×

Numerical simulation of the aerobreakup of a water droplet. (English) Zbl 1419.76540

Summary: We present a three-dimensional numerical simulation of the aerobreakup of a spherical water droplet in the flow behind a normal shock wave. The droplet and surrounding gas flow are simulated using the compressible multicomponent Euler equations in a finite-volume scheme with shock and interface capturing. The aerobreakup process is compared with available experimental visualizations. Features of the droplet deformation and breakup in the stripping breakup regime, as well as descriptions of the surrounding gas flow, are discussed. Analyses of observed surface instabilities and a Fourier decomposition of the flow field reveal asymmetrical azimuthal modulations and broadband instability growth that result in chaotic flow within the wake region.

MSC:

76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
76L05 Shock waves and blast waves in fluid mechanics
76M12 Finite volume methods applied to problems in fluid mechanics
76N15 Gas dynamics (general theory)

References:

[1] Aalburg, C.; Leer, B. V.; Faeth, G. M., Deformation and drag properties of round drops subjected to shock-wave disturbances, AIAA J., 41, 12, 2371-2378, (2003) · doi:10.2514/2.6862
[2] Allaire, G.; Clerc, S.; Kokh, S., A five-equation model for the simulation of interfaces between compressible fluids, J. Comput. Phys., 181, 577-616, (2002) · Zbl 1169.76407 · doi:10.1006/jcph.2002.7143
[3] Batchelor, G. K., The stability of a large gas bubble rising through liquid, J. Fluid Mech., 184, 399-422, (1987) · Zbl 0641.76102 · doi:10.1017/S0022112087002945
[4] Castrillon Escobar, S., Rimbert, N., Meignen, R., Hadj-Achour, M. & Gradeck, M.2015Direct numerical simulations of hydrodynamic fragmentation of liquid metal droplets by a water flow. In 13th Triennial International Conference on Liquid Atomization and Spray Systems. ILASS. · Zbl 1460.76803
[5] Chang, C. H.; Deng, X.; Theofanous, T. G., Direct numerical simulation of interfacial instabilities: a consistent, conservative, all-speed, sharp-interface method, J. Comput. Phys., 242, 946-990, (2013) · Zbl 1299.76097 · doi:10.1016/j.jcp.2013.01.014
[6] Chen, H., Two-dimensional simulation of stripping breakup of a water droplet, AIAA J., 46, 5, 1135-1143, (2008) · doi:10.2514/1.31286
[7] Coralic, V.2015 Simulation of shock-induced bubble collapse with application to vascular injury in shockwave lithotripsy. PhD thesis, California Institute of Technology, Pasadena, CA.
[8] Coralic, V.; Colonius, T., Shock-induced collapse of a bubble inside a deformable vessel, Eur. J. Mech. (B/Fluids), 40, 64-74, (2013) · Zbl 1408.76602 · doi:10.1016/j.euromechflu.2013.01.003
[9] Coralic, V.; Colonius, T., Finite-volume WENO scheme for viscous compressible multicomponent flows, J. Comput. Phys., 274, 95-121, (2014) · Zbl 1351.76100 · doi:10.1016/j.jcp.2014.06.003
[10] Engel, O. G., Fragmentation of waterdrops in the zone behind an air shock, J. Res. Natl Bur. Stand., 60, 3, 245-280, (1958) · Zbl 0088.19001 · doi:10.6028/jres.060.029
[11] Gojani, A. B.; Ohtani, K.; Takayama, K.; Hosseini, S. H. R., Shock Hugoniot and equations of states of water, castor oil, and aqueous solutions of sodium chloride, sucrose, and gelatin, Shock Waves, 26, 1, 63-68, (2016) · doi:10.1007/s00193-009-0195-9
[12] Guildenbecher, D. R.; López-Rivera, C.; Sojka, P. E., Secondary atomization, Exp. Fluids, 46, 371-402, (2009) · doi:10.1007/s00348-008-0593-2
[13] Han, J.; Tryggvason, G., Secondary breakup of axisymmetric liquid drops. Part II. Impulsive acceleration, Phys. Fluids, 13, 6, 1554-1565, (2001) · Zbl 1184.76209 · doi:10.1063/1.1370389
[14] Hanson, A. R.; Domich, E. G.; Adams, H. S., Shock tube investigation of the breakup of drops by air blasts, Phys. Fluids, 6, 8, 1070-1080, (1963) · doi:10.1063/1.1706864
[15] Harlow, F. H. & Amsden, A. A.1971 Fluid dynamics. Tech. Rep. LA-4700. LASL.
[16] Hinze, J. O., Critical speeds and sizes of liquid globules, Appl. Sci. Res., A1, 273-288, (1949) · doi:10.1007/BF02120335
[17] Hsiang, L. P.; Faeth, G. M., Near-limit drop deformation and secondary breakup, Intl J. Multiphase Flow, 18, 5, 635-652, (1992) · Zbl 1144.76394 · doi:10.1016/0301-9322(92)90036-G
[18] Hsiang, L. P.; Faeth, G. M., Drop deformation and breakup due to shock wave and steady disturbances, Intl J. Multiphase Flow, 21, 4, 545-560, (1995) · Zbl 1134.76557 · doi:10.1016/0301-9322(94)00095-2
[19] Igra, D. & Takayama, K.2001aExperimental and numerical study of the initial stages in the interaction process between a planar shock wave and a water column. In 23rd International Symposium on Shock Waves. The University of Texas at Arlington. · Zbl 1051.76045
[20] Igra, D.; Takayama, K., Numerical simulation of shock wave interaction with a water column, Shock Waves, 11, 219-228, (2001) · Zbl 1051.76045 · doi:10.1007/PL00004077
[21] Igra, D. & Takayama, K.2001c A study of shock wave loading on a cylindrical water column. Tech. Rep. vol. 13, pp. 19-36. Institute of Fluid Science, Tohoku University. · Zbl 1051.76045
[22] Jain, M.; Prakash, R. S.; Tomar, G.; Ravikrishna, R. V., Secondary breakup of a drop at moderate Weber numbers, Proc. R. Soc. Lond. A, 471, 20140930, (2015) · doi:10.1098/rspa.2014.0930
[23] Jalaal, M.; Mehravaran, K., Transient growth of droplet instabilities in a stream, Phys. Fluids, 26, 012101, (2014) · doi:10.1063/1.4851056
[24] Johnsen, E.2007 Numerical simulations of non-spherical bubble collapse with applications to shockwave lithotripsy. PhD thesis, California Institute of Technology, Pasadena, CA.
[25] Johnsen, E.; Colonius, T., Implementation of WENO schemes in compressible multicomponent flow problems, J. Comput. Phys., 219, 715-732, (2006) · Zbl 1189.76351 · doi:10.1016/j.jcp.2006.04.018
[26] Johnsen, E.; Colonius, T., Numerical simulations of non-spherical bubble collapse, J. Fluid Mech., 629, 231-262, (2009) · Zbl 1181.76137 · doi:10.1017/S0022112009006351
[27] Joseph, D. D.; Belanger, J.; Beavers, G. S., Breakup of a liquid drop suddenly exposed to a high-speed airstream, Intl J. Multiphase Flow, 25, 1263-1303, (1999) · Zbl 1137.76623 · doi:10.1016/S0301-9322(99)00043-9
[28] Kapila, A. K.; Menikoff, R.; Bdzil, J. B.; Son, S. F.; Stewart, D. S., Two-phase modeling of deflagration-to-detonation transition in granular materials: reduced equations, Phys. Fluids, 13, 10, 3002-3024, (2001) · Zbl 1184.76268 · doi:10.1063/1.1398042
[29] Khosla, S., Smith, C. E. & Throckmorton, R. P.2006Detailed understanding of drop atomization by gas crossflow using the volume of fluid method. In 19th Annual Conference on Liquid Atomization and Spray Systems. ILASS.
[30] Lane, W. R., Shatter of drops in streams of air, Ind. Engng Chem., 43, 6, 1312-1317, (1951) · doi:10.1021/ie50498a022
[31] Liu, Z.; Reitz, R. D., An analysis of the distortion and breakup mechanisms of high speed liquid drops, Intl J. Multiphase Flow, 23, 4, 631-650, (1997) · Zbl 1135.76481 · doi:10.1016/S0301-9322(96)00086-9
[32] Meng, J. C.2016 Numerical simulations of droplet aerobreakup. PhD thesis, California Institute of Technology, Pasadena, CA.
[33] Meng, J. C.; Colonius, T., Numerical simulations of the early stages of high-speed droplet breakup, Shock Waves, 25, 4, 399-414, (2015) · doi:10.1007/s00193-014-0546-z
[34] Mohseni, K.; Colonius, T., Numerical treatment of polar coordinate singularities, J. Comput. Phys. Note, 157, 787-795, (2000) · Zbl 0981.76075 · doi:10.1006/jcph.1999.6382
[35] Murrone, A.; Guillard, H., A five equation reduced model for compressible two phase flow problems, J. Comput. Phys., 202, 664-698, (2005) · Zbl 1061.76083 · doi:10.1016/j.jcp.2004.07.019
[36] Pelanti, M.; Shyue, K. M., A mixture-energy-consistent six-equation two-phase numerical model for fluids with interfaces, cavitation and evaporation waves, J. Comput. Phys., 259, 331-357, (2014) · Zbl 1349.76851 · doi:10.1016/j.jcp.2013.12.003
[37] Perigaud, G.; Saurel, R., A compressible flow model with capillary effects, J. Comput. Phys., 209, 139-178, (2005) · Zbl 1329.76301 · doi:10.1016/j.jcp.2005.03.018
[38] Pilch, M.; Erdman, C. A., 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, (1987) · doi:10.1016/0301-9322(87)90063-2
[39] Quan, S.; Schmidt, D. P., Direct numerical study of a liquid droplet impulsively accelerated by gaseous flow, Phys. Fluids, 18, 102103, (2006) · doi:10.1063/1.2363216
[40] Quirk, J. J.; Karni, S., On the dynamics of a shock-bubble interaction, J. Fluid Mech., 318, 129-163, (1996) · Zbl 0877.76046 · doi:10.1017/S0022112096007069
[41] Ranger, A. A. & Nicholls, J. A.1968Aerodynamic shattering of liquid drops. In AIAA 6th Aerospace Sciences Meeting. AIAA.
[42] Saurel, R.; Petitpas, F.; Berry, R. A., Simple and efficient relaxation methods for interfaces separating compressible fluids, cavitating flows and shocks in multiphase mixtures, J. Comput. Phys., 228, 1678-1712, (2009) · Zbl 1409.76105 · doi:10.1016/j.jcp.2008.11.002
[43] Simpkins, P. G.; Bales, E. L., Water-drop response to sudden accelerations, J. Fluid Mech., 55, 629-639, (1972) · doi:10.1017/S0022112072002058
[44] Stapper, B. E. & Samuelsen, G. S.1990An experimental study of the breakup of a two-dimensional liquid sheet in the presence of co-flow air shear. In AIAA 28th Aerospace Sciences Meeting. AIAA.
[45] Takayama, K. & Itoh, K.1986 Unsteady drag over cylinders and aerofoils in transonic shock tube flows. Tech. Rep. vol. 51. Institute of High Speed Mechanics, Tohoku University, Sendai, Japan.
[46] Tanno, H.; Itoh, K.; Saito, T.; Abe, A.; Takayama, K., Interaction of a shock with a sphere suspended in a vertical shock tube, Shock Waves, 13, 191-200, (2003) · doi:10.1007/s00193-003-0209-y
[47] Theofanous, T. G., Aerobreakup of Newtonian and viscoelastic liquids, Annu. Rev. Fluid Mech., 43, 661-690, (2011) · Zbl 1299.76217 · doi:10.1146/annurev-fluid-122109-160638
[48] Theofanous, T. G.; Li, G. J., On the physics of aerobreakup, Phys. Fluids, 20, 052103, (2008) · Zbl 1182.76756 · doi:10.1063/1.2907989
[49] Theofanous, T. G.; Li, G. J.; Dinh, T. N., Aerobreakup in rarefied supersonic gas flows, Trans. ASME J. Fluid Engng, 126, 516-527, (2004) · doi:10.1115/1.1777234
[50] Theofanous, T. G.; Mitkin, V. V.; Ng, C. L.; Chang, C. H.; Deng, X.; Sushchikh, S., The physics of aerobreakup. Part II. Viscous liquids, Phys. Fluids, 24, 022104, (2012) · doi:10.1063/1.3680867
[51] Wadhwa, A. R.; Magi, V.; Abraham, J., Transient deformation and drag of decelerating drops in axisymmetric flows, Phys. Fluids, 19, 113301, (2007) · Zbl 1182.76809 · doi:10.1063/1.2800038
[52] Xiao, F.; Dianat, M.; Mcguirk, J. J., Large eddy simulation of single droplet and liquid jet primary breakup using a coupled level set/volume of fluid method, Atomiz. Sprays, 24, 4, 281-302, (2014) · doi:10.1615/AtomizSpr.2014007885
[53] Zaleski, S.; Li, J.; Succi, S., Two-dimensional Navier-Stokes simulation of deformation and breakup of liquid patches, Phys. Rev. Lett., 75, 2, 244-247, (1995) · doi:10.1103/PhysRevLett.75.244
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.