Assessment of geometry effects affecting shock-induced cavitation within a droplet is investigated for the first time. To do this, we use a thermodynamically well-posed multiphase numerical model accounting for phase compression and expansion, which relies on a finite pressure-relaxation rate formulation and which allow for heterogeneous nucleation. These geometry effects include the shape of the transmitted wave front, which is related to the shock speed to droplet sound speed ratio and the droplet geometry (cylindrical vs spherical). Phenomenological differences between the column and the droplet configurations are presented. In addition, the critical Mach number for cavitation appearance is determined for both cases: between M = 1.8 and M = 2 for the column, and between M = 2 and M = 2.2 for the droplet. Based on the transmitted wavefront geometry, with Mach number varying from 1.6 to 6, two cavitation regimes have been identified, and the transition has been characterized: an exponentially (M < 4.38) and a linearly (M > 4.38) increasing bubble-cloud volume. On more applied aspects, we also investigate the influence of the bubble cloud on the interface disruption and compare the results against the pure liquid droplet test case. A parallel with the technique of effervescent atomization is eventually presented.
REFERENCES
1.
D.
Guildenbecher
,
C.
López-Rivera
, and
P.
Sojka
, “
Secondary atomization
,” Exp. Fluids
46
, 371
(2009
).2.
T.
Theofanous
, “
Aerobreakup of Newtonian and viscoelastic liquids
,” Annu. Rev. Fluid Mech.
43
, 661
–690
(2011
).3.
S.
Sembian
,
M.
Liverts
,
N.
Tillmark
, and
N.
Apazidis
, “
Plane shock wave interaction with a cylindrical water column
,” Phys. Fluids
28
, 056102
(2016
).4.
N.
Kyriazis
,
P.
Koukouvinis
, and
M.
Gavaises
, “
Modelling cavitation during drop impact on solid surfaces
,” Adv. Colloid Interface Sci.
260
, 46
–64
(2018
).5.
L.
Biasiori-Poulanges
and
H.
El-Rabii
, “
Shock-induced cavitation and wavefront analysis inside a water droplet
,” Phys. Fluids
33
, 097104
(2021
).6.
L.
Biasiori-Poulanges
and
K.
Schmidmayer
, “
A phenomenological analysis of droplet shock-induced cavitation using a multiphase modeling approach
,” Phys. Fluids
35
, 013312
(2023
).7.
K.
Ando
, “
Effects of polydispersity in bubbly flows
,” Ph.D. thesis (
California Institute of Technology
, 2010
).8.
J. C.
Meng
and
T.
Colonius
, “
Numerical simulations of the early stages of high-speed droplet breakup
,” Shock Waves
25
, 399
–414
(2015
).9.
H. F.
Okorn-Schmidt
,
F.
Holsteyns
,
A.
Lippert
,
D.
Mui
,
M.
Kawaguchi
,
C.
Lechner
,
P. E.
Frommhold
,
T.
Nowak
,
F.
Reuter
,
M. B.
Piqué
,
C.
Cairós
, and
R.
Mettin
, “
Particle cleaning technologies to meet advanced semiconductor device process requirements
,” ECS J. Solid State Sci. Technol.
3
, N3069
(2014
).10.
Y.
Tatekura
,
T.
Fujikawa
,
Y.
Jinbo
,
T.
Sanada
,
K.
Kobayashi
, and
M.
Watanabe
, “
Observation of water-droplet impacts with velocities of O(10 m/s) and subsequent flow field
,” ECS J. Solid State Sci. Technol.
4
, N117
(2015
).11.
L.
Biasiori-Poulanges
and
H.
El-Rabii
, “
Multimodal imaging for intra-droplet gas-cavity observation during droplet fragmentation
,” Opt. Lett.
45
, 3091
–3094
(2020
).12.
J. E.
Field
,
J. P.
Dear
, and
J. E.
Ogren
, “
The effects of target compliance on liquid drop impact
,” J. Appl. Phys.
65
, 533
–540
(1989
).13.
R.
Saurel
,
F.
Petitpas
, and
R.
Abgrall
, “
Modelling phase transition in metastable liquids: Application to cavitating and flashing flows
,” J. Fluid Mech.
607
, 313
–350
(2008
).14.
M.
Pelanti
and
K.-M.
Shyue
, “
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
).15.
R. W.
Forehand
,
K. C.
Nguyen
,
C. J.
Anderson
,
R.
Shannon
,
S. M.
Grace
, and
M. P.
Kinzel
, “
A numerical assessment of shock–droplet interaction modeling including cavitation
,” Phys. Fluids
35
, 023315
(2023
).16.
K.
Schmidmayer
,
J.
Cazé
,
F.
Petitpas
,
E.
Daniel
, and
N.
Favrie
, “
Modelling interactions between waves and diffused interfaces
,” Int. J. Numer. Methods Flow
95
, 215
–241
(2023
).17.
O.
Le Métayer
,
J.
Massoni
, and
R.
Saurel
, “
Elaborating equations of state of a liquid and its vapor for two-phase flow models
,” Int. J. Therm. Sci.
43
, 265
–276
(2004
).18.
R.
Saurel
,
F.
Petitpas
, and
R. A.
Berry
, “
Simple and efficient relaxation methods for interfaces separating compressible fluids, cavitating flows and shocks in multiphase mixtures
,” J. Comput. Phys.
228
(5
), 1678
–1712
(2009
).19.
K.
Schmidmayer
,
F.
Petitpas
,
S.
Le Martelot
, and
E.
Daniel
, “
ECOGEN: An open-source tool for multiphase, compressible, multiphysics flows
,” Comput. Phys. Commun.
251
, 107093
(2020
).20.
E. F.
Toro
, Riemann Solvers and Numerical Methods for Fluid Dynamics
(
Springer Verlag
,
Berlin
, 1997
).21.
B.
Van Leer
, “
Towards the ultimate conservative difference scheme III. Upstream-centered finite-difference schemes for ideal compressible flow
,” J. Comput. Phys.
23
, 263
–275
(1977
).22.
K.
Schmidmayer
,
F.
Petitpas
, and
E.
Daniel
, “
Adaptive Mesh Refinement algorithm based on dual trees for cells and faces for multiphase compressible flows
,” J. Comput. Phys.
388
, 252
–278
(2019
).23.
B.
Dorschner
,
L.
Biasiori-Poulanges
,
K.
Schmidmayer
,
H.
El-Rabii
, and
T.
Colonius
, “
On the formation and recurrent shedding of ligaments in droplet aerobreakup
,” J. Fluid Mech.
904
, A20
(2020
).24.
Y. A.
Pishchalnikov
,
W. M.
Behnke-Parks
,
K.
Schmidmayer
,
K.
Maeda
,
T.
Colonius
,
T. W.
Kenny
, and
D. J.
Laser
, “
High-speed video microscopy and numerical modeling of bubble dynamics near a surface of urinary stone
,” J. Acoust. Soc. Am.
146
, 516
–531
(2019
).25.
J. J.
Quirk
and
S.
Karni
, “
On the dynamics of a shock–bubble interaction
,” J. Fluid Mech.
318
, 129
–163
(1996
).26.
G.
Nykteri
and
M.
Gavaises
, “
Droplet aerobreakup under the shear-induced entrainment regime using a multiscale two-fluid approach
,” Phys. Rev. Fluids
6
, 084304
(2021
).27.
S. D.
Sovani
,
P. E.
Sojka
, and
A. H.
Lefebvre
, “
Effervescent atomization
,” Prog. Energy Combust. Sci.
27
, 483
–521
(2001
).28.
J. R.
Blake
and
D. C.
Gibson
, “
Cavitation bubbles near boundaries
,” Annu. Rev. Fluid Mech.
19
, 99
–123
(1987
).29.
W.
Lauterborn
and
T.
Kurz
, “
Physics of bubble oscillations
,” Rep. Prog. Phys.
73
, 106501
(2010
).30.
O.
Supponen
,
D.
Obreschkow
,
M.
Tinguely
,
P.
Kobel
,
N.
Dorsaz
, and
M.
Farhat
, “
Scaling laws for jets of single cavitation bubbles
,” J. Fluid Mech.
802
, 263
–293
(2016
).31.
J. C.
Meng
and
T.
Colonius
, “
Numerical simulation of the aerobreakup of a water droplet
,” J. Fluid Mech.
835
, 1108
–1135
(2018
).© 2023 Author(s). Published under an exclusive license by AIP Publishing.
2023
Author(s)
You do not currently have access to this content.