B. 2009 Single-drop fragmentation determines size distribution of raindrops. Nat. Phys. 5 (9), 697702.CrossRefGoogle Scholar
Villermaux, E. & Eloi, F. 2011 The distribution of raindrops speeds. Geophys. Res. Lett. 38 (19), L19805.CrossRefGoogle Scholar
Wang, Y., Dandekar, R., Bustos, N., Poulain, S. & Bourouiba, L. 2018 Universal rim thickness in unsteady sheet fragmentation. Phys. Rev. Lett. 120 (20), 204503.CrossRefGoogle ScholarPubMed
Xu, Z., Wang, T. & Che, Z. 2022 Droplet breakup in airflow with strong shear effect. J. Fluid Mech. 941, A54.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 (11), 114103.CrossRefGoogle Scholar

Ade et al. Supplementary Movie 1

Transitional breakup of a water droplet at We = 11.4.

Download Ade et al. Supplementary Movie 1(Video)
Video 1.7 MB

Ade et al. Supplementary Movie 2

Single-bag breakup of a water droplet at We = 12.6.

Download Ade et al. Supplementary Movie 2(Video)
Video 1.4 MB

Ade et al. Supplementary Movie 3

Dual-bag breakup of a water droplet at We = 34.8.

Download Ade et al. Supplementary Movie 3(Video)
Video 1.1 MB

Ade et al. Supplementary Movie 4

Time-series focused holograms at We = 12.6.

Download Ade et al. Supplementary Movie 4(Video)
Video 3.1 MB

Ade et al. Supplementary Movie 5

Time-series focused holograms at We = 34.8.

Download Ade et al. Supplementary Movie 5(Video)
Video 3.1 MB