Seakeeping analysis of two medium-speed twin-hull models

Journal of Ship Production and Design, Vol. 3 1 , No. 3, August 2015, pp. 192-200 http://dx.doi.Org/10.5957/JSPD.31.3.140020

Seakeeping Analysis of two Medium-speed Twin-hull Models

T h e use of twin-hull ships for high-speed passenger and car-passenger transportation is w i d e s p r e a d , whereas their potential use for high-speed cargo transportation w a s estimated as limited. T h e present article discusses the seakeeping performance of t w o twin-hull models of an innovative m e d i u m - s p e e d container ship design. Their hull form w a s the result of a t h o r o u g h hydrodynamic optimization performed at the School of Naval Architecture a n d Marine Engineering of N T U A aiming to minimize the calm water resistance within the EU-funded project "EU-CargoXpress." T h e seakeeping analysis w as performed by applying numerical tools a n d also by performing a series of expenments in the towing tank of N T U A and M A R I N T E K . T h e obtained results are presented and discussed.

K e y w o r d s : seakeeping; twin-hull; containership; numerical analysis; model tests

1. Introduction

T W I N - H U L L SHIPS are extensively used f o r high-speed passen-ger and car-passenpassen-ger transportation. M a n y designers and ship-builders investigated the possibility to operate them also as fast cargo ships without m u c h success yet. W i t h i n the research project "EU-CargoXpress" o f the European U n i o n Seventh F r a m e w o r k Program, an alternative potential use o f the t w i n - h u l l s concept as m e d i u m speed t w i n - h u l l container ships has been investigated. A f t e r an extensive h u h f o r m optimization a i m i n g to m i n i m i z e calm water resistance, the seakeeping analysis o f the resulting h u l l f o r m s was performed by applying numerical tools and also by p e r f o r m i n g a series o f experiments i n the t o w i n g tanks o f N T U A and M A R I N T E K .

M o r e specificaUy, calculations have been p e r f o r m e d using three d i f f e r e n t approaches o f varying c o m p l e x i t y and theoreti-cal consistency. T h e f i r s t one is based on strip theory adapted to t w i n - h u l l vessels. The second is a f u l l y three-dimensional ( 3 D ) approach based on the distribution o f pulsating Green sources over the wetted surface to calculate the v e l o c i t y potential using appropriate c o n e c t i o n terms to account f o r the f o r w a r d speed. The third also f u l l y 3 D approach is based on the distribution o f Rankine sources over the wetted and the free surface to satisfy the linear free surface condition. The n u m e r i c a l results are c o m -pared w i t h each other and w i t h experimental measurements. T h e v a l i d i t y o f the applied approaches is discussed.

Manuscript received by JSPD Committee July 14, 2014; accepted August 19, 2014.

2. Numerical tools 2 . 1 . S t r i p theory method

A m o n g the various codes i m p l e m e n t i n g s t r i p theory f o r t w i n - h u l l s , the codes M O T 3 5 and M O T 2 4 6 ( M c C r e i g h t & Lee 1976) w e r e selected to calculate the d y n a m i c response i n regular waves. T h e codes use the m o d i f i e d s t r i p theory o f Salvesen et a l . ( 1 9 7 0 ) , d i s r e g a r d i n g the transom stern terms, c o u p l e d w i t h the c l o s e - f i t h u l l f o r m representation proposed by F r a n k ( 1 9 6 7 ) , as extended b y Lee et al. ( 1 9 7 1 ) to t w i n - h u l l sections, to solve the t w o - d i m e n s i o n a l p o t e n t i a l f l o w p r o b l e m . T h e y also take i n t o account the viscous c o m p o n e n t s a p p l y i n g appropriate s e m i e m p i r i c a l c o r r e c t i o n terms and can i n c o r p o -rate the e f f e c t o f f o i l s , a l t h o u g h this c a p a b i l i t y has not been used i n our evaluations because the vessel is not quite fast. The theoretical background o f M O T codes is presented i n detail by Lee (1976).

2.2. Three-dimensional G r e e n source panel method

T h e second approach is a f u l l y 3 D panel m e t h o d f o r the evaluation o f the responses o f marine structures at zero speed, subject to incident regular waves, developed b y Papanikolaou (1985) and based on the distribution o f zero-speed pulsating Green sources over the wetted surface to express the radia-tion and d i f f r a c t i o n potentials. T h i s procedure was extended by Papanikolaou et al. (1990) f o r the case o f a vessel advancing w i t h f o r w a r d speed based on a s i m p l i f i c a t i o n o f the exact free

J O U R N A L O F S H I P P R O D U C T I O N AND D E S I G N 192 A U G U S T 2015 2158-2874/15/3103-0192$00.00/0

surface boundaty c o n d i t i o n , enabling the use o f the zero-speed pulsating Green source f o r the solution o f the resulting bound-ai7 value problems. A computer program ( N E W D R I F T ) based o n this procedure was developed and extensively used and validated against available experimental results f o r a series o f vessels t r a v e l i n g i n general w i t h l o w to moderate f o r w a r d speed (at Froude numbers up t o 0.35). The software has been also extended to treat m u l t i h u U vessels and i n particular cata-maran and S W A T H ships.

2.3. Three-dimensional R a n k i n e source panel method The third approach refers to the 3 D time-domain, panel code S W A N 2 (2002). The general formulation is described by Sclavounos (1996), whereas the specific time-domain solution was presented i n detail b y K i i n g (1994). The software implements a f u l l y 3 D approach based on the distribution o f Rankine sources over the wetted and the free surface. The linear free surface condition is satisfied, whereas i t has the capability o f taking into account the nonlinear FroudeKrylov and hydrostatic forces. This option, h o w -ever, was not activated i n the calculation presented here, because i t led to some diverging dynamic responses. Fuitheimore, i n the use o f S W A N 2 , an iterative procedure was added to converge to the actual dynamic draft and t r i m o f the vessel at each speed. A sensitivity analysis was conducted to define a suitable extent o f the free surface g i i d i n the longitudinal and lateral directions as w e l l as the respective number o f panels fitted o n the wetted surface o f the vessel.

3. T h e test c a s e s

The studied h u l l f o r m s are the result o f an extensive o p t i m i -zation p e r f o r m e d i n the f r a m e w o r k o f the E U - f u n d e d research project EU-CargoXpress. The objective o f this project was to deliver a small innovative container ship f o r coastal operation based o n the t w i n - h u l l c o n f i g u r a t i o n . The h u l l f o r m o p t i m i z a t i o n has been p e r f o r m e d using an innovative procedure developed b y N T U A based o n the integration o f suitable software tools, i.e., the ship design software N A P A f o r the design o f h u l l f o r m s , an in-house computational f l u i d dynamics code f o r the evaluation o f resistance i n calm water and a general purpose m u l t i o b j e c t i v e o p t i m i z a t i o n software ( m o d e F R O N T I E R ) to set up the o p t i m i z a t i o n p r o b l e m and to control the overall process. The core o f the procedure is a parametric model developed w i t h i n N A P A f o r the completely automatic generation o f alter-native h u l l f o r m s based o n a set o f design parameters. A series o f parametric models has been developed, each one o f them being adapted to diverse design requirements, as defined d u r i n g the evolution o f the project. Using these parametric models, 15 d i f f e r e n t optimization studies have been p e i f o r m e d ; f r o m each one o f them, several hundreds o f alternative h u l l f o r m s have been automatically

T a b l e 1 Main p a r t i c u l a r s of t w i n - h u l l E U - C a r g o X p r e s s

Main Characteristic, Symbol, Hull A H u l l B

Displacement, A (mt) 3000 2514.2

Length at waterline L^y^ (m) 77.610 82.648

Breadth overall B (m) 21.000 21.000 Breadth, demihull (m) 7.130 6.160 Draft, T (m) 4.680 4.096 Trim by stern r, (m) 0.334 0.520 L C G fwd of A P ( m ) 37.310 38.789 VCG above B L (m) 12.540 12.100 Metacentric height, GM (m) 5.080 11.130 Hull separation, 5 (m) 13.870 14.840

Service speed (knots) 15.000 13.000

Roll Radius of Gyration, Rxx (m) 6.500 7.800

Pitch Radius of Gyration, fin- (m) 17.800 19.750

F i g . 1 Seakeeping test in N T U A with hull form A

derived and evaluated. A m o n g them t w o d i f f e r e n t h u l l f o r m s have been f i n a l l y selected based on then favorable hydrodynamic char-acteristics to be further investigated and model-tested. The m a i n particulars o f the t w o h u l l forms are tabulated i n Table 1.

The t w o h u l l f o r m s have been model-tested b y N T U A and M A R I N T E K . Three models have been constructed, one based o n the first huU f o r m and t w o based o n the second one (Figs. 1-3). N T U A p e r f o r m e d resistance and seakeeping tests i n head seas f o r the f i r s t h u l l f o r m (Zaraphonitis et a l . 2011) and resistance tests i n upright and heeled c o n d i t i o n f o r the second h u l l f o r m . M A R I N T E K performed self-propulsion and seakeeping tests i n head seas f o r the second h u l l f o r m (Rambech 2012). Seakeeping calculations applying numerical tools have been p e r f o r m e d f o r both h u l l f o r m s b y N T U A .

As can be seen f r o m F i g . 1, a h u l l f o r m w i t h a r e l a t i v e l y large bulbous b o w was selected f o r m o d e l A , whereas a rather

Nomenclature

Hi/i = significant wave height (m)

R A O = Response Amplitude Operator R M S = root mean square

R V M = relative vertical motion R V V = relative vertical velocity

g = gravitational acceleration Tp = modal period (seconds)

U = forward speed CDo = wave frequency

a = encounter frequency

a„. = wave amplitude

k -- wave number

P = wave heading (P = 1 8 0 ° for head waves) (tü) = spectral density of incident wave

S,((o) = spectral density of response /

Fig. 2 Resistance tests in NTUA with huli form B

Fig. 3 The model of hull form B used for the seai<eeping tests in MARINTEK

unconventional b o w shape w i t h a reverse p r o f i l e inclination at and above the waterline was selected f o r model B .

4. S e a k e e p i n g results for hull form A

The f n s t h u l l f o r m was o p t i m i z e d f o r a service speed o f 15 knots. However, the seakeeping tests and calculations have been p e r f o r m e d f o r a comparatively reduced speed o f 13 knots. This is because i t was anticipated that a vessel o f such a small size w o u l d not be able to sustain its design speed at the sea states under consideration.

The dynamic performance o f h u l l f o r m A was n u m e r i c a l l y evaluated at a set o f regular waves w i t h periods i n the range f r o m 2 seconds to 15 seconds. Furthermore, the seakeeping behavior o f the vessel was investigated i n three realistic seaways, modeled according to the Bretschneider f o r m u l a t i o n . The conesponding significant wave heights and peak periods are listed i n Table 2.

T a b l e 2 T e s t e d w a v e s p e c t r a for hull f o r m A

Sea State Hy, (m) Tp (seconds)

A 2 7.7

B 3 8.6

C 4 10.3

The derivation o f the responses i n irregular seaways i n the cases o f the strip theory code M O T and the 3 D Green Source Panel M e t h o d software N E W D R I F T was earned out as f o l l o w s f o r the response /:

5,(co) = S,,{iü)RAO\ (1) I n the case o f the t i m e - d o m a i n code S W A N 2 , the statistical

results were derived b y a p p l y i n g fast F o u r i e r t r a n s f o r m on the respective time histories. Head (P = 1 8 0 ° ) , b o w - q u a r t e r i n g (p = 1 3 5 ° ) , and beam (P = 9 0 ° ) waves were considered. T h e f o l l o w i n g responses were evaluated d u r i n g the n u m e r i c a l analy-sis: heave, p i t c h , r o l l , v e r t i c a l acceleration at the b o w , at the Center o f G r a v i t y ( C G ) and at the stern. M o d e l tests at the same sea states have been conducted i n the T o w i n g T a n k o f the L a b o r a t o r y f o r Ship and M a r i n e H y d r o d y n a m i c s o f N T U A . A s a result o f budgetary l i m i t a t i o n s o f the CargoXpress p r o j e c t , i t was not possible to include tank tests i n regular waves i n the test p r o g r a m . The dimensions o f the f a c i l i t y , w i t h a length o f 91 m , breadth o f 4.56 m , and a depth o f 3.00 m , a l l o w o n l y f o r tests i n head waves.

I n the f o l l o w i n g , the numeiical predictions i n regular waves are presented f o l l o w e d by the respective results i n random seaways. The latter w i l l be compared w i t h the respective experimental results.

4 . 1 . R e g u l a r wave results

I n Figs. 4 - 1 1 the Response A m p l i t u d e Operator ( R A O ) curves f o r heave, p i t c h , and r o l l responses o f h u l l f o r m A are plotted on the basis o f the numerical results using all three methods described i n Section 2. A l l R A O curves are made n o n d i m e n -sional f o l l o w i n g the guidelines o f I T T C (1984). Heave has been nondimensionalized by the wave amplitude (a,,.), whereas p i t c h and r o l l b y the product o f the wave amplitude times the wave number (a„,.A'). Accelerations are divided by {g.a.JLwd to become n o n d i m e n s i o n a l . T h e h o r i z o n t a l axis i n a l l the plots presented here coiTesponds to the wave period.

F o l l o w i n g these figures, N E W D R I F T predicts a m o r e acute peak f o r the heave m o t i o n , whereas all three codes estimate quite w e l l the heave resonant period. The f i r s t o f the t w i n peaks o f the heave m o t i o n that may be observed i n the results o f N E W D R I F T code both i n head and bow-quartering waves cor-responds to the heave resonance, whereas the second one is a

HEAVE RAO, 180 deg 3.00 2.50 -*-MOT-Sd HEWOBin "J no

S

S

Fig. 4 Heave Response Amplitude Operator (RAO) curves, head waves

HEAVE RAO, 135 deg PITCH RAO, 135 deg

0.00

4.00 6.00 8.00 10.00

PERIOD (sec) - >

12.00 14.00

F i g . 5 Heave Response Amplitude Operator (RAO) curves, bow-quartering waves

HEAVE RAO, 90 deg

8.00 10.00 PERIOD (sec) ~> 14.00 8.00 10.00 PERIOD (sec) ~> 12.00 14.00

F i g . 8 Pitch Response Amplitude Operator (RAO), bow-quartering waves

PITCH RAO, 90 deg

8.00 10.00 PERIOD ( s e c ) - >

14.00

F i g . 6 Heave Response Amplitude Operator (RAO), beam waves F i g . 9 Pitch Response Amplitude Operator (RAO), beam waves

3.50

0.00

PITCH RAO, 180 deg

4.00 6.00 8.00 10.00

PERIOD (sec)~>

12.00 14.00 1.00

ROLL RAO, 135 deg

8.00 10.00 12.00 14.00 PERIOD (sec)~>

F i g . 7 Pitch Response Amplitude Operator (RAO), head waves F i g . 10 Roll Response Amplitude Operator (RAO), bow-quartering waves

resuk o f the heave and pitch coupling. The pitch R A O curves derived by S W A N 2 do not present any peak, whereas a sharp peak is observed i n the predictions o f the two other codes. I n contrast to the heave m o t i o n , the pitch responses around resonance, predicted by the strip theory code M O T , are quite higher than those predicted by N E W D R I F T both f o r head and bow-quartering waves.

The numerical predictions f o r the R A O curves o f the r o l l response are plotted i n Figs. 10 and 1 1 . M O T takes i n t o account viscous damping components i n the calculations using appro-priate e m p i r i c a l f o r m u l a e . However, a r o l l resonance is observed i n the M O T predictions; whereas even w i t h o u t d a m p i n g c o m -ponents, the results obtained w i t h S W A N 2 do not exhibit any peak at a l l .

ROLL RAO, 90 deg 160

8.00 10.00 PERIOD (sec)-->

14.00

F i g . 11 Roll Response Amplitude Operator (RAO), beam waves

T h e numerical predictions f o r the vertical acceleration at the b o w and stern o f h u l l f o r m A are plotted i n Figs. 12-15 f o r head and bow-quartering waves using all three prediction codes. A relatively better agreement among the three codes may be observed i n the acceleration results f o r the bow area than those f o r the stem. A shaip peak is predicted by N E W D R I F T at the bow area, whereas S W A N 2 gives the smaller peak responses w i t h the M O T 3 5 results being generally i n between the other t w o curves. For the stern area, the higher responses are pre-dicted by M O T 3 5 w i t h the l o w e r results once again prepre-dicted

160

8 9 10 PERIOD ( s e c ) - >

F i g . 12 Bow vertical acceleration, head waves

8 9 10 PERIOD (sec)~>

F i g . 14 Stern vertical acceleration, head waves

F i g . 13 Bow vertical acceleration, bow-quartering waves

8 9 10 PERIOD (sec)">

F i g . 15 Stern vertical acceleration, bow-quartering waves

by S W A N 2 . T w o distinct peaks are predicted by N E W D R I F T , con'esponding to the heave and p i t c h resonant periods.

4.2. D y n a m i c responses in seaways

T o compare the numerical predictions, derived by the three methods under consideration, w i t h the experimental measure-ments obtained w i t h a scale m o d e l o f h u l l f o r m A , the root mean square ( R M S ) dynamic responses i n the three sea states listed i n Table 2 have been calculated. The R M S predictions f o r the heave and p i t c h responses as w e l l as f o r the vertical acceler-adon at the ship's bow, stem, and at the center o f gravity, obtained numericaUy ( f o r head and bow-quartering seas) and experimen-tally (only f o r head seas), are listed i n Tables 3 and 4 . I n addition, the predicted R M S values f o r sway, r o l l , and yaw motions, derived by M O T 246 and S W A N 2 f o r oblique seas (bow-quartering and beam seas), are presented i n Table 5.

A c c o r d i n g to the results presented i n Table 3, f o r the head sea case, the numerical predictions o f heave m o t i o n b y M O T 3 5 are i n better agreement w i t h the m o d e l tests than the other t w o codes. I n the case o f the p i t c h m o t i o n , better agreement w i t h the experiments is shown by N E W D R I F T . The results obtained by S W A N 2 are smaller than those obtained by the other t w o codes and by the tank tests, whereas M O T 3 5 gave the larger p i t c h predictions.

I n b o w - q u a r t e r i n g seas (Table 4 ) , M O T 3 5 and S W A N 2 are p r e d i c t i n g s i m i l a r results f o r the heave m o d o n , whereas the

T a b l e 3 C o m p a r i s o n of r e s u l t s in h e a d w a v e s T a b l e 5 S w a y RiVIS, b o w - q u a r t e r i n g a n d b e a m w a v e s (m)

Sea State Experimental M O T 3 5 N E W - D R I F T S W A N 2 Heave R M S predictions, head waves (m)

SS A 0.389 0.399 0.517 0.354

S S B 0.647 0.609 0.802 0.576

S S C 0.880 0.965 1.075 0.842

Pitch R M S predictions, head waves (degrees)

S S A 1.563 2.000 1.803 1.209

SS B 2.490 2.735 2.714 1.925

SS C 3.018 5.208 3.307 2.505

Vertical acceleration R M S at bow, head waves (g)

SS A 0.221 0.221 0.305 0.182

S S B 0.319 0.315 0.438 0.269

S S C 0.333 0.552 0.487 0.313

Vertical acceleration R M S at C G , head waves (g)

SS A 0.069 0.072 0.102 0.066

S S B 0.099 0.103 0.146 0.096

S S C 0.099 0.174 0.163 0.111

Vertical acceleration R M S at stern, head waves (g)

S S A 0.127 0.279 0.191 0.119

SS B 0.185 0.379 0.272 0.170

SS C 0.210 0.763 0.301 0.198

R M S , root mean square; S S , sea state; C G , center of gravity.

T a b l e 4 C o m p a r i s o n of r e s u l t s in b o w - q u a r t e r i n g w a v e s

Sea State MOT35 N E W D R I F T S W A N 2 Heave R M S predictions, bow-quartering waves (m)

SS A 0.384 0.527 0.386

S S B 0.618 0.801 0.617

S S C 0.812 1.064 0.883

Pitch R M S predictions, bow-quartering waves (degrees)

S S A 1.766 1.472 1.069

SS B 2.677 2.147 1.633

SS C 3.672 2.534 2.025

Vertical acceleration R M S at bow, bow-quartering waves (g)

SS A 0.209 0.249 0.156

S S B 0.311 0.343 0.221

SS C 0.431 0.367 0.245

Vertical acceleration R M S at C G , bow-quartering waves (g)

SS A 0.062 0.099 0.066

S S B 0.090 0.136 0.096

S S C 0.129 0.147 0.111

Vertical acceleration R M S at stern, bow-quartering waves (g)

SS A 0.241 0.156 0.106

SS B 0.368 0.213 0.148

SS C 0.499 0.229 0.164

R M S , root mean square; S S , sea state; C G , center of gravity.

N E W D R I F T predictions are c o m p a r a t i v e l y higher. T h e smaller p i t c h motions i n b o w - q u a r t e r i n g seas are predicted again b y S W A N 2 and the larger ones b y M O T 3 5 w i t h the N E W D R I F T predictions b e i n g somewhere i n the m i d d l e . The predicdons o f the v e r t i c a l acceleration at the b o w , stern, and at C G derived w i t h S W A N 2 f o r the head seas case are generally i n good agreement w i t h the experimental measurements. N E W D R I F T is u n i f o r m l y o v e r p r e d i c t i n g the experimental results, whereas M O T 3 5 is i n good agreement at l o w e r sea states but gives

M O T 3 5 S W A N 2

Sea State 135° 90° 135° 90°

Sway R M S , bow-quartering and beam waves (m)

SS A 0.130 0.337 0.106 0.267

SS B 0.235 0.570 0.195 0.444

S S C 0.268 0.739 0.322 0.725

Roll R M S , bow-quartering and beam waves (degrees)

S S A 0.708 2.276 0.326 0.969

S S B 1.052 3.333 0.737 1.964

S S C 1.225 4.895 1.709 3.537

Y a w R M S , bow-quartering and beam waves (degrees)

SS A 0.313 0.086 0.283 0.165

S S B 0.458 0.129 0.452 0.283

S S C 0.608 0.179 0.611 0.501

R M S , root mean square; S S , sea state.

the higher predictions at the higher sea state, especially at the stern.

I n the bow-quartering seas, S W A N 2 gives the smaller predic-tions o f the vertical acceleration among the three codes. The M O T 3 5 predictions are close to S W A N 2 at C G but much higher at the ends (particularly at the stem). T h e N E W D R I F T predictions are higher at C G but somewhere between the other t w o codes at the ship ends.

Regarding the lateral motions, reasonable discrepancies are observed i n all three cases (sway, r o l l , and y a w ) as depicted i n Table 5. I n particular, the r o l l m o t i o n R M S predictions i n beam seas derived w i t h S W A N 2 are s i g n i f i c a n d y smaller than those derived by M O T 3 5 ( i n beam seas, the difference is up to b y 5 7 % at the smaller sea state and by 2 8 % at the highest sea state). The o n l y exception is the case o f bow-quartering waves at the highest sea state, where the S W A N 2 prediction o f the R M S r o l l m o t i o n is 4 0 % higher than that o f M O T 3 5 .

The already observed discrepancies i n the case o f regular waves among the three numerical prediction codes are therefore apparent also i n the case o f the dynamic behavior i n seaways, although the results i n this case p e r f o r m better because they are integrated over the respective spectra.

5. S e a k e e p i n g results for hull form B

The second h u l l f o r m was o p t i m i z e d f o r a service speed o f 13 knots. A scale model o f h u l l f o r m B equipped f o r selfpropulsion was tested by M A R I N T E K at the f o l l o w i n g c o m b i -nations o f sea state and speed:

SS A : Hi/2, = 2.0 m and Tp = 7.7 sec at f / = 11.4 knots SS B : Hi/3, = 3.0 m and Tp = 8.6 sec at U = 10.7 knots The measured speed d u r i n g the experiments w i t h the self-propelled scale m o d e l was reduced i n comparison w i t h the design speed to account f o r the added resistance o f the ship i n waves.

The numerical seakeeping analysis has been performed applying the computer code S W A N 2 (2002) both i n regular and h r e g u -lar incident waves at the 7 5 % payload departure c o n d i t i o n f o r

f i v e wave headings ( 0 ° , 4 5 ° , 9 0 ° , 1 3 5 ° , and 180°). Calculations i n iiregular waves have been p e r f o i m e d at the same sea states and f o r w a r d speed as those o f the tank tests.

5 . 1 . R e g u l a r wave results

The seakeeping behavior o f the second h u l l f o r m i n head-to-beam regular waves was calculated w i t h the 3 D panel method, time-domain code S W A N 2 . The calculation encompasses a range o f periods w i t h i n the Bretschneider spectra, con'esponding to the listed t w o sea states. Because the t w o speeds that were used during the tank tests w i t h sea states A and B (11.4 and 10.7 knots, respectively) are quite close to each other, plots o f the R A O curves are provided o n l y f o r the l o w e r speed.

The numerical predictions derived w i t h S W A N 2 are presented in Figs. 16-19 f o r surge, heave, p i t c h , and r o l l motions. The translational motions are nondimensionalized by the wave ampli-tude (a,,.), whereas the rotational m o t i o n s are d i v i d e d by the product o f the wave a m p l i t u d e times the wave number (a„..i') to become nondimensional.

Some differences m a y be observed i n the behavior o f the two h u l l f o r m s i n regular waves. A shaip heave resonance f o r the three headings tested is observed i n F i g . 17 f o r h u l l f o r m B , w h i c h is not present i n the results obtained by S W A N 2 f o r

Surge 9 0 - 1 8 0 deg.

Pitch 9 0 - 1 8 0 deg.

6 8 PERIOD (sec)

F i g . 16 Nondimensional surge motion

Heave 9 0 - 1 8 0 deg.

14

6 8 PERIOD (sec)

F i g . 17 Nondimensional heave motion

14 1,20 1,00 0,80 0,60 0,40 0,20 0,00 -*-Pitch- ISOdeg. j : - ^ - P i t c h - ï 3 5 d e g . - ^ P i t c h - g O d e g . ! i . _i

-—

/

F i g . 18 Nondimensional pitch motion

Roll 9 0 - 1 3 5 deg. 14 2,00 1,60

5

/

/

F i g . 19 Nondimensional roll motion

h u l l f o r m A . The p i t c h responses o f h u l l f o i m B i n head and bow-quartering waves are quite smaUer than those o f h u l l f o r m A , whereas i n beam seas, the p i t c h response o f both h u l l f o i m s is very small. The r o l l responses o f h u l l f o r m B i n bow-quartering and beam waves are relatively larger than those o f h u l l f o r m A , e x h i b i t i n g a resonant peak, w h i c h is not present i n the results o f the f i r s t h u l l f o r m obtained w i t h S W A N 2 , presented i n Figs. 10 and 11.

5.2. D y n a m i c responses in seaways

U s i n g the S W A N 2 time-domain code, the time histories o f the dynamic responses o f h u l l f o r m B were derived f o r a period o f 1800 seconds (30 minutes) f o r f i v e headings f r o m head seas ( 1 8 0 ° ) to f o l l o w i n g seas (0°) i n 4 5 ° steps. The t i m e step was 0.05 seconds, corresponding to sampling frequency o f 20 H z . The n u m e r i c a l l y derived time histories were analyzed using fast Fourier transformation and the R M S values were calculated.

A comparison o f the obtained numerical results w i t h the results o f the tank tests conducted by M A R I N T E K f o r the heave and p i t c h motions and f o r the vertical acceleration at C G and at the ship's b o w is presented i n Table 6. A s may be obsei-ved f r o m this table, the numerical predictions are i n good agreement w i t h the experimental measurements. Heave m o t i o n is underestimated

T a b l e 6 C o m p a r i s o n of p r e d i c t i o n s in irregular l i e a d s e a s

6. C o n c l u s i o n s

Sea State A B

Prediction method Experimental Numerical Exp. Num.

R M S heave (m) 0.238 0.221 0.388 0.370

R M S pitch (degrees) 1.047 0.926 1.547 1.433 R M S acceleration at bow (g) 0.148 0.147 0.195 0.192 R M S acceleration at C G (g) 0.044 0.044 0.057 0.058

R M S , root mean square; C G , center of gravity.

by 7 . 1 % at sea state A and b y 4.6% at sea state B . Pitch motion is underestimated by 11.6% at sea state A and by 7.4% at sea state B . The differences i n the vertical accelerations both at the bow and at the vessel's C G are i n all cases less that 2 % .

The f u l l set o f the obtained numerical results f o r the f i v e d i f -ferent headings is summarized in Table 7. The m a x i m u m heave response is obtained at beam seas ( 9 0 ° ) , whereas the m a x i m u m pitch m o t i o n occurs at head ( 1 8 0 ° ) and bow-quartering ( 1 3 5 ° ) waves. The m a x i m u m values f o r the vertical accelerations are exhibited i n the b o w area o f the vessel i n head and bow-quaitering waves. I n comparison to the bow vertical accelerations, those in the stem area are reduced by approximately 3 0 % - 3 5 % when sailing i n head or bow-quartering waves, whereas the v e r t i c a l accelerations amidships are reduced b y approximately 7 0 % i n head or b o w - q u a r t e r i n g waves. A c c o r d i n g to the o r i g i n a l plans, the wheelhouse was to be located i n the f o r w a r d part o f the ship, quite close to the b o w .

I n this case, the vertical accelerations at the wheelhouse are expected to be quite high w i t h the vessel f a i l i n g to f u l f i l l the corresponding operability criterion f o r merchant ships estab-lished by the N o r d i c Project i n head or bow-quartering incident waves o f sea state B , whereas the criterion is m a r g i n a l l y f u l -f i l l e d i n sea state A . The r o l l response is marginal i n beam seas w i t h sea state B ( / / i / 3 = 3 m , Tp = 8.6 seconds); hence, it m i g h t be useful to consider fitting some k i n d o f active stabi-l i z i n g fins to the h u stabi-l stabi-l f o m r .

The results f r o m the analysis o f the seakeeping p e r f o r mance o f t w o variants o f an i n n o v a t i v e mediumspeed c o n -tainer ship design o f the t w i n - h u l l c o n f i g u r a t i o n are presented and discussed. The t w o h u l l f o r m s resulted f r o m a t h o r o u g h h y d r o d y n a m i c o p d m i z a t i o n p e r f o r m e d at the S c h o o l o f N a v a l A r c h i t e c t u r e and M a r i n e E n g i n e e r i n g o f N T U A a i m i n g to m i n i m i z e the c a l m water resistance w i t h i n the E U - f u n d e d p r o j e c t " E U - C a r g o X p r e s s . "

The seakeeping analysis was p e r f o i m e d by applying numerical tools and also by p e r f o r m i n g a series o f experiments i n the t o w i n g tank o f N T U A and M A R I N T E K . The Laboratory f o r Ship and Marine Hydrodynamics is a member o f I T T C since its establish-ment and participates i n all uncertainty evaluation studies organized by I T T C . A 5% eiTor i n the dynamic responses is considered reasonable i n the experimental evaluation o f the regular and r a n d o m wave results using models w i t h a length exceeding 2 m .

The results f o r h u l l f o r m A were obtained by three different numerical codes o f vai7ing complexity and theoretical consistency. These results have been compared w i t h each other and w i t h the tank tests measurements and the accuracy o f the used numerical procedures has been discussed. One o f these codes, i.e., S W A N 2 , was selected to be used f o r the numerical evaluation o f the second h u l l f o r m .

B y comparison o f the available experimental results, i t may be observed that the second h u l l f o r m exhibits s i g n i f i c a n t l y l o w e r vertical responses i n head iiTegular waves b y 3 0 % ^ 0 % in comparison w i t h the first variant. The same conclusion m a y be derived f r o m the comparison o f the results derived b y S W A N 2 f o r the R M S responses i n head and bow-quartering irregular seas f o r the heave and pitch motions and the vertical accelerations at C G and at the b o w area.

W i t h respect to the r o l l response, however, as a result o f the m u c h higher GM value o f the second h u l l f o r m ( A l t h o u g h the demihull breadth o f h u l l f o i m B is smaller than that o f h u l l f o r m A , its waterplane area at equal displacement is approximately 8% larger. I n addition, h u l l f o r m B is tested at a reduced displacement.

T a b l e 7 R e s p o n s e s in i r r e g u l a r w a v e s f r o m h e a d s e a s (180°) to f o l l o w i n g s e a s (0°)

Heading 180° Heading 135° Heading 90° Heading 4 5 ° Heading 0° Heading

Sea Stale A B A B A B A B A B Hw (m) 2.0 3.0 2.0 3.0 2.0 3.0 2.0 3.0 2.0 3.0 Tp (seconds) 7.7 8.6 7.7 8.6 7.7 8.6 7.7 8.6 7.7 8.6 R M S surge (m) 0.210 0.373 0.223 0.372 0.053 0.080 0.337 0.540 0.318 0.505 R M S heave (m) 0.221 0.370 0.251 0.435 0.354 0.575 0.180 0.354 0.143 0.268 R M S pitch (degrees) 0.926 1.433 0.916 1.351 0.184 0.241 0.643 0.978 0.579 0.940 R M S sway (m) 0.000 0.000 0.096 0.196 0.362 0.617 0.309 0.551 0.000 0.000 R M S roll (degrees) 0.000 0.000 0.653 1.244 2.625 3.809 0.569 0.875 0.000 0.000 R M S yaw (degrees) 0.000 0.000 0.283 0.493 0.239 0.350 0.934 1.360 0.000 0.000 R M S acceleration at bow (g) 0.147 0.192 0.138 0.178 0.031 0.042 0.013 0.028 0.007 0.027 RMS acceleration at C G (g) 0.044 0.058 0.037 0.050 0.040 0.051 0.005 0.009 0.003 0.010 R M S acceleration at stern (g) 0.093 0.134 0.090 0.123 0.059 0.069 0.014 0.029 0.008 0.035 R M S R V M at bow 1.017 1.423 0.867 1.151 0.305 0.384 0.621 0.844 0.422 0.695 R M S R V M at stern 0.659 0.994 0.510 0.737 0.568 0.737 0.925 0.960 0.364 0.424 R M S R V V at bow 0.498 0.652 0.432 0.544 0.132 0.154 0.111 0.154 0.051 0.088 R M S R V V at stem 0.395 0.514 0.276 0.367 0.237 0.294 0.170 0.198 0.043 0.080

R M S , root mean square; C G , center of gravity; R V M , relative vertical motion; R V V , relative vertical velocity.

resulting i n an increased BM value. Consideiing also its relatively reduced VCG, h u l l f o r m B has a significantly increased GM value (11.130 m ) i n comparison w i t h a GM value o f 5.080 m o f h u l l f o r m A . ) , the situation is reversed and, according to the n u m e r i -cal results, the second h u l l f o r m exhibits considerably higher r o l l responses i n bow-quartering and beam irregular waves b y 7 0 % - 1 7 0 % i n comparison w i t h the f i r s t h u l l f o r m , whereas i n the stem quartering seaways, its r o l l response is smaller by approxi-mately 5 0 % . I t should be stressed, h o w e v e r , that the d e r i v e d n u m e r i c a l seakeeping results f o r the t w o h u l l f o r m s are n o t directly comparable, because they coiTespond to d i f f e r e n t loading conditions (according to the l i g h t weight and payload specifica-tions provided b y the designer) and d i f f e r e n t sailing speeds.

Acl<nowledg ments

T h e research leading to these results has received f u n d i n g f r o m the European U n i o n ' s Seventh F r a m e w o r k Programme (FP7/2007-2013) under grant agreement no. 233925.

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