Droplet deformation is the first stage of all aerodynamically induced-breakups, considerably affecting the characteristics of the atomization. In the present study, using an adaptive volume of fluid method, two and three-dimensional direct numerical simulations have been performed to understand droplet deformation. A high Reynolds number and a range of relatively high Weber numbers are chosen, addressing the shear breakup of droplets in a stream. The study is focused on the initiation and growth of instabilities over the droplet. The role of Kelvin-Helmholtz and Rayleigh-Taylor instabilities in wave formation and azimuthal transverse modulation are shown and the obtained results for the most amplified wave-numbers are compared with instability theories for zero and non-zero vorticity layers. The present results for the most amplified wave-numbers and deformation topologies are in good agreement with the previous experimental results.
REFERENCES
1.
L. P.
Hsiang
and G. M.
Faeth
, “Drop properties after secondary breakup
,” Int. J. Multiphase Flow
19
(5
), 721
–735
(1993
).2.
L. P.
Hsiang
and G. M.
Faeth
, “Drop deformation and breakup due to shock wave and steady disturbances
,” Int. J. Multiphase Flow
21
(4
), 545
–560
(1995
).3.
C. H.
Lee
and R. D.
Reitz
, “An experimental study of the effect of gas density on the distortion and breakup mechanism of drops in highs peed gas stream
,” Int. J. Multiphase Flow
26
, 229
–244
(2000
).4.
C. S.
Lee
and R. D.
Reitz
, “Effect of liquid properties on the breakup mechanism of high-speed liquid drops
,” Atomization Sprays
11
, 1
–19
(2001
).5.
H.
Zhao
, H. F.
Liu
, W. F.
Li
, and J. L.
Xu
, “Morphological classification of low viscosity drop bag breakup in a continuous air jet stream
,” Phys. Fluids
22
, 114103
(2010
).6.
E.
Villermaux
and B.
Bossa
, “Single-drop fragmentation determines size distribution of raindrops
,” Nat. Phys.
5
, 697
–702
(2009
).7.
D. R.
Guildenbecher
, C.
López-Rivera
, and P. E.
Sojka
, “Secondary atomization
,” Exp. Fluids
46
(3
), 371
–402
(2009
).8.
S.
Quan
and D. P.
Schmidt
, “Direct numerical study of a liquid droplet impulsively accelerated by gaseous flow
,” Phys. Fluids
18
, 102103
(2006
).9.
B. T.
Helenbrook
and C. F.
Edwards
, “Quasi-steady deformation and drag of uncontaminated liquid drops
,” Int. J. Multiphase Flow
28
, 1631
–1657
(2002
).10.
A. R.
Wadhwa
, V.
Magi
, and J.
Abraham
, “Transient deformation and drag of decelerating drops in axisymmetric flows
,” Phys. Fluids
19
, 113301
(2007
).11.
J. Q.
Feng
, “A deformable liquid drop falling through a quiescent gas at terminal velocity
,” J. Fluid Mech.
658
, 438
–462
(2010
).12.
S.
Khosla
, C. E.
Smith
, and R. P.
Throckmorton
, “Detailed understanding of drop atomization by gas cross flow using the volume of fluid method
,” in Proceedings of ILASS-AMERICAS 2006
, Toronto, Canada
, 2006
.13.
J. B.
Bell
, P.
Colella
, and H. M.
Glaz
, “A second-order projection method for the incompressible Navier–Stokes equations
,” J. Comput. Phys.
85
, 257
–283
(1989
).14.
S.
Popinet
, “Gerris: A tree-based adaptive solver for the incompressible Euler equations in complex geometries
,” J. Comput. Phys.
190
(2
), 572
–600
(2003
).15.
S.
Popinet
, “An accurate adaptive solver for surface-tension-driven interfacial flows
,” J. Comput. Phys.
228
, 5838
–5866
(2009
).16.
J.
Han
and G.
Tryggvason
, “Secondary breakup of axisymmetric liquid drops. II. Impulsive acceleration
,” Phys. Fluids
13
, 1554
(2001
).17.
M.
Ohta
, S.
Yamaguchi
, Y.
Yoshida
, and M.
Sussman
, “The sensitivity of drop motion due to the density and viscosity ratio
,” Phys. Fluids
22
, 072102
(2010
).18.
R. D.
Cohen
, “Effect of viscosity on drop breakup
,” Int. J. Multiphase Flow
20
(1
), 211
–216
(1994
).19.
P.
Marmottant
and E.
Villermaux
, “On spray formation
,” J. Fluid Mech.
498
, 73
–111
(2004
).20.
B. M.
Summer
and J.
Fredsøe
, Hydrodynamics around Cylindrical Structures
, Advanced Series on Ocean Engineering
Vol. 26
(World Scientific Publishing
, London
, 2006
).21.
S.
Chandrasekhar
, Hydrodynamic and Hydromagnetic Stability
(Oxford University Press
, London
, 1961
).22.
E.
Villermaux
, “On the role of viscosity in shear instabilities
,” Phys. Fluids
10
, 368
–373
(1998
).23.
D.
Kim
, M.
Desjardins
, M.
Hermann
, and P.
Moin
, “Toward two-phase simulation of the primary breakup of a round liquid jet by a coaxial flow of gas
,” Annual Research Briefs
(Center for Turbulence Research
, 2006
).24.
P.
Dimotakis
, “Two-dimensional shear layer entrainment
,” AIAA J.
24
, 1791
–1796
(1986
).25.
E.
Villermaux
and C.
Clanet
, “Life of a flapping liquid sheet
,” J. Fluid Mech.
462
, 341
–363
(2002
).26.
E.
Villermaux
and H.
Rehab
, “Mixing in coaxial jets
,” J. Fluid Mech.
425
, 161
–185
(2000
).27.
A.
Prosperetti
, “Motion of two superposed viscous fluids
,” Phys. Fluids
24
(7
), 1217
(1981
).28.
D.
Fuster
, G.
Agbaglah
, C.
Josserand
, S.
Popinet
, and S.
Zaleski
, “Numerical simulation of droplets, bubbles and waves: State of the art
,” Fluid Dyn. Res.
41
(6
), 065001
(2009
).29.
J. B.
Keller
, A.
King
, and L.
Ting
, “Blob formation
,” Phys. Fluids
7
, 226
(1995
).30.
Lord
Rayleigh
, “On the instability of a cylinder of viscous liquid under capillary force
,” Philos. Mag.
34
(207
), 145
–154
(1892
).31.
C.
Weber
, “Disintegration of liquid jets
,” Z. Angew. Math. Mech.
11
(2
), 136
–159
(1931
).32.
M.
Jalaal
and K.
Mehravaran
, Breakup of a Liquid Drop Falling Through a Quiescent Media: A DNS Study
(Bulletin of the American Physical Society
, 2011
), p. 56
.33.
M.
Jalaal
and K.
Mehravaran
, “Fragmentation of falling liquid droplets in bag breakup mode
,” Int. J. Multiphase Flow
47
, 115
–132
(2012
).34.
S.
Quan
and D. P.
Schmidt
, “A moving mesh interface tracking method for 3D incompressible two-phase flows
,” J. Comput. Phys.
221
(2
), 761
–780
(2007
).35.
36.
E. K.
Poon
, S.
Quan
, J.
Lou
, M.
Giacobello
, and A. S.
Ooi
, “Dynamics of a deformable, transversely rotating droplet released into a uniform flow
,” J. Fluid Mech.
684
, 227
(2011
).37.
S.
Temkin
and H. K.
Mehta
, “Droplet drag in an accelerating and decelerating flow
,” J. Fluid Mech.
116
(1
), 297
–313
(1982
).38.
R.
Clift
, J. R.
Grace
, and M. E.
Weber
, Bubbles, Drops and Particles
(Dover Publications
, Mineola
, 1978
).© 2014 AIP Publishing LLC.
2014
AIP Publishing LLC
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