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OCR for page 385
Frequency Domain Numerical and Experimental Investigation
of Forward Speed Radiation by Ships
M. Guilbaud, ' J. Boin, ' M. Ba
(~Laboratoire d'Etudes Aerodyna~miques UMR CNRS,
2 CEAT-Universite de Poitiers, ENSMA, France)
ABSTEtAC r
b f is paper w p~ese t m e perimental md
mm~erical mve tig rti m of f ne mdiati m eft t of c sh p wif h
fmward ped m fne fiequency domau~ Ihe te ts were
pe founed m c reci ubt 3 water chxmel Foxes, momeris
md wave~lwrti m were meas ed m series 60 Ce=0 6 md
0 8 shp mod is m forced heave md pit h osc3kticns A
veloci y based fs t crd r Bommdary 3 me t Medhod was
dew~lop d usi 3 he forward ped dift ach m radicti m
G'en fmctim The cakubticns of f is fmction md its
denvrtives as w 11 as it inbr rti m m flat paneL were
pef med by conholk 3 bodh fne accmacy md fne
c mputational time Ihe Fourier inbr rtion was done usi 3
m Admuti e Simps m medhod wih c p~escubed eucr b
whrt m~ns he miace heg rticns, c mix~r43 m m :rical
tech iqre (Gmss medhod wih c mmber of pohs whicha~e
f nctim of fne ddstar~e betwe fne fleld pomt md fne
so :ce paneb md m analytical heg rtion q~eed m fne
Stok s fneorem to hansf m fne bommda~y heg al ho c
co tour one, fne ~emamsr43 Fouri r inbr cls ~r fne compl:x
expone tisl f nchm a~e fnen computed wifh fne same
AdmbLve medhod was used Fcr fhe wave prtt m
cal 3kticns, m exh mokti m tech iqre was used to obtam
improved m3merical ~e 3 ts fcr c fleld poh located m he
fie miace
INTRODUCTION
A pohed out byOkLu 3 mdWff~(1996 md
OkLu 3 (199S), fne compari m of mes :ed md cal 3kt d
global forces (cr mohom) m ships mm mg m wave is not
m effcie t ch k fcr fne validbty md he quliy of c
mm~erical medhod This is d e to fne fact f rt hi kmd of
dab rep~eseris m heg abd effect mvol mg pie ty of
factcrs md not only fluid mechmics but also mechcmcs So
fne te t ~e flt a~e not alway clear concemmg fne qulity of
fne pr 6ctim gi~n by mmencal mehod Seakeepi g
experime ts are gen:raly shp motim mes em nts cr
global force measureme ts fcr forced moti m tesb; ll~s,
fney only give ~es3ts w ich a~e not accmrte enough to
mve tigrte he viDd y of he mod 11i g of fl wbymm~erisal
medhod Com~que tly, it is also neces~ary to mes :e 1~1
dab 3ch as p~ e ddsh~buti m cr fie miace elevati m
ar md fne ships m crd r to hcve c bett r mmde~md g of
fne medhod of compubtion F w experimental dsta a~e
cv3ibbk m 6 is 3bj :ct Some experimer~l ~e 3 ts obtamed
fi m fie mod is m waws cr m fDxd mod ~ m foxed
mohm mbefommifcrexample,OkLu 3 mdWff~(1996
or OkLu 3 (199S) h y d scribe some diffactim md
radicti m wave prtt ms fcr fne OBS f m or S ries 60
Cs=0 S hip mod Is mm mg m wi~es, u mg several probes
1 rted on c prth pamllel to fne d pkoeme t of he mod I
md hen 3tract fne knear compone t of fne fs t hiumomc
by dab pmcessmg Iwashib et ol (19931 e also Okhu 3
(199S), ~o p~ese t pres 3~e mecsurement of fne
diff;ctim probkm fcr c V C shp mnn~ng m wiwes
Fmth mmore, fcr fie mod ~ m wiwes, te t encrs a~e
p~ese t bodh m motim md force md mome t
measureme ts Finally, radicti m md difflach m are not eEiy
to sepiu rte, ewn ff t i w 11 kmovm f rt difflacti m wiwes
vmi h more rmidyf m fne radicti m ones
Ihe experimental workp~ese tedhne hi s to give
bodhglobal mdl~lds~ mhydodynami radiatimfl wm
ord r to c mpiae fnem wih fne mm~erical medhod m he
fiequency domrm mmd r d velopme t Fcr fne exp~imental
work w use he forced moticns fcr heave md cr pit h
moticns A fs t experimental pknar moti m syst m, Guyot
(I 995, Guyot md Guik md (1995) wtu built to shrdy c
S ries 60 modl wihablock m ffcie t Ce=0 6 mdwihc
le gth L=0 6m It is m improwd v~si m of he d ice used
by D h m m et ol (19921 Some d fl flhes were
encow tered wh n t mg to obtam m accmrte wiwe prtt m
m m d e, m piati 3kr, to fne weak amplit d s mes :ed
Therefore, fne set-up hi i ben modfled to p f m te ts m
c mod I wih c I ngth of L 1 2m Fnces md mome ts md
clso wne patbm mes emeris hi ve ben done wifh two
modls, one mwhi hCs=0 6 mdfne of nerwihO S,mordr
to shrdy fne irdhence of he block cceffcie t b~fhences of
OCR for page 386
frequency, free-stream velocity were investigated in the EXPERIMENTALSTUDY
recirculating water channel of the Ecole Centrale de Nantes. Experimental set-up
The test apparatus enables to separate the radiation waves,
which are not directly visible in a towing tank, from the
mean steady wave pattern.
The numerical method developed is a velocity
based panel method using the diffraction-radiation with
forward speed Green function, satisfying a linearized free-
surface boundary condition. The main advantages with
respect to the Rankine methods (described in a large review
by Sclavounos, 1996) is the reduction of the size of the linear
system to be solved, the automatic satisfactory of the
radiation condition (particularly difficult to insure in the
Rankine methods whatever are the values of the frequency
and of the forward speed) and of course, of the free surface
boundary condition. The use of the corresponding Green
function prevents any problem related to the existence of
boundaries of the computational domain on the free surface,
responsible for wave reflections difficult to suppress in the
Rankine methods. Furthermore, due to the fact that no grid is
present on the free surface, there is no filtering of the smaller
wavelengths. Although the corresponding Green function for
seakeeping calculations in the frequency domain around
bodies with forward speed is quite difficult to compute and
relatively time consuming, the progress of computers during
the last years as well as the improvements of the algorithms
of computation enable us to develop numerical codes running
on a cheap workstation or PC in less than 2 hours for the
computation of pressure distribution, forces and moments.
The fastest and more accurate techniques of calculation are
the steepest descent method, Iwashita and Okhusu (1989,
1992), Brument et Delhommeau (1997) or Brument (1998)
using the Steepest descent method for the function and its
derivatives or Iwashita (1992) for boundary integrations of
this function, the method of the Super Green function
developed by Chen and Noblesse (1998), or the Adaptative
Simpson method for the function, Nontakaew et al. (1997),
or for surface integrations on panels, Boin et al. (2000~. But
to have an accurate method to compute free surface flows, it
is necessary to accurately calculate not only the Green
function but also the boundary integrals on panels and the
line integrals on the waterline. We have developed a mixed
technique for the surface integration using both a numerical
Gauss method (with a number of points which are function
of the distance between the field point and the source
element) and an analytical method of integration, derived
from the Stokes theorem, closer to the source element, Boin
et al. (2000~. All these methods give accurate results in
moderate computational times. We present here such a
velocity-based method for non-lifting flows. Nevertheless, it
is well known that these computations are very difficult and
it is quite important to check the results with test
measurements.
............
^:
............. ~
1 Motor- 2 Model- 3 Dynamometer
4 Translation rod - 5 Heave motion transducer
6 Pitch motion transducer - 7 Rotation rod
Figure 1 Planar motion generator
OCR for page 387
7he experiment were p f med m fne te t-
secti m (2m wid md Im high) of fne n:ci arkti g water
cham~el f fne Ecok Cerhale of Nmtes wh re fne maximal
veloci y is 1 7m s 7he photog mh m fgure I show he
pkne moh m genembr it i mcde of two cam~rarlcsh ft
sytems di~n by m elechi motcr (1) wih vari~ole
rotsti m speed 7hese sysbms give c msoidal conhoDed
moti m to fne hip mod 1 2), w ich m be eidner c pm
h~ m oveme t f ough he rod (4) (he pit h rod (7) bei g
decoupled, cr c pm pit h mowme t wifh fne rod (7 (he
h~rod(4)bei gd oupkd Wifhfnecombinatimoftwo
eccenhics, it is also possi k to obtam c heave-pit h
combined moti m wi h c varkibk phase kg betw~ heave
md pi h moh ms 7.1se mod I position is ~eccrd d wifh fne
h p of c heave knear hansducer (5 cr c pit h linear
hansd cer (6 7.1se mod I is fDosd to he moti m device
f ough eidner c 3 compone t dynsmometer cr c rigid
mod lus (3) used for fne wave pattem mms emeris 7he
cenhe of rotation, whi h also coue pcnd to fne cenhe of
m ment, i m fne pEme of he undishnbed wabr lewl md is
located et 0 603 md 0 560 m fi m fne forepart of fne model
for fne Ce=0 6 md 0 3 ~espechve y 7.1se pit h moti m i also
hansmitt d et fne waterlme lewl of fne mod I pi h rod
(7)1 7he maxinul mpk d s cvaikible a~e O to 2 m md 0
to 6° fcr heave md pit h ~espectively
7he positi m of fne pEme moti m genemtor m be
mowd by 90°, i e locat d hori ontally (m teed of ve tit~3y
fcr fne heave md pit h moticns, fg ~e 1) md f s i ~ole to
prod cc way md yaw motiom, Non~ew et ol (1996
b f case, c new dynam ometer is used
Models end test eondidom
Two series 60 Ce=06 md 0 3 ship mod is
(1~1 2m) were buit Th s ~aracten ti s a~e giwn mt~le 1;
fne dmff~sicns are based m he criginal m thodLcal seri s,
Todd (19631 Th mod is a~e made of composite materiels
(carb m fbre) m crd r to ml mise fne ine tic compone ts m
fne force measureme ts Th u weights a~e O 3 md Ikg fcr fne
Cs=0 6 md 0 3 mod is ~espectively Th te ts were canied
out for bo h mod is, fcr pme h ahe md pm pit h moti ms
wih IOSmm md I 3° as amplit d ~espechvely Global
forces md momeris hcve been reccrd d fcr f~equff~ci s
mgi g fi m 2 75 to 3 25Hz ffF=0 04, 2 5 to 6Hz at F=0 2
md 03 Fcr he wave~levation, fne mesureme ts Wff
p f med for f=0 S9 md 1 06H at F=0 12 ¢=022 md
027 md f=3 md 39H at F=02 md 03 (fne tet
mdticns a~e mmaised m tsbk 2 md 31 b crd r to
~educe fne reflffti m f fne waves m fne sid waks of fne
t t section at ve y I w velocity, he flow velocity arommd
~1/4 was incresed fcr he global mesureme ts Th
R y old m mber of fne te ts w ~e R=1 6g 10 F=0 04),
054mdl2105 F=02 mdO3)
Ce 06 OS
Lm 12 12
Bm 01574 O1516
H m 0 0629 0 0726
5 mS 0 23 5 0 324
V 0 007 0 012
T~ole 1: Ship se s
U FH ~ F
ms
04 OS7 022 012
04 107 027 012
07 3 135 02
07 392 176 02
1 297 190 03
1 385 247 03
T~ole 2: Te t condih ms fcr fie
mf aos eLvati m mes emeris
U(m/s) f(Hz) ~ F
0 13 2 75 to 3 25 0 22-0 27 0 04
07 25to6 125to27 02
10 25to6 175to38 03
T~ole 3: Te t conddLcns fcr force mesureme ts
Th dynamometff used i composed of 3 miniahne
force hansd ffS; forces md m me ts a~e uncoupl d by he
use of edk s B f ore bei g com~Kted to f ne anslog to d6gital
conve ter, eiffhic sig ffS Wff amplffed usi g bmd pass
flltffs Sbti w ights Wff used f r caLbrati m to d tffmine
fnecaLbratimmahi fcrdned3~'edchon
Linmr d6 pEceme t hansd ffS ~eccrd fne
moticns Thy a~e not used to mec:ne fne motim
amplit d s but to give fne refesnce kg fcr he motion
Ho~vff, fne kgs h~ ben confft d fi m parasit kgs
inhod ced by fne knesr hansd ffS md by fne dsts
acqui iti m t m by fne mms cd phase kgs duri g fne
ine tis mes emeris wifh fne k own value of I SO°
Fcr fne force mecsureme ts, te ts had to be
pe f med twice, wifh fre mod I oscillaimg m a~r ~m dis
forces) cr m watff (total fomes) at fne same fiequency Then,
fne ine tic forces w ~e subtnct d fi m dse tobl ones to
obtsm dse hyd odynamic ones Guyot md Guilb md (1995
have shovm dsat dse ~esuLs a~e equivale t f he cabb~ti m
mah ff is mplied before dse signsl ansly is (hff mplied to
dse forces cr mome t) cr i dff b d is knt case, dse signsl
ansly i is mplied di:nschy to dse elff h ic signcL We used d is
kntsolutimhffe Onceglob~f~swff dtffmi~daddd
mass md di mpi g cceffcieris Wff calarkted k wm also
necessary to mms e dse hyd odynamic ~e tcri g to obti m
dse cdd dmass cceffcieris Thi wm done at dse
cone pondi g Froud mmber to tske mto accowt dse tme
shape of d~e m m fiff suriNce by meEnri g dse d fffff~ces
bffWff dse fomes md m me t m dse mod I bcated at dse
e~ffmeposticnsofdsemotion
OCR for page 388
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Representative terms from entire chapter:
wave amplitudes
Wave patterns measurements
Free-surface elevations were measured using a
resistive probe which consists of two parallel chromel wires
of 0.2mm in diameter and 150mm in length which were
lOmm apart and held by a Plexiglas frame to avoid electric
perturbations. These two wires were mounted as one branch
of a Wheastone bridge supplied by a 3kHz alternative
current to prevent water electrolysis. After demodulation
and amplification, a signal with voltage directly related to the
depth of immersion was obtained. As for the force
measurements, band pass filtering processed the signal. In
order to obtain a good accuracy in the neasurements of
wave-amplitudes, a probe calibration was done for each flow
velocity. For each one, the curve voltage-immersion was
approximated by a five-order polynomial, in order to
determine the probe immersion. A slight influence of flow
velocity was also found, justifying, thus, this procedure. The
free-surface mesh was obtained over one side of the model
(the flow being symmetrical) each 40mm for x and y co-
ordinates close to the hull, figure 2. This mesh was finer than
that used in a former work (Guy ot, 1995~. The measurement
area was l8SOmm streamwise and 360mm crosswise. During
these tests, we took care to have a significant measurement
domain upstream of the bow in order to highlight the
upstream wave phenomena close to ~=1/4. In short, the
wave-elevation contour cartography included 350
measurement points, see for example figure 2 for the CB=0.6
model.
n ~~
n no
l
Figure 2 Part of the free surface where the elevations was c:
measured g1.2m)
Acquisition system and signal analysis
The experimental set-up included a Pentium
lOOMHz personal computer, with an acquisition card
Keithley DAS1600 (with an internal clock of lOMHz) and a
sample and hold SSH-4/A module (thus the time lag between
the channels during the acquisition did not exceed dons).
Four channels were used for the global measurements (3 for
forces and moment and one for the motion) and two channels
only for the wave pattern measurements (one for the model
position recorder and the other for the free-surface probe).
The probe motion was semi-automatic: automatic along the x
co-ordinate with the help of a stepper motor driven by the
computer, and manual along the y direction. During the tests,
an optical device located close to the motor adjusted the
frequency of motion (motor rotation). As already shown
(Guyot 1995), data reduction depends on the number of
acquisition points: 6000 for the force measurements and for
the wave patterns, 1024 samples were recorded for each
channel. The data treatment procedure was as follows:
a) Rough determination of the motion frequency fin of the
model by a Fourier analysis. This frequency was the initial
value for the following calculations;
b) Probe-signal's Fourier analysis around this frequency
value for the range fini-O.lHz
0.025
0.02
0.015
Ad:
C'
0.01
0.005L
_ \
~ ._W
f(HZ)
Figure 4 Damping coefficients for the heave motion
0.0006
0.0005
0.0004
0.0003
0.0002
0.00 01
· CB=0.6 F=0.2
— ~ — CB=0.6 F=0.3
—-+-— CB=0.8 F=0.2
\ ~ ~ CB =0 .8 F= 0 .3
\
\
If
_~
0.0001 ( ) 1 2 3 4
f(HZ)
Figure 5 Added mass coefficients for the pitch motion
n nnnn
nnnn.~
0.0004
0.0003
By:
C'
0.0002
0.0001
-0.0001 n 1
tt . GB=O.6 ~0.2
\, — ~—- CB=0.6 F=0.3
'\ —-+-— CB=0.8 F=0.2
1\ ~ ~ CB=0.8 F=0.3
~ .
\\ \\
At'
11 ~
i
.. ~ I I I /1 I I I I I I I I I I I I I I I I
2 3 4
f(HZ)
Figure 6 Damping coefficients for the pitch motion
The added-mass coefficient CMjj = Mjj / (r Ln )
and the damping one CAjj = Ajj / (r wL n ) for
j = 3 ¢7 = 5), or j = 5 ,7 = 3) where w= 2pf, versus
CB=0.6 F=0.2
~ CB=0.6 F=0.3
~ = CB_O 8 F=0 3 the frequency f (in Hz) for the 2 ship models and the two
values of the Froude number are plotted in figures 3 to 6.
Figures 3 and 4 correspond to the heave motion.
The effect of the Froude number is relatively weak, except at
lower frequencies for the added-mass CM33. In figure 3 the
model shape has a stronger effect, CM33 increasing with the
block coefficient. It must be noticed than when the frequency
decreases, CM33 is very sensitive to errors in the
hydrodynamic restoring coefficients. Concerning the damping
coefficients, figure 4, these two parameters show weak
influences, except at the lower values ~ the frequency,
leading to high values of CA33.
Figures 5 and 6 are for the pitch motion, CM55 and
CA55. Conclusions are similar for the heave motion, the effect
of the kind of model (value of ~) being greater than the
Froude one, particularly on CM55, figure 5. No important
coefficient variations were observed close to ~=1/4.
Wave pattern measurements
Flow close to ~=1/4
Figure 7 Wave pattern close to ~=1/4 (heave)
T= 0 , 2 7
Figure 8 Wave pattern close to ~=1/4 (pitch)
One of the first aims of this work was to
investigate the wave-elevation contours close to =0.25 for
both CB=0.6 and 0.8 models. It is known that below this
critical value of it one part of the waves field propagates
upstream of the model. Beyond =0.25 a wedge appears at
the bow and stops this propagation, thus the waves are
exclusively convected downstream inside this V-shape
pattern (the wave group velocity is lower than the ship
forward velocity). Figures 7 and 8 show the wave-amplitude
contours for both heave and pitch motions for the CB=0.6
model. The upper half and lower parts of each figure
correspond to ~=0.22 and 0.27 respectively. The form of the
waterline of the CB=0.6 model is also plotted and the white
area around the hull corresponds to a non-investigated zone
(this domain was not accessible to the free-surface probe).
For the heave at ~=0.22 (figure 7), two waves can be seen
close to both the bow and the stern, and their crests are
roughly parallel to the hull axis. The relatively large height of
these waves is probably linked to a reflection phenomenon
on the channel lateral walls. When the motion frequency
increases ¢=0.27), the upstream perturbations vanish and
the more pronounced wave-elevations are located at the
downstream end of the model. An increase of ~ leads to the
formation of the V-shape pattern, as will be shown in the
next paragraph. Figure 8 shows the wave-elevation contours
for the pitch motion. At ~=0.22 stronger perturbations are
convected upstream of the model (in comparison with the
heave motion); the wave pattern stays relatively
homogeneous along the hull downstream. The pattern at
~=0.27 shows the emergence of a new flow state: upstream,
the wave-elevations decrease strongly. However, the wave-
amplitudes pattern remains slightly rough; downstream, a
perturbed wave field is observed, nevertheless the heights are
slightly smaller in comparison with the upstream
measurements.
The results corresponding to the G~=0.8 model
close to ~=1/4 are not reported in the present paper. Indeed,
this model generated larger wave-elevations, which were
reflected on the channel walls. The obtained wave pattern
was strongly disturbed and difficult to analyse. These
measurements are less accurate than those obtained at higher
values of the Brard parameter due to the low flow velocity
enabling wall reflection of waves close to the model and to
the weak amplitudes.
Flow at~>l/4
Figures 9 to 14 show the different wave-elevation
patterns for both CB=0.6 and 0.8 models. The upper half and
lower parts of each figure refer to the CB=0.6 and 0.8 models
respectively for the same test configuration. The wave-
elevation measurements highlight the effect of four
parameters on the free-surface waves: the motion frequency
imposed to the model, the flow velocity (Froude number),
the type of 1~11 movement (heave or pitch) and the ship
block coefficient.
Figure 9 Wave amplitudes (heave motion; F=0.2; f=3Hz)
The recorded wave patterns have the same
characteristics whatever the test configurations and the model
motion: two zones in V-shape with the tip in the upstream
direction are visible with strong amplitude values, at the bow
and the stern (these amplitude values being stronger at the
stern). The whole wave field is contained in this V-shape
pattern.
Figure 10 Wave amplitudes (pitch motion; F=0.2; f=3Hz)
Figure 11 Wave amplitudes (heave motion; F=0.2; f=4Hz)
The opening angle of this wedge and the wave-
amplitudes are decreasing functions of the motion frequency:
the figures 9 and 11 for heave motion, for the CB=0.8 model
for instance, How a decrease of the wave amplitudes just
behind the bow and downstream from the stern when the
frequency increases from 3 to 4Hz. Moreover, the frequency
increase prevents the propagation of strong wave-amplitudes
in the flow field as shown for example in figures 10 and 12
for CB=0.6 and 0.8, in the case of pitch motion. The wave-
amplitudes are quickly damped far from the model. The
highest waves are located close to the stern (particularly for
the pitch motion). A diminution of the two V-shape zone
angles is also observed.
Figure 12 Wave amplitudes (pitch motion; F=0.2; f=4Hz)
Figure 13 Wave amplitudes (heave motion; F=0.3; f=3Hz)
Figure 14 Wave amplitudes (pitch motion; F=0.3; f=3Hz)
The increase of the flow velocity induces the same
behaviour: for the CB=0.6 and 0.8 models, figures 9 and 13
clearly show that the wave-amplitudes decrease and the front
V-shape pattern is less visible when the Froude number
increases; the bow waves are reduced and the region of strong
amplitude moves from nearly x/L=0.2 at Fr=0.2 to about 0.4
for Fr=0.3 for the CB=0.8 model. A similar observation can
be done for pitch motion, figures 10 and 14. However it
should be pointed out that the frequency effect seems more
pronounced in comparison with Froude number one; the
wave amplitude variation is weaker in this last case.
Figures 9 and 1O, both for CB=0.6 and 0.8,
emphasize that on pitch motion, the back V-shape pattern
presents higher wave amplitudes in comparison with the
heave one, but the areas of strong wave amplitudes are
reduced. This fact can also be observed at a higher frequency,
figures 12, F=0.2 and f=4Hz.
For the same test configuration, the block
coefficient effect is quite pronounced: figure 9 for instance
provides stronger wave amplitudes for CB=0.8, but the wave
angle seems to have the same value. For the CB=0.8 model,
just behind the bow wave, a local area of low wave
amplitudes appears, and three areas with high amplitude are
clearly seen close to the hull (see also the CB=0.8 figure 11,
for a frequency increase). The bow wave and front V-shape
pattern vanish with the increase of the flow speed (figure 13,
CB=0.8), only the stern wave is present, with the same
amplitude but a smaller area. Results are similar for pitch
motion, figures 1O, 12 and 14.
Analysis of flow
Unsteady wave motion
/_W
An\ ~
' ~ ~ PITCH
Figure 15 Model positions during motion
The advantage of this kind of experiments is to
underline the evolution of the free-surface unsteady part,
which is defined by z=Asin(mt+(p3, where A is the
amplitude, by removing the steady component which,
because of its high values, hides the unsteady phenomena.
The time variation is quite similar for both models, but the
CB=0.8 model results show a more pronounced wave-
amplitude pattern in comparison with the other model. These
results are therefore presented in this paper in order to make
the understanding easier.
t/T=7/8
Figure 16 Unsteady wave pattern during a period for the
CB=0.8 model in heave motion (F=0.3 and f=3Hz)
t/T=1/8
t/T=1/4
t/T=3/8
Cr=1/?
t/T=5/E
tlT=3/4
t/T=7/8
Figure 17 Unsteady wave pattern during a period for the
CB=0.8 model in pitch motion (F=0.3 and f=3Hz)
Th mod I po ithns dwi g c p riod are giwn m
figme 15: fzheave at VT=1/4, fr mod I is m he high t
position; f r low st r cmre p md to VT=3/4 For f r
h~ motion, f r flgw 16 sh ws f r fie smiace m tedy
compone t dmmg c penod T. fz eight posithns eve y
VT=I/S (fi m VT=0 to 7/S), at F=0 29 md ~190 (f r flow
c mes fi m f r nghtl
A it m be otw~d fr waves pred out
pzalkl to 6r h 11 ax~s md mow away downsheam md
slightly sid way fi m 6r ship dwi g c penod (fo3 w f r
wave d velopme t fi m VT=1/2 to 7/S) Fz 5/S VT 7/S
fr fio t mdbackpekshevefr wmephw~e kg; fr model
~each s its lovm t posihon at VT=3/4, wh ~e fhe peks em
to be mz~inul Th se mwbady wave move away im id f r
V-bap pattems, whicha~e is~ble mflgme l3 ~ zz pa~t)
A mall peak is inble ju t r~z f r b w (t pical f z f r
C =0 5 mod ll
Figme 17 cone pond to f r pit h motion of f r
hip wifh f r wme block c rffcie t C =0 5 md 6r same
te t condbtiom The time VT=1/4 md 3/4 w 9 r to he moti m
wh ~e f r tem is m I w md high posthns ~ew,sectively
(hgme 1) Fr m VT=3/4, c c~e t ju t adz he tem mbe
obw~d its h ight inc~ses fz VT=7/S, md at t=O, f is
c~e t is d id d m two by mo mg away downshem md
goi gsid way fi mbrhu3 Atbrwunetmefrbackc~et
a~ea bee mes ksgz As pre iously d zzibed (f ze 14,
I wz pa~t), f r krge t emplit d s a'e heated r z f r ten~
NUMERICA1 STUDY
MettrmeVesd model
A velocity besed pMri medhod usi g c so :ce
diwbutim wifh fhe diflaction-mdiatimfor~zd ped
G'en fwrti m was d velop d wifhout tskmg ho accowt
fhe lidi g effects es c fu t tep T r fluid is assum d to be
inc mpwss~ble md m v~scous T r f e wuface md 6r
watz hri ht are a~umed to be of hfmite e tent A uwMd,
fhe tobl fl w mommd c ship wifh c mwz ~t for~zd ped
Ux m wa~es m be d ompowd ho c te y fl w, not
comid ~ed hme, md ho m um~ady fl w Fz m
in obtional fl w, f r velocity pot tial m be uw d We wi3
assume fnat fhe te y md umtedy pa~ts of f r velocity
pote tial a~e md prnd t md w only uw he kst r mmd r
6r f m t7,zy,~)e '~ Fl w is described mcoght-hwfled
refe~e f~me frced to f r ship T r ~y phrr is he m m
undiwwbed fi e miace; x axis is m f r d ecti m of m oh m
md thr ~s i vedical m upwzd d ectioa The w,satisl
pa~t of f r mm tedy potential mm t wli fy f r mkce
equati m mf rfluilf rbodyconddh m mbodyS:
(M) = (V+ Q 0
4~ =z+z'+i[(x
md
G.=
x')sosq+ y y')sinq]
j4[g(Z6+8,(Z;~] Z~[s,(Zi+g(Z~;')] 9
:W 4~
;~4 Z[s,Z;+g(Z;~] <[g,(Z;+g(Z~')]
t ~4,~i i9
2XKcQi)(e~ + )
4I K[g,(K;)+g,(K )] K~[g,(Ki)+s,(Ki)] 9
.~ ~fi4~
Th limits of heg ati mfor G~ a:
if t<0 25, q, q,~,~,.
if 0 25
Th body is d id d ho n, colmm of n~ panels
giVDg N = n, n~ panels m hebody Totake advan~ge
of fne mmet y of fhe boat fcr non ii ti g flow, only one
ha/f of fne hu3 is discretised C nseque tly, fne wsterline is
also d id d ho n~ segme ts Th medhod d velop d i c
com mt pmel mehod B - tim (7 leadsto fne fo3Ow g
equatimwifhurlmov.n sJ md sl fcrth cal-ubtim:
Y'~ 3
at s, + ~ b~s = c,, I = I, , N (10)
Coeffci ts a~ md bl to be computed are
~espectively gi~n by bommdxy md line heg als m fne
denvatives of fne G~en 9 nchorr hieg als m fne f mch m
also hsve to be p founed to c mpute usi g q (5 fne
velocity pote ticl f need d m qs (8) cr (9) Th G'en
f mcti m isc mputedas mBa md Guilbmd (1995; fne only
di fe~e i f tt fne Fourier heg sti m is p f med h ~e
by m ad ,mtive quadrature medhod proposed by Ly ess
(1970) md Mal m md Simpsm (19751 whle he
heg ati m sbp d ~ses as fne inbg md becomes more
osci hti g wih c p~escabed eucr, im~ad of c fom h crd r
~ Kutts medhod Bsch herval is d ided ho 2 parts,
fne mt gml on fne whole he~val md fne sum of he 2
heg als mbue 2 sub dom~ns a~e comput dwihc 5 pohs
Simps m mehod md fne results c mpared Nor~ew et
ol (1997 Th pmcedne is pmsued mtil convergers:e is
obtamed it i easy to ~ebte fne eucr m fne whole domam
md fne coue pond g eucr m one of fne sub-domams,
Gutt m (1983) Th mehod ~ed ces th CPU times md
giws accmste ~esult fcr my vahe of fne parameters
Never~eless, not only do fne G'en fmction md it fs t
denvatives hsve to be c mput d accmutely, but also fne
bommdny md co tour heg sls mvolved m fne eq~tion (7
Fcr th bommdxy inbg;ls m panels Kceffcie ts a~ m
~uati m (10)1 fne accu;cy of fne heg sti m by c Gmss
mehod has been co xolled Bom et ol 2000) by
compari g wifhfne ~esuts of m armytical heg sti mbased
mbue Stokes fneorem transf ml g th miace hqgrals ho
co tourones,foll wi gBougis(1981):
I = f ~ f(z~+,) f(z~)
s dz ~=r z~+~ z~
Coeffci ts A~ meq~tim (lI)arecomputed
u mg fne follow g prop ties of fne c mplex hegfa
g~ (x) = g~ (x) -; g~ (x) = g~ (x) - +—f
( ) md ( ) a~e he fmt md second drivatiws of fne
f nctims wifh ~esp t to fne pammeter ~ For fne
heg stiom 0=1 to 3):
g~ (x)dx = g~ (x) + in x
dx g~(x)dx=g~(x)+(x+~)lnx x
Th txm Go, of ff~ ~uded m aemdynamics cr
hydrodynamics usi g Rarlcirx's si~mlarties, will not be
~udi d h ~e Fcr G. md G~, fne foil wi g e p~essicns a~e
obtsmed:
OGd= B I dd
~ a~ x ~ ~ ,
{~Ct[K,~t K4]+( 1) C't(K,D'~ K2D'~)}
fcr F12 cr 3 md:
(12)
C' =(q+irsinq(x x) F irsinq)~+t y)
hft(xt,yt,z~) is fne nod k of c panel wifh M~+~=M~;
th outxu tn~rncltohepaneli n,~,=(p,q,r) md
F x G~, w obtam:
[|g,(~)d;] I
D~= ~ ' j=1,2
~1
dG~ /dxds~ I
pL~
1,+12+13+14
Th txms I~ m he doove e p~essi m a~e vey simitn to
~uati m (12) wifh d fere t cceffcie ts msbad of D~
mvolvcg of ner values of c x fne modf. d compkx
fmcticns Detads m be fommd m Bom et ol, 2000
Q Dmt ties ( )' a~ e d d ced fi m th ( ) ones by repk i g X
by X'. wif f x 1=12:
C = K~ Z + Z~ + i (x X
· )c~sq+(y y )sinq .
i ncenzng th G'en f mction, coeffcieris a~e
obt~ned wit similar e p~essions by repboi g fne m iqre
heg~als for D by double heg ati m wif ~e pect to
Fmdnemmce,w haveth follow g~elations:
For th i teg ati m m a segme t, a simibr
e p~essimto luatim(ll) mbeobt~ned:
df dl = f (X~ ) f ' )
i dx x~ x,
(l3)
hs eq~ations (11) md (13), fne Founer heg ations
a~e also p fcrned wit fne Simps m Adspative mef od
already used for fne G'en f mcti m FinaDy a tech iqre to
calculab fne bommdxy hqgrals was used it mixes a
mm~erical Gmss mef od of hegcti m wit m analyical
one Tbemmber of Gmss poiris requzedtohave agood
accmacyrmgesfi mam~ueone,farfi mth soucepanel
md puticularly upsheam, to 224 G mss pohs close to it
As fne c mputational time for fne analytical mef od of
heg ati m i mce or less equivale t to fne m mencal one
wif 4 G mss pomt, fne analytical mef od is mce effcie t
close to th panel Iherefce, w have d id d to use fne
mm~ericalmef od(wit fnemmberofGmsspohsrangi g
fi m I to 4)for feldpoiris out of a vedical cymder cenhed
on fne so :ce panel wif a mdi s eq~al to 8 t mes fne panel
ler~ds, exaspt m a zone lim ted by mgl s ami~ md am=,
d fm d m fgure 18, wh ~e it is not poss~ble to c mpute
accmate y dne hegcl owr G~, ewsn wit a large rnmb~x of
Gmss pomt hs t e cylmd r, bof hegrals m G~ md G~
are heg ated analytically Detads of fne mef od a~e
e~plamedmBometo/ 2000)
Ihe values of th fmit g mgles mdne fgure 18 h~ been
dtxmiredfi mmmxicaltesb; msi gl panel mdafeld
poh descabi gfnewhol ft iddomambyva~ymgbothfne
Fmud mmber mdfnemotimf~equency
Figure 18Limiti g mglesforfre d f ti moffnezonewh ~e
ftse heg als m G~hsve to be calcubtedanalyica6y
Tbey have shovm f~tt ami~ is a f mch m of fne
B;rdparamet rgi~nby
if t < 0 27, am~ = 05O
(r ~n) (14)
if t>O27,a =160 72 e 02
d i mme dffculttofmd me p~essimfor am=,butw
have chosen:
x ~ = 18l tf t 0 27
Neverffielex, ff f ns m ixed t h iqre of bommdxy
heg ati m used for fnese kmd of catulatiom is efficie t
wh n fne feld pomt a~e not to close to fne fie surface,
mm~erlcal dfficuthes arue wh n calculalmg f ne wave patbm
fi m equati m (9), fne feld pohs bel g m f is case on fne
fie nface (z=O) his is qrite e id t for fhe fu t mw of
panels close t to fne fie :r face, none of fne 2 lnbg atl m
tech lqres (mmerlcal or anslytlcal) gives com t ~esults
Bett r heg ation is made usl g fne armytical mehod by
~ed cl g fne p~escrll~d euor to IO ~ mdbylncre mg fne
mmber of teps dnl g fne ad ,mtative heg ati m to 10000,
but o ly ff LS-O I We fnen d id d to compute fne
heg als for f is value of z md to exh molate fne values to
z=0 Results hsve ben shovm to be nmrly md pmd t of
ftse m thod of e xmolatim used We are tdl workmg m
ftse lmproveme t of ftse cal-ulati m of fnese hegels Similar
dwelopmeris m be also done for fne heg als owr fne
wabrllne segme ts
Flnstly, eq~ati m (10) led to a linear sysbm of
uatlons ft tt m be mve t d gi mg fne so :ce hffuibes
m fne panels Afx r ha mg obtamed fnese hff~sities, fne
p~ e is computed by eqmhon (8) md by mt g ati m m
fnebodysurface,fnefeces mdmoment m hebody Such
a computer cod has ben d~lop d wlhout lnc ml g
waves to c mpare fhe ~esults with fne p~ese t te t ~esults
md with fne m merlcal ~esults obtamed by Nontsksew et
ol (1997 foraftatplate m way mdyawmotionsusl g a
vod:xlattlcemethodNmnerical~esults mdfnec mparl m
withfne te t mes eme ts wlllbe p~ese ted md dscussed
mdnene tparagrmh
C mputationsl t mes for p~essme, feces
md m me ts a~e t pica6y 2 hours m a FC for 4 panels
md 7 hours for fne c mputations of 200 pohs on fne fx e
surface for one value of fne fiequency md of fne Froud
m mb~x
NUMERICA1 FESULTS AND COMPAb'lSON WIIH
TEST MEAS[~d
Senes 60 hulls
O012 ~
00
O007
0 005
Figurel9cAdd d~sscceffici tsfcrS ries60C =08h 11
mheave moh m F=0 2; a/L - 0 009; 490 panels)
Figurel9bDampi gcceffici tsfcrS nes60C =08h 11
m heaw moti m F=0 2; a/L=0 009; 490 panels)
Fig e 19 md20 plots dne cdd dmass md dsmpi g
cceffici ts wrsus fne m dmff~sional fiequency
f =fL/U fcrdneS nesC =08h 11fcr hetwomoticns
wifh 490 paneh et F=02 Tne heave amplit d was
a/L=0 009 mdfne pit h one ~=1 8° Tne dnhed knes a~e fcr
fne m merical ~esults (wi hout fne waterline heg al) md fne
symbols a~e fcr fne te t mes eme ts Tnese ~esults show
o~ilkdicns prob~oy d e to he e isbnce of imgmk
fiequff~cies To ~em dy f is probl m, w h~ cdd d c
miace of flat hori or~l md slighdy i mened panels
(-O 5% of fne total body le gth) msid fne fie- miace wh ~e
c zero velocity condbtion is sati fed The ~esults obtamed
mg 6 is t h iq e fcr npp~essi g fne inegmbr f~ ncies
a~e shovm by he f 111ine The fmt inegmbr fiequff~cies h~
ben effechvey ~mowd (J<4s), shwig m
improwme t of fne ~esultg but fne~ e till inegmbr
fiequff~cies et high r values Work is m prog ess to impmve
fnese ~esu ts Neverffieless, w m obse~e c good agreme t
betven computaticns md mes eme ts fcr J s 4 5.
pa~ticukr y fcr fne heave mohon b suits a~e also good fcr
CA s but calcubted ~esults owr p~edLct fne te t ~esults The
agreme t is less good fcr C!dss but fne varicti m of fhi
coefficie t wifh J > 4 5 is quclibLve y p~edLcted md f is
coeffici t has ve y weak values
Fig e20cAddd~ssccefficierisfcr Sries60C =08
h 11 mpit hmoti m F=0 2; ~=1 8°; 490 panels)
Figure 20b Dampi g coeffici ts fcr S nes 60 C =0 8 h 11 m
pit hmoti m F=0 2; ~=1 8°; 490panels)
Figm~es 21 d pict fne plots of fne m tecdy wahc
cmplit d pattems arommd fne S rie-60 C =0 8 et F=0 2 md
~1 75 (f=3 9Hz) fcr heave motion (top g mh md fcr pit h
one (bottom one). The upper part of each graph shows the
numerical results and the lower one the test measurements;
the higher plot represents the heave motion and the lower
one the pitch one. The motion amplitudes are the same than
previously. The same general wave patterns can be observed
with the V shape already mentioned and some regions with
high amplitudes at the bow, middle part and end. The
calculations show particularly a zone with high wave
amplitude behind the hull. This fact has not been explained
yet, but it has already been mentioned, Brument et al.
(1998~.
SeI?eS 60 CB=0.8, F=0.2, f=3.9HZ, a=10.8
v_
04 .
03 _
no :
0.001 0.0~ 0.~3 0004 00050.0060.0070.0030.0~ on o.a2 0014
Calculation
..
1~
..~
1
Figure 21 Comparison of wave height amplitudes for a series-
60 CB=0.8 model in forced heave or pitch motion
(F=0.2; f=3.9Hz; ~=1.75;a/L=0.009 or ~=1.8°)
n no _
v .v ~
o. 015 _
Present calculations (245 panels)
Present calculations (400 panels)
Present tests
0.5 0.25 o -0.25 -0.5 -075
x/L
Figure 22 Comparison of wave height amplitude for a series-
60 CB=0.8 model in forced heave motion at y/L=0.166
(F=0.2; f=3Hz; ~=1.35;a/L=0.009)
Present calculations (245 panels)
— ——— Present calculations (400 panels)
· Present tests
v. v, TV
0.01 _
n nnQ~
Figure 23 Comparison of wave height amplitude for a series-
60 CB=0.8 model in forced heave motion at y/L=0.166
(F=0.2; f=3.9Hz; ~=1.75;a/L=0.009)
For a quantitative comparison, figures 22 Ad 23
plot the longitudinal relative wave amplitude (h/L) profile for
y/L=0.166 for the Series 60 C4=0.8 hull in heave motion at
respectively f=3 and 3.9Hz and F=0.2. Full line is for 245
panels and the dashed line for 400 panels. The symbols are
for the test measurements. The increase of the number of
panels lead to weak variation of the wave profile but with a
smoother curve. In figure 22 (f=3Hz), some discrepancies
appear between computations and measurements but this
frequency is close to an irregular one. At the contrary, in
figure 23 (f=3.9Hz), the agreement is better except at the hull
end where, as already mentioned, the calculations overpredict
the wave amplitude; this frequency is located between two
irregular frequencies, so the results are better and the
agreement with the test results is more fair, except behind the
hull, as already mentioned.
Flat plate in forced sway motion
Figures 24 and 25 plot the added-mass and damping
coefficients CM22 = 2M22 / (r SL) and CA22 = - 2A22 / (r SO )
versus the non-dimensional circular frequency V for a
surface-piercing flat plate of aspect ratio AR=0.5 at Froude
number F=0.32 in forced sway motion. The shape of the
plate is a Wigley hull defined by:
y/B = 1 _(z/T)2 1 - (2x/L)2 *
(1 + O .2(2x/L) ~ +
+(z/T) 1 - (z/T) 1 - (2x/L)
with L=lm, T=0.5m and b=0.02m. The mean amplitude is
oc=0°. The present results (full lines) are compared with the
calculations of Nontakaew et al . (1997) using a vortex lattice
method based on the same diffraction-radiation with forward
ped G~ flm ti m as m he p~ese t sh~dy fcr c zero
6 ickness flct pkte (dssh d line1 Ag ement is ~ekdively
good whm it is consid r d fl assumpti m fcr fl~ese kst
calcubticns, pa~dicukr y fcrhigh vahes of ~ Neverffieless,
ewn et high vahes of ~, c :ves hcve simibr shapes
Figure 24 Add d mass cceffici ts f cr c WigLy- shaped flct
pkte m way moti m F=0 32; AR=0 5; 4 0 panels)
32 ~ ." -';~
27 ~ I / -
2 ~ /
2; ~ '
12 [-`
07 ~ /
02 ~ /
' ~ ' ' 2 ' ' 3 ' ' 4 ' ' 5
\
Figure 25 Dampi g cceffici ts fcr cWigey-shmed flct
pkte m way moti m F=0 32; AR=0 5; 4 0 panels)
CONCLUSION
We hcve pre t d some experimental md
mmencal ~esults m he fiequency domcm conceneng he
radicti m fl w ammmd shp mod is of S ri s 60 wih block
ccefficie t C =0 6 md 0 3 m fomed oscilhticns of heave cr
pit h moti ms Add d~ss md d mpi g ccefficieris were
mes cd as well as fl~e m te y fie-suriNce elevati m
a ommd fl~e h 11 Ihe mes em nt s sh w c sh o g i fluer~e
of he block ccefficie t wh:n compared wih fl~e Froud
mmber bo6 m global forces md also fle suriNce
elevaticns Fmth mmore, fl~e umte y radicti m wave pattem
evoluti m duri g c p riodhas ben analysedby ~emov~ng fl~e
m m fle miace eLvatim fl m fl~e mesureme ts Ihe
g mh sh w waves, oneried alo g fl~e lo git dinal axis,
hahelk g downsheam md sid way fl m he model, boflh
starti gfl mfl~efore mdbackpartsoffl~eh 11 Thesewaves
moved m Vshme a~s fl~at m be dose~ed m he wave
amplit d plots Fcr heave motion, he upsheam md
downsheam wave hcve fl~e ~oout same phase kg, wh3e fl~e
phase kg is ctout 130° fcr fl~e pit h motioa Close to fl~e
~mhs value of fl~e Brard pa~m ter rO=1/4, fffl~e wave
p attem chmges fl m wave h ahefli g m fl~e whok d mam ff
~<1/4to only downsheam wave ffml/4,no ~,mvarictim
of fl~e f or ces cceffici ts are fl~en obse~ed
Calcukdicns hcve be p fonned wiflh c com mt
panel mehod usi g fl~e dff6~cti m ;dicti m wiflh fo ward
ped G'en flnctim Boflh he zccmacy of fl~e G'en
flmch m md d rivatives but zlso of he i teg ati m m ftat
panels hsve ben conh ofled Ihe compari m of zdd d mass
md dsmpi g cceffici ts fcr S :ries 60 h fls h ws ~ektive y
go d zgreme tbetwe m~ued mdcal-uk4 dvalues Ihe
~esuts obtamed wih fl~e cod dvelop d m fl~e p~ese t
sh~dyhsve zlso ben compared wih ofl~er mm~erical ~esults
zvaibbk fcr z ftat pkte m forced way moti m md z~e m
~ektizely good zgrem nt hese ~alcukdicns sh w zlso flhe
p~eseme of ineg kr flequ~cies zt h h vahes of fl~e ~ed ced
flequff~ci s O y fl~e f t inegmk flequff~ci s hsve ben
supp~ cd md he tech iq~e usedhas to be improwd Some
dfficulti s mpearfor hefle miaceelwatimcal-ukdicns,
padicukrly m fl~e wake of he mod I wh ~ess fl~e wzze
zmplit ds z~e ovem~edcted by fl~e computatims
Neverffiekss, fl~e wave pattem i q~zlitatively conectly
~ep~ese ted by fl~e computaticns Fmth mmore, fl~e fle
miaceamplit d z~enotaccmatewhnfl~eflequencyi too
clme of m megular cne
Finslly, work is m prog ess fu t to improve fl~e
tech iq~e used to supp~ess he megmbr flequency, to tudy
fl~e seakepi g of ships m regmbr wzzes md to inh od cc he
wabrline inbg zl c mputstional cod conhofli g fl~e
zccmacy of fl~e i teg zls m he segme ts of fl~e waterkne
The i fluer~e of fl~e k4ter will be mve tigated fcr several
kmds of boats Ihe ktmg eft t wiflbe zlso inhod ced to
dml wih boats m yawed fl ws zs sailmg bosb; cr
man~i g ships b 6 is case, inbg zls deali g wih he
second d rivati es of fl~e G'en flm ticns hsve to be
consid ~ed More c mp ms m z~e to be done boflh m global
d~z md kcal ones A sh~dy of fl~e calcubti n of fl~e wz~
zmplit d behmd fl~e h 11 mu t be pmsed m order to
und r~md he ovem~edhi m of fl~e fle miace elevati m m
flhis zone
AKNOWLEDG~d
The mfhors t atef lly fnarlc fne DGA-DR iT
( French Ml ishy of D fers~e) for its t ant n°95-068 used to
fmarre fne e perimental pa~t of hi sbad Th mfhms
fnar~c also GD h mem md its t oup of LMFDHN
MR CNRS n°6598) of E ok L nh~e d Naries P;rs~e)
for m my exchmge md d6 us i m ~oo t f is st dy
BEt; EREtNCEd
Be M end Gbilh~md M, "A fast medhod of evaluati m fm
he twnskti g md pulsatmg G'en's f nchon," 8hiD
TechmoloevR s, VoL 42, April 1995, pp 68-80
Boin JP., Be M. end Guttb~md M., "Semkepi g
computaticns usi g fne ship mohm G'een's fmction,"
P ~linos of ISOP 2000 Ccnfe3nce, Vol. V, Seadk
USA), Mcy2000
Boutis J.,'dtd d k diflactim-mdiatimdanslems
d m flotteur md6fomkible mim6 d me it sse moy m~e
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DISCUSSION
V. Bertram
Hamburg Ship Model Basin, Germany
The authors present detailed measurements to
validate advanced seakeeping computations for a
publicly available hull form. Together with recent
experiments by Prof. Iwashita in Japan, these are the
first such benchmark data available to the general
public and I am sure that the world-wide community
of researchers will be grateful for this.
Iwashita t 11 showed in transversal wave cuts for
diffraction waves near the bow for the Series 60 CB =
0.8 that even a "fully 3-d" Rankine singularity
method is not able to reproduce the local unsteady
wave field in this region, although it improved results
over GEM computations. I wonder if the authors have
tried similar transverse cuts for radiation waves and
found similar results.
Have results been compared with Iwashita's X/L-O 9
experiments for the same geometries to obtain a o o, _ .
feeling for the accuracy of these very difficult
measurements?
Both Rankine singularity methods and Green
function methods for ships at considerable forward
speed are still not at a stage where we can be satisfied
with the results when we look at local effects like
waves which indicate also to some extent how local
pressures are likely to differ. How will we overcome
these shortcomings in the future? Will sophisticated
potential flow solvers, perhaps RSM in the near field
coupled to GEM in the far field, in the frequency X/L=0.6
domain ever be sufficient to get local pressures with
sufficient accuracy?
~-0 .0 05
n n1
_
0.0 05 _
1. Iwashita, H. "Prediction of Diffraction Waves of
a Blunt Ship with Forward Speed Taking account
of the Steady Nonlinear Wave Field", 2
Numerical Towing Tank Symposium NuTTS'99,
Rome, 1999.
AUTHOR'S REPLY
Unfortunately, we have not obtained the paper from
Iwashita t11 mentioned by Professor Bertram in spite
of asking it from library, so no comparison has been
yet made. Nevertheless, we are interested to make
such comparison.
We have tried also to compare the transverse
cuts computed and measured. The figure 1 show such
cuts for the Series 60 ~=0.6 hull in heave motion at
F=0.2 and f=4Hz, far from irregular frequencies. The
agreement seems to be correct close to the stern but
some discrepancies can be shown closer to the bow
for low values of Y/L. Nevertheless, it is quite
difficult with our probe to make measurements very
close of the model. Other comparisons are being done
in different cases and for different values of the flow
parameters.
Concerning the last point evoked in the
comments of Prof. Bertram, more comparisons with
local measurements are needed to validate the various
codes, Rankine or Green, as wave pattern or pressure
distribution. But, we think that probably close to the
hull these kinds of inviscid methods are not very
accurate and that a coupling between viscous method
close to the body and inviscid one, able to represent
precisely the far field may be a track to follow to
improve the numerical methods.
Reference:
1. Iwashita, H. "Prediction of Diffraction Waves of a
Blunt Ship with Forward Speed Taking account of
the Steady Nonlinear Wave Field", 2n~ Numerical
Towing Tank Symposium NuTTS'99, Rome, 1999.
· Te sts ~ cost
- ~ ~ CompL tatbn (cost
/, \ ~ Te sts ~ sin ~
/ \ ~ CompL tatbn (sin)
2/~\ I /~
-u.u<` ~ 0.1 0.2 0.3 0.4
Y/L
n n1
-0 0 1 5
Heave a3/L=O.OO9
Serie 60 Cb=0.8, F=0.2 ,f=4Hz,l=1.79
Figure 1
