Based on adaptive mesh refinement, the SIM (Sharp-Interface Method) is utilized to numerically study the interaction between a shock wave and a liquid column as well as the evolution of the flow field. The SIM consists of the LSM (Level Set Method) and the GFM (Ghost Fluid Method). The LSM tracks the gas-liquid interface, and the GFM generates the virtual domains near the interface based on the gas-liquid interface condition. The hybridized GFM has been developed by integrating the Riemann GFM and the modified GFM together, which ensures the accuracy of the interface Riemann problem in the small deformation region of the interface while ensuring that the large interface deformation can be processed correctly. By comparing with the experimental results and the numerical results in previous literature, the good agreement shows that the above algorithm can accurately simulate the interactions between shock waves and liquid columns along with achieving the evolutions of the sharp gas-liquid interfaces. Based on the algorithm above, the interactions between the shock waves and the inviscid, the Newtonian, and the shear-thinning liquid columns are simulated, respectively. The numerical results indicate that the viscous effect can cause the bending of the liquid column and large deformation in the high shearing region. However, the shear thinning effect alleviates the bending and the deformation of the liquid column in the high shear region.
REFERENCES
1.
A. R.
Hanson
, E. G.
Domich
, and H. S.
Adams
, “Shock tube investigation of the breakup of drops by air blasts
,” Phys. Fluids
6
, 1070
–1080
(1963
).2.
J. A.
Nicholls
and A. A.
Ranger
, “Aerodynamic shattering of liquid drops
,” AIAA J.
7
, 285
–290
(1969
).3.
M.
Pilch
and C. A.
Erdman
, “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
,” Int. J. Multiphase Flow
13
, 741
–757
(1987
).4.
D. D.
Joseph
, J.
Belanger
, and G. S.
Beavers
, “Breakup of a liquid drop suddenly exposed to a high-speed airstream
,” Int. J. Multiphase Flow
25
, 1263
–1303
(1999
).5.
L.-P.
Hsiang
and G.
Faeth
, “Deformation and secondary breakup of drops
,” in 31st Aerospace Sciences Meeting
(AIAA
, 1992
), p. 814
.6.
L.-P.
Hsiang
and G.
Faeth
, “Secondary drop breakup in the deformation regime
,” in 30th Aerospace Sciences Meeting and Exhibit
(AIAA
, 1992
), p. 110
.7.
L.-P.
Hsiang
and G. M.
Faeth
, “Drop deformation and breakup due to shock wave and steady disturbances
,” Int. J. Multiphase Flow
21
, 545
(1995
).8.
X.
Wang
, D.
Yang
, J.
Wu
, and X.
Luo
, “Interaction of a weak shock wave with a discontinuous heavy-gas cylinder
,” Phys. Fluids
27
, 064104
(2015
).9.
L.
Zou
, S.
Liao
, C.
Liu
, Y.
Wang
, and Z.
Zhai
, “Aspect ratio effect on shock-accelerated elliptic gas cylinders
,” Phys. Fluids
28
, 036101
(2016
).10.
T. G.
Theofanous
, G. J.
Li
, and T. N.
Dinh
, “Aerobreakup in rarefied supersonic gas flows
,” J. Fluids Eng.
126
, 516
–527
(2004
).11.
T. G.
Theofanous
and G. J.
Li
, “On the physics of aerobreakup
,” Phys. Fluids
20
, 052103
(2008
).12.
A.
Wierzba
and K.
Takayama
, “Experimental investigation of the aerodynamic breakup of liquid drops
,” AIAA J.
26
, 1329
–1335
(1988
).13.
T.
Osuka
, E.
Erdem
, N.
Hasegawa
, R.
Majima
, T.
Tamba
, S.
Yokota
, A.
Sasoh
, and K.
Kontis
, “Laser energy deposition effectiveness on shock-wave boundary-layer interactions over cylinder-flare combinations
,” Phys. Fluids
26
, 096103
(2014
).14.
J.
Nagy
, A.
Horvath
, C.
Jordan
, and M.
Harasek
, “Turbulent phenomena in the aerobreakup of liquid droplets
,” CFD Lett.
4
, 112
–126
(2012
).15.
A. L.
Klein
, W.
Bouwhuis
, C. W.
Visser
, H.
Lhuissier
, C.
Sun
, J. H.
Snoeijer
, E.
Villermaux
, D.
Lohse
, and H.
Gelderblom
, “Drop shaping by laser-pulse impact
,” Phys. Rev. Appl.
3
, 044018
(2015
).16.
J.
Sinclair
and X.
Cui
, “A theoretical approximation of the shock standoff distance for supersonic flows around a circular cylinder
,” Phys. Fluids
29
, 026102
(2017
).17.
D.
Obreschkow
, P.
Kobel
, N.
Dorsaz
, A.
de Bosset
, C.
Nicollier
, and M.
Farhat
, “Cavitation bubble dynamics inside liquid drops in microgravity
,” Phys. Rev. Lett.
97
, 094502
(2006
).18.
D.
Obreschkow
, N.
Dorsaz
, P.
Kobel
, A.
de Bosset
, M.
Tinguely
, J.
Field
, and M.
Farhat
, “Confined shocks inside isolated liquid volumes: A new path of erosion?
,” Phys. Fluids
23
, 101702
(2011
).19.
M.
Jain
, R. S.
Prakash
, G.
Tomar
, and R. V.
Ravikrishna
, “Secondary breakup of a drop at moderate weber numbers
,” Proc. R. Soc. A
471
, 20140930
(2015
).20.
J. C.
Meng
and T.
Colonius
, “Numerical simulations of the early stages of high-speed droplet breakup
,” Shock Waves
25
, 399
–414
(2015
).21.
S.
Sembian
, M.
Liverts
, N.
Tillmark
, and N.
Apazidis
, “Plane shock wave interaction with a cylindrical water column
,” Phys. Fluids
28
, 056102
(2016
).22.
D. P.
Garrick
, M.
Owkes
, and J. D.
Regele
, “A finite-volume hllc-based scheme for compressible interfacial flows with surface tension
,” J. Comput. Phys.
339
, 46
–67
(2017
).23.
D. M.
Anderson
, G. B.
McFadden
, and A. A.
Wheeler
, “Diffuse-interface methods in fluid mechanics
,” Annu. Rev. Fluid. Mech.
30
, 139
–165
(1998
).24.
S.
Marella
, S.
Krishnan
, H.
Liu
, and H. S.
Udaykumar
, “Sharp interface cartesian grid method I: An easily implemented technique for 3D moving boundary computations
,” J. Comput. Phys.
210
, 1
–31
(2005
).25.
H.
Liu
, S.
Krishnan
, S.
Marella
, and H. S.
Udaykumar
, “Sharp interface cartesian grid method II: A technique for simulating droplet interactions with surfaces of arbitrary shape
,” J. Comput. Phys.
210
, 32
–54
(2005
).26.
Y.
Yang
and H. S.
Udaykumar
, “Sharp interface cartesian grid method III: Solidification of pure materials and binary solutions
,” J. Comput. Phys.
210
, 55
–74
(2005
).27.
R. R.
Nourgaliev
, T. N.
Dinh
, and T. G.
Theofanous
, “Adaptive characteristics-based matching for compressible multifluid dynamics
,” J. Comput. Phys.
213
, 500
–529
(2006
).28.
R. W.
Houim
and K. K.
Kuo
, “A ghost fluid method for compressible reacting flows with phase change
,” J. Comput. Phys.
235
, 865
–900
(2013
).29.
C.-H.
Chang
, X.
Deng
, and T. G.
Theofanous
, “Direct numerical simulation of interfacial instabilities: A consistent, conservative, all-speed, sharp-interface method
,” J. Comput. Phys.
242
, 946
–990
(2013
).30.
K. W.
Thompson
, “Time dependent boundary conditions for hyperbolic systems
,” J. Comput. Phys.
68
, 1
–24
(1987
).31.
K. W.
Thompson
, “Time-dependent boundary conditions for hyperbolic systems, II
,” J. Comput. Phys.
89
, 439
–461
(1990
).32.
R. P.
Fedkiw
, “The ghost fluid method for viscous flows
,” in Innovative Methods for Numerical Solutions of Partial Differential Equations
(World Scientific
, 2002
), p. 111
.33.
34.
R.
Saurel
and R.
Abgrall
, “A simple method for compressible multifluid flows
,” SIAM J. Sci. Comput.
21
, 1115
–1145
(1999
).35.
L.
Zhang
, C.
Yang
, and Z.-S.
Mao
, “Numerical simulation of a bubble rising in shear-thinning fluids
,” J. Non-Newtonian Fluid Mech.
165
, 555
–567
(2010
).36.
K.
Luo
, C.
Shao
, Y.
Yang
, and J.
Fan
, “A mass conserving level set method for detailed numerical simulation of liquid atomization
,” J. Comput. Phys.
298
, 495
–519
(2015
).37.
C.
Wang
, T.
Liu
, and B.
Khoo
, “A real ghost fluid method for the simulation of multimedium compressible flow
,” SIAM J. Sci. Comput.
28
, 278
–302
(2006
).38.
L.
Jiang
, H.
Ge
, C.
Feng
, and D.
Chen
, “Numerical simulation of underwater explosion bubble with a refined interface treatment
,” Sci. China: Phys., Mech. Astron.
58
, 1
–10
(2015
).39.
P.
Colella
and P. R.
Woodward
, “The piecewise parabolic method (PPM) for gas-dynamical simulations
,” J. Comput. Phys.
54
, 174
–201
(1984
).40.
P.
Colella
, D. T.
Graves
, T. J.
Ligocki
, D.
Martin
, and B.
Van Straalen
, “AMR Godunov unsplit algorithm and implementation
,” Technical Report, Applied Numerical Algorithms Group, NERSC Division, Lawrence Berkeley National Laboratory
, 2003
.41.
G.-S.
Jiang
and D.
Peng
, “Weighted eno schemes for Hamilton–Jacobi equations
,” SIAM J. Sci. Comput.
21
, 2126
–2143
(2000
).42.
C.-W.
Shu
and S.
Osher
, “Efficient implementation of essentially non-oscillatory shock-capturing schemes
,” J. Comput. Phys.
77
, 439
–471
(1988
).43.
F.
Losasso
, R.
Fedkiw
, and S.
Osher
, “Spatially adaptive techniques for level set methods and incompressible flow
,” Comput. Fluids
35
, 995
–1010
(2006
).44.
W. H.
Press
, S. A.
Teukolsky
, W. T.
Vetterling
, and B. P.
Flannery
, Numerical Recipes in C
(Cambridge University Press
, 1988
).45.
B.
Lalanne
, L. R.
Villegas
, S.
Tanguy
, and F.
Risso
, “On the computation of viscous terms for incompressible two-phase flows with level set/ghost fluid method
,” J. Comput. Phys.
301
, 289
–307
(2015
).46.
D.
Igra
and K.
Takayama
, “Investigation of aerodynamic breakup of a cylindrical water droplet
,” Atomization Sprays
11
, 20
(2001
).© 2019 Author(s).
2019
Author(s)
You do not currently have access to this content.