A survey of research on slamming impact pressure

29 MEl 1980

ARCHIEF

MPR AsSocATrS, iNC.

CoP/e:'

Lab. y. Scheepsbouwkunde Technische Hogschoi

_:"

Deift A SURVEY OF RESEARCH ON SLAMMING IMPACT PRESSURE

by F. Sellars 4

Prepared for

16th American Towing Tank Conference Sao Paulo, Brazil

August 9-13, 1971

This research was carried out under the

f _{Naval Ship Systems Command}

General Hydromechanics Research Program Subproject SR 009 01 01, administered by the Naval Ship Research and Development Center.

Prepared under the Office of Naval Research Contract N00014--7 1-C-0045

Reproduction in whole or in part is permitted for any purpose of the United States Government

I. INTRODUCTION AND SUMMARY

The impact of the bottom structure of a ship's hull on the water surface has been termed 'slamming". The hydrodynamic loads produced by such impacts can cause damage and to date a reliable design technique for pre

dicting them is lacking. The purpose of this review is to cover recent

experi-mental and theoretical study of ship slamming. Differences in test results

and in comparisons between theory and experiment for both magnitude of pressure and frequency of occurrence of slamming are noted. Next, scaling laws for slamming impact pressure, together with instrumentation scale effects, are reviewed and resolution of differences in test results is discussed.

The slamming pressures treated in this review are termed "impact pressures. They are of short duration and are of local extent. The local geometry of a ship's bottom structure in the region of slamming impacts is flat in a number of cases and for flat impacts the relative velocity of the body at the time of impact, V, is taken as constant during the period

of occurrence of the impact pressure. Hydrodynarnic slamming theories,

Reference (1), consider the flux of momentum due to reduction of body velocity and setting the fluid into motion and thus are not considered to apply to the local impact pressures.

L

II. THEORY AND EXPE.MENT

An examinatioii of seakeeping model and two-dimensional

drop test peak impact pressure data in light of a theoretical _{pressure that}

takes account of model material and elastic characteristics, Reference (2),

indicated qualitative agreement with theory. This theory neglected effects

of air and experimental pressures were found to lie below the theoretical pressure. _{Theoretical analyses of cushioning effects of entrapped air on} pressure, References (3) and (4), have assumed that the structure is rigid

and comparison of drop test data with these theories, References (5) and

(4), has shown that experimental pressures lie substantially below theory. These discrepancies between theories and experiment have led to further work and a theoretical model that considers the coupled effects of an elastic structure and cushioning by air bubbles entrapped in the water has

been used to obtain a relation for the peak impact _{pressure, Reference (8).}

The absolute peak impact pressure is determined and results are discussed later in this paper under the review of scaling laws.

Experimental measurements of slamming pressures in labora-tories have covered drop tests of stiffened plate structures and unstiffened

plates and tests with seakeeping1' models in waves. The term "seakeeping'

model applies to a three dimensional ship form model in waves. Materials

of construction have included metals, wood, and plastic and recent

experi-ments are summarized in Table (I),

Type of Experiment Drop Tests Drop Tests Drop Tests Drop Tests Drop Tests

Seakeeping and Drop Tests Drop Tests Drop Tests Seakeeping Test TA:BLE I SUMMARY OF EXPERIMENTS Model Reference Aluminum Block (6) Aluminum Plates (5)

2-D Wood Ship Sections (7)

Steel, Aluminum and

Lucite Plates (9)

2-D Wood and Aluminum

Ship Sections (10)

3-D Wood Mariner Model

(il)

Steel Plates and Stiffened

Plates (12)

Steel Stiffened Plate

Structures (13)

3-D Fiberglass Merchant

Form (14)

A comparison of impact pressure versus relative velocity at

im-pact, Figure (1), shows that for the same impact velocity, pressures recorded

in drop tests are noticeably larger than those determined from seakeeping model tests. In addition, experiments with a two-dimensional model of station

3-1/2 of a Mariner form and a 5 foot model of a Mariner form have covered a

comparison of drop tests of both the two-dimensional and three-dimensional

models and tests of the seakeeping model in waves, Reference (11).

Compari-son of gauge pressures as a function of relative velocity at impact indicated

that for the same velocity the 2-D drop test gave the highest pressure, drop

tests with the 3-D model resulted in lower pressure and that tests in waves

resulted in the lowest pressure of the three.

The frequency of occurrence of slamming has been experimentally determined in long-time sample model tests of a fiberglass seakeeping model

of a cargo ship, Reference (14). The experimental intervals corresponded to

from 5. 4 to 10. 9 hours full scale operation and thus _{are expected to lead to}

Laccurate determination of

frequency of occurrence. Comparison of experi-mentally determined frequency of occurrence of slamming with theoretical

predictions showed the theory to be high by a factor of from 1.8 to 5.4. Instances

where full scale determination of frequency of slamming _{have differed from}

theory are discussed in Reference (15).

-¡000.0

100.0

10.0

10

CU1WARISOU OF 1UPACT PRESSURE

-RELAT IOS OBTA ILD FRC1 EXPER IMEUf S O MODELS

FIGURE I

-5-.

I A I _1 S-2A -t-MF-3 f

/0/

/

r

ir

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-z'-T

'1JT I AND r OS-2 CB-,j,

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H--MAR DROP UER - STA. 3-TEST 2

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I

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ORt

-

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t

G XOS-2 EP VKG-3 1AR CB-I S-2A

¿NAR---3

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RELATiVE VELOCTY I1 FT./SEC. w V) V) w o-w -'X 1.0

Scaling laws applicable to the simulation of peak impact pressure are reviewed. The purpose of this review is to provide a basis for study of differences among slamming experiments noted previously.

The results for absolute slamming pressure, P2, obtained in Reference (8) lead to the identification of scaling parameters. These are summarized below: p1C1

ôcpC

_SS

V

pG

₁₁

V

o;

Vi oPi cP1 with V = i p1C1

OC

¡s

s

OC

Io o and

Pi

C1

G::

c,p C o o Where: B = width of model

b = width of plate panel

P1 absolute ambient pressure

P2 = _{absolute impact pressure}

V _{relative velocity at impact}

impact area parameter, Reference (2)

-6-ILl. REVIEW CF SCALING LAWS

structure to fluid impedance ratio

Non-dimensional relative velocity

mixture impedance ratio

p, C1

mass density and wave speed for structure

' C mass density and speed of sound for pure liquid

p, Cs

= mass density and speed of sound for air, water mixture

In addition, from consideration of the relative magnitude of momentum flux terms

b = Panel scale ratio,

B

E =

- - , panel parameter,

lb

h

Other parameters determined from general consideraons of structure-fluid interactions, References l6), _{(17), and (18), include Reynolds number, Froude} number, Weber number, and Cauchy number.

These parameters are defined below

2 2

oV

pV

Cauchy No. Inertia force = o o

00

Elastic force E 2

P1CL

Froude No. Inertia force = VO

Gravitational force

r

Reynolds No. Inertial force VBo

Viscous force Z)

Weber No. = Inertial force = 1/2 V B

Surface tension force ô

where

CL = speed of sound in model material

E = èlastic modulus of structure

kinematic viscosity of liquid

o = surface tension

The effect of Reynolds.' number is evaluated in Reference (18)

which shows the Reynolds' number has a negligible effect. Experiments which

covered variation of surface tension, Reference (6), indicate that its effects

may be neglected. The Weber number covers surface tension forces and hence

need not be scaled.

The Froude number gives the relative magnitude of inertial forces

to gravity forces. The Cauchy number gives the relative magnitude of inertial

forces to elastic forces and it is proportional to (V/V1)2. If the materials in a model are the same as the full scale structure, then the invariance of

(Vo/V1)2 requires that V be the same in both model and full size. _This

intro-duces a dilemma since Froude scaling requires velocity to be proportional to

the square root of the scale ratio. _{As noted in the introduction to this review,}

gravitational forces which are associated with reduction of body velocity V are considered small in comparison to inertia forces, hence Vo/V1 is to he used in correlations of data for impact pressure rather than Froude number.

Model data have been correlated on the basis of Vo/V1 in

Reference (8). Some results are shown in Figure (2) for two groups of models

with similar structure impedance ratio C and correlation of non-dimensional impact pressure for different models on the basis of Vo/V1 is noted when C is held constant. Characteristics of the models. covered in this figure are

given in Table II.

ioo, o 10.0 LEGEND C LO 1.0 10.0 y_o vi

MODEL RESULTS FOR IMPACT PRESSURE

C = 0,4OandC = 9.0 FIGURE 2

-9-100.0 1000.0

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flj 8J'

EtE EF t-1r

_-Hr-'

fl-i-MARINER 3 0.39 KG 3,4 0.38

VEP

.40 o S-2 9, c: os-z 9.5

(1) estimate Model Ref. Overall Size SUMMARY OF MODELS ' C BI b td (Inches) h (inches) Material Gas Liquid Mariner (3-1/2) 11 5.5' x .79' x .37' Pine Air Fresh 1. 114 .705 .39 1.0 .375" & 0.50" . 1875 & .500" .25 OS-2 10 26. 5" x 33" x 30"

Pine & Alum. Air

Fresh 0.36 1.0 9.50 1.0 .375" & 3.5" .00214 J-IO .500" .00358 CB-i 12 26. 5" x 20" (4" x ¿6. 5" x 1/2") Steel Air Fresh 2.54 1.0 3. 18 5.0 37511(1) 0.50" . 1975 H2 O KC-3&4 12 80" x 90" (8" x 18" z .125") Steel Air Salt 20.4 1.0 .38 10.0

50''

0.125" 1.0 H2 O Er' i 15-3/4" , 26-1/4" Steel Air Fresh 20.4 1.0 .40 1.0 3751,11) 0.25" .375 x 1/4' H20 13 10' 2" x 7' 9" (9" x 30" x 1/2" Steel Air Fresh 5.74 1.0 1.42 10.3 . 50' 0.50" .25 H2 O S-ZA .6 2" Diameter Aluminum Air Fresh .24 9. 10 1.0 37S 2.0" .047 H20 3-UY 7 12" z 12" x 4" Maple Air Fresh . 13 2.04 1.0 .5011(1) 4.0" .031 H2 O

IV. INSTRUMENTATION SCALE EFFECTS

Instrumentation used to measure and record slamming impact pres sure can lead to scale effects. Two possible sources of scale effects which can result in errors in measurement o.f peak impact pressure are

revi ewe d.

Effects of Pressure Transducer Size

Scale effects due to the finite size of a pressure transducer are

evaluated by means of an impact area parameter _a. The impact area

para-meter is covered in Reference (2), and is defined by

i D

Where D the diameter of the surface area of the plate that is impacted by water and h = plate panel thickness. When the impact diameter D is greater than or equal to the diameter of the pressure transducer, ed. no size scale effect is

expected, while in cases where the transducer diameter t is greater than the

impact diameter D, a reduction in the peak pressure measured due to a size scale effect is likely. This may be evaluated by defining a transducer area

parameter,

_{a; as}

i td

where d = diameter of the pressure transducer.

Cases have been no;ed, Reference (8), where _{sizes of pressure}

transducers used in drop tests of relatively flexible _{structures can lead o}

attenuation of peak impact pressure. Instrumentation Frequency Response

Slamming impact pressures have been noted to have a short

dura-tion. Impact pressure pulse durations of from 2 x io to 10 x l0- seconds

have been observed in drop tests of metal structures, Reference (12). In order to prevent attenuation of peak impact pressure measurements the pressure transducer and associated recording instrumentation must have a frequency response that is flat to a high enough frequency to cover the impact pressure pulse. A pulse period of 2 x iü seconds corresponds to a frequency of 500 Hz.

As an example of this effect it has been noted, Reference (19), that instrumentation used in recent full sa1e measurements of slamming pres sure on the S.S. Wolverine State had a frequency response flat only to

50 Hz and thus would not be expected to record true peak slamming pressures.

-Type of Experiment

rD

V. DISCUSSION

The results of the theoretical analysis for _{a flat impact with s}

truc-ture elastic forces and with entrapped air accounted for, Reference (8), require

that both the ratio of structure-to-fluid impedance CI6 _{and non-dimensional}

relative velocity o/ be scaled in order scale peak impact _pressure.

The different types of experiments conducted by laboratories _have

been found to fall into different regimes of structure impedance _{C and} V01

1

These are compared below and properties of the models covered are summarized in Table II.

C

Vo/\;1 p2/p1

This comparison shows that the experiments compared on the basis of relative

impact velocity V0 inFire (1), fall into markedly diff erent areas when

struc-tural impedance ratios C and non-dimensional impact _velocity V01 _are

con-i

sidered. Because of this, the observed differences in _{pressure noted are to}

be expected.

13 -Drop Tests of Blunt Rigid

Bodies

Drop Tests of Plates

Seakeeping Model 9. 1 9. 0 -0.40 0.40 20 to 1000 20.0 to 200.0 2.0 to 10.0 1.0 to 100.0 1.0 to 20. 0 1.0 to 2.0

Several of the models tested were geometrically similar to station

3-1/2 of the Mariner, These models were

Model Mariner 3-1/2 os-2 s-Uv C 0.39 9. 50 2.04

and it is seen that they fall into different groups with regard to their structural characteristics. Because of this their impact pressure measurements are not expected to correlate.

The five foot long pine Mariner model has a structural impedance ratio that is similar to that for a panel in a steel stiffened plate structure C = 0. 40

and the seakeeping model data fall in the velocity region 2.0

<

o/

<10,0. i

An estimate of the structure impedance ratio for a full scale steel _{cargo ship}

V

gives C 0. 65 and slams are expected rn the velocity region of 30 < o/ < 90.

1

Thus, although the seakeeping model has a structural impedance C that is close

to a full scale cargo ship the seakeeping model tests do not scale the cargo ship

peak impact pressures due to the differences in non-dimensional velocity V01

Impact pressure data from experiments by oihers has been converted

to ratios of absolute impact pressure to ambient pressure and correlated on the

basis of a theoretical model structure impedance ratio and _{a non-dimensional}

impact velòcitv, Reference (8).

-The use of absolute pressure rather than gauge pressure in Reference (8) is dictated by considerations of the speed of a shock wave in

a liquidas mixture.

This work concludes that: (1) impact pressure results

from drop tests of models whose non-dimensional velocity and structure impedance ratio correspond to full scale values provide a satisfactory design

basis, nd (2) seakeeping model impact pressure data does not appear to be

a reliable design basis for peak pressure, although such tests are useful for the evaluation of the frequency of slamming.

Further work is required to establish a reliable design technique for slamming impact loads and areas for investigation include:

Establishment of confidence in scaling lavis based on (Vo/V1) by extra-polation of model data to full scale ships for which slamming pressure data is available.

Review of factors involved in discrepancies noted between theory and experiment for frequency of occurrence of slamming.

Analysis of the mechanics of air bubble entrapment in water during a slam

so that the relative mass of air entrapped may be predicted. The relative

REF EREN CES

Chu, Wen-Hwa and Abramson, H. N., "Hydrodynamic Theories of

Ship Slamming - Review and Extension, " Journal of Ship Research Vol. 4, No. 4, March, 1961..

Sellars, F. H., "The Influence of Structural Characteristics on Slamming Impact Pressures, " Journal of Shio Research, Vol. 15, No. 1,

March, 1971.

Verhagen, J. H. G., "The Impact of a Flat Plate on a Water Surface,

Journal of Ship Research, Vol. 11, No. 4, December, 1967.

Lewis on, G., "On the Reduction of Slamming Pressures, " Transactions,

RINA, Vol. 112 (1970).

Gerlach, C. R., "Investigation of Water Impact of Blunt Rigid

Bodies-Size Scale Effects, " Technical Report No. 2, Southwest Research

Institute Project No. 02-2036, November, 1968.

Gerlach, C. R., "Investigation of Water Impact of Blunt Rigid

Bodies-Real Fluid Effects, " Technical Report No. 1, Southwest Research

Institute Project No. 02-2036, December, 1967.

Gerlach, C. R. and Astleford, W. J., "Investigation of Water Impact of

Blunt Bodies, " Final Report, Southwest Res carch Institute Project No. 02-2036, December, 1970.

Sellars, F. H., "Slamming Impact Pressure, " MPR-282, Report being prepared for NSRDC, June, 1971.

Kamel, A. M., "Shock Pressures Caused by Waves Breaking Against

Coastal Structures, ' Research Report H-68-2, U. S. Army Engineer

Waterways Experiment Station, September, 1968.

Ochi, M. D., and Schwartz, F. M., "Two-Dimensional Experiments on

the Effect of Hull Form on Hydrodynamic Impact, " DTMB Report 1994, May, 1966.

Ochi, M. D., and Bonilla-Norat, J., "Pressure-Velocity Relationship in Impact of a Ship Model Dropped onto the Water Surface and in Slamming in Waves," NSRDC Report 3153, June, 1970.

Chuang, 5. L., "Investigation of Impact of Rigid and Elastic Bodies, NSRDC Report 3248, February, 1970.

-REFERENCES - Continued

Lewis on, G., and MacLean, W. M., "On the Cushioning of Water Impact

by Entrapped Air, Journal of Ship Research, VoI. 12, No. 2,

June, 1968.

Oakley, O. H., "An Analytical and Experimental Study for Prediction

of Ship Impact Forces in a Seaway. " Report No. 69-6, Massachusetts Institute of Technology, Department of Naval Architecture and

Marine Engineering, August, 1969.

Loukakis, T. A., "Computer Aided Prediction of Seakeeping Performance

in Ship Design, " Report No. 70-3, Massachusetts Institute of

Technology, Department of Naval Architecture and Marine Engineering, August, 1970.

Abramson, H. N., "1-lydroelasticity - Some Problems and Some Solutions, "

ASME, Fluid-Solid Interaction Symposium, 1967.

1-Teller, S. R., _{"Structural Similitude for Impact Phenomena, " DTMB}

Report 1071, April, 1958.

Baker, W. E., Westine, P. S., Garza, L. R., and Hunter, P. A.,

"Water Impact Studies of Model Apollo Command Module, Appendix

A-Impact Simulation, ' Final Report, SWRI Project No. 02-1541,

August, 1965.

Henry, J.R. and Bailey, F.C.,

"Slamming of Ships: A Critical Review

of the Current State of Knowledge, " SSC-208, 1970.

17