Geodesic
On the influence of droplet size on the breakup induction period in the flow behind a shock wave
Sibirskij žurnal industrialʹnoj matematiki, Tome 27 (2024) no. 3, pp. 165-176 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper, we computationally study the influence of the initial diameter of a water droplet on the dynamics and breakup induction period in the flow behind a passing shock wave. For this purpose, a series of calculations were performed for a fixed Weber number $\text{We} = 400$ and a variable initial diameter $d = 1.4, 2.8, 5.6$ mm of the water droplet. The numerical technique is based on the VOF method, the LES model is used to take into account turbulence, and the technology of adapted dynamic grids is used to describe the behavior of the interfacial boundary at main turbulent scales; this has made it possible to resolve secondary water droplets up to 20 $\mu$m in size. The droplet shape, the flow structure near and in the droplet wake, and the nature of mass entrainment were investigated. As a result of the calculations, the dependences of the breakup time on the dimensionless droplet diameter were obtained, the breakup induction time was determined, and the time constant of droplet interaction with the flow was calculated to estimate the droplet breakup lag.
Keywords: mathematical modeling, VOF method, LES model, dynamic grid, shock wave, aerodynamic droplet breakup, breakup induction time. 
@article{SJIM_2024_27_3_a11,
     author = {A. A. Shebeleva and A. V. Minakov and S. V. Poplavski and V. M. Boyko},
     title = {On the influence of droplet size on the breakup induction period in the flow behind a shock wave},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {165--176},
     year = {2024},
     volume = {27},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2024_27_3_a11/}
}
TY  - JOUR
AU  - A. A. Shebeleva
AU  - A. V. Minakov
AU  - S. V. Poplavski
AU  - V. M. Boyko
TI  - On the influence of droplet size on the breakup induction period in the flow behind a shock wave
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2024
SP  - 165
EP  - 176
VL  - 27
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/SJIM_2024_27_3_a11/
LA  - ru
ID  - SJIM_2024_27_3_a11
ER  - 
%0 Journal Article
%A A. A. Shebeleva
%A A. V. Minakov
%A S. V. Poplavski
%A V. M. Boyko
%T On the influence of droplet size on the breakup induction period in the flow behind a shock wave
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2024
%P 165-176
%V 27
%N 3
%U http://geodesic.mathdoc.fr/item/SJIM_2024_27_3_a11/
%G ru
%F SJIM_2024_27_3_a11
A. A. Shebeleva; A. V. Minakov; S. V. Poplavski; V. M. Boyko. On the influence of droplet size on the breakup induction period in the flow behind a shock wave. Sibirskij žurnal industrialʹnoj matematiki, Tome 27 (2024) no. 3, pp. 165-176. http://geodesic.mathdoc.fr/item/SJIM_2024_27_3_a11/

[1] Villermaux E., “Fragmentation”, Annu. Rev. Fluid Mech., 39 (2007), 419–446 | DOI | MR | Zbl

[2] Nicholls J. A., Ranger A. A., “Aerodynamic shattering of liquid drops”, AIAA J., 7 (1989), 285–290 | DOI

[3] Benjamin M. A., Jensen R. J., Arienti M., “Review of atomization: Current knowledge and future requirements for propulsion combustors”, At. Sprays, 20 (2010), 485–512 | DOI

[4] B. E. Gel'fand, S. A. Gubin, and S. M. Kogarko, “Types of droplet fragmentation in shock waves and their characteristics”, Inzh.-Fiz. Zh., 27:1 (1974), 119–126 (in Russian)

[5] V. M. Boiko, A. N. Papyrin, and S. V. Poplavskii, “Dynamics of droplet breakup in shock waves”, J. Appl. Mech. Tech. Phys., 28:2 (1987), 263–269 | DOI

[6] B. E. Gel'fand, S. A. Gubin, E. N. Timofeev, and S. M. Sheparnev, “Breakup of a liquid drop aggregate in shock waves”, J. Appl. Mech. Tech. Phys., 19:6 (1978), 742–746 | DOI

[7] Boiko V. M., Lotov V. V., Papyrin A. N., “Ignition of Liquid Fuel Drops in Shock Waves”, Prog. Astron. Aeronaut., 132 (1991), 205–219

[8] B. E. Gel'fand, V. N. Kramarenko, and V. S. Solov'ev, “State of the art and tasks of research into detonation in the liquid-droplet-gas system”, Coll. Detonation, 1977, 28–39 (in Russian)

[9] Dinh T. N., Li G. J., Theofanous T. G., “An Investigation of Droplet Breakup in a High Mach, Low Weber Number Regime”, Proc. 41st AIAA Aerosp. Sci. Meet. Exhibit., 2003, 30–35

[10] V. M. Boiko and S. V. Poplavskii, “Particle and drop dynamics in the flow behind a shock wave”, Fluid Dyn., 42 (2007), 433–441 | DOI | Zbl

[11] Ranger A. A., Nicholls J. A., “Shape and surrounding flowfield of a drop in a high-speed gas stream”, AIAA J., 8:9 (1970), 7120–1722 | DOI

[12] V. M. Boiko and S. V. Poplavski, “On the dynamics of drop acceleration at the early stage of velocity relaxation in a shock wave”, Combust. Explos. Shock Waves, 45:2 (2009), 198–204 | DOI | MR

[13] Ortiz C., Joseph D. D., Beavers G. S., “Acceleration of a liquid drop suddenly exposed to a high-speed airstream”, Int. J. Multiph. Flow, 30:2 (2004), 217–224 | DOI | Zbl

[14] Gelfand B. E., “Droplet breakup phenomena in flows with velocity lag”, Progr. Energy Combust. Sci., 22:3 (1996), 201–265 | DOI

[15] V. M. Boiko and S. V. Poplavski, “Experimental study of two types of stripping breakup of the drop in the flow behind the shock wave”, Combust. Explos. Shock Waves, 48:4 (2012), 440–445 | DOI

[16] Theofanous T. G., Li G. J., “On the physics of aerobreakup”, Phys. Fluids, 20 (2008), 1–14 | DOI

[17] Minakov A. V., Shebeleva A. A.,Strizhak P. A., Chernetskiy M. Yu., Volkov R. S., “Study of the Weber number impact on secondary breakup of droplets of coal water slurries containing petrochemicals”, Fuel, 254 (2019), 1100094 | DOI

[18] Poplavski S. V. Minakov A. V., Shebeleva A. A., “An early stage of the drop interaction with shock wave: airflow, deformation, destruction”, J. Phys. Conf. Ser., 1359 (2019), 012032 | DOI

[19] Poplavski S. V. Minakov A. V., Shebeleva A. A., Boyko V. M., “On the interaction of water droplet with a shock wave: Experiment and numerical simulation”, Int. J. Multiph. Flow, 127 (2020), 103273 pp. | DOI

[20] Guildenbecher D. R., Lopez-Rivera C., Sojka P. E., “Secondary atomization”, Exp. Fluids, 46 (2009), 371–402 | DOI

[21] Sharma S., Singh A. P., Rao S. S., Kumar A., Basu S., “Shock induced aerobreakup of a droplet”, J. Fluid Mech., 929 (2021), A27 | DOI | MR | Zbl

[22] Rossano V., Cittadini A., De Stefano G., “Computational Evaluation of Shock Wave Interaction with a Liquid Droplet”, Appl. Sci., 12 (2022), 1349 | DOI

[23] S. V. Poplavski, “Parametric study of droplet breakup behind a shock wave by the sheet striping mechanism”, J. Appl. Mech. Tech. Phys., 63:3 (2022), 408–417 | DOI | DOI

[24] Aggarwal S. K., Peng F., “A review of droplet dynamics and vaporization modeling for engineering calculations”, J. Eng. Gas Turbines Power, 117 (1995), 453–461 | DOI

[25] Minakov A. V., “Numerical algorithm for moving boundary fluid dynamics problems and its testing”, Comput. Math. Math. Phys., 54:10 (2014), 1560–1570 | DOI | MR | Zbl

[26] A. M. Frank, Discrete Models of Incompressible Fluid, Fizmatlit, M., 2001 (in Russian) | MR

[27] Tavangar S., Hashemabadi S. H, Saberimoghadam A., “CFD simulation for secondary breakup of coal-water slurry drops using OpenFOAM”, Fuel Process. Technol., 132 (2015), 153–163 | DOI

[28] Kothe D. B., Rider W. J., “Volume tracking of interfaces having surface tension in two and three dimensions”, Proc. 34th AIAA Aerosp. Sci. Meet. Exhibit., 1996, 859

[29] Hirt S. W., Nichols B. D., “Volume of fluid (VOF) method for the dynamics of free boundaries”, J. Comput. Phys., 39 (1981), 201–226 | DOI

[30] Brackbill J. U., Kothe D. B., Zemach C. A., “Continuum method for modeling surface tension”, J. Comput. Phys., 100 (1992), 335–354 | DOI | MR | Zbl

[31] Smagorinsky J., “General Circulation Experiments with the Primitive Equations. I. The Basic Experiment”, Mon. Weather Rev., 91 (1963), 99–164 | 2.3.CO;2 class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI