In this paper, a nonlinear boundary element method (BEM) is developed for investigating air cavity formation during the high-speed water entry of wedges. A technique is proposed for dynamic re-gridding of free surface boundaries. This technique applies to both equally and nonequally spaced grids, and it is able to suppress the numerical instabilities encountered using a BEM for simulating free surface flows. The authors also develop a purely numerical method to simulate nonviscous flow separation, which occurs when the flow reaches the knuckle of the wedge. The present nonlinear BEM has been verified by comparisons with similarity solutions. We also compare numerical results with experimental results. Finally, we give a numerical prediction of the evolution of the cavity until the closure of the cavity, and the influence of the initial entry velocity, wedge mass, and deadrise angle on the characteristics of the transient cavities is investigated.

References

References
1.
Von Karman
,
T.
,
1929
, “
The Impact of Seaplane Floats During Landing
,”
National Advisory Committee for Aeronautics
,
Washington, DC, Report No. NACA-TN-321
.
2.
Wagner
,
H.
,
1932
, “
Über Stoss- und Gleitvogänge an der Oberfläche von Flüssigkeiten
,”
Z. Angew. Math. Mech.
,
12
(
4
), pp.
193
235
.10.1002/zamm.19320120402
3.
Cointe
,
R.
, and
Armand
,
J. L.
,
1987
, “
Hydrodynamic Impact Analysis of a Cylinder
,”
ASME J. Offshore Mech. Arct. Eng.
,
109
, pp.
237
243
.10.1115/1.3257015
4.
Dobrovol’skaya
,
Z. N.
,
1969
, “
On Some Problems of Similarity Flow of Fluid with a Free Surface
,”
J. Fluid Mech.
,
36
, pp.
805
829
.10.1017/S0022112069001996
5.
Zhao
,
R.
, and
Faltinsen
,
O. M.
,
1993
, “
Water Entry of Two-Dimensional Bodies
,”
J. Fluid Mech.
,
246
, pp.
593
612
.10.1017/S002211209300028X
6.
Vinje
,
T.
, and
Brevig
,
P.
,
1981
, “
Nonlinear Two Dimensional Ship Motions
,”
Proceedings of the 3rd International Conference on Numerical Ship Hydrodynamics
,
Paris
, pp.
257
266
.
7.
Greenhow
,
M.
, and
Lin
,
W. M.
,
1985
, “
Numerical Simulation of Nonlinear Free Surface Flows Generated by Wedge Entry and Wave Maker Motions
,”
Proceedings of the 4th Numerical Conference on Ship Hydrodynamics
,
Washington, D.C.
8.
Yim
,
B.
,
1985
, “
Numerical Solution of Two Dimensional Wedge Slamming With a Nonlinear Free-Surface Condition
,”
Proceedings of the 4th Numerical Conference on Ship Hydrodynamics
,
Washington, D.C.
9.
Greenhow
,
M.
,
1987
, “
Wedge Entry into Initially Calm Water
,”
Appl. Ocean Res.
,
9
, pp.
214
223
.10.1016/0141-1187(87)90003-4
10.
Kihara
,
H.
,
2004
, “
Numerical Modeling of Flow in Water Entry of a Wedge
,”
Proceedings of the 19th International Workshop on Water Waves and Floating Bodies
,
Cortona, Italy
.
11.
Longuet-Higgins
,
M. S.
, and
Cokelet
,
E. D.
,
1976
, “
The Deformation of Steep Waves on Water I. A Numerical Method of Computation
,”
Proc. R. Soc. London, Ser. A
,
350
, pp.
1
26
.10.1098/rspa.1976.0092
12.
Zhao
,
R.
,
Faltinsen
,
O. M.
, and
Aarsnes
,
J. V.
,
1996
, “
Water Entry of Arbitrary Two-Dimensional Sections With and Without Flow Separation
,”
Proceedings of the 21st Symposium on Naval Hydrodynamics
,
Trondheim, Norway
.
13.
Yettou
,
E.
,
Desrochers
,
A.
, and
Champoux
,
Y.
,
2006
, “
Experimental Study on the Water Impact of a Symmetrical Wedge
,”
Fluid Dyn. Res.
,
38
, pp.
47
66
.10.1016/j.fluiddyn.2005.09.003
14.
Blagoveshchensky
,
S. N.
,
1962
,
Theory of Ship Motions
,
Dover Publications, Inc.
,
New York
.
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