Slamming on forced oscillating wedges at forward speed, Part I: Test results

DeiftUniverefty of Technology Ship Hydromechanics Laboratory

Mekeiweg2

2628 CD Oath The Netherlands Phone 015 - 78 6882

LUI

_{G ON FORCED OSCILLATING}

ES AT FORWARD SPEED.

P1RT I: TEST RESULTS.

Report No. 888/1991

W. Beukeimn* and D. Radev"

I.S.:P., Vol. 39, Nr.420, 1992

Ship Hydromechanics Laboratory, Deift University of

Technology, The Netherlands.

**

_{Bulgarian Ship Hydromechanics Centre, Var, Bulagria,}

INTERNATIONAL SHIPBUILDING PROGRESS

Volume 39, no. 420

CONTENTS

M.Rf Haddara and fl Cumming, 'Experimental Investigation into

the Physics of Roll Damping of a Long, Slender Hull Form'

_323-343

Jianbo Hua, 'A Study of the Parametrically Excited Roll Motion

of A RoRo-Ship. in Following and Heading Waves'

_345-366

L.J.M. Adegeest, 'Linear and Nonlinear Hydrodynainic FOrces

Acting on a Sgmented Heaving Wigley Mod1'

_367-389

G. Deliporanides, 'Finite Element Shaft Alignment on Elastic

Foundation'

_391-397

D. Radev and W. Beukelman, 'Slamming on Forced Oscillating

Wedges at Forward Speed', Part I

- Test Results

399-422

J.J.W. Nibbering, 'Structural Safety and Fatigue f Ships'

_423-435

ON FORCED OSCILLATING

SPEED.

PART I: TEST RESULTS

D.

Radev* and W. Beúkeiman**

*

Bulgarian Ship Hydródynamics Centre, Varna,

Bulgaria.

Research Fellow at Ship Hydromechanics Lab.,

Deif t University of Tèchnology,

The Netherlands.

Ship Hydromechanics Lab., Deif.t University

of Technology, The Netherlands

As follow-up of former research forced, vertical

oscillation experiments have been performed to

detennine peak pressures and rise times for four

metal wedges with diffreflt dead rise angles.

These pressures have been meaSured as function

of vertical oscillation speed,

trim angle and

forward speed.

The results in general show that the peak values

of the impact pressures are proportional to the

sqiared value of the vertical speed,

however,

also the influence of forward speed appeared to

be signifkcant

in most of the existing

mathema-tical models this relation has unsufficiently

accounted for as shown here. Application of the

prediction models in this respect is urgently

required.

D

ES AT FORWARD

Nomenclature

B

beam

R

depth

proportionality constant

L

length

rn'

sectional added mass

N'

sectional damping

p

.pres sure

s

vertical displacement.

(upwards positive)

t

time

U

forward speed

V

vertical speed

(upwards positive)

half width of the submerged cross section

on the waterline

trim angle (bow up positive)

dead rise angle

p

mass density of fluid

1. introduction

It

is well known that for nonnal ship types

voluntary speed reduction is in generai required

to avoid slanmdng.

For modern high speed craft, however, slamming

is becoming an important problem.

In this research the attention therefore will 'be

focussed at high forward speeds in relation to

'Usual calculation methods related to lower ship

speeds are mentioned in '[1]

and. will be

consid-ered in section 4.

In the past slamming has experimentally been

in-vestigated at the Ship Hydromechanics Laboratory

of the Deift University in the Netherlands by

forced oscillation of a segmented shipmodel

[:1]

For

p].edi'ction

a

calculation model

based on

strip-theory and

fluid momentum exchange has

been developed showing that the peak pressures

are proportionally related t'o the squared

verti-cal velocity.

In case of usual moderate ship

speeds the agreement between measurements and

predictions appeared to be rather satisfactory.

It should be remembered that the forward speed

is

.

only accounted for in case of a trim angle as

the arise of a vertical component of the forward

velocity.

The next research with 'a fòrced oscillated

rec-'tangular' and triangalar cylinde

at high forward

speeds

[21] (in

Dutch)

showed

less

reliable

results.

This might have been due to the influence of a

bow wave in the vicinity of the. pressure

trans-ducers, but also due to the elasticity of the

polyester material or/and a remaining

defonna-tion of the bottom resulting in phenomena as air

inclusion.

For this reason it was decided to construct four

stiff metal wedges with dead rise angles of O,

0.5, 1.0 and 10 degrees.

From preceeding calculations and test's it viz.

withn small dead rise angles up to

i

or

2

degree.

For each wedge five pressure transducers were

placed on a transverse line near the rear side

of the wedge.

With those wedges oscillating experiments have

been carried out to determine maximum slamming

pressures and rise times dependent on vertical

oscillation

speed,

high

forward

speed,

trim,

'angle (bow Up)' and dead rise angle.

The test results in general showed for the peak

values of the slamming pressures proportionality

to the squared value of the vertical speed and

also a strong: influence of forward speed. This

last relation was not accounted for in most of

the existing calcuIat'ion models..

In part II an extension and improvement of the

calculation model as descr±bed in[l]

will be

presented

especially

with

respect

to

the

influence

of

forward

speed and 3-D

effects.

Moreover it appeared from the test results that

the. peak pressures' increase with trim angle,

while the rise times decrease with trim angle,

vertical and forward velocity.

There

is

'also

observed a slight reduction of the peak. pressure

from' the centre i:ine of the wedge to the edge

and

a

strong

reduction

for

the

wedge

with

highest dead rise angle.

2. 'Test description

As.

said before

in

the introduction the last

research [2]

related to slamming showed results

with a strong dispersion. This research has been

carried out wi'th a triangular and rectangular

cylinder manufactured, from glass

fibre

r5in-f orced polyester. The pressure transducers were

placed at the forward part of the model while

trim angles were adjusted with the bow up. From

the observations it appeared that a strong bow

wave

was

always' present

in vicinity

of'

the

pressure. transducers so that the actual trim

angle in most cases was not according to the

required nominal trim angle if one looks at the

position of the water-level. Moreover it

appear-ed that the low elasticity of the polyester

material not only caused an actual, but also a

permanent deformation resulting in a not desired

air inclusion.

To avoid all these objections and to continue

the

experimental

and

analytical

slamming

research stiff metal wedges were constructed

with the pressure transducers as aft as

possi-ble. Carrying out a heaving motion including a

trim angle with the bow up resulted in a direct

and first contact of that rear part of the wedge

in which the pressure transducers were mounted,

so that no pressure wave was present at the

moment of impact.

2.1. Wedges

Four wedges with small dead rise angles were

constructed as shown in figure 1 and table 1.

The dimensions are:

L

X

B

X

H = 0.50

X

0.25

X

0.25m

From former research

[2]

it appeared that high

peak pressures only arise for small dead rise

angles, up to 1 or 2 degree. For this reason the

wedges (except nr.4) have such restricted

dead-rise angles. Wedge nr.4 with a dead dead-rise angle

of .10 degrees was chosen to demonstrate the fall

in the peak pressures.

Five

pressure

transducers

were.

placed

on

a

transverse line 10 mm from the aft edge of the

wedge as denoted in figure 2 Showing the wedge's

bottom.

Table i

Figure 2. Wedge's bottom.

Wedge nr.

Dead rise ß

Half beam (3m)

mm

degree

mm

3. 0 0

125

2 1

0.46

125

3

2.5

1.15

125

Transdúcers nr.

I and 3 have the saine distance

of 40 mm t'o

the centre of the wedges and are

supposed to show equal peak preSures.

The pressure transducers in a transverse row

should show the peak pressures as function of

the distance form the centre line.

it. should be noticed that although the. situation

of the wedges i-s meant to approach. a 2-D

condi-tion, 3-D effects' may play an. important role.

2.2. Instrumentation

The. wedges were instrumented with five miniature

semi-conductor pressure transducers. These were

positioned as indicated in figure 2.

The' main characteristics 'of

these transducers

were as follows':

Manufacture

Type

Range

Acceleration

sens i.t ivity

Temperature :drif t

Natural frequency

in air

Diameter of membrane:

Druck Ttd.

PDCR'42

7OkPa, (IO psi.)

of full scale

output ¡g

02% of FSO/°C'

>70kHz

5mm.

To reduce thermal shock at the. instants that the

transducer touched the water, a very thin rubber

coating was applied to the membrane,. Due to thiS

coating and the masS öf the water the natural

frequency was reduced to a lower value. It was

difficult to assess' the amount of this reduction

but juding from manufacturers data and some

ex-periments it appeared plausïble that the

band-width was still higher then 35kHz

Assuming in

addition that the. non-specified-relative damping

factor was' lower then i

(typIcal values for

pressure transducers range from .5 to

.7')

the

rise time can be calculated to be less then

Ì6s.

Rise time is defined here as the time it takes

the transducer output to rise from 10% to 90% of

its final value in response to a step pressure

change.

As the rise times of the .sianuning. pulses 'fell in

the range of .2mg 'to 12.Sms the rise time of the

pressure transducers was not a limiting factor,

nor did its eventual (moderate) overshoot mf

lu-ence the results.

The. slamming peaks were recorded on an

instru-mentation recorder and a UV-recorder. The

band-width of the. UV-recorder was too small to record

the slamming puises accurately and was only used

f r control purposes durng the experiment.

The actual processing, of the data was done af ter

the. experiment. The data-tapes were replayed and

the slamming puises fed to. 'a digital.

oscillos-cope.

From each measurement run five puises from each

transducer were catched and. the rise time and

magnitude. of them me:sured. 'The resulting values

of the five pulses were averaged to reduce the

large fluctuations that plague this type of

ex-periment. AS rise time was taken the time

'in-terval between the 0% start value of the pulse

and the first

(local) maximum value of it. The

magnitude was the global maximum of the pulse.

Some selected pulses were fed to a computér via

the scope's interface and plotted.

'2.3.. TeaL program

Each wedge

was

forced oscillated as

heaving

motion in vertical direction wi.th an adjusted

trim angle in such a way that the average

posi-tion of

the

transducers

was. situated in the

zero position of the harmonIc motion and the

transduc-ers hit the water surface with maximum

oscilla-tion speed.

If the vertical displacement of oscillatión is

characterized as

S =

Sa COS(Ot

(1).

wIth,:

w

= oscillation frequency

amplitude of oscillation

it follows that the maximum vertical speed

be-comes

V=

(2)

The following program has been performed for

each wedge:

I. One oscillation-frequency with three

diffe-rent amplitudes delivered three vertical

Five trim angles with bow up (positive) were

considered viz:

0,

0.5, 1.0, 2.0 and 2.5 degrees and for

wedge nr.1 also

a

=:

3 degrees.

Three forward speed

were adjusted viz:

U = 1.0 rn/s

U = 2.0 rn/s

U = 3.0 rn/s

speeds viz:

w =

12 rad/s with 5a = 0.02m

V

= 0.:24: m/s

w = 12 rad/s with 8a = 0.04m

V

= 0.48 rn/s

w =

12 rad/s with

_8a

0.06m

V = 0.72 rn/s

By means of these experiments it was possib]e to

measure peak pressures and rise times as

func-tion

of vertical

speed,

trim, angle,

forward

speed, dead rise angle and transverse 'postion..

It should be remarked that for ail trim

condi-tions' except a = 0° no influence of the forward

part of the wedge was present.

The measured data are presented in the tables 2'

to5 for each wedge.

Accurate determination of

peak pressures and

rise times was not always póssible especially in

the case of i rn/s forward speed showing mostly

low pressure values and uncertain rise 'tïmes.

in the tables 2 to 5 peak pressure values below

ikPa are not reported. Ail presented data are.

average values of f ive oscillations..

3. Results and inaiysis

From the test restilts as presented in the tables

2 to 5' and the figures 3 to 6 the f:ollowïng

ten-dencies may be derived for the. peak pressures

and rise times with respect to the parameters

'considered:

3.1.. influence of trim angle a

See f;igure 3.1, 3.2, 3.3. and 3.4

Peak pressure,: In general increase, with trim

angle. 'fOr dead rise angle ß > 0.5

degree,. but with. almost no

varia-tion at the. maximum dead rise

angle. ß = 10 de,g.r.

For dead: rise

angle ß < 0.5 dgree. a strong

variation With trim angle may be

observed with minimum values at

about a = 0 5 degree trim angle

Almost equal and small. values for

the peak. pressures' could be

esta-blished for:

V = 0.24 rn/s and U = .i

2, 3 rn/s

V = 0,48 rn/s and U = I rn/s

V = 0.72 rn/s and U = 1rn/s

Rise. time

: A Strong reduction if, the trim

angle a increases.

3.2. Influence of dead rise angle ß

See figure 4.1, 4.2, 4..3 and 4.4..

'Peak pressure: A strong increase from' ß = O up

to ß = 1.15 degree followed by a

strong reduction at .ß

= 10 dègr.

This tendency has been confirmed

by

the

experiments

of

Chuang

[15]

Rise time

:

influence of p on rise times is

rather small,.

3.3. influence of vertical, speed. V

See figure 5.1, 5.2, 5.3 and 5.4.

Peak pressure: Strong, almost quadratic1

in-crease with. vertical 'speed V,

especially at p

0 degree.

.Small increase for p = 110 degree.

Rise time

: Significant reductiön with

in-crease of vertical speed V.

3.4. Influence of forward speed U

See figure 6.1,. 6.2, 6.3 and 6.4.

Peak pressure.: In many cases' a strong increase

wth sometimes quadratic

respect to the fOrward speed U.

Rise

time

':

Rather strong redudtion with

increase of' forward speed U.

3.5. influence of transverse positIon

See tables 2 to 5.

Peak pressure: Moderate reduction to the. edge

and to the centre. line with an

optimum value at transducer

nr.1-3.

Rise

time

Moderate redúction to the edge.

3 ..6. Review of the results

Some remarkable tendencies could be seen from

the test resuÏts.

in general the highest peak pressures occur at

the lowest dead rise angles., but not resulting

in extreme maximum values for zero dead rise

angle as one might be expected.

The peak pressure increases when the deadrise

angle decreases for the same equal trim 'angles

'(Figs.

3.1,

3.2,

3.3 and. 3.4.). 'The fluctuation

of the peak. pressure as a function'

.

Of the trim

angles is lower for big deadrise angles.. The

influence

of.

the transverse position'

s

sig-nificant for small deadr±se angles' and the value

of the peak pressure tends to be constant for

high deadrise angles

The maximum value of the

peak 'preBsue is in the range of 1.15° deadri'se

angle ('Fig.

4 . .1,

4.2,, 4.3, and. 4.. 4).

The experiments confirmed the. wellknown relation

that the peak vaiues 'of the slaning pressures

are proportional

t'o

the squared value of the

vertical speed.

estab-lished with respect to the forward speed. This

last relation was not accounted for in most of

the existing calculation models. This' influence

might be important expecially for high forward

speeds as already mentioned by Watanabe

[3],

Takemoto etal

[4], and Beukeiman [21.

'in 'the prediction model as p.resent'ed'in

_[1]

the

forward speed influence has only been introdúced

with the vertical component öf this speed in the

case of a trim angle. It should be noticed from

the measured results that also for zero trìm

angle significant forward speed influence was

observed,

The experimental results generally show a f

luc-.tuating increase of the peak pressures with trim

angle ('bow up)'.

in transverse line these pressures 'reduce t'o the,

centre line and the edge of the wedge.

The general picture for the rise times

is,

a

decrease with trim angle, vertical and forward

velocity.

See talle 2 to

15

4,. Comparison with calculation methodE

4.1. Bottom impact pressures

Most existing calculation methods for bottom

im-pact pressures

f 1., 5, 6, 7, 8, 9,

10,

11, 12,

.13,

14, 15,

16,] determine these pressues

relat-ed to the squarrelat-ed vertical velocity only as:

p = kpV2

(3)

with,:

k = proportionality constant

p = mass density

V = vertical velocity

in the case of forced heave oscillation around

the watersurface 'with vertical displacement

this impact pressure may also be expressed as

p = kp2

(5)

The proportionality constant k for wedges and

cones may be determined by the Wagner wedge

im-pact theory [17], the Chuang cone imim-pact theory

and NRSDC drop tests of wedges and cones

Sorne of the above mentioned calculation methods

[1,

14,

16]

introduce the forward speed mf

lu-ence as the vertical component of the forward

speed in case of a trim angle.

I.t might be remarked here that in the present

research forward speed influence was also

ob-served for zero trim angle. There is a

scatter-ing in the value of the proportionality constant

k for the mentioned calculation methods. Some of

them use k

30 among which e.g. Takezawa [61.

Calculations according to t'his method are shown

in the figures 5.2 related .to wedge nr.2,

(ß

0.46 degrees) with trim angle a

= 0.5 and 2,5

degrees.

From these figures it might be obvious that the

calculated forward speed influence is too small.

compared to the measurements, while the

calcu-lated values

show an overestimation

for

the

lower forward speeds.

With

respect

to

the

remaining

calculation

methods

[1, 7,

13,

14]

it has been established

that

the

predictions

for

the

low dead

rise

angles

show very high values for the impact

pressures. For this reason the results were not

presented in the related f ±g.ires.

in case of wedge nr.4 with the highest dead rise

angle

(ß

= 9.98 degrees)

the computed results

according to M.D.

Ochi

[7]

are presented in

figure

5.4

showing reasonable agreement with

the measurements at the smallest trim angle (a

0.5 degrees)

4.2.. Fluid

innmentum

exchange

Another method with a restricted forward speed

influence is that of Beukelman, [I].

The impact pressure is determined on base of

fluid momentum exchange: and strip theory

result-ing in the followresult-ing expression.:

I ,

dm'

= - (N + -

2

₊

_m

) (:6)

2Yw

ds

with,: N' = sectional damping

rn'

= sectional added mass

Yw= half width of the submerged

cross section on the waterline

s

_{= 8a cos,t}

vertical displacement

The

first term with sectional damping

is

of

minor importance and may be neglected.

in case of forward speed with a trim angle

_a

(bow up) the total vertical speed will be:

=

-

t sifla

(7)

The saine

objiections as mentioned before holds

for this type of forward: speed influence: it is

too

estricted and zero for zero trim angle.

An extension of this method will be presented in

part

II

taking into account more significant

forward speed influence and 3-D effects.

The calculated results generally show the same

tendency as mentioned earlier.: very high peak

values for the wedges with the low dead rise

angles.

So

calculated results are

only presented

in

figure 5.4. for wedge nr ..4 with the highest dèad

rise angle (ß = 9.98 degr.). It is striking, that

for this

case. too low calculated válues are

shown.

4.3. 3-D wedge

impact

It is

also

worthwhile to mention separately the

calculation method

of, Stavbry-Chuang

[141

and

:Chuang

(:1973) [16]

to detennine impact pressures

for three dimensional models at high forward

speed. The pressure that acts normal to the hull

bottom in the slamming area,

may

be separated

into two components:

The impact pressure

pj due to the velocity

component of the craft normai to the water

surface.

The planing pressure Pp due to: the velöcity

component of the craft tangential to the

wa-ter surface..

The planing pressure acting normal to the. hull

bottom is:

Pp

3pV2cOsßeh

(8)

with ßeh

=

'effective impact angle in

the

horizontal

longitudinal plane.

The totai pressure due to velocity components of

the craft both normal and tangent to the wave

surface is therefore:

Pt

=

Pi

+

Pp

(9)

For low speeds the planing pressure is usually

sin li compared 'to the impact pressure.

Making use of

_{for our case extrapolated 3-D}

predictions as presented in Chuangs report

[16]

(figures

Ba,

8h,

12',

13,

2) one calculated

nr.4

_(ß

=

9.98

degrees)

showing

reasonable

agreement with the test results.

Nevertheless it remains remarkable that Chuang

found by experiment and 3-D calculation that a

change in forward velocity will not alter the

magnitude of. the impact. pressure if the vertical

velocities remain the same.

5. Conclusions and recnnimcndat ions

Analysis of the test results fr the wedges

con-sidered and comparison with existing calculatïon

methods delier the; following :conclisions and

recommendations:

i. The measured peak pressures show a clear

pro-portionality t'o the squared values of the

vertical speed, but also a significant mf

lu-ence of the relatively h'igh forward speed

even at zero trim angle.

Peak pressures generally als,o demonstrate a

fluctuating increase with trim angle (bow up)

especially 'at the lower d'ead rise angles. A

strong increase of these pressures with d'ead

rise angle coul'd be' established up' to 1.15

degree dead rise angle. For IO degree a

strong pressure reduction was observed.

For an accurate determination of the mf

lu-ence of dead' rise angle on the peak pressures

more tests with additional, dead rise, angles

are required.

in transverse line of 'the wedges reduction of

the 'peak pressurés to the centre line and the

edge could. be observed.

4'. Rise times of the peak pressures decrease

rather strongly with trim. an:ie,, vertical and

forward velocity, but the influence of

Most existing calculation me.tI.ods show too

high pressure predictions and in ali cases

the forward speed influence is very poorly

represented.

Extensive further research to the influence

of forward speed, 3-D and surface effects is.

required.

6. References

f 1] Beukeiman,. W.,

'Bottom impact pressures due to forced

oscillation'., International Shipbuilding

Progress, Volume 27, No.309, May 1980:,.

[

2] Beukelman,. W.,

'Slaming. pressures. on the cylinder

sur-faces due to forced oscillation', Report

Nr.728, Ship Hydromechanics Laboratory,

Deif t University of Technology, Noeniber

1986 (in Dutch)

31 Watanabe, I..,

'Effects of the three dimensionality of

ship hull on wave impact pressure', Jöunal

of the Soc.

o.f. Naval Architects of Japan,

pp. 163-174,. Volume 162, 1987.

[ 4]

Takemoto, H., Hashlzume, Y. and .Oka, S.,

'Full scale measurements of wave impact

loads and hull response of a ship in

waves', Journài of the. Society of Naval

Architects of Japan, Volume. 158, 1985.

51 Ochi, M.K. and Motter, L.E.,

'Prediction of slamming characteristïcs and

hull responses for ship design'

,

SNNE 81,,

1973,. pp. 144-176.

6] Takezawa, S. and Hasegawa, S.,

'On the characteristics of water impact

pressures acting on a hull surface among

waves', Journal of the Society of Naval

Architects of Japan, Volume 13, 1975.

E

7] Ochi, Margaret 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.

8] Ochi, M. K.,

'Prediction of occurrence and s.everity of

ship slÏaxmning at sea', 5th Symposium on

Naval Hydrodynamics, Bergen, Norway, 1964

[9)1 Tasai, F.,

'A study on the seakeeping qiai.ities of

full ships', Report of Research institute

for Applied Mechanics,, Japan, Volume XVI,

No.55, 1968.

Ochi., M.K.,

'Model experiments on ship strength and

slamming in regular waves', Trans. SN,

Volume 66, 19518.,

Hagiwara1 K. and Yuhara,, T.,

'Fundamental study on wave impact loads on

shIp bow'

Cist report), Selected papers

from Journal of the Society of Naval

Archi-tects of Japan, Volume 14, 1976.

(12] Chuang, S.L.,

'Experiments on flat-bottom slamming',

Journal of Ship Research, March 1966,

_pp.

10-17.

[13] Kaplan, P. and Malakhof f, A.,

'Hard structure slamming of SES craft in

waves', AIAA/SN

Advanced Marine Vehicles

Conference, San Diego, April 19178.

[14] Stavovy, Alexander B. and Chuang, S.L.,

'Analytical determination of siaimning

pres-sures for high-speed vehicles In waves',

Journal of Ship Research, December 1976,

pp. 190-198.

[15:] Chuang, S.L.,

'Experiments on sianmiing of wedge-shaped

bodies', Journal of Ship research,

Septem-ber 1967, pp. 190-198.

Chuang, S. L.,

'Slamming tests of three-dimensIonal models

in calm water and waves', NSRDC, Report

4095, September 1973.

Wagner, VIi.,

'Uber stoez.- und Gleitvorgânge an der

Ober-fläche von Flüssigkeiten', Zeitschrift für

Angewandte Mathematik und Mechanik., Volume

12, No.4, pp. 193-215, August 1932.

Chuang, S.L.,

'Theoretical investigations on slanuning of

Cone-Shaped bodies', Journal of Ship

Research, Vol.13, No.4, .1969.

Chuang, S.L. and Mime, D.T.,

'Drop tests of cones to investigate, the

three-dimensional effects of slamming',

NSRDC,, Report 3543, 1971.

965UU p 6?. I100?D I V 10186 0 UA0I12 OIR. 7 60. 1 2 3 4 5 1 0 3 4 5 0 2 2.4 2.2 2.1 2.3 2.3 2.1 1.3 1.7 3.0 1.7 S L) 1.3 2.5 1.6 1.5 1.0 1.6 1.2 3.3 2.5 0.5 2 1.0 2.1 2.5 -

1.5

---S 0.6 1.5 2.3 - - 1.7 1.0 2 2.2 1.4 8.0 - 1.7 3 1.2 1.0 1.4 1.3 1.2 0.24 1 2.3 2.2 2.1 0.6 2.0 2 3.0 2.1 3.7 3.3 2.1 3 3.9 2.5 0.2 2.0 2.4 3 6.2 - 7.0 2.2

1.5

---2.3 2 2.0 3.1 1.0 1.0 2.4 3 3.0 2.7 3.4 2.5 2.7 1 1.2 - - 3.4 1.7 3.0 2 2.5 1.5 1.0 1.0 2.2 3 4.6 2.9 2.7 1.2

3.3

---0 2 0.5 4.0 3.5 5.3 2.3 1.0 2.2 0.0 2.0 1.0 3 18.5 10.6 12.5 14.2 4.3 1.1 3.2 1.2 1.1 1.0 0.3 8 4.3 4.0 6.1 1.0 0.4 2.3 1.3 1.0 1.2 3.0 3 3.2 3.4 4.9 - 3.0 2.1 0.0 2.0 - 5.3 1.0 2 3.5 5.7 6.3 0.6 3.4 12.0 10.2 12.7 10.4 7.5 2 7.5 3.6 1.0 0.5 4.3 7.2 7.3 7.2 6.4 -0.05 1 2.1 1.3 2.2 9.3 1.3 2.0 1 13.0 0.2 82.0 12.5 4.1 5.0 7.2 7.4 6.1 -3 83.3 10.0 88.3 1.0 2.2 5.5 0.5 3.6 - -1 4.5 2.4 4.1 2.8 2.5 2 12.7 6.7 0.0 0.4 6.3 3.9 3.2 6.8 4.4 -3 23.6 5.2 15.4 12.8 6.1 3.6 3.7 1.5 4.0 4.0 1 4.1 3.1 0.7 2.6 3.0 2 11.7 10.0 11.0 10.9 7.3 6.0 5.5 6.7 1.1 9.1 3 12.5 0.6 10.6 11.2 6.7 3.1 6.0 3.0 5.0 4.4 0 1 7.5 7.2 6.3 6.5 7.3 1.0 2.3 8.0 1.8 0.5 3 20.4 33.1 52.0 31.6 29.0 0.0 1.1 0.6 0.7 0.6 0.5 2 5.3 5.1 0.4 7.3 10.4 14.1 10.3 14.1 5.3 5.0 3 85.0 13.3 07.3 - 14.0 1.0 2 5.0 15.3 31.1 12.4 4.0 2.6 2.3 2.4 1.8 1.1 3 17.5 23.1 13.3 04.3 10.6 0.72 2.0 2 17.5 15.0 06.3 9.3 11.7 0.5 0.8 0.6 0.4 0.7 3 22.6 15.1 20.7 14.5 12.3 0.3 0.5 0.3 0.3 0.6 1 2.0 2.0 2.1 3.6 2.3 3.4 2.7 3.7 3.3 2.3 2.5 2 21.3 01.1 29.4 00.1 12.6 0.0 0.7 0.4 0.6 1.0 3 34.1 32.2 33.1 23.0 23.1 0.2 0.4 0.2 0.2 0.9 1 1.1 2.0 2.2 2.5 1.4 5.0 3.8 4.7 3.3 3.1 3.0 2 22.2 20.7 21.6 13.2 12.6 0.2 0.2 0.2 0.2 0.2 3 26.4 29.5 31.2 24.3 22.0 0.2 0.3 0.2 0.1 0.2 PR2U2Z p OP. 0200111W 0 V /. 10114 U IR416011 NR. IRANR 60. MUU I Z 3 4 5 1 2 9 4 3 0.24 0 2 3 4.1 3.5 4.02.0 3.6 0.3 3.12.0 1.61.6 0.9 2 3 3.5 1.0 2.7. 1.02.0 1.61.3 2.7 1.0 2 3 9.0 1.0 1.50.7 3.5 1.6 2.01.4 2.0 1.4 2.0 1 2 3 1.0 3.7 4.2 3.6 1.0 2.6 1.1 3.6 3.2 -2.4 5.7 2.3 3.0 3.6 0.3 1 2 3 6.6 1.6 4.0 -2.4 1.7 6.0 3.5 4.1 3.0 5.5 3.3 1.0 3.2 3.6 1.6

---

7.2 -3.0

Z

---0.40 0 2 3 4.7 12.7 4.3 12.3 4.6 14.5 3.0 11.5 8.1 9.6

---

4.8 5.7 4.0 4.6 0.3 11 3 5.1 6.0 4.55.1 7.6 0.0 4.0 7.6 3.4 0.6 09.6 9.0 15.0 6.013.67.7 -7.7 -1.0 1 2 3 1.5 0.5 6.3 1.4 5.0 6.9 3.7 5.1 6.9 0.1 5.1 6.4 1.3 4.6 1.932.36.331.76.111.56.2 7.7 7.2 4.4 7.1 2.0 1 2 3 2.4 84.6 00.6 1.6 10.3 13.0 2.5 11.2 16.6 5.1 0.0 16.0 3.17.4 6.6 6.8 6.5 5.8 7.5 3.9 5.5 5.5 -3.6 2.0 1 2 3 4.2 10.8 14.1 3.7 22.7 6.3 4.6 13.7 15.0 2.5 13.8 15.2 3.3 0.6 6.5 5.0 6.2 6.7 0.3 6.4 6.0 5.6 -6.5 3.0 2 0.72 0 2 3 4.2 33.6 3.3 32.0 4.3 33.6 4.4 26.321.26.3 1.6 1.0 8.6 0.0 1.4 0.6 1.0 0.7 1.0 0.6 0.0 12 3 0.5 3.6 12.3 2.2 0.5 15.0 8.4 6.6 05.3 1.7 4.7 14.616.00.6 1.6 0.6 5.40.7 3.50.6 1.80.7 0.5 0.7 1.0 1 2 3 1.8 14.5 25.6 -19.0 14.1 1.6 19.6 20.9 1.4 13.3 17.0 1.3 5.0 11.0 1.6 6.6

---

1.6 1.0 0.4 2.0 1 5 3 1.4 15.3 16.2 -05.6 17.7 3.2 10.1 07.0 2.8 6.7 15.3 3.0 7.4 0.5 0.4 0.5 0.1 0.50.3 0.8 0.5 1.0 -5.5 1 2 3 4.2 10.4 33.6 2.6 00.6 33.7 4.2 18.2 31.4 3.6 14.3 24.7 1.5 5.8 19.1 0.0 0.9 0.6 0.4

...

0.5 0.2 0.5 0.3 0.5 0.3 3.0 2

Table 2

Table 3

P. 0

l

WZ! 60.2 P - 0.46 2237m

Table 4

0- 1.23 DXZ3

Table 5

SIRX! PIR P003IRJRO p 67. 02STDIR i

..

V I. TRISO

D..1.

O IIRASI95RI95 SIR. ?RMSDUCTR 60.

a a s 4 3 0.24 a a s a.a a.o1.3 2.41.7 1.63.5 1.7 2.2 o.s a 3 i.o2.0 -1.1 1.61.7 1.12.7

---a.o ia a.ea.a

4.0 -2.3 2.2 1.4 3.0 2.3 3.03.0 2.6

i.---

---2.0 12 3 1.3 2.7 4.3 3.3 1.4 2.1 1.6 4.1 2.6 3.15.0 2.0

2.2

---2.3 1 2 3 2.1 3.4 4.6 1.5 3.5 2.4 3.0 1.7 4.1 2.0 2.5 3.2 2.2 3.8 3.4 3.0 1 0.46 0 2 3 4.3 14.9 11.04.312.74.7 4.1 53.3 3.7

3...

4.2 4.0 4.4 4.0 4.] 0.3 2 3 3.2 15.1 2.06.603.15.4 3.49.0 3.4 7.7 .4.0 -6.0 5.1 10.5 0.3 -6.2 0.0 i1 3 1.0 7.3 20.3 1.0 6.2 10.1 1.2 3.0 13.3 2.0 5.0 11.3 2.8 6.0 10.3 4.3 6.53.3 50.6 3.5 21.0 6.0 -7.4 2.0 2 3 16.2 13.3 7.36.912.60.2 12.713.2 3.0 0.2 6.23.0 3.94.0 3.05.5 0.17.0 -0.1 2.5 12 3 9.4 02.4 14.4 1.7 0.4 23.0 2.9 13.0 11.2 0.0 0.0 14.3 2.24.7 6.13.4 3.35.0 4.93.4 5.40.6 -3.0 2 0.72 0 2 3 0.4 35.3 7.0 32.4 23.29.231.10.0 10.00.3 1.27.3 0.00.0 7.00.0 0.10.4 3.10.0 0.1 12 3 1.0 9.7 33.0 2.0 11.0 27.7 2.9 11.0 20.4 0.7 9.0 29.9 0.1 - 0.10.4 00.4 0.7 10.02.7 0.37.6 0.5 1.0 2 3 14.3 30.0 12.4 27.3 17.3 33.3 24.6 26.1 6.0 0.40.3 0.00.3 0.00.2 0.20.3 0.7 -2.0 1 2 3 2.7 06.3 31.0 2.6 15.4 24.3 2.4 21.9 24.0 3.2 15.2 33.3 2.4 3.3 17.7 7.00.2 0.00.3 0.20.0 1.20.2 4.5 0.4 2.1 2 2 3 4.4 20.0 32.4 2.6 00.0 20.6 3.4 20.3 30.7 3.1 10.7 25.0 2.3 4.1 24.3 0.30.1 3.70.3 6.20.1 6.5 0.2 2.20.2 3.0 2 060225552 p klo OOS210IR t

.

V oF. TRIM 0500.,!.

U 55953025X02 OR. TRA9501JCTR ISO.

i 2 3 4 3 2.24 0 2 3 1.6 1.2 8.0 0.0

1.5 ...

0.3

i-

2 3 1.1 2.3 a.. 1.0 2.21.4 1.3

---

...

1.0 12 3 -2.9 0.7 4.2 1.4 2.01.9 1.31.2 1.0 2.0 2 3 1.2 1.0 -1.2 2.22.0 1.20.0 1.1 2.3 12 3 4.1 1.2 0.0 2.4 -1.5 4.4 0.0 12.4 0.5 7.1 1.1

1.________

3.0 2 0.40 0 2 2 3 0.2 3.3 4.4 1.0 2.5 3.1 7.2 4.1 3.0 1.0 9.1 4.1 4.7 0.4 2.0 2.1 - 2.1 - -0.3 1 2 3 2.0 4.3 4.4 3.0 2.7 3.2 3.2 3.0 4.4 2.4 4.0 4.1 2.7 4.2 4.2 1.0 12 3 3.0 4.2 4.2 3.1 2.2 3.2 3.0 4.0 9.9 2.1 3.0 4.7 2.3 1.0 4.5 .

---

. 0.0 2.0 5 2 3 4.1 4.3 4.3 2.3 2.0 3.0 4.0 4.0 4.4 4.5 3.0 4.1 0.0 4.1 3.0 2.1 2 3 4.1 4.5 2.13.3 3.04.4 3.04.4 4.12.0 3.0 2 -: - -0.72 0 1 2 3 1.0 10.0 9.3 1.3 3.7 10.0 1.0 9.2 6.3 3.0 20.6 0.7 4.0 7.0 0.1 0.00.4 0.70.3 0.60.4 0.70.4 2.70.5 0.5 21 3 2.3 0.5 0.4 1.5 3.4 9.9 2.0 0.0 0.5 4.3 0.0 0.4 0.7 0.0 0.90.4

---

0.00.3 0.00.4 0.70.2 -0.6 2.0 2i 3 2.3 6.0 10.7 1.7 4.4 00.1 2.4 0.5 9.3 4.0 10.0 0.0 7.2 7.3 0.00.5 . 0.0 0.3 0.0 0.4 70 0.6 0.6 2.2 -0.7 2.0 1 2 3 0.0 0.1 0.2 2.2 3.0 9.6 3.0 0.0 00.3 3.6 0.0 7.6 10.0 0.3 0.2 6.0 0.7 0.0 -0.7 0.3 -0.3 0.2 0.6 0.0 0.5 0.0 2.1 0.7 2.3 12 3 6.9 7.0 00.3 7.3 6.6 0.0 3.3 0.2 0.3 3.0 0.3 7.7 0.7 0.2 10.2 4.0 0.0 0.3 0.4 0.4 0.0 -0.6 0.3 -0.7 0.6 0.9 0.0 0.7 3.0 3

30 20 ÇckPa 10 O

Lo

U - 2.O1rn/s

V

O24 rn/s

1 2 s

-- degrees

Figure 3.1. Peak, pressure. as functión of trim

angle a.

J.

J,'

30

Lo.46

U» 1.00 rn/s

V « 0.72 rn/s

a

p

(kPa)

00

degrees

Figure 3.2. Peak pressure

_{as function of trim}

angle a.

30 o

4j

U - 3,. 00 rn/s

0.72 rn/s

J 2 3 a -

degrees

V = -0.48

/'Ç

U - 3.00 rn/s

1 2 3

a

-

degrees

a

-

degreee

a

degrees

Figure 3.3. Peak

_{pressure as. function of trim}

o

U2.0Om/s

V 0.72 rn/s 3° (kPa) Io U 3,100 V 0.72 in/s '_-:.'..8:_.__o_-. .1 0 a

_degrees,

FIgure 3.4. Peak

_{pressure as function.o:f trim}

angle

.

0o,

U 3.. 00 /s V 10.24 rn/s e

_i

_q- a

a

_degrees

_a

_degrees

30

t

00 (kPaJ

t

'2

p

(kPa]1

2C

p

(kPaJ l0 30 -U

3.00 s/s

V

0.24 oz/s

: o s so

degrees

'l0

fi

degrees

Figure 4.1. Peak pressure as function of

dead-rise angle ß.

30

\ \

_\'.

\

\\

.E

\.;\\\

a

1.0°

U

3.00 s/s.

V

0.72 rn/s

degrees

Figure 4.2. Peak pressure as

_function

of

dead-rise angle ß.

fi 5 10

degrees

20

(kPaj

lo o o lo

o 1 U

_{1.00 rn/s}

V

0.24 rn/s

10 p

degrees

o Io p

degrees

Figuze .4.3. Peak

_{pressure as function of}

dead-rise angle p.

Figure 4.. 4. Peak pressure as. 'function

f

dead-rise angle p.

p Oo

o V U

.1 rn/s

o V U

2 rn/s

VU-.3 rn/s

0.24 0.F. 07i V

rn/s

o V U = 1 rn/s

o V U - 2

rn/s

Y U = 3 rn/s

O

V U = i rn/B

O V U = 2 rn/s

.

Y U

3 rn/s

Figure 5.1. Peak pressure as function of

verti-cal velocity V.

o y

u

=

In/s

U = 2 rn/s

T

Y U '= 3 rn/s

a

_2.5e

Figure 5.2. Peak

_{pressure as function of}

verti,-cal velocity V.

3Ò

t

20

p

[kPa]

o 0.24 V 0.72

In/s

- - U = i m/

o V U

2 rn/s

Y U

3 rn/s

r

-. ,/

- )?

o-- <---ç-J

,

e V U = I rn/s

o V U - 2 rn/s

-. V U = 3 rn/s

Figure .5.3. Peak pressure as function of

verti-cal velocity V.

-Figure 5.4. Peak pressure as function of

vertI-cal ve.ocity V..

Figure 6.1. and 6.2. Peak

_{pressure as function,}

-of forward speed U.

U rn/B

U. -- rn/s

Figure 6.3:.

and 6.4.

_{Peak pressure}

_as.functjon

SLAMMING SIMULATION, ON

PENETRAT-ING WEDGES AT FORW7RD SPEED

-by

W.. Beuke1Tnrn,

DeIft. University

Technology

and

D. Radev, Bulgarian Ship

Hydro-dynamics Laboratory

Report No.. 888-P

1991.

Deift :Unlvo(ty of Technology Ship Hydromachañics Laboratory Mekelweg,2

2628 CCDe!ft

The Netherlands

INTERNATiONAL

'SYMPOSIUM

ON

HYDRO

-

_ANÓ

AERODYNAMICS

IN MARINE

:ENGIN'EERING

M

_'91

incorporating the 20 Jubileé

_Session.

of the Scientific and

_{M.ethodölogical}

Seminar

on Ship Hydrodynamics

dedicated

_{to the 20 Anniversary of.}

the Bulgarian Ship Hydrodynamics

Centre

PROCEEDINGS, VOLUME 2

ABSTRACT

This paper presents theoretical and

experimental slamming investigation of 3-D

penetrating wedges at forward speed. The research is a continuation of the, method of Beukelman 1980 C33, including forward speed influence and 3-D hydrodynamic effects using the momentum theory. The tests were carried

ut with four metal wedges and different

dmdrise

angles on the basi,s of forced

vertical oscillation by the Ship

HydrDdynamics Laboratory (SHL) at Delft

IJniversity of Technology.. The influence of

the forward speed appeared to be significant. Time simulation has been performed for the wedge enteringr into the water. The

cal'culati.oñ results' have 'been compared with

experemantal data in such' away that the in5luence of the parameters considered is

clearly demonstrated.

NOMENCLATURE

B. waterline beam of wedge g acceleration of grävity

H _depth

local reduction coefficient of added mass along longitudinal direction L waterlÇne length

5'

sectional added mass sectional damping P pressure S _{vertical displacément} T _draught t _time U' _{forward speed'}

V _{vertical speed (upwards positive)}

XO,VO,ZO right hand coordinate system, fixed In space

Asote professor, Ing.

Research Scientist, Ph.D.

p u

58I

right hand coordinate system, at the water level moving with the wedge speed

right hand coordinate system, fixed to the wedge

half

width of the submerged' cross section on the waterline

trim angle deadrise angle

mass density of fluid

circular frequency of oscillation

1. 'INTRODUCTION

During the last few years the efforts have been continued to determine the slamming.

pressure mainly in two directions:

- momentum theory C2, 9, 10, 19, 22, 2, 24].,

- impact theory C2. 20.. 21, 22, 23).

Miyamoto, T.anizawa C.l] studied water impact experimentally and; numerically for wedges

with small deadrise angles. The authors

presented a mathematical model including air

influence.

Kaplan CII] used á quasi three dimensional representation of the added mass of the

section (without taking account of the

frequency domain) for advanced marine vehïcles,on the basis of the momentum theory,. Matusiak and Rantanen C131 proposed a unified method for the hydrodynamic loads. The linear portion of hydrodynamic loads was produced by the classical Uriear seakeeping strip theory. The non-linear terms represent prImarily the impact loads called slamming. The added mass and damping, of the. sections as a function of

the draFt are evaluated b,y the 2-D close-fit method (Bedel,, Lee, t971ì.

Takemoto,. Hashizumi, Oka C273 measured the

wave impact load and the hull responses for

a patrol boat, while the boat was run in

DL..c-1r1XÌ.JG B X?1LJLr'X OP.J DN PE 4ETFT X FiG LJEDGEB

-.T FDRWD BPEED

W. BEUKELMAN

Del.ft University of Technology Ship Hydrodynamics Laboratory, Mekelweg 2

2628 CD Del,f t, The Netherlands

D. RADE V'

Bulgarian Ship :Hydrodynamics Centre 9003 yama, Bulgaria

severe waves at different encounter frequencies and speeds.

Beukèlman (3 presented a two dimensional method on the basis' of strip-theory (7],

using Frank Close-Fit method for added mass

calculation (83e

The present research was .perfored with

penetrating 3-D wedges at forward speed in

the most d1sputed zone: deadrise angles O-3,, where the classical 2-D theory of Wagner

(293 gives Infinite results for prissure, different from the test data of Chuang (5, 25] and others (6) . This paper presents a

continuation of the method of Beukelman including the forward speed

influence

and the

3-D hydr.odynamic effects.

2. PREDICTION METHOD FOR DETERMINING THE

SLAMMING PRESSURE ON PENETRATING WEDGES AT

FORWARD SPEED.

The proposed calculation method is based on the momentum theory including forward speed

(13] and 3-D effects. The coordinate systems relative to which the wedge is penetrated

with vertical velocity V and forward speed U

are presented in Fig.i. The right hand

coordinate system (Xo,Yo,.Z,)) is fixed in

the space. The

Z0 -

axis Is vertically

upwards, the

Xo -

axis is i,n the direction

of the forward speed of the wedge. 'The coordinate system O.(X,Y,Z) Is moving with

constant

forward speed U. The (X,Y) plane l's

situated in the still water sUrface, X in the direction of' the wedge speed U and Z positive upwards. The, system CCXD,YD,Z) Is fixed to

the wedge, C being the main corner point of

the wedge. The relation between the different coordinate systems is, as follows:

X0 X + X cosce - Z9 sin«

C j)

Zc + X1.. mm« + _cos«,

where « is trim angle, Xc, Zc. are coordinates

of the cornerpoint C.

For the wedge, there is _{a linear. correl ati on}

between Y,... and ZE.:

Z0 tQß Yj

For pure heaving _{oscillation of the}

wedge with forward speed, the following applies:

Ut

Zc = s' = si.. cosut

The hydroynamj _{force per unit length acting}

on each. h.eaving _{section at position X is}

calculated by _{using Newman's formuia}

(1'977 _r13.

58-2

Fx(X,Z) - C(X,Z) Cm'CX,Z,w)+

+ _. N'(X,Z,w)])

-The operator . is the total derivativa wi'th

respect to time t, defined as:

dò

a

dt at ÒX

- the difference, between cross-sectional area in motlòn and in still water. All the above Variables are function of time. Applying formula (Z) for the derivative, equation (4') c'an be' written as follows:

din' .Fz'(X,Z)= -m"-N'-

-ds

- Us -

dX9 dN' o dN'

- -

SS + -

Us de dX8 'a a as .a

where 5Z for calm water and -

- s.

at as at às

For slamming pressure,, the following equation

Is obtained: i a .. . din'. din'

p(X,Z)=-- (m's+Ns+ __2- Us +

2 ÒY ds dX dN'. dN' + -,--ss, - Us') ds dX9

The slamming' pressure achieves infinite value for the flat bottom wedge (B0'), or for the

central point (Y = O) on the wedge. Making

comparison with the' method of Beukel'man (3]

'for the evaluation of the slamming pressure, the first three terms in (7) are the same. The fourth term is the

influence

of the f orward speed, including the change. of the

added mass in X direction (123:. The remaining terms show the influence of the damping derivatives, together with the

vertical and the forward speed In fixed

displacement s.

For calculation of the heave force load as..

well as the peak pressure of the wedge entering the water, It is necessary to know the added mass and' damping. coef4icients in

the time domain. Fortypical 3-D wedge forms. calculations are performed using the - SRL method Cl., 163 or Meyerhof f method (143,, to

obtain the local reduction factor 3 (B/L,

X/L). Thi.s 4actr 'consists of the ratio

between 2-D. and 3-D coefficient including

general , geometrical Forni and relative.

position of

the cros section

along the

longitudinal direction,.

In the present study the calculation of the slamming pressure Is simply based on the time derivation of 'the momentum of the added mass

derivativas. in the time domain simulation, at every moment of penetration there are

1ways new wedges with the came initiai

9lobal ratio of parameters but with the change of the local position of the starting arosa section X/L. On the basis of few characterIstic points for added mass and damping coefficients and their derivatives

with respect to Z and X the approximated curve is obtained for the duration of the.

simulation. This fitting is done by using

orthogonal polynomials. The error obtained

is too small, so that its influence for

determination of the derivatives is neglected.

3. TESTS

3.1.Test Description

Four stiff metal wedges with deadrise angles

0',,0.46, i..l'5,9.98' were constructed as

shown in Fig.2. The dimensions are: L x B x

H 0.50 x O.25 x 0.25m Five pressure transducers were placed on a transverse line 10mm from the aft edge of the wedge as

denoted in Fig.2 showing the wedge's bottom

Transducers Nrc. 1 and 3 have the same distance of 40 mm to the centre of the wedges

an are supposed to show equal peak

pressures. The pressure transducers in a

transverse, row should show the peak pressures

as 'Function. of the distance form the.centre

line. Each wedge was forced oscillated, as

heaving motion in vertical, direction with an

adjusted trim angle in such a ' way that the

average position of the transducers was

situated in the zero position of the harmonic motion and the still water. level. This means that the transducers hit the water surface

with maximum oscillation speed. The

'Following program has been performed for each

wedge:

- One oscillation frequency with three vertical speeds viz:

u = 12 radis, 'V 0.24m/s,0.48m/s,O.72m/s.

- Five trim.angl'es with 'bow up (positive)

Were considered viz:

0", 0.5, 1-.0, 2.0' and 2. and for

Wedge Nr.1 also «

3.

Three forward speeds were adjusted viz:

'U = .1.0 rn/s , 2.0 rn/s , 3.0 rn/s.

means of these experiments it was possible

tQ -rneaU _{peak pressures and rise times as}

a function _{of vertical speed, trim angle,}

forward speed, dead. rise angle andtransverse

58-3

position.

All

presented data are average values of five oscillations.

.2.Resu1tc and analveim

Some remarkable tendencies could b

established from the test results. The peak pressure increases when the deadrice angle decreases for the same equal trim angles (Figs.3).The fluctuation of- the peak pressure as a function of the trim angles Is làwer for

big deadrise angl-esThe. influence of the transverse position is significant for small

deadrice angles and .the value of the peak.

pressure tends ta be constant for 'high

deadrise angles.The maximum value of the 'peak pressure.i,s in the range of'S l.15 deadrise angle (Figc.4).The .xperiments confirm the wel l.known relation that the peak pressure are

proportional to the squared value of the

vertical speed, but less pronounced for ß=10 as may be seen from Figs..r1oreover, a very strong influence on the peak pressure could be established with respect to the forward

speed, in a moderated way however, for ß00

as shown in Fig.6.The general picture for the rice times shows a decrease with the trim angle, the vertical and the forward speed.

- .3.Comparison with the existino calculation methods

host of the existing calculation methods for bottom impact pressures C 3, 4, , 17, lB

25, 26 1 determine these pressures related to

the squared vertical 'velocity' only. Some of

the above mentioned caÍculation methods C3,

5, 25] introduce the _forward speed , in-fluence as the horizontal component of the vertical speed' in case of a trim 'angle. It

might 'be marked here that in the present research the forward speed influence was also observed for zero trim angle. There is a scattering In the value of the

proportionality constant k for the mentioned -calculation methods.Bome of them use k 60

among which eig. Takezawa. C26].Cal'culations

according to this method are shown in the Fig.5 related to wedge Nr.2 (B 0 .46')

with trim angle « 0.5' and 2.5. From these figures it might be obvious that the

calculated forward speed Influence is too

small compared to the measurements, while

the calculated values ' show an - over eStimation for the lower forward speeds.

-With respect to the remaining

calculation methods C3, 18, 25] it

has been established that the predictions for the low deadrise angles show very high values for the impact pressures. For this, reason the results were not presented in the related figures. In case of wedge Nr.4 wIth the

computed resulte according to MD.Ochi t18 are presented in FIgs.5 showing reasonable agreement w*th the measurements at' the smallest trim angle

(« - 0.5')'

Another method with s restricted forward ' speed influence is that of Beukelman

C3.

The impact pressure is determined on the basis of the fluid momentum theory.

The same objections as mentioned before hold for this type of forward speed influencet it

is too restricted and zero for zero trim

angle. The calculated results generally show

the same tendency as mentioned esrliert very high peak values for the wedges with the loÑ

deadrise 'angles (B < 3). So calculated results are only presented in Figs.5 for

wedge Nr.4 with the highest deadrise angle (B = 9.99') It is striking' that for this case too low calculated values are shown.

It is also worthwhile to mention separately the calculation method of Stavovy-Chuang C251

and Chuang (1973) (53 used to determine the impact pressures for three dimensional models

at high forward speed. Making use in our

case the extrapolated 3-D predictions as

presented in Chuangs report (53 (Figures Ba,

Bb, 12, 13, 21.)one calculated value coul,d be

presented in Fig. s for wedge Nr.4 (P

9.99) showing reasonable agreement with the

teGt results. Nevertheless it remains

remarkable thatChuang 4ound thata change of.

the forward velocity does not alter the magnitude of the impact pressure if the vertical velocities remain the same.

4. NUMERICAL EXPERIMENTS

4.1 Geometrical oarameters of test wedaes, Irs this research, the object of investigation are 3-D wedges. The geometrical form of every wedge is determined by the following ratiost

T L tg« (B)

T tgß

Table' t. Geometricai characterjgtjcs of different 3-D wedges.

58-4

The ratio between L and B is derived from _th, above two expressions,

(9)

B

2tg

The main linear parameter is absent _for

wedges, _{because th. global dimensions of}

th,

wedges are determined, only by _their

proportions. The global geometrical ratios: of all the four test - wedges are shown ri

Table 1.

It is seen that the largest differences of characteristics for the wedges lie 'between a deadrise angle less than 2' and a deadrise angle of 9.98'. From the

table, it is understood that the big

influence is not only from the deadrise angle but also from the trim angle. The

different variants of these two angles give a different proportions of the main wedge

parameters. For the first, second and third

wedge with deadrise angle less than 2' the ratio.L/B is very small:

L B

This means that it is not appropriate to apply the strip theory directly for the

calculation of 2-D hydrodynamic coefficients. _{This' is} the reason for'

applying 3-D calculation methods in this

investigation. In Fig,. 7 the changes of the

wetted area for the first wedge in time domain are shown.

4.2.Hvdradvnamc coefficients

The _{hydrodynamic coefficients are calculated}

using the Meyerhoff 3-D potential method and

Frank Cloce-Fit method. In Fig.B' the added

mass per unit length calculated by Frank Close-Fit method is presented. It is seen

changing 'the dead,-ise angle on the added, mass

that for the same frequency the effect of

coefficient is not significant, _{whereas for}

the same deadrjse angle, the difference i'n added mass coeffjcjeñt is very high, while changing the frequency from 0'- 12s'.

graphs on Fi;g.9 give the change of the added mass in longitudinal direction _{of the} wedge (deadrise angls P 9.98") in the time domain. The momentum added mass is shown in the time domain for a fixed strip relative to

(X, Y, Zn) coordinate system.

Fig. 10 presents the added mass

calculations by the strip theory and by the

Meyerhoff 3-D potential method with _deadrise angle p w 0.09' and trim angle « w

The big difference between these two _methods

is there, where _{the penetration increases.}

The deviation of the added mass during the initial stage of wedge penetration is _{not so} large but this result has a significant influence on the value of the derivatives.

The l WEDGE - RATIO PARAMETERS L " L B i' 1.1 ßO.09', _{0.092 114.6 1250} 1.2. B=0.09, .50' 0.018 22.9 12S0' 2.1 1=0.46', 0.458 114.6 250 2.2 _{B0.46' 0.092 22.9 250} 3.1 B=1.15', 1.146 1146:. 100 3.2 B=1.iS', _{0.229 22.9} 100 4.1 P=9.98, 10.053 114.6 11.4 4.2

ß999',

_{2.009 22.9 11.4}

COMPARISON WITH TEST RESULTS

Figs. .11 - 13 show the slamming pressures

calculated by the prisent method in

comparison with the tests results . Every

ligure gives information regarding the

geometrical characteristics of the wedge

(deadrise angle and trim angle) and the

kinematic conditions. Also the distribution

of the points of investigation is shown.The graphs on Fig.1l give the comparison between

the test points and the predicted results of

the peak pressure in the time domain. The correction of added mass te détermined by usi ng Meyerhoff's 3-D method. The result is

rather high for calculation with 2-D

coefficients.

ood correlation for the

deadrise angle B O.46 is seen in the case

of the change of vertical speed. Where forward speed is changed, the deviatioñ from the test points ii bigger. When comparing the peak pressure in the time domain for the different wedges (B

0.46, P

98) the rapid change in the peak pressure for wedges

with small deadrise angle is clearly shown.

In Fig. 12 the test points and the predicted results of the peak pressure are shown as a function of the vertical speed for two

forward

peed.

The difference In predicted

results for changing the forward speed is too

small. The explanation is that the term

which includes forward speed in formula (7)

has scali influence for flat wedges c«>

0's).

Fig. 13 presents the test points and predicted results of the peak pressures as a function of the forward speed. For V 0.24 H/S the

results are better than those for V 0.72

MIS.

On the basis of the analysis from the

obtained results, the following remarks can be made with respect to the method presented in the paperi

t. the term proortional to the squared

vertical strip speed includtng the derivative of the added mass has the largest Influence, specially' in the case of the flat wedges (B

-> 0);

* the last two terms iA formula (7),

which include the displacement and damping

coefficient have small contribution for flat

wedges (ß -> 0'), because displacement is

small (5 -> 0)

t the influence of thi term which

consists of forward speed and derivative of added mass in X direction is higher for

Wedges with greater trim angles.

CONCLUSIONS AND RECOMMENDATIONS

On _{the basis of the performed investigation}

the fol lowing conci usi'on and recommendations

58-5

can b. drawn.

- the, proposed expanded method is hereby suggested for evaluation of the peak pressure including 3-D

effects

and forward speed in4lu.nc. A tim. simulation program on

penetrating wedges at forward 'speed is

realized;

- the test results shows a significant influence of the relatively high forward

speed. Peak pressures generally also

demonstrat, a fluctuating increase with trim angle Cbcw up) especially at the lower deadrise angles. A strong increase of these pressures with - deadrise angle could be established up to 1.15' deadrise angle. For 9.98' a' strong pressure reduction was observed. For an accurate determination of

the influence of deadrise angle--on---thepeak

pressures more tests with additional deadrise angles are required;

- while considering 3-D effects (including the influence of thi global

geometrical parameters and the local .position

of the cross section), the evaluation of the peak pressure for flat wedges gives relatively good. agreement i.iith test results;

- the influence of the term, which represents the effect of the forward speed is tncreased' for wedges with larger trim angles;

- the term proportional to the vertical strip speed squarid multiplied by 'the derivative of the added mass has the most dominant influence for evaluation

of

the peak pressure;

- further Investigations require evaluation of the hydrodynamic coefficients on the bests of the advanced 3-D methods, as

well as thé free surface effects;.

- the experience from such slamming simulation .

o the penetrating wedges at

forward speed can be applied for ship slamming.

AKNDWLEDGEMENT

This Investigation is carried out in the Ship Hydrodynamics Laboratory at Deif t University of Technology. Tha part re1tod t

tPIQ tt

rQsults is realized by' tng.W. Seukelman. The prediction method is developed 'by Dr. D. Radev during his research-féllowship in

Dell t. The authors would like to express

their sincere gratitude to the Department staff of the Ship Hydrodynamics Laboratory for undertaking such noble research.

REFERENCES'

C 1] Adegeest, L.J.M., "Analysis of a Three Dimensional Method for the Calculation of the

'Distribution of Hydrodynamic Coe4fjcients

University of Technology, SHL, Report No.

84-S, 1989.

C 2] Selik, O.,, Bishop, R.E.D. arid Price,

W., lnfl',uence of Bottom and Flare Slamming

on Structural Responsee", Trane. RINA 1987.

'C 3] Beukelman, W., "Bottom ImpactPressure

düe to Forced Oscillation", ISP Volume 27,

1990.

C 41 Beukelman, W., "Slamming pressures on the cylinder surfaces due to forced oscillation", Deif t LJniversity of Technology,

SHL, Report No.729, November 1986 (in Dutch).

Chuang, 9., "Slamming Tests of Three-Dimensional Models in Calm Water and Waves", NSRDC Report'No.'4095, 1973.

Faltinsen, O., "Sea Loads on Ships and

Offshore Structures", Cambridge University

Press, .1990.

Gerritsma, J. and Beukelman, W.,,

"Analysis of the Modified Strip Theory for the calculation of Ship Motions and Wave Bending Moments", ISP Volume 14, 1967.

Frank, W.. and Salvesen, W., 'The Frank

Close-Fit Method Computer Program", NSRDC Report No.3289, 1970.

C 9). Jensen,. J. and .Pedersen, P.1., "Wav.e

induced Bending Moments in Ship- A Quadratic Theory", Trans. RINA, 1978.

ClO] Mansour, A. and d'Olivei'ra, J., "Hull

Bending Moment Due to Ship Bottom Slamming in Regular Waves"., JSR Volume 19, 1975.

Cli) Kaplan, P., "Analysis and Prediction of Flat Bottom Slamming Impact of Advanced Marine Vehicles in Waves",, ISP Vol.34, 1987. C12]. Keuning, J., "Distribution of Added Mass and Damping Along the length of a Ship Model

Moving at High Forwárd Speed,", Deif t

University of Technology, SHL, Report . No. 617-P, i988..

C13] Matusiak, J. and Ratanen, A., "Digital Simulation of the Nòn-llnear Wave Loads and Response o'4 a Non-rigid Ship", CADMO 19,96, Washington D.C.

C143 Meyerhof, W.,, "Added masses of Thin Rectangular Plates. Calculated from Potential Theory", JSR Volume 15, 1970.

CIS) Miyamoto, T. and Tanizawa, K., "A Study

of _{the Impact Load on Shi,p Bow", 2nd Report,}

Journal of the Society of Naval Architects of Japan, Volume 159, 1985.

58-8

Ciò] Mynett, A. and Keuning, J. , "Ocean Wá,

Data Analyses arid Ship Dynamics", Memorial

Symposium to Professor R.E.D. Bishop,. London, 1990.

C17].Ochi, M.K. and Motter, L., "Prediction

of' Slamming Characteristics and Hull

Responses for Ship Design", SNAME 81, 1973.

CIBI Ochi, 'Margaret 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.

('191 Petersen', J. and Marnte, L.,

"Comparison of Non-Linear Strip Theory Predictions and Model Experiments", PRADS

1989, Varna.

(20] Radev, D., "Numerical Realization of

'problem for Entry of Rigid Circular Cylinder

in Compressible Fluid", IV th IMAEM Congress

1987, Varria.

C21.] 'Radev, D., "6eneral Approach to Ship

Bottom Slamming Investigation" IV th IMAEM Congress 1987, Yama.

(222 Report .of Committee 11.2 "Dynamic Load Effects', 10th ISSC 1988, Denmark.

Report of the ITTC Seakeeping Committee,

Proc. of the 19th ITTC, 1990, Madrid.

Soares, C., "Transient Response of Ship Hulls to Wave Impact", ISP Volume 36, 1908.'

Stavovy, A. and Chuang, S., "Anal,itiça'l

Determination of Slamming Pressures for

High Speed Vehicles in Waves", JSR 1976. Tákezawa, S. and Hasegawa, S., "On the characteristics of water impact pressures actingon a hull surface among waves", Journal

of the. Societyof Naval Architects of Japan,

Volume 13, 1975.

Takemoto, H., Hashizumi., Y. and Oka,

S., "Full Scale Measurement of Wave Impact

Loads and Hull Responces of a Ship in Waves",

Ist Report, Journal of the Society of Naval

Architects of Japan,, Volume 158, 1985.

(29] Watanabe, I., "Effects of tho three

dlmensional.lty of ship hull on wave ' impact

pressure,", Journal of the Society of Naval

Architects of Japan, Volume 162, 1987.

(29] Wagner, V., "Uberstosz- und

gleitvorgan-ge an der Oberfiache von F.lussigkeiten',

Zeitschrift fur Angewandte Mathematik Und Mechanik", Vol. 12, No.4, 1932.

('.1-o (kP3)

/_,

\

o.

-,

SS

-

. 30 10

-58-7. a U - 3.00H/8 V- 0 .48 H/S

Figure 3. Peak pressure as function of trim angle s.

30

10

Figure 4. Peak/pressure as function of de:drise angle =

.

Figure 1. Coordinate Systems. Penetration of 3-D wedge Figure 2. View at the wedge's

in different times. bottom with

pres-sure transducers. i 2O o 5 [01 .10