Experimental assessment of interference resistance for a Series 60 catamaran in free and fixed trim-sinkage conditions

ELSEVIER

C o n t e n t s lists a v a i l a b l e at S c i V e r s e S c i e n c e D i r e c t

Ocean Engineering

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / o c e a n e n g

Experimental assessment of interference resistance for a Series 60 catamaran

in free and fixed trim-sinkage conditions

Antonio Souto-Iglesias *, David Fernandez-Gutiérrez, Luis Pérez-Rojas

Model Basin Researcli Croup (CEHINAV), Naval Arcliitecture Department (FTSIN). Tedmical University ofMadtid (UPM). 28040 Madrid Spain

A R T I C L E I N F O

Article liistory:

Received 24 February 2012 Accepted 3 June 2012 Editor-in-Chief: A.I. Incecil< Available online 10 July 2012 Keywords: Interference resistance Interference factor Series 60 Catamaran Free t r i m Fixed t r i m Fixed sinkage Free sinkage Free m o d e l Captive model A B S T R A C T T h e i n t e r f e r e n c e r e s i s t a n c e o f m u l t i h u l l s t a l d n g i n t o a c c o u n t t h e t e s t c o n d i t i o n ( f i x e d o r f r e e m o d e l ) is e x p e r i m e n t a l l y s t u d i e d . E x p e r i m e n t s h a v e b e e n c a r r i e d o u t w i t h a c o m m e r c i a l c a t a m a r a n m o d e l a n d m o r e e x t e n s i v e l y w i t h a Series 6 0 c a t a m a r a n . T h e i n f l u e n c e o f t h e t e s t i n g c o n d i t i o n ( f i x e d o r f r e e ) t o g e t h e r w i t h t h e i n f l u e n c e o f h u l l s e p a r a t i o n has b e e n a n a l y s e d . T h e r e l e v a n c e o f t h e s e e x p e r i m e n t a l r e s u l t s i n t h e s e p a r a t i o n o p t i m i s a t i o n t e c h n i q u e s b a s e d o n s l e n d e r b o d y flow s o l v e r s is d i s c u s s e d . © 2 0 1 2 E l s e v i e r L t d . A l l r i g h t s r e s e r v e d . 1. I n t r o d u c t i o n A s i g n i f i c a n t b o d y o f l i t e r a t u r e a n a l y s i n g m u l t i i i u i l s t i y d r o -d y n a m i c s ( C l i e n e t al., 2 0 0 3 ; I n s e l a n -d M o l l a n -d , 1 9 9 2 ; M i g a l i et al., 2 0 0 1 ; M o l l a n d et al., 1 9 9 6 ; T u r n e r a n d T a p l i n , 1 9 6 8 ; Y e u n g e t al., 2 0 0 4 ) , m a i n l y considers slender b o d y s i m p l i f i c a t i o n s a n d f o c u s o n m o d e r a t e a n d h i g h speed r e g i m e s . B r o g l i a et a l . ( 2 0 1 1 ) a n d Z a g h i et al. ( 2 0 1 1 ) use i n s t e a d a N a v i e r - S t o k e s s o l v e r to s i m u l a t e m u l t i h u l l s , finding a g o o d a g r e e m e n t f o r the resistance v a l u e s a n d d e s c r i b i n g c o m p l e x i n t e r f e r e n c e e f f e c t s at h i g h Froude n u m b e r s r e g i m e s .

M o s t o f these analyses assume a fixed m o d e l c o n d i t i o n c o n s e q u e n t l y r e d u c i n g t h e c o m p u t a t i o n a l e f f o r t . This, c o m b i n e d w i t h t h e slender b o d y a s s u m p t i o n , a l l o w s f o r t h e s i m u l a t i o n o f a w i d e r r a n g e o f c o n f i g u r a t i o n s i n t e r m s o f s e p a r a t i o n a n d v e l o c i t y f o r a reasonable c o m p u t a t i o n a l e f f o r t . W i t h these types o f codes, i t is t h e r e f o r e feasible t o set u p a s e p a r a t i o n o p t i m i s a t i o n f r a m e -w o r k i n e a r l y d e s i g n phase ( M o r a e s et al., 2 0 0 7 ; Y e u n g a n d W a n , 2 0 0 7 ) .

I n Souto-lglesias et a l . ( 2 0 0 7 ) , t h e i n t e r f e r e n c e resistance o f m u l t i h u l l s w a s analysed b y assessing its r e l a t i o n s h i p w i t h t h e

• C o r r e s p o n d i n g author. Tel.: -F34 913367156; fax: + 3 4 915442149. E-mail addresses: antonio.soutoS'upm.es (A. Souto-lglesias), fg.david(S)gmaiI.com (D. F e r n a n d e z - G u t i é r r e z ) ,

I u i s . p e r e z r o j a s ® u p m . e s (L. Pérez-Rojas).

0029-8018/$ - see f r o n t matter © 2012 Elsevier Ltd. All rights reserved. http;//dx.doi.org/10.1016/j.oceaneng.2012.06.008

shape a n d a m p l i t u d e o f t h e w a v e t r a i n b e t w e e n t h e h u l l s f o r a s p e c i f i c c o m m e r c i a l vessel design. The f r e e m o d e l c o n d i t i o n w a s t h e n c o n s i d e r e d m a k i n g i t m o r e d i f f i c u l t t o i d e n t i f y i n t e r f e r e n c e e f f e c t s d u e t o s u b s t a n t i a l l y d i f f e r e n t d y n a m i c t r i m s a n d sinkages b e t w e e n t h e m o n o h u l l a n d t h e c a t a m a r a n . T h i s case s t u d y is h e r e i n r e v i s i t e d b y c o n s i d e r i n g t h e fixed m o d e l c o n d i t i o n .

I n a d d i t i o n t o t h e c o m m e r c i a l vessel, a Series-60 (S60) catam a r a n has b e e n e x p e r i catam e n t a l l y s t u d i e d . Its h u l l shape s i g n i f i -c a n t l y -changes f r o m t h e f o r m e r , e x p a n d i n g t h e g e o m e t r y types analysed. A l t h o u g h t h e S60 is a w e l l k n o w n h u l l f o r e x p e r i m e n t a l a n d c o m p u t a t i o n a l analyses ( T o d d , 1 9 6 4 ; K i m a n d Jenkins, 1 9 8 1 ; T o d a e t al., 1 9 8 8 , 1 9 9 2 ; N a k a t a k e a n d Takeshi, 1 9 9 4 ; T a r a f d e r a n d S u z u k i , 2 0 0 8 ) , t o t h e a u t h o r s ' k n o w l e d g e , its b e h a v i o u r as a m u l t i h u l l has n o t y e t b e e n e x p e r i m e n t a l l y d e s c r i b e d a n d such k n o w l e d g e m a y be u s e f u l f o r CFD p r a c t i t i o n e r s w o r k i n g o n m u l t i h u l l h y d r o d y n a m i c s . I n Y e u n g et a l . ( 2 0 0 4 ) t h e i n t e r f e r e n c e r e s i s t a n c e o f a S60 c a t a m a r a n w a s n u m e r i c a l l y s t u d i e d n e g l e c t i n g t r i m a n d sinkage i n f l u e n c e s . T h e y p r o v i d e d t h e v a l u e o f t h e i n t e r f e r e n c e f a c t o r f o r a w i d e range o f s e p a r a t i o n s a n d speeds a n d a s i g n i f i c a n t i n s i g h t i n t o t h e c o m p l e x i t y o f t h e m u l t i h u l l w a v e i n t e r f e r e n c e p h e n o m -ena. T h e i r p r e d i c t i o n s have b e e n c o n t r a s t e d w i t h e x p e r i m e n t a l results i n t h e p r e s e n t paper. The p a p e r is o r g a n i s e d as f o l l o w s : first, a i m i n g at p r e s e n t i n g t h e p r o b l e m a n d t h e n o t a t i o n , t h e i n t e r f e r e n c e resistance is d e f i n e d . Second, t h e c o m m e r c i a l vessel case t h a t w a s s t u d i e d

N o m e n c l a t u r e m h m o n o h u l l

V k i n e m a t i c v i s c o s i t y ( m ^ / s )

cat c a t a m a r a n RF f l a t p l a t e f r i c t i o n resistance ( N )

CF f r i c t i o n resistance c o e f f i c i e n t RT t o t a l resistance ( N )

CT t o t a l resistance c o e f f i c i e n t Rw w a v e resistance ( N )

Cw w a v e resistance c o e f f i c i e n t Rwmli w a v e resistance o f m o n o h u l l ( N )

v a r i a t i o n o f b o w d r a f t i n f r e e m o d e l c o n d i t i o n ( m ) Rwcat w a v e resistance o f c a t a m a r a n ( N ) v a r i a t i o n o f s t e r n d r a f t i n f r e e m o d e l c o n d i t i o n ( m ) Re Reynolds n u m b e r g g r a v i t y ( m / s ^ ) S60 Series 6 0 Fn Froude n u m b e r s s e p a r a t i o n ( m ) IF i n t e r f e r e n c e f a c t o r V v e l o c i t y ( m / s ) L l e n g t h b e t w e e n p e r p e n d i c u l a r s ( m ) u n d e r t h e f r e e t r i m c o n d i t i o n i n Souto-lglesias et a l . ( 2 0 0 7 ) is r e v i s i t e d , t h i s time, c o n s i d e r i n g t h e f i x e d t r i m c o n d i t i o n e f f e c t o n i n t e r f e r e n c e resistance. T h i r d , a S60 c a t a m a r a n is a n a l y s e d c o m -p a r i n g t h e e x -p e r i m e n t a l data u n d e r f i x e d a n d f r e e t r i m t e s t c o n d i t i o n s w i t h t h e e x i s t i n g data f o u n d i n t h e p r e v i o u s l y m e n -t i o n e d l i -t e r a -t u r e . Finally, a s u m m a r y o f -t h e d r a w n c o n c l u s i o n s t o g e t h e r w i t h f u t u r e w o r k s are p r o v i d e d . w a v e resistance i m p l i e s c h a n g i n g t h e d e n o m i n a t o r o f Eq. ( 1 ) t o t h e t o t a l resistance, since as a f o r e m e n t i o n e d , f r i c t i o n c o m p o n e n t s cancel o u t i n t h e n u m e r a t o r . The v a l u e o f t h e i n t e r f e r e n c e f a c t o r is i n v e s t i g a t e d i n t h e p r e s e n t paper b y l o o k i n g at t h e i n f l u e n c e o f t h e t e s t i n g c o n d i t i o n f o r t w o vessels, n a m e l y a c o m m e r c i a l vessel a n d a Series 6 0 (S60). The c h a r a c t e r i s t i c s o f b o t h m o d e l s are presented i n T a b l e 1.

2. I n t e r f e r e n c e r e s i s t a n c e

I n m u l t i h u l l s , t h e r e is u s u a l l y a s t r o n g i n t e r f e r e n c e b e t w e e n t h e w a v e systems g e n e r a t e d b y each h u l l . This i n t e r f e r e n c e c a n e i t h e r be f a v o u r a b l e o r u n f a v o u r a b l e t o t h e g l o b a l resistance o f t h e h u l l . To p r o p e r i y characterise t h i s e f f e c t , t h e i n t e r f e r e n c e f a c t o r IF is d e f i n e d as t h e r a t i o o f t h e d i f f e r e n c e b e t w e e n t h e w a v e resistance o f t h e c a t a m a r a n , Rwcm. a n d t w i c e t h e w a v e resistance f o r c e o f a m o n o h u l l , Rwmh '• JP ^ Rwcat^^2Rwmh Ideally, t h e v a l u e o f t h e i n t e r f e r e n c e f a c t o r s h o u l d be k e p t as s m a l l as possible, n e g a t i v e i f achievable ( Y e u n g a n d W a n , 2 0 0 7 ) . To c o r r e c t l y c a l c u l a t e t h e i n t e r f e r e n c e f a c t o r , t h e f r i c t i o n resistance has t o be s u b t r a c t e d f r o m t h e t o t a l resistance o b t a i n e d i n t h e e x p e r i m e n t s . A i r d r a g and c o r r e l a t i o n a l l o w a n c e are c o n s i d e r e d n e g l i g i b l e i n the p r e s e n t analysis. T h e w a v e resistance is o b t a i n e d v i a t h e H u g h e s ( L u n d e et al., 1 9 6 6 ) d e c o m p o s i t i o n . RT = Rw + a+k)RF (2) w h e r e k is t h e f o r m factor, a s s u m e d i d e n t i c a l f o r b o t h t h e m o n o h u l l a n d t h e c a t a m a r a n cases. Rp is t h e f r i c t i o n resistance o f a f l a t p l a t e w i t h e q u i v a l e n t w e t t e d surface, c o m p u t e d f r o m t h e f r i c t i o n d r a g c o e f f i c i e n t ( Q ) o b t a i n e d v i a t h e ITTC 1 9 5 7 c o r r e l a -t i o n l i n e f o r m u l a : ( l o g , o ( R e - 2 ) ) 2 T h e r e is a s t r o n g d e p e n d e n c e b e t w e e n t h e w a v e resistance a n d t h e v a l u e set f o r t h e f o r m f a c t o r . This s i g n i f i c a n t l y affects t h e e x t r a p o l a t i o n p r o c e d u r e b u t m o d e r a t e l y i n f l u e n c e s t h e v a l u e o f t h e i n t e r f e r e n c e f a c t o r IF w h i l e m a i n t a i n i n g its sign, t h e reason b e i n g t h a t t h e f r i c t i o n a l c o m p o n e n t s o f t h e resistance cancel o u t i n t h e n u m e r a t o r o f Eq. ( 1 ) . T h e r e f o r e , e s t a b l i s h i n g w h e t h e r t h e i n t e r f e r e n c e effects are f a v o u r a b l e o r u n f a v o u r a b l e does n o t d e p e n d o n e v e n t u a l u n c e r t a i n t i e s o f t h e f o r m f a c t o r c o m p u t a t i o n p r o c e d u r e . The i n t e r f e r e n c e f a c t o r is s o m e t i m e s d e f i n e d c o n s i d e r i n g t h e t o t a l resistance ( Z a g h i et al., 2 0 1 1 ) . A c c o r d i n g t o t h e H u g h e s resistance d e c o m p o s i t i o n , u s i n g t h e t o t a l resistance i n s t e a d o f t h e 3. C o m m e r c i a l v e s s e l 3.1. General

This vessel is c o m m o n l y used i n t h e t r a n s p o r t o f goods a n d f i s h t o a n d f r o m a sea f a r m . T h e m a i n d i m e n s i o n s o f t h e m o d e l are presented i n T a b l e 1. T h e r e f e r e n c e s y s t e m c o n s i d e r e d , t h e n o t a t i o n s d e s c r i b i n g t h e h u l l s e p a r a t i o n a n d t h e vessel g e o m e t r y are s h o w n i n Fig. 1 . T h e s e p a r a t i o n (s) is d e f i n e d as t h e d i s t a n c e b e t w e e n each h u l l ' s c e n t r e l i n e , a n d is m a d e n o n d i m e n s i o n a l w i t h t h e l e n g t h b e t w e e n p e r p e n d i c u l a r s (s/L).

The free m o d e l c o n d i t i o n studied i n Souto-lglesias et al. ( 2 0 0 7 ) was aimed at finding the relationship b e t w e e n the interference f a c t o r

Table 1

iVlain dimensions o f the case studies.

M a i n features Commercial vessel S60 Units

Length between perpendiculars (L) 2.208 2.500 m

Beam ( m h ) 0.238 0.333 m D r a f t 0.120 0.133 m W e t t e d surface ( m h ) 0.885 1.062 m^ Displacement ( m h ) 84.35 65.70 kg Block coefficient 0.653 0.600 Length-beam ratio 9.28 7.51 B e a m - d r a f t ratio 1.98 2.50

and the a m p l i t u d e o f the w a v e system i n b e t w e e n the t w o hulls. The present study completes the previously m e n t i o n e d w o r k by p e r f o r m i n g tests i n f i x e d m o d e l c o n d i t i o n using this geometry, thus e l i m i n a t i n g the effects o f sinkage and t r i m m o v e m e n t s . A photograph t a k e n d u r i n g the tests o f this paper's experimental campaign is s h o w n i n Fig. 2. Further i n f o r m a t i o n about this h u l l is included i n Souto-lglesias et al. ( 2 0 0 7 ) i n c l u d i n g its 3 D geometrical d e f i n i t i o n as an IGES file, provided as a supplementary material.

The f o l l o w i n g tests w e r e c a r r i e d o u t : • M o n o h u l l , f r e e m o d e l • M o n o h u l l , f i x e d m o d e l • C a t a m a r a n , s / L = 0 . 3 8 8 , i n f r e e m o d e l c o n d i r i o n • Catamaran, s / L = 0 . 3 8 8 , i n f i x e d m o d e l c o n d i t i o n The s e p a r a t i o n ( s / L = 0 . 3 8 8 ) w a s c h o s e n f o r h a v i n g t h e m o s t i n t e r e s d n g i n t e r f e r e n c e e f f e c t s , as f o u n d i n Souto-lglesias et al. ( 2 0 0 7 ) . A test m a t r i x c o m p r i s i n g o f t h e speeds s h o w n i n T a b l e 2 w a s i n i t i a l l y devised. The speed range o f m a i n i n t e r e s t c o r r e -sponds t o Froude n u m b e r s b e t w e e n 0.2 a n d 0.4. For t h e Froude n u m b e r 0.375 t h e e x p e r i m e n t w a s r e p e a t e d 5 rimes i n o r d e r t o assure t h a t m e a s u r e m e n t u n c e r t a i n t i e s r e m a i n c o n s i d e r a b l y s m a l l e r t h a n t h e i n t e r f e r e n c e e f f e c t s t o analyse. A c o l l e c t i o n o f e x t r a v e l o c i t i e s w a s r u n f o r t h e range 0.3 < f n < 0.4 i n o r d e r t o

Fig. 2. Picture of commercial vessel-model test.

Table 2

Froude numbers and velocities considered for the commercial vessel tests. Point Fn V ( m / s ) 1 0.100 0.465 2 0.150 0.698 3 0.200 0.931 4 0.250 1.164 5 0.300 1.396 6 0.350 1.629 7 0.375 1.745 8 0.375 1.745 9 0.375 1.745 10 0.375 1.745 11 0.375 1.745 12 0.400 1.862 13 0.450 2.094 14 0.500 2.327 15 0.550 2.560

p r o p e r t y characterise t h e resistance h u m p . V i d e o s o f these e x p e r i m e n t s , p r o v i d e d as s u p p l e m e n t a r y m a t e r i a l , can be f o u n d o n l i n e at h t t p : / / c a n a l . e t s i n . u p m . e s / f t p / 2 0 1 2 / S 6 0 /

3.2. Results

T h e r e s u l t i n g e x p e r i m e n t a l curves are p r e s e n t e d i n Fig. 3. I t can be o b s e r v e d t h a t there is a s i g n i f i c a n t d i f f e r e n c e i n t h e r e s u l t s f o r t h e fixed a n d f r e e m o d e l c o n d i t i o n s , w i t h t h e f r e e m o d e l resistance b e i n g larger t h a n t h e fixed m o d e l i n a l l cases, as i n K i m a n d Jenkins ( 1 9 8 1 ) f o r a S60 m o n o h u l l a n d M o r a e s e t a l . ( 2 0 0 4 ) f o r t h e W i g l e y h u l l . W i t h r e g a r d t o t h e d i f f e r e n c e s b e t w e e n m o n o h u l l a n d catamaran, t h e t e n d e n c y i n t h e m o n o h u l l resistance is m o n o t o n i c w h i l s t a clear h u m p can be a p p r e c i a t e d f o r t h e c a t a m a r a n c o n f i g u r a t i o n . Focusing o n t h e h u m p r e g i o n , these c h a r a c t e r i s t i c s are discussed i n d e t a i l i n w h a t f o l l o w s n e x t . I n o r d e r t o a d e q u a t e l y e s t i m a t e t h e i n t e r f e r e n c e f a c t o r f o r a c o n t i n u o u s range o f Froude n u m b e r s , t h e resistance curves w e r e fitted w i t h NURBS (Fig. 4 l e f t a n d right). I n t h e s e figures, t h e m a r k e r s c o r r e s p o n d t o t h e r a w e x p e r i m e n t a l data. The i n t e r f e r -ence f a c t o r r e f e r s t o a c o m p a r i s o n b e t w e e n w a v e resistances w h i c h have b e e n o b t a i n e d f r o m t h e t o t a l resistance f o l l o w i n g t h e p r o c e d u r e d e s c r i b e d i n Section 2 a n d c o n s i d e r i n g a f o r m f a c t o r o f 0.24. T h e f o r m f a c t o r has been t a k e n as t h e s a m e f o r t h e c a t a m a r a n a n d t h e m o n o h u l l . Fig. 4 l e f t a n d right s h o w t h e d i f f e r e n c e s i n w a v e a n d t o t a l resistance i n t h e h u m p r e g i o n ( 0 . 3 < F n < 0 . 4 ) b e t w e e n the m o n o h u l l a n d t h e c a t a m a r a n f o r t h e f r e e a n d fixed m o d e l c o n d i t i o n s r e s p e c t i v e l y . I t c a n be seen t h a t t h e w a v e resistance a n d t h e t o t a l resistance f o l l o w a s i m i l a r t r e n d , a l t h o u g h as p r e v i o u s l y m e n t i o n e d , t h e v a l u e s r e m a i n l o w e r f o r t h e fixed t r i m c o n d i t i o n . Favourable i n t e r f e r e n c e regions c o r r e s p o n d i n g t o those w h e r e t h e c a t a m a r a n resistance is s m a l l e r t h a n t w i c e t h a t o f t h e m o n o h u l l can also be o b s e r v e d .

The i n t e r f e r e n c e f a c t o r is c a l c u l a t e d f r o m t h e s e data w i t h t h e r e s u l t s s h o w n i n Fig. 5. W h i l e i t is a p p a r e n t t h a t t h e values are d i f f e r e n t f o r 0.3 < F n < 0.34, a v e r y s i m i l a r p a t t e r n is o b t a i n e d f o r Fn > 0.34. O v e r a l l , t h e t e n d e n c y o f t h e i n t e r f e r e n c e f a c t o r s f o r t h e f r e e a n d fixed m o d e l c o n d i t i o n s is s i m i l a r , w i t h s o m e d i f f e r e n c e s i n t h e IF v a l u e s f o r t h e Froude n u m b e r s b e t w e e n 0.3 a n d 0.34. This fits w i t h w h a t w a s e x p e c t e d f r o m a n a l y s i n g t h e t r i m angles o f t h e m o n o h u l l a n d c a t a m a r a n c o n f i g u r a t i o n s i n f r e e m o d e l c o n d i t i o n , as discussed i n Souto-lglesias e t a l . ( 2 0 0 7 ) .

Results r e g a r d i n g sinkage a n d t r i m are p r e s e n t e d i n Fig. 6. T h e y are m a d e n o n d i m e n s i o n a l u s i n g t h e t y p i c a l l e n g t h V^jg (Eqs. ( 4 ) a n d ( 5 ) ) , as i n K i m a n d Jenkins ( 1 9 8 1 ) .

Trim = -(Azt<,„,-AZstern)2g/V^ (4)

Sinkage = -{Aztow+AZstern)g/V'^ (5)

F n

0.3 0 . 3 1 0.32 0.33 0 . 3 4 0.35 0.36 0.37 0.38 C.39 0.4 F n

0.3 0 . 3 1 <0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.4 F n

Fig. 4. Total and wave resistance, commercial vessel, free ( l e f t ) and fixed ( r i g h t ) conditions.

0.2 0 . 1 0 - 0 . 1 - 0 . 2 1 ^ ^ ^ ^ ^ i 1 ^ ^ " F r e e model " « F i x e d model ; / i \ : ; ^ * • • • \ : * V V T E -0.3 0 . 3 2 0 . 3 4 0.36 0.38 F n

Fig. 5. IF o f commercial vessel for test case s/L=0.388.

0.4 0.08 0.06 0.04 0.02 0 -0.02 -0.04 -0.06 0.3 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.4 F n

Fig. 6. Sinkage and t r i m , commercial vessel.

This typical l e n g t h is the characteristic wave l e n g t h over 2n. A l t h o u g h the sinkage is significant ( < 10% o f the d r a f t ) , its behaviour is very similar f o r b o t h the m o n o h u l l and the catamaran. If w e l o o k at the t r i m , absolute t r i m angles r e m a i n small ( b e t w e e n - 0 . 3 ° and 0.3°, equivalent t o ± 0.06 i n the nondimensional t r i m f r o m Fig. 6 ) w i t h small variations. The t r i m angle reduction a r o u n d F n = 0 . 3 7 f o r t h e catamaran m a y help i n e x p l a i n i n g the favourable interference f o u n d i n the free m o d e l c o n d i t i o n f o r this velocity.

4. S e r i e s 60

4.J. General

The tests h a v e b e e n c a r r i e d o u t w i t h a Series 6 0 ( T o d d , 1 9 6 4 ) c a t a m a r a n ( f i g . 7 ) . The m o d e l characteristics h a v e b e e n p r e s e n t e d i n Table 1 t o g e t h e r w i t h those o f t h e c o m m e r c i a l vessel t e s t case. The d i m e n s i o n ratios are f a i r l y s i m i l a r f o r these t w o vessels b u t

Fig. 7. 560 catamaran model.

1 ! ! l l l l !

1

."".".r-r-..

Fig. 8. S60 (Todd, 1964) body plan (black) and present study (red). (For interpretation of the references to colour i n this figure legend, the reader is referred to the web version of this article.)

t h e h u l l s are s i g n i f i c a n t l y d i f f e r e n t :

1. The S60 has n o c y l i n d r i c a l s e c t i o n c o m p a r e d t o a l o n g o n e f o r t h e c o m m e r c i a l vessel.

2. The S60 has a c o n v e n t i o n a l cruise t y p e a f t b o d y a n d t h e c o m m e r c i a l vessel has a t r a n s o m s t e r n .

3. The S60 has n o k n u c k l e s w h i l e t h e t h e c o m m e r c i a l vessel has a h a r d c h i n .

Prior t o t h e m i l l i n g o f t h e m o d e l s , t h e h u l l g e o m e t r y w a s c o m p u t a t i o n a l l y r e d e f i n e d s t a r t i n g f r o m t h e IGES d e f i n i t i o n u s e d

as b e n c h m a r k i n t h e T o k y o 1 9 9 4 CFD W o r k s h o p . The reason f o r t h i s r e f a i r i n g is t h a t t o o m a n y surface patches w i t h n o t e n o u g h q u a l i t y m a t c h i n g w e r e used i n t h e l a t t e r . F u r t h e r m o r e , a v e r t i c a l e x t e n s i o n o f t h e m o d e l w a s r e q u i r e d t o cope w i t h t h e g e n e r a t e d w a v e s f r o m h i g h Froude n u m b e r tests. T h e m a t c h i n g o f t h e u p d a t e d g e o m e t r y w i t h t h e o r i g i n a l S60 d e f i n i t i o n ( T o d d , 1 9 6 4 ) is g o o d , as can be a p p r e c i a t e d i n Fig. 8. The IGES f i l e used here is p r o v i d e d as a s u p p l e m e n t a r y m a t e r i a l at h t t p : / / c a n a l . e t s i n . u p m . e s / f t p / 2 0 1 2 / S 6 0 / , w i t h t h e a i m t o serve as a s t a n d a r d d i g i t a l d e f i n i t i o n f o r f u r t h e r studies.

The f o l l o w i n g s e p a r a t i o n s have been t e s t e d :

a) , s = 0 . 5 6 5 m , s / L = 0 . 2 2 6 b ) s = 0 . 7 6 8 m , s / L = 0 . 3 0 7 c ) 5 = 0 . 9 7 1 m , s / L = 0 . 3 8 8 d ) s = 0 . 1 1 7 4 m , s / L = 0 . 4 7 0 The r a t i o n a l e b e h i n d t h i s s e l e c t i o n is t h a t , a c c o r d i n g t o t h e c o m p u t a t i o n a l analysis o f a Series 60 c a t a m a r a n b y Y e u n g et a l . ( 2 0 0 4 ) , s / L = 0 . 2 2 6 w a s d e t e r m i n e d as the s e p a r a t i o n r a t i o f o r w h i c h t h e largest f a v o u r a b l e i n t e r f e r e n c e s t a k e place. s / L = 0 . 3 8 8 is t h e s e p a r a t i o n r a t i o w i t h t h e largest f a v o u r a b l e i n t e r f e r e n c e e f f e c t s f o r t h e c o m m e r c i a l vessel case s t u d i e d i n t h e p r e v i o u s s e c t i o n . s / L = 0 . 3 0 7 is t h e m e a n v a l u e o f 0.226 a n d 0.388. s / L = 0 . 4 7 0 is l a r g e r t h a n 0.388 a n d c h o s e n t o e v e n l y space t h e 4 separations. Results are p r e s e n t e d a n d discussed f o r each o f these 4 separations. T h e f o r m f a c t o r used f o r t h e c o m p u t a t i o n o f t h e w a v e c o m p o n e n t o f t h e resistance is t a k e n as 0.0673. T h i s v a l u e w a s d e d u c e d b y M i n a n d Rang ( 2 0 1 0 ) w h o u n d e r t o o k a v e r y t h o r o u g h s t u d y o n t h e d e p e n d e n c e b e t w e e n t h e f o r m f a c t o r a n d t h e Reynolds n u m b e r . As f o r t h e c o m m e r c i a l vessel, i t is a s s u m e d t h a t t h e f o r m f a c t o r f o r t h e m o n o h u l l a n d t h e c a t a m a r a n is t h e same. The v e l o c i t i e s p r e s e n t e d i n Table 3 w e r e r u n f o r t h e m o n o h u l l a n d f o r t h e c a t a m a r a n w i t h a l l f o u r s e p a r a t i o n s i n b o t h f r e e a n d fixed m o d e l c o n d i t i o n s . O n t o p o f t h e p o i n t s p r e s e n t e d i n Table 3, a t o t a l o f 5 e x t r a r u n s w e r e d o n e f o r t h e r e g i o n s o f c o n v e x i t y c h a n g e i n t h e resistance curves. These e x t r a p o i n t s are s h o w n i n t h e resistance curves i n t h e n e x t s e c t i o n . Since i t w a s p r e v i o u s l y

Table 3

Froude numbers and velocities for the S60 catamaran tests.

Point FII V (m/s) 1 0.15 0.743 2 0.20 0.990 3 0.25 1.238 4 0.26 1.288 5 0.27 1.337 6 0.28 1.387 7 0.29 1.436 8 0.30 1.486 9 0.31 1,535 10 0.32 l'.585 11 0.33 1.634 12 0.34 1.684 13 0.35 1.733 14 0.36 1.783 15 0.37 1.832 16 0.38 1.882 17 0.39 1.931 18 0.40 1.981 19 0.41 2.030 20 0.42 2.080 21 0.43 2.129 22 0.45 2.229 23 0.50 2.476 24 0.55 2.724

u n c l e a r w h e r e t h e strongest i n t e r f e r e n c e e f f e c t s w o u l d take place, t h e range o f Froude n u m b e r s is w i d e r t h a n t h e one used f o r t h e c o m m e r c i a l vessel (Table 2 ) . T h e v i d e o s o f these e x p e r i m e n t s , p r o v i d e d as a s u p p l e m e n t a r y m a t e r i a l , can be f o u n d o n l i n e at h t t p : / / c a n a l . e t s i n . u p m . e s / f t p / 2 0 1 2 / S 6 0 / . A p h o t o g r a p h t a k e n d u r -i n g t h e e x p e r -i m e n t s -is p r e s e n t e d -i n F-ig. 9.

4.2. Resistance curves for all separations

T h e resistance curves f o r t h e m o n o h u l l a n d t h e c a t a m a r a n w i t h a l l 4 separations i n fixed a n d f r e e m o d e l c o n d i t i o n s are p r e s e n t e d i n Figs. 10 a n d 1 1 . T h e r e is a s l i g h t h u m p i n t h e resistance curves f o r b o t h fixed a n d f r e e m o d e l c o n d i t i o n s f o r 0.3 < F n < 0.4. I n b o t h c o n d i t i o n s a n d as a g e n e r a l t r e n d , t h e resistance d i m i n i s h e s as t h e s e p a r a t i o n increases, t e n d i n g t o t h a t o f t h e m o n o h u l l . Let us p o i n t o u t t h a t t h e m o n o h u l l resistance has been d o u b l e d f o r t h e c o m p a r i s o n . The t r a n s l a t i o n o f these resuits i n t h e i n t e r f e r e n c e f a c t o r is later discussed.

Fig. 9. Picture of S60 model test.

14 r 1 - 1 1 1 1 1 1 1 1

« •

_f^^y^

i é / /

i é / /

-*- •

£/

Fig. 10. S60, total resistance in free model c o n d i t i o n .

14 12 h 10 4 21¬ 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 F n

4.3. Resistance curves in free and fixed model conditions

The graphs i n Fig. 12 s h o w t h e resistance curves f o r each separation i n fixed and free m o d e l conditions, a n d compare t h e m

0 . 1 0.15 0 . 2 0 . 2 5 0.3 0.35 0 . 4 0.45 0.5 0 . 5 5 F n

w i t h the m o n o h u l l ones. As a general trend, i t can be observed t h a t the resistance is greater i n the free m o d e l c o n d i t i o n t h a n i n the fixed one f o r each separation. This is best appreciated w h e n c o m p a r i n g t h e data f o r the greatest speed. In Section 3.2, a s i m i l a r effect is described

14 12 10 ^ 8 ^ 6 4 2 0 T 1 1 1 1 1 -- • -- 2RT^ (free) - ••»•• R-Tcat (free) - • - 2RTmh (fixed) - - • RTcat (fixed) 1 ' 1 1 L - I 1 1 1—. 1 -0 . 1 -0.15 -0 . 2 -0.25 -0.3 -0.35 -0 . 4 -0 . 4 5 -0.5 -0 . 5 5 F n 12 10 —1 1 n 1 r ' ' ' ' 4 , » • - • - 2RTml, (free) • e - RTcat (free) - • - 2 R T „ J , (fixed) R T „ t (fixed) _ , . , . - , „ . . r v — " u..,„.,.,-.-f--y> ., , , , , , , , 0 . 1 0.15 0 . 2 0 . 2 5 0.3 0 . 3 5 0 . 4 0 . 4 5 0 . 5 0 . 5 5 F n 12 10 - 2 R T m h (free) - R T o a t (free) - 2 R T m h (fixed) - R T c a l (fixed) 0 . 1 0 . 1 5 0 . 2 0 . 2 5 0.3 0 . 3 5 0 . 4 0 . 4 5 0.5 F n 0 . 5 5

Fig. 12. S60, total resistance i n fixed and free model conditions. Top l e f t : s/L=0.226, Top Right: s/L=0.307, D o w n l e f t : s/L=0.388, D o w n Right: s/L=0.470.

12 10 h o A 6 0.3 <> • 2RTml, • R T c I — 2R\Vmh . . . . 2 R w „ t <>

.••*

f o r the commercial vessel. As can be appreciated i n Fig. 12, the differences are larger f o r t h e catamaran t h a n f o r the m o n o h u l l and even larger f o r small separations compared t o large ones. This effect was also described f o r the W i g l e y h u l l by Moraes et al. (2004).

For t h e c a t a m a r a n i n f r e e m o d e l c o n d i t i o n , w i t h s / L = 0 . 2 2 6 , t h e g r e a t e s t speeds c o u l d n o t be r e a c h e d due t o t h e g e n e r a t e d w a v e s e n t e r i n g t h e m o d e l . For s / t = 0 . 3 0 7 i n f r e e m o d e l c o n d i t i o n , t h e p l a n n i n g range f o r t h e c a t a m a r a n c o n f i g u r a t i o n is reached. 0.55 0.55

Fig. 14. S60, total and w a v e resistance i n fixed model c o n d i t i o n . Top left: s/L=0.226, Top Right: s/L=0.307, D o w n l e f t : s/L=0.388, D o w n Right: s/L=0.470.

1 0.8 0.6 0.4 0.2 0 -0.2

H-^'....A

Bim Free model

• • Fixed model 0.55 • Y e u n g et al. 2004! ' Free model • Fixed model - 0 . 4 ' 0.3 0.35 0.4 0.45 F n 0.5 0.55 1 0.8 0.6 0.4 0.2 0 - 0 . 2 - 0 . 4 • Y e u n g et al. 2004 ' Free model 1 Fixed model 0.3 0.35 0.4 0.45 F n 0.5 0.55

A. Souto-lglesias et al. / Ocean Engineeting 53 (2012) 38-47

T h i s can be d e d u c e d b y l o o l d n g at t h e flattening o f t h e resistance c u r v e f o r F n = 0 . 5 5 . For s / L = 0 . 3 8 8 , t h e d i f f e r e n c e i n resistance values b e t w e e n t h e m o n o h u l l a n d t h e c a t a m a r a n g r o w s s m a l l e r f o r large Froude n u m b e r s b o t h i n fixed a n d f r e e m o d e l c o n d i t i o n s . T h i s t e n d e n c y is m a d e clearer w i t h t h e largest s e p a r a t i o n ( s y L = 0 . 4 7 0 ) .

4.4. Wave resistance

I n o r d e r t o calculate t h e i n t e r f e r e n c e f a c t o r f o r a c o n t i n u o u s range o f Froude n u m b e r s , t h e resistance curves have been fitted w i t h NURBS. For each case, w a v e resistances have b e e n o b t a i n e d f r o m t h e t o t a l resistance f o l l o w i n g t h e p r o c e d u r e described i n S e c t i o n 2. The curves r e p r e s e n t i n g these results are s h o w n i n Figs. 13 a n d 1 4 f o r f r e e a n d fixed m o d e l c o n d i t i o n s r e s p e c t i v e l y . I n these figures, the m a r k e r s c o r r e s p o n d t o t h e r a w e x p e r i m e n t a l data. Data are presented f o r Fn > 0.3, w h e r e t h e first b e h a v i o u r d i f f e r e n c e s b e t w e e n t h e m o n o h u l l a n d t h e c a t a m a r a n s t a r t t o take place. W e can c o n c l u d e t h a t f o r t h e f r e e m o d e l c o n d i r i o n a n d s m a l l e s t separation, there is no f a v o u r a b l e i n t e r f e r e n c e r e g i o n . For t h e largest Froude n u m b e r s t h e c a t a m a r a n a n d t h e m o n o h u l l resistances t e n d t o converge. I n t h e m i d p a r t o f t h e graphs t h e t r e n d s are m o r e i n t r i c a t e a n d described t h r o u g h t h e IF i n t h e n e x t s e c t i o n .

4.5. Interference factor

U s i n g t h e w a v e resistance curves p r e s e n t e d i n t h e p r e v i o u s s e c t i o n , t h e i n t e r f e r e n c e f a c t o r s f o r b o t h fixed a n d f r e e m o d e l c o n d i t i o n s a n d f o r a l l separations are p r e s e n t e d i n t h i s section.

Results are c o m p a r e d w i t h Y e u n g et a l . ( 2 0 0 4 ) a n d Y e u n g ( 2 0 0 5 ) , w h o c o n s i d e r e d a t h i n - s h i p p o t e n t i a l a p p r o x i m a t i o n t o m o d e l t h e p r o b l e m , w i t h a fixed m o d e l h y p o t h e s i s .

I n t e r f e r e n c e f a c t o r s f o r f r e e and fixed m o d e l c o n d i t i o n s are p r e s e n t e d f o r a l l separations i n Fig. 15. F o c u s i n g o n s / L = 0 . 2 2 6 , i t can be a p p r e c i a t e d t h a t t h e f r e e m o d e l a n d fixed m o d e l i n t e r -ference f a c t o r s are s i g n i f l c a n t l y d i f f e r e n t . A l t h o u g h a c c o r d i n g t o Y e u n g et al. ( 2 0 0 4 ) , w h e r e t h i s last s e p a r a t i o n w i t h F n = 0 . 3 3 p r o d u c e s t h e m o s t f a v o u r a b l e i n t e r f e r e n c e e f f e c t s , t h i s does n o t occur i n t h e p r e s e n t e x p e r i m e n t s . For F n = 0 . 3 3 t h e i n t e r f e r e n c e is u n f a v o u r a b l e a n d t h e m i n i m u m is s h i f t e d t o a r o u n d F n = 0 . 3 8 . The f r e e m o d e l c o n d i t i o n presents o v e r a l l a m o r e u n f a v o u r a b l e b e h a v i o u r t h a n b o t h fixed c o n d i t i o n a n d t h e o r e t i c a l m o d e l . This is r e l e v a n t since i n real a p p l i c a t i o n s , t h e f r e e m o d e l c o n d i t i o n applies. For t h e largest v e l o c i t i e s t h e r e is a c o n v e r g e n c e b e t w e e n the flxed m o d e l c o n d i t i o n results a n d t h o s e o f Y e u n g e t a l . ( 2 0 0 4 ) .

For s / L = 0 . 3 0 7 , i t can be a p p r e c i a t e d t h a t t h e f r e e m o d e l i n t e r f e r e n c e f a c t o r s i g n i f i c a n t l y d i f f e r s f r o m t h e fixed m o d e l one i n t h e range 0.35 < Fn < 0.4. W i t h regards t o t h e c o m p a r i s o n w i t h Y e u n g e t a l . ( 2 0 0 4 ) , i t is n o t i c e a b l e t h a t t h e peak v a l u e o f t h e i n t e r f e r e n c e c o e f f i c i e n t is s h i f t e d t o 0.05 ( f r o m 0.38 t o 0.43 i n t h e e x p e r i m e n t a l results). This s h i f t is also p r e s e n t i n t h e m i n i m u m v a l u e o f t h e i n t e r f e r e n c e f a c t o r . For t h e largest v e l o c i t i e s t h e r e is a c o n v e r g e n c e b e t w e e n t h e e x p e r i m e n t a l results a n d t h o s e f r o m Y e u n g et a l . ( 2 0 0 4 ) i n f r e e a n d flxed m o d e l c o n d i t i o n s . F u r t h e r -m o r e , t h e i n t e r f e r e n c e effects d i -m i n i s h a n d t h e IF t e n d s t o zero, as is t h e case i n Z a g h i et al. ( 2 0 1 1 ) . A n a l o g o u s l y t o w h a t h a p p e n e d f o r t h e c o m m e r c i a l vessel, i n t h e S60 case, the strongest f a v o u r a b l e i n t e r f e r e n c e e f f e c t s are f o u n d f o r s / L = 0 . 3 8 8 . W i t h regards t o t h e c o m p a r i s o n w i t h Y e u n g 0.45 0.35 0.25 0.3 0.35 0.4 0.45 0.5 0.55 F n 0.45 0.35 0.25 0.3 0.35 0.4 0.45 0.5 0.55 F n 0.45 0.35 0.25 0.3 0.35 0.4 0.45 0.5 0.55 F n

et a l . ( 2 0 0 4 ) , t h e peaks a n d valleys i n t h e e x p e r i m e n t s are d e l a y e d w i t h r e s p e c t t o t h e m o d e l . For t h e largest v e l o c i t i e s , t h e c o n v e r -gence o f t h e e x p e r i m e n t a l results f o u n d i n t h i s p a p e r t o t h o s e o f Y e u n g et a l . ( 2 0 0 4 ) is c l e a r l y a p p r e c i a t e d . M o r e a t t e n u a t e d t r e n d s are o b s e r v e d f o r t h e largest separation, s / L = 0 . 4 7 0 .

A n i n t e r e s t i n g g l o b a l r e p r e s e n t a t i o n o f these e f f e c t s across t h e d i f f e r e n t s e p a r a t i o n s is g i v e n . To d o t h i s , a c o n t o u r p r o j e c t i o n o f t h e 3 D g r a p h f o r t h e IF is presented i n Fig. 16. The t e n d e n c i e s o b s e r v e d i n t h e i n d i v i d u a l graphs f o r each s e p a r a t i o n (Fig. 15) are n o w clearer. The c o l o u r scale i n each g r a p h is i n d i v i d u a l i s e d due t o t h e r a n g e o f t h e i n t e r f e r e n c e f a c t o r d a t a f r o m Y e u n g et a l . ( 2 0 0 4 ) b e i n g s i g n i f i c a n t l y shorter t h a n t h e o n e f o u n d e x p e r i m e n -t a l l y . G l o b a l l y -t h e r e are some s i m i l i -t u d e s i n -t h e i n -t e r f e r e n c e p a t t e r n s b u t s o m e d i f f e r e n c e s can be a p p r e c i a t e d . C o m p a r i n g t h e f r e e m o d e l e x p e r i m e n t a l d a t a ( w h i c h is t h e r e a l i s t i c c o n f i g u r a t i o n t o be f o u n d i n f u l l scale) w i t h t h o s e o f Y e u n g et a l . ( 2 0 0 4 ) shows t h a t t h e m o s t f a v o u r a b l e i n t e r f e r e n c e takes place at a s i m i l a r Fn ( 0 . 3 3 ) a n d w i t h a s i m i l a r IF ( a r o u n d - 0 . 2 ) b u t a t a larger separation (0.4 i n s t e a d o f 0 . 2 2 6 ) . T h i s Fn is s i m i l a r t o t h a t f o u n d b y Zaghi et a l . ( 2 0 1 1 ) w i t h a s l e n d e r e r m o d e l . T h e u n f a v o u r a b l e i n t e r f e r e n c e s are s t r o n g e r i n t h e e x p e r i -m e n t a l case w i t h a -m a x i -m u -m o f t h e o r d e r o f 0.7 i n s t e a d o f t h e t h e o r e t i c a l l y c a l c u l a t e d 0.3. I t is s i g n i f i c a n t t h a t t h i s m a x i m u m does n o t t a k e place f o r the smallest s e p a r a t i o n , as is t h e case i n Z a g h i et a l . ( 2 0 1 1 ) . Also, i n e x p e r i m e n t s , t h e r e is a s m o o t h e r t r a n s i t i o n b e t w e e n t h e f a v o u r a b l e a n d u n f a v o u r a b l e regions c o m p a r e d t o t h e t h e o r e t i c a l m o d e l . N o w c o m p a r i n g f r e e a n d fixed m o d e l c o n d i t i o n tests, o t h e r d i f f e r e n c e s can be a p p r e c i a t e d : 1. T h e t r a n s i t i o n b e t w e e n f a v o u r a b l e a n d u n f a v o u r a b l e regions is s h a r p e r f o r t h e fixed m o d e l case. Such a s h a r p t r a n s i t i o n i n the fixed m o d e l case is p r e d i c t e d b y t h e t h e o r e t i c a l m o d e l . 2. For t h e s m a l l e s t separations a n d c o n t r a r y t o w h a t h a p p e n s i n

t h e f r e e m o d e l c o n d i t i o n , t h e r e are f a v o u r a b l e , a l t h o u g h q u i t e m i l d , i n t e r f e r e n c e regions i n t h e fixed m o d e l c o n d i t i o n results. 3. A l t h o u g h t h e u n f a v o u r a b l e i n t e r f e r e n c e regions are s i m i l a r i n

size, t h e f r e e m o d e l ones are m o r e i n t e n s e .

4. T h e m o s t f a v o u r a b l e i n t e r f e r e n c e f a c t o r i n fixed m o d e l c o n d i -t i o n is s m a l l e r -t h a n -t h e f r e e m o d e l one.

S u m m a r i z i n g , t h e f r e e m o d e l c o n d i t i o n t e n d s t o e n h a n c e the f a v o u r a b l e a n d u n f a v o u r a b l e i n t e r f e r e n c e e f f e c t s .

4.6. Sinl<age and trim

T h e o b j e c t o f t h i s s e c t i o n is t o analyse t h e r e l a t i o n s h i p b e t w e e n t h e IF d i f f e r e n c e s i n f r e e a n d fixed m o d e l c o n d i t i o n s a n d t h e d y n a m i c p o s i t i o n (sinkage a n d t r i m ) i n f r e e m o d e l c o n d i t i o n . I t is also r e l e v a n t t o analyse d i f f e r e n c e s i n sinkage a n d t r i m i n f r e e m o d e l c o n d i t i o n b e t w e e n t h e m o n o h u l l a n d t h e c a t a m a r a n ; such values are p r e s e n t e d i n n o n d i m e n s i o n a l f o r m i n Figs. 17 a n d 18, f o l l o w i n g t h e d e f i n i t i o n s hy K i m a n d Jenkins ( 1 9 8 1 ) p r e s e n t e d i n Eqs. ( 4 ) a n d ( 5 ) .

W h e n c o m p a r i n g the S60 data w i t h t h o s e o f t h e c o m m e r c i a l vessel ( F i g . 6), sinkage seems t o be o f t h e s a m e o r d e r b u t t r i m is s i g n i f l c a n t l y l a r g e r f o r the S60. P e n d i n g f u t u r e w o r k , w e b e l i e v e t h i s m a y h a v e a n i n f l u e n c e o n t h e IF b e h a v i o u r change b e t w e e n flxed a n d f r e e m o d e l c o n d i t i o n s . W h e n c o m p a r i n g t h e S60 m o n o h u l l a n d t h e S60 c a t a m a r a n i n f r e e m o d e l c o n d i t i o n , large d i f f e r e n c e s i n s i n k a g e can be a p p r e -c i a t e d f o r 0.3 < F n < 0.42 (Fig. 17). For t h e s h o r t e s t s e p a r a t i o n ( s / L = 0 . 2 2 6 ) t h e sinkage f o r t h e c a t a m a r a n is a r o u n d 50% greater. Also f o r s / i = 0 . 2 2 6 , as can be seen i n Fig. 15, t h e d i f f e r e n c e s i n the IF b e t w e e n f r e e a n d fixed m o d e l are s i g n i f i c a n t b u t n o t m o n o -t o n i c , u n l i k e -t h e sinkage d i f f e r e n c e s , w h i c h are m o n o -t o n i c . 0.141 1 1 21 i i ' ' ' 0.3 0.35 0.4 0.45 0.5 0.55 F n Fig. 17. Sinlfage for the S60.

0.2

| r ; l 1 I 1 1 1

0.3 0.35 0.4 0.45 0.5 0.55. F n

Fig. 18. T r i m f o r the S60.

L o o k i n g at t h e t r i m (Fig. 1 8 ) a n d i n a l l cases, t h e d i f f e r e n c e s are m o r e p a t e n t f o r l a r g e r Fn. B e t w e e n F n = 0 . 3 8 a n d F n = 0 . 4 5 a s i g n i f i c a n t t r i m increase is a p p r e c i a t e d . This s h i f t r e q u i r e s f u r t h e r i n v e s t i g a t i o n i n o r d e r t o e v a l u a t e a possible r e l a t i o n b e t w e e n d i f f e r e n c e s i n t h e IF i n f r e e a n d fixed m o d e l c o n d i t i o n . 5. C o n c l u s i o n s The i n t e r f e r e n c e resistance o f m u l t i h u l l s t a k i n g i n t o a c c o u n t t h e t e s t i n g c o n d i t i o n ( f i x e d m o d e l o r f r e e m o d e l ) has b e e n e x p e r i m e n t a l l y s t u d i e d . E x p e r i m e n t s have b e e n c a r r i e d o u t w i t h a c o m m e r c i a l c a t a m a r a n m o d e l a n d m o r e e x t e n s i v e l y w i t h a Series 6 0 c a t a m a r a n . For t h e c o m m e r c i a l vessel, t h e i n f l u e n c e o f t h e m o d e l c o n d i t i o n has b e e n a n a l y s e d f o r t h e s e p a r a t i o n i n w h i c h t h e s t r o n g e s t i n t e r f e r e n c e e f f e c t s t a k e place. I n t h i s case i t has b e e n s h o w n t h a t t h e i n f l u e n c e o f t h e m o d e l c o n d i t i o n ( f r e e -flxed) is n o t s u b s t a n t i a l . T h i s is c o n s i s t e n t w i t h t h e e x p e r i m e n t s p r e s e n t i n g m o d e r a t e d y n a m i c t r i m - s i n k a g e values a n d s m a l l d i f f e r e n c e s i n d y n a m i c t r i m a n d sinkage b e t w e e n t h e m o n o h u l l a n d t h e m u l t i h u l l c o n f l g u r a t i o n i n f r e e m o d e l c o n d i t i o n .

For the Series 60 m o d e l a range o f separations has been studied and compared w i t h the fixed m o d e l slender body theoretical results. The differences between the free and fixed c o n d i t i o n e x p e r i m e n t a l results are significant, w i t h the free c o n d i t i o n p r o v i d i n g m o r e extreme cases i n t h e favourable and unfavourable interference regimes. The o p t i m u m interference factor ( - 0.2) appears at a Froude n u m b e r o f 0.33, agreeing w i t h theoretical results. Nonetheless, this o p t i m u m interference occurs f o r a substantially larger separation ratio (0.40) t h a n the theoretically predicted (0.226). The t r a n s i t i o n between favourable and unfavourable regions is sharper f o r the fixed m o d e l case. Such a sharp t r a n s i t i o n is i n accordance w i t h the theoretical m o d e l predictions. For t h e smallest separation and

c o n t r a r y t o w h a t happens i n t h e free m o d e l c o n d i t i o n , there are favourable, a l t h o u g h quite m i l d , interference regions i n t h e fixed m o d e l c o n d i t i o n . It has been described t h a t f o r each separation t h e r e is a s h i f t i n t h e m a x i m u m favourable and u n f a v o u r a b l e interference Froude n u m b e r s as compared to t h e theoretical m o d e l . I n general, t h e f r e e m o d e l c o n d i t i o n tends t o enhance the f a v o u r a b l e and u n f a v o u r -able i n t e r f e r e n c e effects. As a final c o n c l u s i o n , w e b e l i e v e t h a t t h e d i f f e r e n c e s d e s c r i b e d i n t h i s p a p e r b e t w e e n e x p e r i m e n t a l r e s u l t s a n d t h e o r e t i c a l p r e d i c t i o n s a n d b e t w e e n t h e w a v e r e s i s t a n c e i n fixed a n d f r e e s i n k -t r i m c o n d i -t i o n s m a y be r e l e v a n -t a-t -t h e d e c i s i o n - m a k i n g l e v e l i n e a r l y m u l t i h u l l h y d r o d y n a m i c d e s i g n . I n a d d i t i o n , a n d since t h e h u l l s t h a t h a v e b e e n t r e a t e d are a s t a n d a r d a n d a f u l l y d e f i n e d one, w e h o p e t h i s p a p e r w i l l be u s e f u l as b e n c h m a r k d a t a f o r n u m e r i c a l a n a l y s i s o f m u l r i h u l l h y d r o d y n a m i c s . A c l c n o w l e d g e m e n t s

The research leading t o these results has received f u n d i n g f r o m t h e Spanish M i n i s t r y f o r Science a n d I n n o v a t i o n w i t h t h e "Programa de Acceso y Mejora de las ICTS", w h i c h p r o v i d e d f u n d i n g f o r c a r r y i n g o u t t h e e x p e r i m e n t a l campaign i n CEHIPAR m o d e l basin. W e t h a n k Elldn M a u r i c i o Botia-Vera, Luise D r a h e i m , D a v i d Feijoo de Azevedo, Carios A r i e l Garrido Mendoza, Francisco P é r e z - A r r i b a s , Roque Velasco-Sopranis, Hugo Gee all f r o m o u r research g r o u p , a n d Libor Lobovsl<y f r o m University o f W e s t Bohemia f o r t h e i r s u p p o r t i n d i f f e r e n t tasks d u r i n g the research t h a t has led t o this paper.

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