Abstract
The varying speed impact of wedge bodies on a water surface is studied numerically and theoretically to provide a fast and accurate prediction of the pressure on the wedge surface and the motion of wedge bodies during the free impact, which can be a two-dimensional (2D) model for the strip theory or 2D + t strategy. The fluid is assumed to be incompressible, inviscid, with negligible gravity effect and surface tension effect. The computational fluid dynamics (CFD) method is based on the volume of fluid (VOF) method and global moving mesh (GMM) method. Various cases of a varying speed impact are shown for the CFD method, and a linear relationship between the pressure coefficient Cp and a dimensionless variable K is observed. To clearly explain the linear relationship between Cp and K, we follow the potential theory to derive the Cp expression based on several assumptions on the free surface drawn from the CFD results. The Cp expression and the motion of wedge bodies for a free impact derived from it are considered as an approximate solution for a varying speed impact. The approximate solution is compared with the existing analytical models and the published experimental data. The approximate solution can work well for different deadrise angles, while the existing analytical models can only be used for small deadrise angles. Good agreement is also obtained between the approximate solution and the experimental test results, including the time history of wedge acceleration and the pressure on the wedge surface.
Issue Section:
Flows in Complex Systems
References
1.
Heymann
,
F.
, 1968
, “
On the Shock Wave Velocity and Impact Pressure in High-Speed Liquid-Solid Impact
,” ASME J. Basic Eng.
,
90
(3
), pp. 400
–402
.10.1115/1.36051142.
Faltinsen
,
O. M.
,
Landrini
,
M.
, and
Greco
,
M.
, 2004
, “
Slamming in Marine Applications
,” J. Eng. Math.
,
48
(3/4
), pp. 187
–217
.10.1023/B:engi.0000018188.68304.ae3.
4.
Kapsenberg
,
G. K.
, 2011
, “
Slamming of Ships: Where Are we Now?
,” Philos. Trans. R. Soc. London A: Math., Phys. Eng. Sci.
,
369
(1947
), pp. 2892
–2919
.10.1098/rsta.2011.01185.
Von Karman
,
T.
, 1929
, “
The Impact on Seaplane Floats During Landing
,” National Advisory Council for Aeronautics (NACA), Langley Field, VA, Report No. 321.6.
Seddon
,
C. M.
, and
Moatamedi
,
M.
, 2006
, “
Review of Water Entry With Applications to Aerospace Structures
,” Int. J. Impact Eng.
,
32
(7
), pp. 1045
–1067
.10.1016/j.ijimpeng.2004.09.0027.
Guo
,
B.
,
Liu
,
P.
,
Qu
,
Q.
, and
Wang
,
J.
, 2013
, “
Effect of Pitch Angle on Initial Stage of a Transport Airplane Ditching
,” Chin. J. Aeronautics
,
26
(1
), pp. 17
–26
.10.1016/j.cja.2012.12.0248.
Qu
,
Q.
,
Hu
,
M.
,
Guo
,
H.
,
Liu
,
P.
, and
Agarwal
,
R. K.
, 2015
, “
Study of Ditching Characteristics of Transport Aircraft by Global Moving Mesh Method
,” J. Aircr.
,
52
(5
), pp. 1550
–1558
.10.2514/1.C0329939.
Iafrati
,
A.
, 2016
, “
Experimental Investigation of the Water Entry of a Rectangular Plate at High Horizontal Velocity
,” J. Fluid Mech.
,
799
, pp. 637
–672
.10.1017/jfm.2016.37410.
Semenov
,
Y. A.
, and
Iafrati
,
A.
, 2006
, “
On the Nonlinear Water Entry Problem of Asymmetric Wedges
,” J. Fluid Mech.
,
547
(1
), pp. 231
–256
.10.1017/S002211200500732911.
Wagner
,
H.
, 1932
, “
Über Stoß-Und Gleitvorgänge an Der Oberfläche Von Flüssigkeiten
,” ZAMM-J. Appl. Math. Mech.
,
12
(4
), pp. 193
–215
.10.1002/zamm.1932012040212.
Mei
,
X.
,
Liu
,
Y.
, and
Yue
,
D. K. P.
, 1999
, “
On the Water Impact of General Two-Dimensional Sections
,” Appl. Ocean Res.
,
21
(1
), pp. 1
–15
.10.1016/S0141-1187(98)00034-013.
Dobrovol'Skaya
,
Z. N.
, 1969
, “
On Some Problems of Similarity Flow of Fluid With a Free Surface
,” J. Fluid Mech.
,
36
(4
), pp. 805
–829
.10.1017/S002211206900199614.
Logvinovich
,
G. V.
, 1972
, Hydrodynmaics of Free-Boundary Flows
,
Israel Program for Scientific Translations
,
Jerusalem
.15.
Korobkin
,
A.
, 2004
, “
Analytical Models of Water Impact
,” Eur. J. Appl. Math.
,
15
(6
), pp. 821
–838
.10.1017/S095679250400576516.
Howison
,
S. D.
,
Ockendon
,
J. R.
, and
Wilson
,
S. K.
, 1991
, “
Incompressible Water-Entry Problems at Small Deadrise Angles
,” J. Fluid Mech.
,
222
(1
), pp. 215
–230
.10.1017/S002211209100107617.
Zhao
,
R.
, and
Faltinsen
,
O. M.
, 1993
, “
Water Entry of Two-Dimensional Bodies
,” J. Fluid Mech.
,
246
, pp. 593
–612
.10.1017/S002211209300028X18.
Peseux
,
B.
,
Gornet
,
L.
, and
Donguy
,
B.
, 2005
, “
Hydrodynamic Impact: Numerical and Experimental Investigations
,” J. Fluids Struct.
,
21
(3
), pp. 277
–303
.10.1016/j.jfluidstructs.2005.04.01119.
Fraenkel
,
L. E.
, and
Keady
,
G.
, 2004
, “
On the Entry of a Wedge Into Water: The Thin Wedge and an All-Purpose Boundary-Layer Equation
,” J. Eng. Math.
,
48
(3/4
), pp. 219
–252
.10.1023/B:engi.0000018157.35269.a220.
Wang
,
J.
, and
Faltinsen
,
O. M.
, 2017
, “
Improved Numerical Solution of Dobrovol'skaya's Boundary Integral Equations on Similarity Flow for Uniform Symmetrical Entry of Wedges
,” Appl. Ocean Res.
,
66
, pp. 23
–31
.10.1016/j.apor.2017.05.00621.
Meyerhoff
,
W. K.
, 1970
, “
Added Masses of Thin Rectangular Plates Calculated From Potential Theory
,” J. Ship Res.
, 14(2), pp. 100
–111
.https://www.onepetro.org/journal-paper/SNAME-JSR-1970-14-2-10022.
Watanabe
,
I.
, 1986
, “
On Hydrodynamic Impact Pressure Acting Upon Flat Bottomed Ships
,” J. Soc. Nav. Archit. Jpn.
,
1986
(159
), pp. 193
–202
.10.2534/jjasnaoe1968.1986.19323.
Watanabe
,
I.
, 1986
, “
Theoretical Investigation on the Wave Impact Loads on Ships
,” Proceedings of 16th Symposium on Naval Hydrodynamics
, Berkeley, CA, Jul. 13–16.24.
Watanabe
,
I.
, 1987
, “
Effects of the Three-Dimensionality of Ship Hull on the Wave Impact Pressure
,” Nav. Arch. Ocean Eng.
,
26
(162
), pp. 33
–47
.10.2534/jjasnaoe1968.1987.162_16325.
Hui
,
S.
, and
Faltinsen
,
O. M.
, 2012
, “
Hydrodynamic Forces on a Semi-Displacement Ship at High Speed
,” Appl. Ocean Res.
,
34
, pp. 68
–77
.10.1016/j.apor.2011.10.00126.
Zhao
,
R.
,
Faltinsen
,
O. M.
, and
Aarsnes
,
J.
, 1996
, “
Water Entry of Arbitrary Two-Dimensional Sections With and Without Flow Separation
,” Proceedings of the 21st Symposium on Naval Hydrodynamics
, Washington, DC, pp. 408
–423
.27.
Carcaterra
,
A.
,
Ciappi
,
E.
,
Iafrati
,
A.
, and
Campana
,
E. F.
, 2000
, “
Shock Spectral Analysis of Elastic Systems Impacting on the Water Surface
,” J. Sound Vib.
,
229
(3
), pp. 579
–605
.10.1006/jsvi.1999.251728.
Luo
,
H.
,
Wang
,
H.
, and
Soares
,
C. G.
, 2012
, “
Numerical and Experimental Study of Hydrodynamic Impact and Elastic Response of One Free-Drop Wedge With Stiffened Panels
,” Ocean Eng.
,
40
(1
), pp. 1
–14
.10.1016/j.oceaneng.2011.11.00429.
Yu
,
P.
,
Ong
,
M. C.
, and
Li
,
H.
, 2018
, “
Effects of Added Mass and Structural Damping on Dynamic Responses of a 3D Wedge Impacting on Water
,” Appl. Sci.
,
8
(5
), p. 802
.10.3390/app805080230.
Yu
,
P.
,
Li
,
H.
, and
Ong
,
M. C.
, 2019
, “
Hydroelastic Analysis on Water Entry of a Constant-Velocity Wedge With Stiffened Panels
,” Mar. Struct.
,
63
, pp. 215
–238
.10.1016/j.marstruc.2018.09.00731.
Wen
,
X.
,
Liu
,
P.
,
Qu
,
Q.
, and
Hu
,
T.
, 2020
, “
Impact of Wedge Bodies on Wedge-Shaped Water Surface With Varying Speed
,” J. Fluids Struct.
,
92
, p. 102831
.10.1016/j.jfluidstructs.2019.10283132.
Wen
,
X.
,
Liu
,
P.
,
Qu
,
Q.
, and
Hu
,
T.
, 2020
, “
Impact of a Plate on an Asymmetric Water Wedge
,” ASME J. Fluids Eng.
,
142
(4
), p. 041301
.10.1115/1.404533033.
Hughes
,
O. F.
, 1972
, “
Solution of the Wedge Entry Problem by Numerical Conformal Mapping
,” J. Fluid Mech.
,
56
(1
), pp. 173
–192
.10.1017/S002211207200225334.
Battistin
,
D.
, and
Iafrati
,
A.
, 2004
, “
A Numerical Model for the Jet Flow Generated by Water Impact
,” J. Eng. Math.
,
48
(3/4
), pp. 353
–374
.10.1023/B:engi.0000018173.66342.9f35.
Hirt
,
C. W.
, and
Nichols
,
B. D.
, 1981
, “
Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries
,” J. Comput. Phys.
,
39
(1
), pp. 201
–225
.10.1016/0021-9991(81)90145-536.
Ubbink
,
O.
, 1997
, “
Numerical Prediction of Two Fluid Systems With Sharp Interfaces
,” Ph.D. thesis,
Imperial College of Science, Technology and Medicine
, London, UK.37.
Muzaferija
,
S.
,
Peric
,
M.
,
Sames
,
P.
, and
Schellin
,
T.
, 1998
, “
A Two-Fluid Navier-Stokes Solver to Simulate Water Entry
,” Proceedings of 22nd Symposium on Naval Architecture
,
National Academy Press
, Washington, DC, pp. 277
–289
.38.
Zhang
,
X.
,
Liu
,
P.
,
Qu
,
Q.
,
Wang
,
R.
, and
Agarwal
,
R. K.
, 2018
, “
Effects of Froude Number and Geometry on Water Entry of a 2-d Ellipse
,” J. Hydrodyn.
,
30
(4
), pp. 738
–749
.10.1007/s42241-018-0040-739.
Zhang
,
X.
,
Liu
,
P.
,
Qu
,
Q.
,
Zhao
,
Y.
,
Hu
,
T.
, and
Agarwal
,
R. K.
, 2018
, “
Numerical Analysis of the Pressure Peak Position Shift With Deadrise Angle in Two-Dimensional Wedge Water Entry
,” ASME J. Fluids Eng.
,
140
(11
), p. 111101
.10.1115/1.404006740.
Yu
,
P.
,
Li
,
H.
, and
Ong
,
M. C.
, 2018
, “
Numerical Study on the Water Entry of Curved Wedges
,” Ships Offshore Struct.
,
13
(8
), pp. 885
–898
.10.1080/17445302.2018.147177641.
Bodaghkhani
,
A.
,
Muzychka
,
Y.
, and
Colbourne
,
B.
, 2018
, “
Three-Dimensional Numerical and Experimental Simulation of Wave Run-Up Due to Wave Impact With a Vertical Surface
,” ASME J. Fluids Eng.
,
140
(8
), p. 081205
.10.1115/1.403936942.
Gurevich
,
M. I.
, 1965
, Theory of Jets in Ideal Fluids
,
Academic Press
, New York.43.
Hughes
,
O. F.
, 1973
, “
Some Characteristics of the Free Surface in the Wedge Entry Problem
,” J. Eng. Math.
,
7
(4
), pp. 367
–375
.10.1007/BF0153542044.
Korobkin
,
A.
, and
Pukhnachov
,
V.
, 1988
, “
Initial Stage of Water Impact
,” Annu. Rev. Fluid Mech.
,
20
(1
), pp. 159
–185
.10.1146/annurev.fl.20.010188.00111145.
Wu
,
G.
, 2012
, “
Numerical Simulation for Water Entry of a Wedge at Varying Speed by a High Order Boundary Element Method
,” J. Mar. Sci. Appl.
,
11
(2
), pp. 143
–149
.10.1007/s11804-012-1116-346.
Yettou
,
E. M.
,
Desrochers
,
A.
, and
Champoux
,
Y.
, 2006
, “
Experimental Study on the Water Impact of a Symmetrical Wedge
,” Fluid Dyn. Res.
,
38
(1
), pp. 47
–66
.10.1016/j.fluiddyn.2005.09.00347.
Carcaterra
,
A.
, and
Ciappi
,
E.
, 2004
, “
Hydrodynamic Shock of Elastic Structures Impacting on the Water: Theory and Experiments
,” J. Sound Vib.
,
271
(1–2
), pp. 411
–439
.10.1016/j.jsv.2003.02.00548.
Wu
,
G.
,
Sun
,
H.
, and
He
,
Y.
, 2004
, “
Numerical Simulation and Experimental Study of Water Entry of a Wedge in Free Fall Motion
,” J. Fluids Struct.
,
19
(3
), pp. 277
–289
.10.1016/j.jfluidstructs.2004.01.00149.
Lewis
,
S. G.
,
Hudson
,
D. A.
,
Turnock
,
S. R.
, and
Taunton
,
D. J.
, 2010
, “
Impact of a Free-Falling Wedge With Water: Synchronized Visualization, Pressure and Acceleration Measurements
,” Fluid Dyn. Res.
,
42
(3
), p. 035509
.10.1088/0169-5983/42/3/03550950.
Yettou
,
E. M.
,
Desrochers
,
A.
, and
Champoux
,
Y.
, 2007
, “
A New Analytical Model for Pressure Estimation of Symmetrical Water Impact of a Rigid Wedge at Variable Velocities
,” J. Fluids Struct.
,
23
(3
), pp. 501
–522
.10.1016/j.jfluidstructs.2006.10.00151.
Youngs
,
D. L.
, 1982
, Time Dependent Multimaterial Flow With Large Fluid Distortion
,
Academic Press
, New York.52.
Payne
,
P. R.
, 1994
, “
Recent Developments in Added-Mass Planning Theory
,” Ocean Eng.
,
21
(3
), pp. 257
–309
.10.1016/0029-8018(94)90002-753.
Zeraatgar
,
H.
,
Malekmohammadi
,
J.
,
Javaherian
,
M. J.
, and
Moradi
,
H.
, 2019
, “
Sampling Rate Effect on Wedge Pressure Record in Water Entry by Experiment
,” Ocean Eng.
,
179
, pp. 51
–58
.10.1016/j.oceaneng.2019.03.00654.
Barjasteh
,
M.
,
Zeraatgar
,
H.
, and
Javaherian
,
M. J.
, 2016
, “
An Experimental Study on Water Entry of Asymmetric Wedges
,” Appl. Ocean Res.
,
58
, pp. 292
–304
.10.1016/j.apor.2016.04.013Copyright © 2021 by ASME
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