A three-dimensional model has been developed of droplet impact onto asymmetric surface geometries. The model is based on RIPPLE, and combines a fixed-grid control volume discretization of the flow equations with a volume tracking algorithm to track the droplet free surface. Surface tension is modeled as a volume force acting on fluid near the free surface. Contact angles are applied as a boundary condition at the contact line. The results of two scenarios are presented, of the oblique impact of a 2 mm water droplet at 1 m/sec onto a 45° incline, and of a similar impact of a droplet onto a sharp edge. Photographs are presented of such impacts, against which the numerical results are compared. The contact angle boundary condition is applied in one of two ways. For the impact onto an incline, the temporal variation of contact angles at the leading and trailing edges of the droplet was measured from photographs. This data is applied as a boundary condition to the simulation, and an interpolation scheme proposed to evaluate contact angles between the leading and trailing edges. A simpler model is then proposed, for contact angle as a function of contact line velocity, and applied to both geometries. The model requires values of only two contact angles, at a rapidly advancing and a rapidly receding contact line. Simulation results compare well with photographic data.

1.
M.
Rein
, “
Phenomena of liquid drop impact on solid and liquid surfaces
,”
Fluid Dyn. Res.
12
,
61
(
1993
).
2.
F. H.
Harlow
and
J. P.
Shannon
, “
The splash of a liquid droplet
,”
J. Appl. Phys.
38
,
3855
(
1967
).
3.
J. E. Welch, F. H. Harlow J. P. Shannon, and B. J. Daly, “The MAC method,” Technical Report LA-3425, LANL, 1966.
4.
G. B.
Foote
, “
The water drop rebound problem: Dynamics of collision
,”
J. Atmos. Sci.
32
,
390
(
1975
).
5.
K.
Tsurutani
,
M.
Yao
,
J.
Senda
, and
H.
Fujimoto
, “
Numerical analysis of the deformation process of a droplet impinging upon a wall
,”
JSME Int. Ser. II
33
,
555
(
1990
).
6.
G.
Trapaga
and
J.
Szekely
, “
Mathematical modeling of the isothermal impingement of liquid droplets in spraying processes
,”
Metall. Trans. B
22
,
901
(
1991
).
7.
FLOW-3D: Computational modeling power for scientists and engineers,” Technical Report FSI-88-00-1, Flow Science, Inc., San Diego, CA, 1988.
8.
C. W.
Hirt
and
B. D.
Nichols
, “
Volume of fluid (VOF) method for the dynamics of free boundaries
,”
J. Comput. Phys.
39
,
201
(
1981
).
9.
H. Liu, W. Cai, R. H. Rangel, and E. J. Lavernia, “Numerical and experimental study of porosity evolution during plasma spray deposition of W,” in Science and Technology of Rapid Solidification and Processing (Kluwer Academic, Dordrecht, 1995), pp. 73–107.
10.
D. B. Kothe, R. C. Mjolsness and M. D. Torrey, “RIPPLE: A computer program for incompressible flows with free surfaces,” Technical Report LA-12007-MS, LANL, 1991.
11.
J.
Fukai
,
Y.
Shiiba
,
T.
Yamamoto
,
O.
Miyatake
,
D.
Poulikakos
,
C. M.
Megaridis
, and
Z.
Zhao
, “
Wetting effects on the spreading of a liquid droplet colliding with a flat surface: Experiment and modeling
,”
Phys. Fluids
7
,
236
(
1995
).
12.
J.
Fukai
,
Z.
Zhao
,
D.
Poulikakos
,
C. M.
Megaridis
, and
O.
Miyatake
, “
Modeling of the deformation of a liquid droplet impinging upon a flat surface
,”
Phys. Fluids A
5
,
2588
(
1993
).
13.
M.
Pasandideh-Fard
,
Y. M.
Qiao
,
S.
Chandra
, and
J.
Mostaghimi
, “
Capillary effects during droplet impact on a solid surface
,”
Phys. Fluids
8
,
650
(
1996
).
14.
M.
Bertagnolli
,
M.
Marchese
,
G.
Jacucci
,
I.
St. Doltsinis
, and
S.
Noelting
, “
Thermomechanical simulation of the splashing of ceramic droplets on a rigid substrate
,”
J. Comput. Phys.
133
,
205
(
1997
).
15.
W.-J.
Chang
and
D. J.
Hills
, “
Sprinkler droplet effects on infiltration. I: Impact simulation
,”
J. Irrig. Drain. Eng.
119
,
142
(
1993
).
16.
A.
Karl
,
K.
Anders
,
M.
Rieber
, and
A.
Frohn
, “
Deformation of liquid droplets during collisions with hot walls: Experiment and numerical results
,”
Part. Part. Syst. Charact.
13
,
186
(
1996
).
17.
S.
Chandra
and
C. T.
Avedisian
, “
On the collision of a droplet with a solid surface
,”
Proc. R. Soc. London, Ser. A
432
,
13
(
1991
).
18.
S. V. Patankar, Numerical Heat Transfer and Fluid Flow (McGraw-Hill, New York, 1980).
19.
D. L. Youngs, “An interface tracking method for a 3D Eulerian hydrodynamics code,” Technical Report 44/92/35, AWRE, 1984.
20.
M.
Rudman
, “
Volume-tracking methods for interfacial flow calculations
,”
Int. J. Numer. Methods Fluids
24
,
671
(
1997
).
21.
D. L. Youngs, “Time-dependent multi-material flow with large fluid distortion,” in Numerical Methods for Fluid Dynamics, edited by K. W. Morton and M. J. Baines (Academic, New York, 1982), pp. 273–285.
22.
J. U.
Brackbill
,
D. B.
Kothe
, and
C.
Zemach
, “
A continuum method for modeling surface tension
,”
J. Comput. Phys.
100
,
335
(
1992
).
23.
I. Aleinov and E. G. Puckett, “Computing surface tension with high-order kernels,” in Proceedings of the 6th International Symposium on Computational Fluid Dynamics, Lake Tahoe, CA, 4–8 September 1995, edited by K. Oshima, pp. 13–18.
24.
D. B. Kothe, W. J. Rider, S. J. Mosso, J. S. Brock, and J. I. Hochstein, “Volume tracking of interfaces having surface tension in two and three dimensions,” Technical Report 96-0859, AIAA, 1996.
25.
A. J.
Chorin
, “
Curvature and solidification
,”
J. Comput. Phys.
57
,
472
(
1985
).
26.
J. Y.
Poo
and
N.
Ashgriz
, “
A computational method for determining curvatures
,”
J. Comput. Phys.
84
,
483
(
1989
).
27.
C. S.
Peskin
, “
Numerical analysis of blood flow in the heart
,”
J. Comput. Phys.
25
,
220
(
1977
).
28.
E. B.
Dussan
V
and
S. H.
Davis
On the motion of a fluid-fluid interface along a solid surface
,”
J. Fluid Mech.
65
,
71
(
1974
).
29.
B.
Lafaurie
,
C.
Nardone
,
R.
Scardovelli
,
S.
Zaleski
, and
G.
Zanetti
, “
Modeling merging and fragmentation in multiphase flows with SURFER
,”
J. Comput. Phys.
113
,
134
(
1994
).
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