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Droplet size distribution in a swirl airstream using in-line holography technique

Published online by Cambridge University Press:  06 January 2023

Someshwar Sanjay Ade ,
Pavan Kumar Kirar ,
Lakshmana Dora Chandrala Open the ORCID record for Lakshmana Dora Chandrala [Opens in a new window]  and
Kirti Chandra Sahu Open the ORCID record for Kirti Chandra Sahu [Opens in a new window]
Someshwar Sanjay Ade
Affiliation:
Center for Interdisciplinary Program, Indian Institute of Technology Hyderabad, Kandi, Sangareddy 502 284, Telangana, India
Pavan Kumar Kirar
Affiliation:
Department of Chemical Engineering, Indian Institute of Technology Hyderabad, Kandi, Sangareddy 502 284, Telangana, India
Lakshmana Dora Chandrala*
Affiliation:
Department of Mechanical and Aerospace Engineering, Indian Institute of Technology Hyderabad, Kandi, Sangareddy 502 284, Telangana, India
Kirti Chandra Sahu*
Affiliation:
Department of Chemical Engineering, Indian Institute of Technology Hyderabad, Kandi, Sangareddy 502 284, Telangana, India
*
†Email addresses for correspondence: [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected]
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Abstract

We investigate the morphology and size distribution of satellite droplets resulting from the interaction of a freely falling water droplet with a swirling airstream of different strengths by employing shadowgraphy and deep-learning-based digital in-line holography techniques. We found that the droplet exhibits vibrational, retracting bag and normal breakup phenomena for the no swirl, low and high swirl strengths for the same aerodynamic field. In the high-swirl scenario, the disintegrations of the nodes, rim and bag-film contribute to the number mean diameter, resulting in smaller satellite droplets. In contrast, in the low-swirl case, the breakup of the rim and nodes only contributes to the size distribution, resulting in larger droplets. The temporal variation of the Sauter mean diameter reveals that for a given aerodynamic force, a high swirl strength produces more surface area and surface energy than a low swirl strength. The theoretical prediction of the number-mean probability density of tiny satellite droplets under swirl conditions agrees with experimental data. However, for the low swirl, the predictions differ from the experimental results, particularly due to the presence of large satellite droplets. Our results reveal that the volume-weighted droplet size distribution exhibits two (bi-modal) and three (multi-model) peaks for low and high swirl strengths, respectively. The analytical model that takes into account various mechanisms, such as the nodes, rim and bag breakups, accurately predicts the shape and characteristic sizes of each mode for the case of high swirl strength.

JFM classification

Drops and Bubbles: Breakup/coalescence Drops and Bubbles: Drops
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 954 , 10 January 2023 , A39
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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References

REFERENCES

Agrawal, M., Katiyar, R.K., Karri, B. & Sahu, K.C. 2020 Experimental investigation of a nonspherical water droplet falling in air. Phys. Fluids 32 (11), 112105.CrossRefGoogle Scholar
Agrawal, M., Premlata, A.R., Tripathi, M.K., Karri, B. & Sahu, K.C. 2017 Nonspherical liquid droplet falling in air. Phys. Rev. E 95 (3), 033111.CrossRefGoogle ScholarPubMed
Apte, S.V., Mahesh, K., Gorokhovski, M. & Moin, P. 2009 Stochastic modeling of atomizing spray in a complex swirl injector using large eddy simulation. Proc. Combust. Inst. 32 (2), 2257–2266.CrossRefGoogle Scholar
Balla, M., Tripathi, M.K. & Sahu, K.C. 2019 Shape oscillations of a nonspherical water droplet. Phys. Rev. E 99 (2), 023107.CrossRefGoogle ScholarPubMed
Beér, J.M. 1974 Combustion aerodynamics. In Combustion Technology (ed. H.B. Palmer & J.M. Beér), pp. 61–89. Elsevier.CrossRefGoogle Scholar
Bentley, W.A. 1904 Studies of raindrops and raindrop phenomena. Mon. Weath. Rev. 32, 450–456.Google Scholar
Berg, M.J. 2022 Tutorial: aerosol characterization with digital in-line holography. J. Aerosol Sci. 165, 106023.CrossRefGoogle Scholar
Candel, S., Durox, D., Schuller, T., Bourgouin, J.F. & Moeck, J.P. 2014 Dynamics of swirling flames. Annu. Rev. Fluid Mech. 46, 147–173.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
Chaitanya, G.S., Sahu, K.C. & Biswas, G. 2021 A study of two unequal-sized droplets undergoing oblique collision. Phys. Fluids 33 (2), 022110.CrossRefGoogle Scholar
Dai, Z. & Faeth, G.M. 2001 Temporal properties of secondary drop breakup in the multimode breakup regime. Intl J. Multiphase Flow 27 (2), 217–236.CrossRefGoogle Scholar
Falk, T., et al. 2019 U-Net: deep learning for cell counting, detection, and morphometry. Nat. Meth. 16 (1), 67–70.CrossRefGoogle ScholarPubMed
Gao, J., Guildenbecher, D.R., Reu, P.L. & Chen, J. 2013 a Uncertainty characterization of particle depth measurement using digital in-line holography and the hybrid method. Opt. Express 21 (22), 26432–26449.CrossRefGoogle ScholarPubMed
Gao, J., Guildenbecher, D.R., Reu, P.L., Kulkarni, V., Sojka, P.E. & Chen, J. 2013 b Quantitative, three-dimensional diagnostics of multiphase drop fragmentation via digital in-line holography. Opt. Lett. 38 (11), 1893–1895.CrossRefGoogle ScholarPubMed
Gao, P., Wang, J., Gao, Y., Liu, J. & Hua, D. 2022 Observation on the droplet ranging from 2 to 16 $\mathrm {\mu }$m in cloud droplet size distribution based on digital holography. Remote Sens. 14 (10), 2414.CrossRefGoogle Scholar
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, 107–122.CrossRefGoogle Scholar
Guildenbecher, D.R., Gao, J., Reu, P.L. & Chen, J. 2013 Digital holography simulations and experiments to quantify the accuracy of 3d particle location and 2d sizing using a proposed hybrid method. Appl. Opt. 52 (16), 3790–3801.CrossRefGoogle ScholarPubMed
Guildenbecher, D.R., López-Rivera, C. & Sojka, P.E. 2009 Secondary atomization. Exp. Fluids 46 (3), 371–402.CrossRefGoogle Scholar
Haan, F.L. Jr., Sarkar, P.P., Kopp, G.A. & Stedman, D.A. 2017 Critical wind speeds for tornado-induced vehicle movements. J. Wind Engng Ind. Aerodyn. 168, 1–8.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), 1070–1080.CrossRefGoogle Scholar
Hsiang, L.P. & Faeth, G.M. 1993 Drop properties after secondary breakup. Intl J. Multiphase Flow 19 (5), 721–735.CrossRefGoogle Scholar
Ibtehaz, N. & Rahman, M.S. 2020 MultiResUNet: rethinking the U-Net architecture for multimodal biomedical image segmentation. Neural Netw. 121, 74–87.CrossRefGoogle ScholarPubMed
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
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 (2177), 20140930.Google Scholar
Katz, J. & Sheng, J. 2010 Applications of holography in fluid mechanics and particle dynamics. Annu. Rev. Fluid Mech. 42 (1), 531–555.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
Kostinski, A.B. & Shaw, R.A. 2009 Raindrops large and small. Nat. Phys. 5 (9), 624–625.CrossRefGoogle Scholar
Krzeczkowski, S.A. 1980 Measurement of liquid droplet disintegration mechanisms. Intl J. Multiphase Flow 6 (3), 227–239.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
Kumar, S.S., Li, C., Christen, C.E., Hogan, C.J. Jr., Fredericks, S.A. & Hong, J. 2019 Automated droplet size distribution measurements using digital inline holography. J. Aerosol Sci. 137, 105442.CrossRefGoogle Scholar
Kumar, A. & Sahu, S. 2019 Large scale instabilities in coaxial air-water jets with annular air swirl. Phys. Fluids 31 (12), 124103.CrossRefGoogle Scholar
von Lenard, P. 1904 Über regen. Meteorol. Z 6 (249), 92–62.Google Scholar
Lewellen, D.C., Lewellen, W.S. & Xia, J. 2000 The influence of a local swirl ratio on tornado intensification near the surface. J. Atmos. Sci. 57 (4), 527–544.2.0.CO;2>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
Marcotte, F. & Zaleski, S. 2019 Density contrast matters for drop fragmentation thresholds at low Ohnesorge number. Phys. Rev. Fluids 4 (10), 103604.CrossRefGoogle Scholar
Marmottant, P. & Villermaux, E. 2004 On spray formation. J. Fluid Mech. 498, 73–111.CrossRefGoogle Scholar
Marshall, J.S. & Palmer, W.M. 1948 The distribution of raindrops with size. J. Meteorol. 5, 165–166.2.0.CO;2>CrossRefGoogle Scholar
Merkle, K., Haessler, H., Büchner, H. & Zarzalis, N. 2003 Effect of co-and counter-swirl on the isothermal flow-and mixture-field of an airblast atomizer nozzle. Intl J. Heat Fluid Flow 24 (4), 529–537.CrossRefGoogle Scholar
Patil, S. & Sahu, S. 2021 Air swirl effect on spray characteristics and droplet dispersion in a twin-jet crossflow airblast injector. Phys. Fluids 33 (7), 073314.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), 741–757.CrossRefGoogle Scholar
Rajamanickam, K. & Basu, S. 2017 On the dynamics of vortex–droplet interactions, dispersion and breakup in a coaxial swirling flow. J. Fluid Mech. 827, 572–613.CrossRefGoogle Scholar
Ronneberger, O., Fischer, P. & Brox, T. 2015 U-net: Convolutional networks for biomedical image segmentation. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (ed. N. Navab, J. Hornegger, W. Wells & A. Frangi), vol. 9351, pp. 234–241. Springer.CrossRefGoogle Scholar
Schlottke, J. & Weigand, B. 2008 Direct numerical simulation of evaporating droplets. J. Comput. Phys. 227 (10), 5215–5237.CrossRefGoogle Scholar
Shanmugadas, K.P., Chakravarthy, S.R., Chiranthan, R.N., Sekar, J. & Krishnaswami, S. 2018 Characterization of wall filming and atomization inside a gas-turbine swirl injector. Exp. Fluids 59 (10), 151.CrossRefGoogle Scholar
Shao, C., Luo, K., Chai, M. & Fan, J. 2018 Sheet, ligament and droplet formation in swirling primary atomization. AIP Adv. 8 (4), 045211.CrossRefGoogle Scholar
Shao, S., Mallery, K., Kumar, S.S. & Hong, J. 2020 Machine learning holography for 3d particle field imaging. Opt. Express 28 (3), 2987–2999.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
Soni, S.K. & Kolhe, P.S. 2021 Liquid jet breakup and spray formation with annular swirl air. Intl J. Multiphase Flow 134, 103474.CrossRefGoogle Scholar
Srivastava, R.C. 1971 Size distribution of raindrops generated by their breakup and coalescence. J. Atmos. Sci. 28 (3), 410–415.2.0.CO;2>CrossRefGoogle Scholar
Suryaprakash, R. & Tomar, G. 2019 Secondary breakup of drops. J. Indian I. Sci. 99 (1), 77–91.CrossRefGoogle Scholar
Szakall, M., Diehl, K., Mitra, S.K. & Borrmann, S. 2009 A wind tunnel study on the shape, oscillation, and internal circulation of large raindrops with sizes between 2.5 and 7.5 mm. J. Atmos. Sci. 66 (3), 755–765.CrossRefGoogle Scholar
Taylor, G.I. 1963 The shape and acceleration of a drop in a high speed air stream. Sci. Pap. GI Taylor 3, 457–464.Google Scholar
Villermaux, E. 2007 Fragmentation. Annu. Rev. Fluid Mech. 39, 419–446.CrossRefGoogle Scholar
Villermaux, E. & Bossa, B. 2009 Single-drop fragmentation determines size distribution of raindrops. Nat. Phys. 5 (9), 697–702.CrossRefGoogle Scholar
Villermaux, E. & Eloi, F. 2011 The distribution of raindrops speeds. Geophys. Res. Lett. 38 (19), L19805.CrossRefGoogle Scholar
Wang, C., Chang, S., Wu, H. & Xu, J. 2014 Modeling of drop breakup in the bag breakup regime. Appl. Phys. Lett. 104 (15), 154107.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
Wierzba, A. 1990 Deformation and breakup of liquid drops in a gas stream at nearly critical Weber numbers. Exp. Fluids 9 (1–2), 59–64.CrossRefGoogle Scholar
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

The animation depicts different holography reconstructed planes at different depths. This corresponds to figure 3.

Download Ade et al. Supplementary Movie 1(Video)
Video 4.9 MB

Ade et al. Supplementary Movie 2

The vibrational breakup mode in Figure 5 (Sw = 0).

Download Ade et al. Supplementary Movie 2(Video)
Video 10.4 MB

Ade et al. Supplementary Movie 3

The retracting bag breakup mode in Figure 5 (Sw = 0:47).

Download Ade et al. Supplementary Movie 3(Video)
Video 8 MB

Ade et al. Supplementary Movie 4

The bag breakup mode in Figure 5 (Sw = 0:82).

Download Ade et al. Supplementary Movie 4(Video)
Video 7.8 MB
Supplementary material: PDF

Ade et al. Supplementary Material

Ade et al. Supplementary Material

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