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Review Articles

Hull Slamming

[+] Author and Article Information

Department of Mechanical Engineering
and Energy Processes,
Southern Illinois University,
Carbondale, IL 62901-6603
e-mail: abrate@engr.siu.edu

Manuscript received September 19, 2011; final manuscript received February 1, 2013; published online February 26, 2013. Assoc. Editor: Kazuo Kashiyama.

Appl. Mech. Rev 64(6), 060803 (Feb 26, 2013) (35 pages) doi:10.1115/1.4023571 History: Received September 19, 2011; Revised February 01, 2013

This report presents an in-depth review of the current state of knowledge on hull slamming, which is one of several types of slamming problems to be considered in the design and operation of ships. Hull slamming refers to the impact of the hull or a section of the hull as it reenters the water. It can be considered to be part of a larger class of water entry problems that include the water landing of spacecraft and solid rocket boosters, the water landing and ditching of aircraft, ballistic impacts on fuel tanks, and other applications. The problem involves the interaction of a structure with a fluid that has a free surface. Significant simplifications can be achieved by considering a two-dimensional cross section of simple shape (wedge, cone, sphere, and cylinder) and by assuming that the structure is a rigid body. The water is generally modeled as an incompressible, irrotational, inviscid fluid. Two approximate solutions developed by von Karman (1929, “The Impact on Seaplane Floats During Landing,” NACA Technical Note NACA-TN-32) and Wagner (1932, “Uber stoss und Gleitvorgange an der Oberache von Flussigkeiten,” Z. Angew. Math. Mech., 12, pp. 192–215) can be used to predict the motion of the body, the hydrodynamic force, and the pressure distribution on the wetted surface of the body. Near the intersection with the initial water surface, water piles up, a jet is formed, and the solution has a singularity in this region. It was shown that nearly half of the kinetic energy transferred from the solid to the fluid is contained in this jet, the rest being stored in the bulk of the fluid. A number of complicating factors are considered, including oblique or asymmetric impacts, elastic deformations, and more complex geometries. Other marine applications are considered as well as applications in aerospace engineering. Emphasis is placed on basic principles and analytical solutions as an introduction to this topic, but numerical approaches are needed to address practical problems, so extensive references to numerical approaches are also given.

Copyright © 2011 by ASME
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References

Figures

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Fig. 1

Three phases in the impact of a projectile in water (Mackey [9]): (a) flow formation, (b) open cavity (or cavity running), (c) closed cavity

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Fig. 2

Cylinder of unit length floating on a liquid. The external force per unit length f is balanced by the vertical components of the two surface tensions σ. The geometry is defined by the wetting angle θ.

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Fig. 3

Von Karman's momentum approach. Penetration depth ζ and deadrise angle β.

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Fig. 4

Water pile-up near the edge, as estimated by Wagner [7]

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Fig. 5

Velocity of the wedge as a function of the penetration depth for three values of the deadrise angle β=5 deg,15 deg,30 deg when Vo = 1 m/s and M = 100 kg

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Fig. 6

Experimental results and theoretical predictions for the example of Carcaterra and Ciappi [36] ((a) maximum force versus initial velocity, (b) time to maximum force versus initial velocity, (c) product F*t* in Eq. (3.13) versus initial momentum)

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Fig. 7

Wagner's model (top: wedge entering the water; bottom: Wagner's expanding plate model)

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Fig. 8

Water entry of a wedge (Greenhow [52], reproduced with permission from Elsevier)

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Fig. 9

Water entry of a wedge with small deadrise angle showing the three flow regions (I: outer flow region; II: inner flow region; III: jet flow region)

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Fig. 10

Local coordinates in the inner region

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Fig. 11

Air cushioning of flat bottom body prior to water entry

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Fig. 12

(a) Asymmetric water impact of a wedge; (b) oblique water impact of a wedge

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Fig. 13

Floating wedge subjected to an impulsive start

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Fig. 14

Impact of flat-bottom body on shallow water. Compressive wave propagating downwards through the water.

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Fig. 15

Impact of flat-bottom body on shallow water. The shock wave reflected from the bottom and the outflow of the liquid from beneath the body is still not developed (adapted from Korobkin [98]).

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Fig. 16

Asymptotic expansion model for the third stage (adapted from Korobkin [98])

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Fig. 17

Two degree of freedom model for water impact

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Fig. 18

Elastic wedge model: two beams pinned at the vertex and connected by a rotational spring

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Fig. 19

Penetration of the initial water level by a sphere

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Fig. 20

Water entry of a steel sphere

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Fig. 21

Water entry of a golf ball

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Fig. 22

Water entry of a ping pong ball

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Fig. 23

Nondimensional force F˜=F/(πρR2Vo2) versus the nondimensional penetration depth ζ/R for three spheres with different specific densities: steel ball, aluminum ball, ping pong ball

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Fig. 24

Water entry of Apollo capsule (Cappelli et al. [116])

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Fig. 25

Acceleration versus time for vertical impact of Apollo capsule

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Fig. 26

Acceleration versus penetration depth for vertical impact of Apollo capsule

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Fig. 27

Sphere impacting the surface of the water with an oblique linear velocity V and an angular velocity ω

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Fig. 28

Oblique impact of a sphere on the surface of a fluid. (a) Contact between the fluid and the water; (a) total force F and (b) lift and drag components.

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Fig. 29

Water entry of a cone

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Fig. 30

Oblique impact of a projectile with a conical tip (Gurney [139])

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Fig. 31

History of the hydrodynamic force for a horizontal cylinder during vertical water entry in terms of the nondimensional force F˜=F/(πρVo2R) and the nondimensional time t˜=Vot/R obtained from (a) Eqs. (4.44) and (4.46) and (b) Eq. (4.48)

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Fig. 32

Model for stone skipping problem (adapted from Nagahiro and Hayakawa [175])

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Fig. 33

Transient response of a SDOF system to a sine pulse: nondimensional displacement versus nondimensional time (Eq. (5.2)). Quasistatic response QS and response for three values of the ratio TL/TN: 0.5, 0.2, 0.1.

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Fig. 34

Shallow water entry of a rigid body (adapted from [201,202]). I: region beneath the entering body; II: the jet root, III: the spray jet; IV: the outer region.

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Fig. 35

Elastic spherical shell impacting the water surface (adapted from Bingman [210]). Solid line: initial shape; dashed line: deformed shape.

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Fig. 36

Ditching of airplanes (Thompson [350])

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Fig. 37

Attitudes of space capsule before water landing (McGehee et al. [411]). (a) Positive attitude, (b) zero attitude, (c) negative attitude. Dash-dot line: flight path.

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Fig. 38

Hemispherical wave in water after a 18-in-diameter ball impacted the surface and penetrated 7.8 cm. The velocity at that instant is 3520 ft/s (1072.9 m/s), which is 35% less than the impact velocity (McMillen [111], reproduced with permission from the American Physical Society).

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Fig. 39

Polar coordinates used in Eqs. (9.3) and (9.4) for the impact of a sphere on the water surface

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Fig. 40

Drag coefficient Cd as a function of Reynolds number Re (Eq. (9.11))

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Fig. 41

Shock wave generated by the impact of a projectile on a water-filled tank with an initial velocity of 1243 m/s (Petitpas et al. [449], reproduced with permission from Elsevier)

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Fig. 42

Formation of a wave front for a supersonic projectile

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