The interaction effects on
a catamaran traveling with
forward speed in waves
A.P. vafl't Veer and F.R.T. SiregarReport 1037-P 1:995
FAST'95 Third mt. Conference on Fast Sea
Transportation, Lübeck, Sept. 25-27, '95
TU Deift
Faculty of Mechanical Engineering and Marine TechnologyShip Hydromechanics Laboratory Deift University of Technology
VOLUME i
of the
ThIrd hiternationa Conference
on
Fast Sea Transportation
Lübeck-Travemünde
Germany
September 25-2v 1995
Schiffbautechnische Gesellschaft
FAST'95:
LA 7799Ith?
Third International Conference
on Fast Sea Transportation
Lübeck-Travernünde, Germany
September 25-27, 1995
Editor:
C.E:L. Kruppa
Institut für Schiffs- .und Meerestechnik Technische Universität Berlin
V®'ULUllt
Schiffbautechnische Gesellschaft
THE INTERACTION EFFECTS
'ON A CATAMARAN
TRAVELING WITH FORWARD
SPEED IN WAVES
A.P. van 't Veer Deift University of Technology The Netherlands
F.R.T. Siregar Deift University of Technology The Netherlands
Abstract
In the last decade there has been an increasing interest in the application, of advanced marine vehicles, such as catamaran vessels. Due to the effect of waye interaction between the two hulls
of such a vessel the seakeeping behaviour is more difficult to predict than for a monohull vessel,
in which case the strip theory can often be applied with succes. Application of the, strip theory to catamaran vessels could be very Worthwhile since the strip theory is widely used and is a very fast prediction tool. Therefore the strip theory program ASAP was developed in which the
sectional hydrodynamic coefficients for a twin cross section can be calculated using different wave
interaction schemes. The program is validated with model test results of a Wigléy catamaran model sailing at forward speed in head waves. It was found that 'the hydrodynamic välues are in most cases better, predicted with the new developed interaction 'scheme. The prediction of the heave and pitch' transfer function were also slightly improved by this scheme.
.1
Introduction
To predict the seakeeping behaviour of a (monohull) vessel the strip theory is a widely applied method. The main advantage ofthe strip theory is that it is a very fast and relativesimple method.
An extension of the strip theory to more advanced vessels, for example catamaran vessels, is worth considering since 3D methods which include forward speed are still very time consuming and only
limited avaible at the moment.
To stud.y the wave interaction effects between the two hulls three regions can be considered. In the first region the vessel is sailing at a very low speed and the. Waves generated by the ship motions are travelling alimost perpendicular to 'the opposite hull' (zero or 'low forward speed region)... The
pröblem can therefore be considered as a 2D problem, and the wave interaction effects between the two hulls are classified as. 2D interaction effects. The sitution is schemetically presented in
Figure 1.
When the forward speed increases the wave interaction becomes more complicated since the waves will be swept back in the Wake of the vessel (intermediate speed region). Therefore waves
generated at a particular section of the hull will interact on the other hull at a more aftly positioned
section. The problem. of wave interaction is now fuily 3D and the most accurate way to include this kind of 3D wave interaction will be a 3D forward speed diffraction method. However, for several reasons already mentioned before, the solution method choosen for this region will be the strip theory and to include, in some way, the 3D effects, a correction scheme was developed. The 3D wave interaction is schematically drawn in Figure 1.
Above a certain forward velocity of the vessel, in relation with the wave frequency, the waves
generated at one hull are not able to reach the other hull (high speed region). Thus no wave
interaction effects between the two hulls is possible and the problem of a catamaran vessel can be simplified to the problem of a monohull vessel sailing at high speed, see Figure 1.
The most interesting region is the region were wave interaction between the two hullsoccurs.
A numerical scheme, based on the strip-theory method has been developed to model these effects. Validation of the numerical results is performed using model experiments of a Wigley catamaran
model. It will be shown that with inclusion of this interaction scheme the motion of a catamaran
travelling at a forward speed in head waves can be predicted with reasonable accuracy.
2
The numerical model
A strip theory program was developed (called ASAP; A Seakeeping Analysis Program) to calculate
the motions of a catamaran vessel in a seaway.
The calculation of the sectional hydrodynamic coefficients is 'based on the Frank close fit method, Frank (1967). The extension of his method to twin section configurations is described
by Lee, Jones and Bedel (1971). To avoid the irregular frequencies in this method, which are due
to the eigen frequency of the waves inside a section, the method has recently been extended by closing the section with a few segments on top of the section at the waterline (a socalled 'lid').
To obtain the overall hydrodynamic coefficients the Salvesen, Tuck and Faltinsen (1970) method is used, except in the 3D correction scheme where the overall coefficients are calcùlated according
to the modified strip theory. These coefficients can be found in for example Journée (1992). The
modified coefficients are used since it is possible that W.hen the 3D correction scheme is 'applied
the sectional hydrodynamic coefficients are calculated using different interaction schemes along
the hull of the vessel.
As can 'be seen in Figure 1, the wave interaction in the intermediate speed range takes place between two diffèrent sections. Waves generated by section a travel to section b but due to the
forward speed of the vessel, waves generated by section b does not interact on section a. Therefore,
the 2D calculation method for a twin section configuration, as presented by Lee et al. (1971) can
not be applied. However, the method can easily be extended to include this one-way interaction.
2.1
One-way interaction scheme
A calculation scheme based on the Frank close fit method is used to calculate the hydrodynamic
effects of a twin section which is subject to one-way interaction. When the one-way interaction is projected on the earth fixed reference plane, the second section (section b in Figure 1) experiences
the incoming waves from the first section (section a in Figure 1) as beam waves. Calculation
results for a catamaran section in beam waves have been given by Kim (1972) and his results were
used to validate the ASAP calculations.
In the Frank close fit method the wetted surface of each section is devided into a limited number
of straight segments. On each segment a source potential of constant strength is assumed. Using
a Green's function the influences coefficients between all the segments on both hulls are calculated,
resulting in a matrix of influence coefficients. For a twin hull section this matrix consists of four blocks. 'The two diagonal blocks are filled with the influence coefficients of a section on itself, while the two off-diagonal blocks are filled with the cross coupling coefficients. For a twin hull
section consisting of two sections A and B this leads to the foHowing system of equations:
(A-A
Af*B\I(cTARHS
\B.-A
B-B)TB)
When equation (1) is solved a source distribution along the wetted contour of the section is obtained, from which the hydrodynamic values can be calculated. For a twin hull configuration with a symmetry plane in between the two sections the problem is reduced to solving the source
strength distribution on one hull. The influence coefficients A -+ B can be taken into account in
the diagonal blocks, reducing the number of unknows.
To model the one-way wave interaction the matrix of influence coefficients consists of four blocks but oniy one block with offdiagonal terms has to be filled with influence coefficients. The other öff-diagonal block is filled with zeros since no waves are travelling in that direction.
Thus, if section A experience influence from section B but not vica versa, the matrix of influence coefficients becomes,
(A-A AB(1ARHS
O
The source distribution on section A obtained from equation (2) now includes the (one-way)
interaction effects from section B.
As can be seen in Figure 2 it is possible that waves generated in the forward part of the vessel interact with more than one section, since the waves in between the two hulls can travel from one
hull to the other hull and vica versa. However, it is assumed that the effect of the second and
higher interaction .waves are of second order in relation with the first interaction wave. Therefore
orly the first interaction wave is taken into account.
2.2
Overall calculation scheme
The overall. hydrodynamic values and motions are calculated using three different interaction
schemes. In scheme zero (SO) it is assumed that there is no wave interaction between two opposite
sections, which is the monohull approach in scheme two (S2) the sectional valuesare calculated
using 2D wave interaction between two opposite sections. The one-way interaction is modeled by scheme three (S3). When scheme, three isapplied the di.rection of the outgoing waves is calculated
for each frequency. It is then possible to calculate where. the waves generated at one hull will interfere at the other hull. For the sections which experience wave influence from the other hull the corrected one-way interaction scheme is applied. For the sections in the. forward part of the.
hull the. zero interaction scheme is used since these sections do not experience any wave interaction from the other hull..
3
Numerical results
3.1
2D interaction
In Figure 3 results are presented for a twin hull semi-cylinder section. The 2D (twoway)
hydro-dynamic coefficients are plotted and compared w.ith model experiments in 2D, taken from Lee et aL (1971). The agreement 'between model experiments and the numerical results is excellent.
The negative peak in the hydrodynamic mass curve around frequenc-y 0.5 is the first resonance
peak of the watercolumn between the two sections. This watercolumn oscillates' with the same
frequency as the cross section, see Figure 6. The ffrst resonance frequency can be approximated
with the following formula:
(2)
/
pgA,pg(HB)
- VpV+mzz
Np(HB)T+rnzz
where A is the water plane area, V is 'the volume of the water column and = pirr2/2 is the ad'ded mass of the' water column which is approximated by the. mass of half the undèr water
column, H is the hull separation at the waterline, B is the beam of the section and T 'is the draught.
Using equation (3) the first resonance peak is approximated at w2B/2g = 0.56, which agrees very
well with the experiments and the ASAP calculations.
Other resonance frequencies in heave occur when the wave frequency is an odd or even value of the distance between the two sections, in formula:
nA = 2(b
- a)
k(b - a) =- a)
mr n = 1,2, ... (4)For the configuration used above these resonance frequencies occur at the frequencies (n=1) 3.14,
(n=2) 6.28, etc, from which tke first can be spotted in Figure 3.
The Frank close fit method as originally proposed by Frank (1967) fails to give a solution at
certain, socalled, irregular frequency where the method fails numerically due to the eigen solution
of the waves inside a section. However, when the section is closed with a few segments on the waterline inside the section, it is seen in Figure 3 that the irregular frequencies disappear from the solution (first irregular frequency could be expected around 1.7).
3. 2
One-way interaction
In the Figures 5 and 6 the numerical results are presented using three interaction schemes The hydrodynamic values in heave for a twin section without wave interaction between the two cross sections (scheme SO), are equal to the hydrodynamic values for a monohull section in
heave. As a comparison the monohull experimental data from Vugts (1968) are presented as well.
When the results of the two-way (2D) interaction scheme (scheme S2) are compared with the results of the one-way interaction scheme it is seen that in this calculation example the first interaction peak disappears. The calculations were performed with two equal sections, spaced at HS/B = 2 which is exactly the same spacing as has been used in the 2D calculations (H3 is the
distance between the two centerlines of the hulls). Since the sections are equal it is not possible to
obtain negative hydrodynamic mass since the amplitude of the incomingwaves from one section
can never be greater than the amplitude of the outgoing waves from that section. The overall
wave load is directly coupled .with the wave amplitude or the fluid damping of a section, which is
clearly seen from the Figures 5 and 6.
4
Model experiments
In 1992 a model test research project was carried o.ut in the towing tank of the Delft Ship Hydrodynamics Laboratory with a segmented Wigley hull. The project was initialised to study the interaction effects along the length of the vessel for different forward speed of the model.
The Wigley monohull hull was towed in the vicinity of the tank wall, thus simulatinga Wigley
catamaran model by using the tank wall as the symmetry plane of the vessel.
The series of experiments consisted of: forced heave oscillätion tests with a segmented model,
restrained model tests with a segmented model, and motion tests with a whole model. The segmented model was build up with eigth segments. The test results are published in a report by
Siregar (1995).
The underwater part of the mathematical Wigley hull is described by the following formula:
(i -C2)('
C2)(1 2)+c2(1 C8)(i
2)4 (5)where represents the x-coordinate with C E [-1, 1] and where represents the z-coordinate with
E [-1, 0]. The main particulars of the model are given in Table 1.
The model experiments were carried out with three different hull spacings, resulting in H/B values of 1.04, 2.iiO and 3.14, and for each hull spacing the model tests were performed at three different Froude numbers, 0.15, 0.30 and 0.45. The hull separation H is defined as the distance between the two midship seçtions at the waterline.
5
Results
5.1
Zero speed
Hydrodynamic values, Figures 7
- 8The overall hydrodynamic mass and fluid damping can not be measured at zero speed in the
towing tank since at zero speed wave reflection from the tank wall disturbes the experiment. The strip theory calculations are therefore compared with 3D diffraction calculations from DELFRAC,
which is a 3D Rankine source based program, developed by Prof. Pinkster at Delft U.niversity. In Figure 7 the results are given for the Wigley monohull. Except for the lower frequencies the agreement between the 2D and 3D results is excellent.
The results for the Wigley catamaran vessel with a hull separation over beam ratio of H/B =
2.10 are given in Figure 8. The hydrodynamic coefficients for the catamaran vessel atzero speed
are calculated with pure 2D interaction (S2) and without taken the interaction into account (SO). If the results are compared with 3D zero speed diffraction calculations, good agreement is found
es-pecially in the higher frequency range. The interaction peak in the 2D calculations is overpredicted
compared to the 3D prediction.
Motion results, Figure 9
The heave and pitch transfer function for the Wigley catamaran are calculated using the strip-theory and the 3D diffraction strip-theory. As can be seen from Figure 9 the agreement is good over
the whole frequency range. The results where interaction is taken into account (S2) are sligthly
better than the results without interaction (SO).
5.2
Non-zero speed
To calculate the position where waves generated at one hull will reach the other hull the reduced frequency r is used. This frequency is defined as the ratio of the forward speed of the vessel (1J)
over the wave velocity (Vr):
U0 U0 U0k U0We
V
)/T
We gIf r is greater than the ship length over the hull separation ratio L/H no wave interaction can
take place since a wave generated at the bow section of the hull can not reach the aft section of other hull anymore.
Hydrodynamic values, Figures 10
- 12The overall hydrodynarnic values are shown in the Figure lO for the Wigley catamaran with the
smaillest H/B value 1.04 sailing at the lowest Froude number 0.15 used in theexperiments. The 3D wave interaction is in' this case the most severe since waves are going almost to the opposite
section.
The limiting hydrodynamic mass and fluid damping coefficients are accurately predicted by
all three interaction schemes. Although at these frequencies the 3D wave interaction' occurs over
more than half the hull length, the effèct of the interaction is very small, due to the high frequency
range. With the corrected scheme (S3) the interaction peak in the .hydrodynamic mass and fluid
damping values are much better predicted than with zero interaction' (SO) or 2D interaction taken (S2) into account.
In Figure lithe hydrodynamic mass and fluid damping values are plotted for the Wigley catamaran at Froude number 0.30 and an H/B ratio of 2.10. In the 'high speed range the results
with the correction scheme are döse two the monohull approach results which agree good with
the experimental results. In the low frequency range scheme three gives a better agreement than
the other two schemes. Since both the 2D and monohull approach gives a worse prediction of the
coefficients in the low frequency range it indicates that at this speed and hull separation the 3D
effects are severe.
At the highest Froude number used in the model experiments the waveinteraction is absent if the encounter frequency i above 7.4 rad/sec, since than bow waves from one hull can not reach the other hull, in Figure 12 it can be seen that the hydrodynarnic mass is predicted reasonable but that in the higher frequency range the fluid damping is predicted to low. The calculations
from scheme three (S3) converge with the calculations from scheme SO, which indicates that the
interaction can indeed be neglected for frequencies higher than around 7.4.
Motion results, Figures 13
- 15The heave and pitch transfer function are plotted in Figure 13 for the Wigley catamaran at
Fn - 0.15 and H/B
_ 1.04. The heave transfer function is predicted quite accurate by the2D calculation scheme. The calculations performed using the monohull approach does not show
the peak in the heave transfer function, which is due to the interaction effects. The calculations with scheme three (S3) give a slightly worse prediction for the heave transfer function than the
calculations with pure 2D interaction (:S2). The pitch transfer function is more difficult to predict
than the heave transfer, as can be seen from the only reasonable agreement between model test
resu:lts and calculations. It indicates that it is important to calculate the distribution of the
hydrodynamic coefficients and forces accurately. Since the correction scheme (S3) gives a poor heave and pitch prediction it also indicates that at this combination of forward speed and hull separation the second wave interaction effects are important.
For Fn=O.30 and H/B = 2.10 the heave and pitch transfer function are plotted in Figure 14. The heave transfer is already quite accurate predicted by scheme two (S2). Up till A/L of 1.2 the results from scheme three and zero show a better agreement since with 2D interaction the results
show high peaks. Around the resonance peak the 2D resultsare slightly overpredicting the model
experiments. The pitch transfer function is difficult to predict, the best resultsare obtained using
zero interaction. It indicates that the distribution of hydrodynamic coefficients and forces, due to the interaction effects, is not very well calculated by the strip theory.
For the highest speed and hull separation, Fn = 0.45 and H/B =3.14, the heave and pitch
transfer function are predicted quite accurate by the zero interaction scheme, indicating that for a catamaran vessèl sailing at high speed the interaction effects are vanishing. The motion results are plotted in Figure 15. Again the agreement between model tests and calculations in heave is better than in pitch.
6
Conclusions
The overall hydrodynamic mass and fluid damping values are accurate predicted when the 3D correction scheme is applied. The heave and pitch transfer function can be predicted with reas-onable accuracy in the low speed range using the 2D interaction scheme and for the high speed range by neglecting the interaction and using the monohull approach. At intermediate forward speed of the vessel the heave but especially the pitch transfer is more difficult to predict. The
monohull approach underpredict the motions while if interaction is taken into account the
mo-tions are overpredicted around the resonance peak. At least for a Wigley catamaran the heave and pitch transfer function are difficult to predict with a strip theory program if interaction plays an important role, which is the case in the intermediate speed range.
References
Frank, W. (1967), Oscillation of cylinders in or below the free surface of deep fluids, Technical
Report 2375, Naval Ship Research and Development Centre, Washington D.C.
Journée, J. M. J. (1992), Experiments and calculations on four wigley hullforms, Technical Report MEMT 21, Deift University of Technology, Ship Hydromechanics Laboratory.
Kim, C.-H. (1972), The hydrodynamic interaction between two cylindrical bodies floating in beam seas, Technical Report SIT-OE-72-1O, Stevens Institute of Technology, New Jersey.
Lee, C.. M., Jones, H.. and Bedel, J. W. (1971), Added mass and damping coefficients of heaving
twin cylinders in .a free surface, Technical 'Report 3695, Department of the Navy Naval Ship
Research and Development Center, Bethesda.
Salvesen, N., Tuck, E. O. and Faltinsen, 0. (1970), 'Ship motions and sea loads', Trans. SNAME
78, 250-287.
Siregar, F. R. T. (1995), Experimental results of the wigley hull formm withadvancing: forward
speed' in head waves, Technical Report 1024, Deift University of Technology, Ships Hydro-dynamics Laboratory.
Vugts, J. H'. (1968), "The hydrodynamic coefficients for swaying, heaving and rolling cylinders in'
a free' surface', mt. Shipbuilding Progress pp. 25 1-275.
= E: 'E I pu p.dm«0L..
-
u .0 013 .0 OFigure 1: Three different interaction schemes
Figure 2: First and second order wave interaction
45 4 35 2.5 '.5 05' u 'C sp.4mnIL..
-
u ut hcpiyFigure 3: Hydrodynamic mass and fluid damping coefficient versus freuency number for twin cylinders with H/B = 2.0
s 0
-2 .3
Figure 4: First interaction peak waveresonance Table 1: Main particulars of Wigley model (H-B)/2 3.5 ' 2.5 1.5 0.5 kB/S
Figure 5: Hydrodynarnic mass and flùid damping coefficient versus frequency number fordifferent wave interaction schemes
Figure 6: Hydrodynamic forces in heave versus frequency number' for different wave' interaction
schemes Length [rnj 2.500 Beam [m] 0.351 Draught [m} 0.139 VOlume [rn'3] 0.06953 L/1B
L/T
18 CB,. 0.5607 CM 0.9090 CWL 0.6933: 0.5 15 2.5. k812 05 1.5 2.5 0.5 1.5 25 Ei0
0.9 0.8 0.7 o 0.8 Ò.5 0.4 03 a 2.2 0.I-lao a I .0 .5 .5 .4 .2 ZOa 100 CT &'3l
Figure 7: Hydrodynaruic
mass and fluid damping coefficient versus frequency number, WIglevmonohuil 1.0 .2 B a. Cme (nch( 5 12
''
'-'Figure 9: F-leave arid Pitch transfer funtion... Wigley catamaran. Fa
= 0.0, H/B
2.10I
A
J
R - &O0 : : OEAC ; -r 1.0 1.5 20 l.a 1.5 2.0 2.5 5.0 7.5 10.0catamaran, Fu = 0.0, H/B=2.10
Figure 8: Hydrodynarnic
mass and uid damping coefficient versus frequency number, WigleyCma (rdI Omêqa fr4IJ
g g 2 3 4 5 6 7 gat) W1gloycmaran, Fn. 0.15:148 1:04 expemImeoI ASAPSO e--ASAPS2 -m---ASAP 53 -'--4--9: a 7 04 3 2 Wiyc.atamarrni. Fn 0.15; 14fB. 1.04 2 3 4 mega s1(IJg 4-Wieycalamaxan, Fn 0.45,168 3.14 000enmeni a ASAPSO
e-ASAPS2 --'4'--ASAPS3 -4--5 6 7Figure 11: Hydrodynamic mass and fluid damping coefficient versus wave frequency, Wigley catamaran, Fn = 0.30, H/B = 2.10
Wigleycalamazen, Fn'. 045. H/B .3:14
Figure 12: Hydrodynamic mass and fluid damping coefficient versus wave frequency, Wigley catamaran, Fn = 0.45, H/B = 3.14 t expenienIa ASAPSO
e--Ji:
ir
u-I expea ASAPSOe ASAPS2---.i---ASAPS2 -k-k'\
i t, .1 . j.,- --' i:-/
... 4... frii
- I ASAPSOe- ASAPS2---4----ASAPS3 f 2 3 4 6 7 3 4 5 6 7omega sqflJg) omnoga sqI(L)
Figure 10: Hydrodynamic mass and fluid damping coefficient versus wave frequency, Wigley
catamaran, Fn = 0.15, H/B 1.04 Weycalamaran, Fn. 030, KB -2.10 Wleycaiamoman. Fn - 030, WO .2.10 2 3 4 gas1(LI9 7 5 3 2 g0 -2 -3 5 4.5 4 3.5 23 Jo 2 1.5 I 0.5
I j 1.6 IA 12 08 06 0.4 02 o
'k'
05 WIJeycatama,an. Fn -0.15. RB. 1.04 IS 2 woo. IwthI 04p 100801' w16yooIoInwon. A. 0,15. RB. 1.04 wIdoyoo60.m60:Fn - 020. RB. 2.10 1.5 2 2.5 3 160 180 IO, 1,4,F'
08, 0.6, 0.4 02' o 4.5 0.5 IS 2 W800 0019011 OOp 1.01981 Wbloy Ianwan. Fn.0.lS. 1419.1.04 WleycoIamwo0. Fn .0,15. RB -,1,04,Figure 13: Heave and Pitch transfer functiön, Wigley' catamaran vessel, Fn = 0.15, H/B = 1.04
Wi0yCal.ma,.fl. F6.030, 100.2,10
3
Figure 14: Heave and Pitch transfer function, Wigley catamaran vessel, Fn = 0.30, H/B = 2.10
00
o.
ASAPS2 ASAPS3---100 ASAPS2----0-.-ASAR 531-t ivi
---rg1P11
000=I.
ASAP S20. ASAPSO'.-V
t4:
.,i
108' iuUi 06 15 2 3 Woo. Iw*th/ 44p 100811 WÇ oOIom*On.' Fo - 030. RB. 2.10 0,5 1S '2 3 WOo.I191h/ 44p 1001911 WI8yC.Iom018fl. Fn .020, RB .2.10 '1,5 2 25 3 15 2 3 *800008011 14P 08'! Woo. 1011911 lolOp 1011911 25 15 3 3 - IS Os 25 IS 05 o Woo. 100801 104p 1001901 WOo.10119111 014p 1601901180
05 15 2
W008 0.98 IOiOp 10.98, .WÇIèy colomá.on. F - 045. lOB -3 14
W1ey60I0m0.8n. Fn .015.168 - 3.14 as 3 5 a 0.6 I8yO0I0l00.on. FO - 0.45.149 .3.14
Figure 15: Heave and Pitch transfer function, Wigley catamaran vessel, Fn = 0.45, H/B = 3.14
u ASAP SO
