The classic study of the water entry of a body has applications ranging from hydroballistics to behavior of basilisk lizards. The availability of Russian supercavitation theory in recent years has allowed for an even greater understanding, and was used to develop a model to predict the dynamic size, shape, and pressure of a naturally or artificially produced underwater cavity. This model combines supercavitation theory, rigid body dynamics, and hydrodynamic theory into a comprehensive model capable of determining the motional behavior of underwater objects. This model was used as the basis for modeling the vertical water entry of solid objects into a free water surface. Results from simulation of water entry of various-sized thin disks compared favorably with published experimental data from the technical literature. Additional simulated data support a disk radius dependence on a relative object depth at cavity closure that was not previously recognized. Cavity closure times are also presented.

1.
Worthington
,
A. M.
, and
Cole
,
R. S.
, 1900, “
Impact With a Liquid Surface Studied by the Aid of Instantaneous Photography, Paper II
,”
Philos. Trans. R. Soc. London, Ser. A
0962-8428,
194A
, pp.
175
199
.
2.
Lee
,
M.
,
Longoria
,
R. G.
, and
Wilson
,
D. E.
, 1997, “
Cavity Dynamics in High-Speed Water Entry
,”
Phys. Fluids
1070-6631,
9
(
3
), pp.
540
550
.
3.
May
,
A.
, 1952, “
Vertical Entry of Missiles Into Water
,”
J. Appl. Phys.
0021-8979,
23
(
12
), pp.
1362
1372
.
4.
Glasheen
,
J. W.
, and
McMahon
,
T. A.
, 1996, “
Vertical Water Entry of Disks at Low Froude Numbers
,”
Phys. Fluids
1070-6631,
8
(
8
), pp.
2078
2083
.
5.
Glasheen
,
J. W.
, and
McMahon
,
T. A.
, 1996, “
Size-Dependence of Water-Running Ability of Basilisk Lizards (Basiliscus Basiliscus)
,”
J. Exp. Biol.
0022-0949,
99
, pp.
2611
2618
.
6.
Glasheen
,
J. W.
, and
McMahon
,
T. A.
, 1996, “
A Hydrodynamic Model of Locomotion in the Basilisk Lizard
,”
Nature (London)
0028-0836,
380
, pp.
340
342
.
7.
Floyd
,
S.
,
Keegen
,
T.
,
Palmisano
,
J.
, and
Sitti
,
M.
, 2006, “
A Novel Water Running Robot Inspired by Basilisk Lizards
,”
Proceedings of the IEEE/RSJ Intelligent Robotic Systems Conference
,
Beijing, China
.
8.
Shi
,
H.-H.
,
Itoh
,
M.
, and
Takami
,
T.
, 2000, “
Optical Observation of the Supercavitation Induced by High-Speed Water Entry
,”
ASME J. Fluids Eng.
0098-2202,
122
, pp.
806
810
.
9.
Gaudet
,
S.
, 1998, “
Numerical Simulation of Circular Disks Entering the Free Surface of a Fluid
,”
Phys. Fluids
1070-6631,
10
(
10
), pp.
2489
2499
.
10.
Pan
,
Y.
, and
Suga
,
K.
, 2003, “
Capturing the Pinch-Off of Liquid Jets by the Level Set Method
,”
ASME J. Fluids Eng.
0098-2202,
125
, pp.
922
927
.
11.
Duclaux
,
V.
,
Caille
,
F.
,
Duez
,
C.
,
Ybert
,
C.
,
Bocquet
,
L.
, and
Clanet
,
C.
, 2007, “
Dynamics of Transient Cavities
,”
J. Fluid Mech.
0022-1120,
591
, pp.
1
19
.
12.
Miller
,
T. F.
, and
White
,
E. R.
, 2008, “
Dynamic Modeling of Water Breathing Powerplants for High Speed Supercavitating Underwater Vehicles
,”
JANNAF Journal of Propulsion and Energetics
,
1
(
1
), pp.
83
100
.
13.
Honghui
,
S.
, and
Takami
,
T.
, 2001, “
Hydrodynamic Behavior of an Underwater Moving Body After Water Entry
,”
Acta Mech. Sin.
0459-1879,
17
(
1
), pp.
35
44
.
14.
Choi
,
J. Y.
, and
Ruzzene
,
M.
, 2006, “
Stability Analysis of Supercavitating Underwater Vehicles With Adaptive Cavitator
,”
Int. J. Mech. Sci.
0020-7403,
48
(
12
), pp.
1360
1370
.
15.
Kirschner
,
I. N.
,
Kring
,
D. C.
,
Stokes
,
A. W.
,
Fine
,
N. E.
, and
Uhlman
,
J. S.
, 2002, “
Control Strategies for Supercavitating Vehicles
,”
J. Vib. Control
1077-5463,
8
(
2
), pp.
219
242
.
16.
Serebryakov
,
V.
, 2003, “
Supercavitation Flows With Gas Injection—Prediction and Drag Redaction Problems
,” CAV 03-OS-7-003, Fifth International Symposium on Cavitation (CAV2003), Osaka, Japan, November 1–4, 2003.
17.
Serebryakov
,
V. V.
, 2009, “
Physical-Mathematical Basis of the Principle of Independence of Cavity Expansion
,”
Proceedings of the Seventh International Symposium on Cavitation
,
Ann Arbor, MI
.
18.
Paryshev
,
E. V.
, 2006, “
Approximate Mathematical Models in High Speed Hydrodynamics
,”
J. Eng. Math.
0022-0833,
55
(
1–4
), pp.
41
64
.
19.
Epshtein
,
L. A.
, 1970,
Methods of Theory of Dimensionality and Simularity in Problems of Ship Hydrodynamics
,
Sudostroenie
,
Leningrad
, p.
207
.
20.
Logvinovich
,
G. V.
, 1969,
Hydrodynamics of Flows With Free Boundaries
,
Naukova Dumka
,
Kiev
, pp.
3.1
3.4
.
21.
Cor
,
J. J.
, and
Miller
,
T. F.
, 2010, “
Theoretical Analysis of Hydrostatic Implodable Cylindrical Volumes With Solid Inner Structures
,”
J. Fluids Struct.
0889-9746,
26
(
2
), pp.
253
273
.
22.
Thorley
,
A. R. D.
, and
Wiggert
,
D. C.
, 1985, “
The Effect of Virtual Mass on the Basic Equations for Unsteady One-Dimensional Heterogeneous Flows
,”
Int. J. Multiphase Flow
0301-9322,
11
(
2
), pp.
149
160
.
23.
Uhlman
,
J. S.
,
Fine
,
N. E.
, and
Kring
,
D. C.
, 2001, “
Calculation of Added Mass and Damping Forces on Supercavitating Bodies
,”
Proceedings of the Fourth International Symposium on Cavitation
,
Pasadena, CA
.
24.
Brennen
,
C. E.
, 1982, “
A Review of Added Mass and Fluid Inertial Forces
,” Naval Civil Engineering Laboratory, Report No. N62583-81-MR-554.
25.
May
,
A.
, 1975,
Water Entry and the Cavity-Running Behavior of Missiles
, Naval Surface Weapons Center/White Oak Laboratory,
U.S. Department of Commerce, National Technical Information Service (NTIS)
,
Springfield, VA
, pp.
2:3
2:9
.
27.
Spurk
,
J. H.
, 2002, “
On the Gas Loss From Ventilated Supercavities
,”
Acta Mech.
0001-5970,
155
, pp.
125
135
.
28.
Schmidt-Nielsen
,
K.
, 1995,
Scaling: Why Animal Size Is Important
,
Cambridge University Press
,
Cambridge
, pp.
60
62
.
29.
Alexseev
,
N. V.
,
Pozdnyakov
,
O. E.
, and
Shorin
,
S. N.
, 1983, “
Study of the Interaction Between a Hot Gas Jet and a Liquid Bath
,”
Inzh.-Fiz. Zh.
0021-0285,
44
(
4
), pp.
537
544
.
30.
Banks
,
R. B.
, and
Chandrasekhara
,
D. V.
, 1963, “
Experimental Investigation of the Penetration of a High-Velocity Gas Jet Through a Liquid Surface
,”
J. Fluid Mech.
0022-1120,
15
, pp.
13
34
.
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