Date Author Address
May 2007 Jakob Pinkster
Deift University of Technology
Ship Hydromechanics Laboratory
Mekelweg 2, 26282 CD Deift
TUDeift
Deift University of Technology
Dolfljn Class Submarine Surfaces Again
by
Jakob Pinkster
Report No. 1533-p
2007
Published ifl Schip & Wart da Zee, May 2007, ISSN 0926-4213, Media Business Press, Rotterdam
de
05/07
Deift University of Technology
Ship Hydromechanics Laboratory
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Dolfijn Class Submarine
Surfaces Again
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Bureau Veritas by.Foto: Frits Waldekker
Wim van Rees en
Chrisaan Pouw
are Master Stu-dents in Marine
Technology on
the same subject.
Henk de Koriing Gaus is lecturer Hydromechanics
at DeIft
Universi-ty.
DoIfij.n Class Submarine
Surfaces Again
One of the courses that Master students in Marine Technology at the Deift University of Technology
have to attend is Introduction of Numerical Methods in Ship Hydromechanics". In this course students
have to simulate a flow of a stationary sailing ship in still water with a free surface and have to make
diffraction calculations to find out what the response operator of the six different motions is. For these simulations students apply advanced software [1] developed at the Laboratory of Ship
Hydromechan-ics. For these calculations the authors chose a previous Royal Netherlands Navy submarine of the
Dolfijn class.
Figure 1: Main frame showing the 3-cylinder
lay-out
et some cnndene wiiih
dthe in andutpüt It is
im-5flW' hihysicaJ itities arë e use of lmeariaatieln
ethiected
1hasebne
e-causeif seareouide the
iuIvill occur. The. &iiput data h e.iilieked
and.ih-tèrprted: areth'e cpmpiitvd 4ta reahtac of qoiite well Lt- .1
on this cam
iu'soitixNt aevrOcrinr1acS?
I'he gnmeiatIr th students is to write a -mim parer thsubjecL 1ç give el reaâler an iuresion-Qf1oe
onten,
Figure 2: DelftShip rendering of the hull
U -
-
U-
U
_IU U
U- UThe vessel that we chose as a sample for
our calculations is a DolfIjn class sub-marine of the Royal Netherlands Navy.
The 3-cylinder concept [2] of these
sub-marines was designed by F. Gunning during the Second World War and in
the 1950s; the design and construction
of the first two subs took place at the RDM in Rotterdam. The Dolfljn and
her sister ship the Zeehond, were deli-vered at the end of the 1950s, two more
vessels would follow in the '60s.
The advantage of the 3-cylinder
con-cept lies in reducing the thickness of the
pressure hull while still obtaining the
same diving depth. This advantage
pays off in lower material costs, a reduc-tion in weight and - taken that the inter-nal volume is the same compared to a 1-cylinder boat - a lower centre of gravity.
As can be seen in figure 1 the three
cylinders are arranged in a triangular
shape. The upper cylinder accommo-dates the crew, navigational equipment
and armament and the lower two cylin-ders house the propulsion machinery, as well as store rooms.
Overall length of these boats is 79.5
me-ter, breadth overall is 7.8 meter and the
draft is 4.8 meter. The total
displace-mentis 1530 tons surfaced and 1830 ton submerged. The main propulsion con-sists of two M.A.N. 12-cylinder diesel engines delivering a total of 4MW with
a top speed of 14.5 knots surfaced.
Sub-merged, the prime movers are two Smit electric motors delivering almost a total of 6MW which gives a top speed of 17
knots.
Geometry
The 3-cylinder concept makes an
inter-esting hull shape, a wide midship that
converts to a slender bow and stem. A
sonar dome is placed under the bow as a bonus.
The hull form was made in Maxsurf
based on a General Arrangement Plan
with a view of some frames. After the
hull was faired, it was exported to Deift-Ship (see figure 2) where it was possible
to make a mesh from the hull. This
mesh was then used in a Matlab
pro-gram to produce a partial cosine-spac-ing mesh.
A cosine-spacing (figure 3) is a way to distribute the panels along the hull and results in having smaller panels in the
bow and the stem. From a numerical point of view, it's better to refine the mesh when the gradients are getting
larger.
Our cosine spacing doesn't run from the
front of the bow to the stern but starts 3.75 meters before the bow. The bow
shape is fairly complex and we thought
it necessary to put more panels in the first part of the hull. The length of the
panels at the end of the cosine spacing is therefore extended into the forward part. of the bow.
The number of panels for the hull is limited to 500 and to determine the
amount of panels to use in transversal and longitudinal direction, we tried to find the optimum where no panel
ex-ceeds its aspect ratio of 1:4. This
result-ed in eight transversal panels all along the hull. In longitudinal direction there
are fifteen panels in the bow and 47 pan-els along the rest of the hull.
Another criterion which should be
tak-en into consideration is
that there
should be at least eight panels placed along one wavelength originating from the vessels wave system. The wave-length is based on the Froude number
which turns out to be 0.267. Rearrang-ing the definition of the wavelength and the Froude number we come to the fol-lowing wavelength;
2it Fn2
X3x9 5 x5 x4
Figure 3: Cosine spacing to distribute the panels on the hull
Xl
WiTh the chosen number of panels
along the hull, we have at least fifteen panels along one wave which is
mea-sured halfway the hull where the panels are the most elongated.
For Delkelv, a mesh is needed for the
free surface, this starts at 0.5 L ahead of
the bow and ends one ship length be-hind the stem. The width is determined by the Kelvin angle of the bow wave of
19.5° and we've added 25% extra width to make sure that there are no reflections of the bow wave with the side of the do-main.
Along the length of the hull, there are a total of eighteen panels. This results in
8.07 panels along one wavelength which
satisfies our requirement for a
mini-mum of eight panels per wave length.
FIgure 4: The final mesh for the free surface and the hull showing the parIel cosine
spac-ing
Numerical Programs
Both Delkelv and Deifrac are based on a panel method to calculate potential flow but they are used for different purposes.
Delkelv is used to calculate the
wave-pattern around the ship (in terms of
pressures and velocities), while Delfrac is used to calculate the ship's response
to waves.
Both programs assume potential flow, this implies that the flow is rotational free, non-viscous and incompressible.
Both programs will be explained in
more detail.
In Delkelv, the panels on the hull are
represented-by sources and dipoles, the free surface is represented by a source distribution. There are several
bound-ary conditions to be satisfied. On the
hull there is a Von-Neumann condition
which states that the flow should be tan-gent to the hull, this is also known as the no-leak condition. For the inner domain
there is a Dirichiet condition resulting from the Laplacian of the velocity vec-tor being zero At the free surface, there
are also two conditions to be met,
known as the kinematic and the
dynam-ic
.undary condiiThaicinematic
b.c. requires that the pressure equals the
Figure 7: Resultsof
Delkelv, showing the wave elevation
accord-ing to a speed of 14.5
kts(Fn = 0.267)
atmospheric pressure. The dynamic
b.c. is a no-leak condition.
With a known incoming velocity of the
flow, it's possible to calculate the source
strengths on the surfaces. Now that the source distribution isalso known on the
free surface,. the wave pattern can be
de-ducted.
Deifrac also uses boundary conditions of the 'Von Neumann' type for the hull but also for the sea bottom. At the free surface, the same two boundary
condi-tions hold. A fifth condition is added
which states that at an infinite distance
from the ship, the radiated waves are
dimmed and eventually wi]l.go to zero.
z=o
Tocalculate a ship's response to waves, the potential describing the wave is in a periodic form. As we assume lineariza-tion of the waves, we can therefore add
iWLTh
Li[ft
flr
9:'Lr LETrI l?N '
T1T1.i ri LIFLI
-_EJtJL
i; wh CL200 0.168 0.176 0.163 0.160 0.138 0.125 -0.188 -0.200Fguea Pressure distribution over the hull
eight different potentials. These eight are the six radiation potentials (due to
the ships motions), the undisturbed
wave potential and the diffraction
po-tential.
The unknownsourcestrengths are cal-culated by using Green's function and are based on the no leak condition on the body. With the sources known, the added mass and damping can be mined. The motions can now be
deter-mined with the coupled equations of
motion for all six degrees of freedom.
Hydrodynamic Coefficients
Before one can start with a numerical
calculation, input parameters have to be
given. For Delkelv this is quite simple,
this is just the forward speed of 14.5
knots.
For Deifrac much more parameters are required. We start with elaborating on
how to determine the CoG (center of gravity), which for a submarine is a
more challenging task than for the aver-age surface ship.
The hull form in the geometty-fuie de-scribes the outer hull and to determine the CoG, everything, enclosed by this hull should be considered. This means also the space which is free flooded by
water. Knowing the displacement in the
three conditions (lightweight/surfaced! submerged) and the volumes given by DelftShip, an estimate can be made of
the CoG. We therefore need the
vol-ume and location of the three pressure
hulls, the fuel tanks, the diving tanks
and the free flooded areas. The pressure
huilsarealso drawn in DelftShip which
gives us an accurate location of the
cen-Frp rf hinyanry&cording to the main
frame in figure 1, an estimate is made. for the volume and the location of the
fueltanks andthe diving tanks. The fuel
tanks are located between the two lower
pressure hulls and the diving tanks are
located alongside the upper pressure hull. The remaining volumes are
as-sumed to be free flooded. The final KG
appears to be 2 meterwhich results in a
CoB - CoG of 0.61 meter.
Deifrac also needs an estimate of the weight distribution which should be
given in the form of the radii of gyration for pitch, yawand roll. The calculations should be performed in a fixed frequen-cy domain.
To make agood estimation for the max-imum frequency of ourdomain, we take
this twice as large as the natural
fre-quency. For a mass-spring system, the dimensionless respotise at the double
natural frequency is not more than a
third of its input and this will only de-crease when damping is included. It is
therefore save to take thefrequency do-main from zero to 2-wa.
The radii of gyration and the natural
frequencies can be estimated according to several rules of thumb which are
giv-en in [3] and [4]. We also like to esti-mate the natural frequencies so that we
can compare them later on with the cal-culations from Deifrac.
For thenatul-al roll frequency we have:
/p.g.v.GMr
We neglected the added inerti term
whereas I, and the radius of
gyra-tion aregiven by:
I=Iç2-p-v
k, nO.289-B. 1+
Pt 6000.0 4600.0 4000.0 3500.0 3000.0 2500.0 2000.0 1600.0 1000.0 600.0 0.0 -600.0 -1000.0 -1600.0 -2000.0 -2600.0 -3000.0 -3500.0 .4000.0 .4600.0 -5000.0 0.112 D.10a 0.088 0.075 0.063 0.0502
0.038 0.025 0.013 0.000 -0013 -0.025 -0.038 -0.050 -0.063 -0.076 -0.088 -0100 -0.113. -0.125 -0.138 -0.150 -0.163 -0.17524 SCHIP&WERF d ZEE - MEl 2007
Figure 9: Velocities vectors on eachhul!ipanel For the natural heave frequency the
fol-lowingho1ds:
jp.gA
(0,,
, WIAnd- forthe natural pitch:frequency:
/p.gS7.GM 4%j J+fl798
with .ç+n(0.32.-L.p.V
Results
The results that we are interested in
from Delkelv are the wave height and the pressure distribution along the hull.
The wave height is shown in figure 7 and clearly shows that there are -two
waves coming from the hull.
The-Kelvin waves and the wave system behind the ship are clearly visible and
one can-see-that these two systems inter-.
2,5 2,0 1,5
a
E 10 0;5 0,0 0FigUre 10: RA0sof the three motionS Without a natural frequency
SCHIP&WERF de-ZEE -MEl 2002
0,5 1 15 frequency [iad1sJ pr 5000.0 4500.0 4000.0 3600.0 3000.0 2600.0 2000.0 1600.0 1000.0 500.0 0.0 -600.0 -1000.0 -1500.0 -2000.0 -2500.0 -30000 -3600.0 -4000.0 -4600.0 -5000.0
act with each other. According to the
Froude number, there should be 2.23. waves along the ship. This is also
con-finned by the flgure..Furthermore-.there
is no reflection of the wave
with-the edge of the domain-so the width and length of the do-main- arechosen correctly.
The pressure distribution
along the hull is particularly
interesting because
of the
sonar dome. In- the following figure, -one can see that there
are high -peaks on- and around
the dome. The transition be-tweenthe.domeand the rest of
the hull
also causes somepeaks. Half way the hull-, the
second small peak-in the
pres-sure is visible and this
com-plies with having two waves alongthehull.
25
A closer look at the bow with a quver plot shows us how the streamlines are
directed around the dome.
The results from Delfrac are plotted as RAOs for different headings and
in-coming waves The- surge, sway and
yaw-motions don't have a natural-
fre-quency and show a normal behavior. The other three motions do. have a nat-ural frequency-because there-is a
spring-term involved in their motions. They
show a more erratic behavior as damp-ing, starts to play a role. The lower
fre-quencies are dominated by the, spring
term, the higher frequencies by the
mass-term.
Potential flowcan't describe the-viscous
damping and these- viscous effects.
would normally damp the heave, roll
and pitch motions around- their natural
frequency. This can best be seen in fig-ure 11 which shows the roll-motion and where-viscous damping is relatively-im-portant. Because the shape.of the hull-is
0. 2,5 2,0 a 1,5 1,0
05
0,0Figure 11: RAOs fortheother threeimotions, showingextrernely,highresponses around their natural frequency
close to a cylindrical shape, in that case
potential damping is very low.
Finally, it is good to check the
calculat-ed resonance frequencies with our
pre-viously estimated ones.
For heave we estimate the added mass according to the previously mentioned formulae as the volume of half a
cylin-der uncylin-der the hull. The natural
fre-quency is then estimated to be O99
rad/s. This isslightly lower thanthe 1.1
rad/s which is calculated by Deifrac. Deifrac can calculate the added mass exactly, the result for a slender ship
turns out to be lower than our estima tion
The natural frequency for roll is
esti-mated to be 1.33 rad/s which complies with thegraph in figure 11. It is slightly higher as weneglected the added inertia term.
For pitch the estimated natural
fre-quency is 1.13 rad/s which is in
agree-ment with figure 11.
Conclusion
NumericaItools are becoming more and more. easy-to-use for investigating ship motions, but one should take care when
making use of them. A proper panel
distribution is essential to avoid nurner-ical instability and to ensurethe reliabil ity of the solution
The solution should always be checked with manual calculations to ensure that
2,5 2,0 E . 1,5 e 0,5 0,0 frequency Iradls] Pitch
no majOr errors are made. The number of waves should be in accordance with the Froude number and the estimated natural frequencies shouldn't be toofar
off the calculatedones.
Even though the hull form was fairly
complex, we tried .toput it in one mesh.
On hindsight, it would have beenbetter to split the mesh in two parts to avoid weird panel transitions from the sonar dome to the hull. One mesh for the hull
which runs from the bow to the stem
and one mesh separately for the sonar
dome.
Nevertheless, we think that with these
simuiations;we have captured sufficient basic;physical propertiesof the complex flow around the hull for the use in apre-liminary design stage
References
H.J. de Koning Gans, Numerical
Methods in Ship Hydromechanics (Deift University of Technology)
K.H.L. Gerretse, Drie-Cylinders
Duikn Dieper (Amsterdam: van Soeren
1992)
J.M.J. Journee and W.W. Massie, Offshore Hydromechanics (Delft Uni-versity of Technology, january2001)
J. Gerritsma, Golven, Scheepsbewe-gingen, Sturenen Manoeuvreren I (Delft University of Technology)
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25 SCHIP&WERF deZEE- MEI2007
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