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] (inDutch)
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
ior
2degree.
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'
ssig-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'othe 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,
(ß0.46 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.
E7] 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 2.21.5
---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 1.23.3
---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 -3.0Z
---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 2Table 2
Table 3
P. 0l
WZ! 60.2 P - 0.46 2237mTable 4
0- 1.23 DXZ3Table 5
SIRX! PIR P003IRJRO p 67. 02STDIR i..
V I. TRISOD..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.a4.0 -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 3.73...
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 ...
0.3i-
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 1.11.________
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 3.0 330 20 ÇckPa 10 O
Lo
U - 2.O1rn/s
VO24 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)
00degrees
Figure 3.2. Peak pressure
as function of trim
angle a.
30 o4j
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 3a
-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 adegrees,
FIgure 3.4. Peak
pressure as function.o:f trim
angle
.
0o,
U 3.. 00 /s V 10.24 rn/s ei
q- aa
degrees
adegrees
30t
00 (kPaJt
'2p
(kPa]12C
p
(kPaJ l0 30 -U3.00 s/s
V0.24 oz/s
: o s sodegrees
'l0
fidegrees
Figure 4.1. Peak pressure as function of
dead-rise angle ß.
30\ \
\'.\
\\
.E\.;\\\
a1.0°
U3.00 s/s.
V0.72 rn/s
degrees
Figure 4.2. Peak pressure as
function
of
dead-rise angle ß.
fi 5 10degrees
20(kPaj
lo o o loo 1 U
1.00 rn/s
V0.24 rn/s
10 pdegrees
o Io pdegrees
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 Vrn/s
o V U = 1 rn/s
o V U - 2
rn/s
Y U = 3 rn/s
OV U = i rn/B
O V U = 2 rn/s
.
Y U3 rn/s
Figure 5.1. Peak pressure as function of
verti-cal velocity V.
o y
u
=In/s
U = 2 rn/s
TY U '= 3 rn/s
a
2.5e
Figure 5.2. Peak
pressure as function of
verti,-cal velocity V.
3Òt
20p
[kPa]
o 0.24 V 0.72In/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 forcedvertical 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 waterlinetrim 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 the3-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 verticallyupwards, the
Xo -
axis is i,n the directionof 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'ssituated 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
adt 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 .awhere 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 dX9The 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 theadded 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 thelongitudinal 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 BeukelmanC3.
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 11.4COMPARISON 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 thedeadrise 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 wedgeswith 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 predictedresults 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 onpenetrating 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.
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/_,
\
o.-,
SS-
. 30 10 -58-7. a U - 3.00H/8 V- 0 .48 H/SFigure 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