Ocean Engineering 90 (2014) 7 2 - 8 3
ELSEVIER
Contents lists available a t ScienceDirect
Ocean Engineenng
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
The work achieved with the sail dynamometer boat "Fujin",
and the role of full scale tests as the bridge between
model tests and CFD
Yutaka Masuyama
Kanazawa Institute of Technology, Actual Seas Ship and Marine Research Laboratory, Yuigaol<a, Anamizu, Housu, Ishil<awa 927-0024, fapan
(D
CrossMarkA R T I C L E I N F O
Article history:
Received 12 November 2013 Accepted 24 June 2014 Available online 23 July 2014 Keywords:
Sail performance Sail dynamometer boat Full scale test Tacking simulation CFD validation
A B S T R A C T
T h e w o r k a c h i e v e d w i t h the s a i l d y n a m o m e t e r boat Fujin w a s reported. A t first, the s a i l s h a p e s a n d p e r f o r m a n c e for u p w i n d c o n d i t i o n s w e r e m e a s u r e d in s t e a d y s a i l i n g c o n d i t i o n s . T h e r e s u l t s w e r e c o m p a r e d w i t h the n u m e r i c a l calculations. T h e database of t h r e e - d i m e n s i o n a l c o o r d i n a t e s o f t h e sail s h a p e s w a s also t a b u l a t e d w i t h t h e a e r o d y n a m i c coefficients. T h e sail s h a p e d a t a b a s e p r o v i d e s a g o o d b e n c h m a r k for the v a l i d a t i o n o f s a i l CFD in f u l l s c a l e level. T h e n , the a e r o d y n a m i c force v a r i a t i o n d u r i n g t a c k i n g m a n e u v e r s w a s m e a s u r e d b y f u j i n , a n d a n e w s i m u l a t i o n m o d e l of t a c k i n g m a n e u v e r w a s p r o p o s e d . T h e s i m u l a t e d results s h o w e d g o o d a g r e e m e n t w i t h the m e a s u r e d d a t a . Finally, t h e s c a l e effect p r o b l e m of w i n d t u n n e l tests w a s d i s c u s s e d . W i n d T u n n e l tests u s i n g m o d e l s a i l s a r e p e r f o r m e d at the r e g i o n of critical R e y n o l d s n u m b e r . T h e r e f o r e , the w i n d t u n n e l test h a d to be p e r f o r m e d v e r y carefully. O n the o t h e r h a n d , the full scale t e s t s u s i n g a sail d y n a m o m e t e r boat a r e free f r o m s c a l e e f f e c t p r o b l e m s a n d a p p e a r m o r e p r o m i s i n g .
© 2 0 1 4 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
Because t h e r e c e n t advances i n c o m p u t a t i o n a l f l u i d d y n a m i c s (CFD) f u r t h e r m o t i v a t e t h e a p p l i c a t i o n o f n u m e r i c a l s i m u l a t i o n s t o p r e d i c t t h e sail p e r f o r m a n c e , t h e r e is a n ever increased n e e d f o r r e l i a b l e e x p e r i m e n t a l data f o r v a l i d a t i o n . W i n d t u n n e l tests can be p e r f o r m e d r e l a t i v e l y easily, b u t scale e f f e c t s r e l a t e d b o t h t o flow a n d s t r u c t u r a l aspects, w h i c h y i e l d i n a c c u r a c y i n sail shape m e a s u r e m e n t s , are always p r e s e n t Full scale o n b o a r d m e a s u r e -m e n t s are f r e e f r o -m scale e f f e c t p r o b l e -m s a n d appear -m o r e p r o m i s i n g , b u t t h e challenge b e c o m e s h o w t o a c c u r a t e l y m e a s u r e t h e forces a c t i n g o n t h e sail. Such studies o n sail f o r c e m e a s u r e -m e n t s w e r e p e r f o r -m e d b y M i l g r a -m et al., M a s u y a -m a e t a l . a n d H o c h k i r c h e t al., w h o b u i l t f u l l - s c a l e boats w i t h o n b o a r d s a i l d y n a m o m e t e r systems.
M i l g r a m e t al. ( 1 9 9 3 ) s h o w e d i n his p i o n e e r i n g w o r k t h a t t h e sail d y n a m o m e t e r boat, Amphetrete, is q u i t e capable. This m e a -s u r e m e n t -s y -s t e m con-si-st-s o f a 3 5 - f o o t b o a t w i t h a n i n t e r n a l f r a m e c o n n e c t e d t o t h e h u l l b y six l o a d cells, w h i c h w e r e c o n f i g u r e d t o m e a s u r e all forces a n d m o m e n t s a c t i n g o n t h e sails. I n his w o r k , t h e sail shapes w e r e also m e a s u r e d a n d used f o r CFD analyses; u n f o r t u n a t e l y , details o f t h e s a i l shape a n d p e r f o r m a n c e data w e r e n o t p r e s e n t e d . H o c h k i r c h a n d B r a n d t ( 1 9 9 9 ) also b u i l t a 3 3 - f o o t
E-mail address: masuyama@neptune.kanazawa-it.acjp
d y n a m o m e t e r b o a t DYNA. The a e r o d y n a m i c f o r c e s a c t i n g o n t h e s a i l w e r e m e a s u r e d a n d c o m p a r e d w i t h t h e r e s u l t s f r o m w i n d t u n n e l tests ( H a n s e n et al., 2 0 0 3 ) . The m e a s u r e d d a t a w e r e also used as i n p u t t o t h e CFD c a l c u l a t i o n a n d a p a r a m e t r i c s u r v e y w a s c a r r i e d o u t ( K r e b b e r a n d H o c h k i r c h , 2 0 0 6 ) . H o w e v e r t h i s w o r k does n o t p r o v i d e a database f o r t h e r e l a t i o n b e t w e e n s a i l shape a n d p e r f o r m a n c e . M a s u y a m a a n d Fukasawa ( 1 9 9 7 ) w e r e e n c o u r -aged b y M i l g r a m ' s w o r k , a n d b u i l t a sail d y n a m o m e t e r b o a t , Fujin. T h e Fujin is a 3 4 - f o o t s a i l i n g cruiser, i n w h i c h l o a d cells, CCD cameras a n d s a i l i n g c o n d i t i o n m e a s u r e m e n t s y s t e m are i n s t a l l e d t o o b t a i n t h e sail forces a n d shapes, a n d t h e b o a t a t t i t u d e , s i m u l t a n e o u s l y . I n t h i s r e p o r t , t h e w o r k a c h i e v e d w i t h t h e s a i l d y n a m o m e t e r b o a t Fujin is p r e s e n t e d , a n d t h e r o l e o f f u l l scale tests i n t h e v a l i d a t i o n o f CFD i n f u l l scale l e v e l is discussed.
2. Sail d y n a m o m e t e r b o a t Fujin
2.1. General arrangement
The Fujin w a s b u i l t i n 1994, Fujin is a 10.3 m - l o n g o c e a n c r u i s e r w i t h a sail d y n a m o m e t e r s y s t e m i n t h e h u l l . Table 1 s h o w s t h e p r i n c i p a l d i m e n s i o n s o f t h e b o a t a n d Fig. 1 s h o w s t h e s a i l p l a n o f t h e Fujin. T h e sail d y n a m o m e t e r s y s t e m is c o m p o s e d o f a r i g i d a l u m i n u m f r a m e a n d f o u r l o a d cells. T h e f r a m e is s e p a r a t e d s t r u c t u r a l l y f r o m t h e h u l l a n d c o n n e c t e d t o i t b y t h e l o a d cells. http://dx.doi.org/10.1016/j.oceaneng.201406.037 0 0 2 9 - 8 0 1 8 / © 2014 Elsevier Ltd. All rigiits reserved.
y. Masuyama / Ocean Engineering 90 (2014) 72-83 73
N o m e n c l a t u r e X, Y Force c o m p o n e n t s a l o n g x a n d y - a x i s ( N )
K, N M o m e n t s a r o u n d x a n d z-axis ( N m ) CL. CL, L i f t f o r c e a n d d r a g f o r c e c o e f f i c i e n t s ( - ) ÏA A p p a r e n t w i n d angle ( A W A ) ( d e g ) CX.CY T h r u s t force a n d side f o r c e c o e f f i c i e n t s ( - ) P D e n s i t y o f w a t e r ( k g m ~ ^ )
SA Sail area ( m ^ ) Pa D e n s i t y o f air ( k g m ~ ^ )
UA A p p a r e n t w i n d speed ( A W S ) ( m s""^) cp Heel angle o r r o l l angle ( d e g ) VB Boat v e l o c i t y ( m s ~ ^ )
¥
H e a d i n g a n g l e ( d e g )T h e g e n e r a l a r r a n g e m e n t o f t h e d y n a m o m e t e r f r a m e is g i v e n i n Fig. 2 ( a ) . The l o a d cells are n u m b e r e d i n t h e f i g u r e . T w o o f these are 1 - c o m p o n e n t load cells a n d t h e others are 2 - c o m p o n e n t ones. T h e d i r e c t i o n s i n w h i c h t h e loads w e r e m e a s u r e d f o r each o f t h e l o a d cells are s h o w n i n Fig. 2 ( b ) . Hence, these l o a d cells f o r m a 6-c o m p o n e n t d y n a m o m e t e r system, a n d t h e i r o u t p u t s 6-can be t r a n s f o r m e d t o the forces a n d m o m e n t s a b o u t t h e b o a t axes u s i n g a c a l i b r a t i o n m a t r i x . A l l r i g c o m p o n e n t s s u c h as t h e mast, c h a i n plates, w i n c h e s , lead blocks, etc. are a t t a c h e d t o t h e a l u m i n u m f r a m e t h r o u g h t h e deck holes.
Table 1
Principal dimensions of Fujin. HULL LOA [m] 10.35 LWL [m] 8.80 BMAX |ml 3.37 BWL [m] 2.64 Disp [ton] 3.86 SAIL I [ml 11.00 J [m] 3.61 P [ml 12.55 E [m] 4.51
Fig. 1. Sciiematic showing the sail plan of Fujin.
2.2. Measurement system
T h e sail shape w a s r e c o r d e d u s i n g pairs o f CCD cameras. T h e l o w e r p a r t o f t h e m a i n s a i l w a s p h o t o g r a p h e d u s i n g t h e CCD camera p a i r d e s i g n a t e d A i n Fig. 3. These w e r e l o c a t e d at t h e m a s t top, 5 0 c m t r a n s v e r s e l y f r o m each side o f t h e mast. The u p p e r p a r t o f t h e m a i n s a i l w a s p h o t o g r a p h e d u s i n g a p o r t a b l e v i d e o c a m e r a f r o m b e l o w t h e b o o m . The l o w e r p a r t o f t h e j i b w a s p h o t o g r a p h e d u s i n g t h e c a m e r a p a i r d e s i g n a t e d B i n Fig. 3, w h i c h w e r e l o c a t e d a t t h e i n t e r s e c t i o n p o i n t o f t h e f o r e s t a y a n d t h e mast, 10 c m t r a n s -v e r s e l y f r o m each side o f t h e mast. The u p p e r p a r t o f t h e j i b w a s p h o t o g r a p h e d u s i n g a p o r t a b l e v i d e o camera f r o m i n s i d e t h e b o w h a t c h . For m e a s u r i n g c o n v e n i e n c e , h o r i z o n t a l stripes w e r e d r a w n
a
Fig. 2. General arrangement of dynamometer frame and directions of measuring components of each load cell.
74 Y. Masuyama / Ocean Engineering 90 (2014) 72-83
Fig. 3. Sea trial condition in light wind with 130% jib.
o n t h e m a i n s a i l a n d j i b a t h e i g h t s o f 10, 20, 4 0 , 6 0 a n d 80% o f each sail. The sail shape images w e r e a n a l y z e d u s i n g t h e sail shape a n a l y z i n g s o f t w a r e , SSA-2D, d e v e l o p e d b y A r m o n i c o s Co. This s o f t w a r e calculates t h e c u r v a t u r e o f t h e sail s e c t i o n b y m a r k i n g several p o i n t s o f t h e sail s t r i p e a n d t h e reference l i n e o n t h e PC d i s p l a y , a n d i n d i c a t e s t h e p a r a m e t e r s such as c h o r d l e n g t h , m a x i m u m d r a f t , m a x i m u m d r a f t p o s i t i o n , e n t r y angle at t h e l u f f , i,e., l e a d i n g edge, a n d e x i t angle at t h e leech, i,e„ t r a i l i n g edge. The o r i g i n a l data a c q u i s i t i o n s y s t e m consisted o f a s i n g l e PC w h i c h g a t h e r e d a l l t h e data. H o w e v e r , t h e s y s t e m w a s r e n e w e d later as a d i s t r i b u t e d s y s t e m u s i n g t h r e e s i n g l e c h i p c o m p u t e r s ( H i t a c h i H 8 -2 6 3 6 ) c o n n e c t e d w i t h t h e C o n t r o l Area N e t w o r k ( C A N ) bus. The CAN is a h i g h - s p e e d , serial bus d e v e l o p e d f o r t h e a u t o m o t i v e e n v i r o n m e n t a n d has a h i g h l e v e l o f noise i m m u n i t y .
3. S t e a d y s a i l p e r f o r m a n c e f o r u p w i n d c o n d i t i o n
3.1. Test condition arid error analysis
A t f i r s t , t h e sail shapes a n d p e r f o r m a n c e f o r u p w i n d c o n d i t i o n s w e r e m e a s u r e d u s i n g m a i n s a i l a n d 130% j i b i n s t e a d y s a i l i n g c o n d i d o n s ( M a s u y a m a a n d Fukasawa, 1997; M a s u y a m a e t al., 2 0 0 7 ) . Close-hauled tests w e r e c o n d u c t e d o v e r a n a p p a r e n t w i n d a n g l e ( A W A ) range o f 2 0 - 4 0 ° , a n d a n a p p a r e n t w i n d speed ( A W S ) r a n g e o f 5 - 1 1 m / s . The e f f e c t o f t h e A W A , a n d t h e d r a f t a n d t w i s t o f t h e m a i n s a i l o n t h e sail p e r f o r m a n c e w e r e m e a s u r e d . Data s a m p l i n g w a s s t a r t e d w h e n t h e s a i l i n g c o n d i t i o n w a s c o n s i d e r e d to be i n steady state. T h e s a m p l i n g r a t e f o r t h e d a t a a c q u i s i t i o n s y s t e m w a s set at 10 Hz. Data s a m p l i n g w a s c o n t i n u e d f o r 90s, a n d d u r i n g t h i s t i m e t h e sail shapes w e r e r e c o r d e d u s i n g t h e CCD cameras. The b o a t w a s steered c a r e f u l l y d u r i n g t h i s t i m e . H o w e v e r i t w a s d i f f i c u l t t o keep t h e v a r i a t i o n i n t h e A W A s u f f i c i e n t l y s m a l l d u r i n g t h e w h o l e o f t h e 90s p e r i o d . T h e r e f o r e t h e steady state v a l u e s f o r t h e a e r o d y n a m i c c o e f f i c i e n t s w e r e o b t a i n e d b y aver-a g i n g t h e daver-ataver-a o v e r aver-a 3 0 - 6 0 s p e r i o d , i n w h i c h t h e A W A w aver-a s closer to t h e t a r g e t v a l u e t h a n d u r i n g t h e w h o l e 90s p e r i o d . For these tests i f t h e range o f d e v i a t i o n o f A W A exceeded + 5 ° , t h e results w e r e d i s c a r d e d . A l l o f t h e m e a s u r e d c o e f f i c i e n t s are p l o t t e d w i t h e r r o r bars i n d i c a t i n g t h e range o f d e v i a t i o n o v e r t h e a v e r a g i n g p e r i o d .
3.2. Numerical calculation method
N u m e r i c a l flow s i m u l a t i o n s w e r e p e r f o r m e d f o r t h e m e a s u r e d sail shapes a n d c o n d i t i o n s . T w o n u m e r i c a l m e t h o d s w e r e used; a v o r t e x l a t t i c e m e t h o d ( V L M ) a n d a R e y n o l d s A v e r a g e d N a v i e r -Stokes (RANS)-based CFD m e t h o d . A v o r t e x l a t t i c e m e t h o d u s i n g a step-by-step p r o c e d u r e d e v e l o p e d b y Fukasawa ( 1 9 9 3 ) w a s e m p l o y e d t o c o m p a r e w i t h t h e results o f a RANS-based CFD c a l c u l a t i o n . Since t h e v o r t e x l a t t i c e m e t h o d can o n l y g i v e i n d u c e d drag, t h e viscous d r a g a c t i n g o n t h e sails a n d r i g g i n g w a s calculated a c c o r d i n g t o M i l g r a m et a l . ( 1 9 9 3 ) . T h e p r o c e d u r e is described i n A p p e n d i x .
The code o f t h e RANS-based CFD m e t h o d w a s FLOWPACK d e v e l o p e d b y Tahara ( 1 9 9 6 ) ; Tahara a n d H a y a s h i ( 2 0 0 3 ) . T h e m e t h o d has a n a u t o m a t i c g r i d d i n g scheme, a n d c o m p l e t e m u l t i -b l o c k d o m a i n d e c o m p o s i t i o n f e a t u r e .
3.3. Sail performance variation with apparent wind angle
Fig. 4 s h o w s t h e p e r f o r m a n c e v a r i a t i o n f o r t h e m a i n s a i l a n d 130% j i b c o n f i g u r a t i o n as a f u n c t i o n o f A W A . Fig. 4 ( a ) a n d ( b ) s h o w t h e v a r i a t i o n o f l i f t a n d d r a g f o r c e c o e f f i c i e n t s C I , C D , a n d t h r u s t a n d side f o r c e c o e f f i c i e n t s Cx, Cy, respectively. I n t h e figure t h e s o l i d s y m b o l s i n d i c a t e t h e e x p e r i m e n t a l results a n d t h e o p e n s y m b o l s i n d i c a t e t h e c a l c u l a t e d results u s i n g t h e V L M a n d t h e RANS-based CFD. For t h e e x p e r i m e n t a l results, b o t h data f r o m t h e s t a r b o a r d (Stbd) a n d p o r t t a c k ( P o r t ) are s h o w n . A l l o f t h e m e a s u r e d c o e f f i c i e n t s are p l o t t e d w i t h e r r o r bars i n d i c a t i n g t h e r a n g e o f d e v i a t i o n o v e r t h e a v e r a g i n g p e r i o d . T h e r e are s o m e discrepancies b e t w e e n t h e data f r o m each tack. D u r i n g t h e e x p e r i m e n t s , e f f o r t s w e r e m a d e t o r e m o v e t h i s a s y m m e t r i c a l p e r f o r m a n c e . H o w e v e r , t h e b o a t speed a c t u a l l y d i f f e r e d o n each tack. I t can be c o n c l u d e d t h a t t h e r e w a s a s l i g h t a s y m m e t r y i n t h e c o m b i n a t i o n o f t h e h u l l , keel, r u d d e r a n d d y n a m o m e t e r f r a m e .
I n t h i s figure, A W A ranges f r o m 2 0 . 3 ° t o 3 7 9 ° f o r t h e p o r t tack. T h e f o r m e r is t h e closest angle t o t h e w i n d t h a t w a s a c h i e v e d , a n d t h e l a t t e r is t y p i c a l o f a close r e a c h i n g c o n d i t i o n , w h e r e t h e sail is t r i m m e d i n t h e p o w e r d o w n m o d e . T h e r e is s o m e scatter i n t h e e x p e r i m e n t a l data because t h i s is m a d e u p f r o m m e a s u r e m e n t s t a k e n w i t h t h e sails t r i m m e d i n s l i g h t l y d i f f e r e n t w a y s . T h e e x p e r i m e n t a l v a l u e o f Cj, i n Fig. 4 ( a ) varies w i t h A W A f r o m 0.91 to 1.58. For t h e close r e a c h i n g c o n d i t i o n , u n f o r t u n a t e l y , t h e sails w e r e n o t w e l l t r i m m e d t o s a t i s f y t h e p o w e r d o w n m o d e . A s a m p l e o f m e a s u r e d sail s e c t i o n p r o f i l e s at t h i s c o n d i t i o n is s h o w n i n a figure a t t a c h e d t o t a b l e 2 ( 2 ) . F r o m t h e figure, i t can be seen t h a t b o t h t h e m a i n s a i l a n d t h e j i b are n o t eased s u f f i c i e n t l y t o c o r r e s p o n d t o t h e large A W A . This is t h e reason f o r t h e d e c r e m e n t i n t h e m e a s u r e d l i f t c u r v e slope o f CL a t t h e r a n g e o f A W A angles o v e r a b o u t 3 5 ° .
The c a l c u l a t e d results f o r CL u s i n g t h e V L M s h o w g o o d agree-m e n t w i t h t h e e x p e r i agree-m e n t s a t A W A angles less t h a n a b o u t 3 5 ° . Over a b o u t 3 5 ° , t h e c a l c u l a t e d results are l o w e r t h a n t h e m e a s u r e d ones. This s h o w s t h a t t h e c a l c u l a t e d results s t r o n g l y i n d i c a t e t h e e f f e c t o f i n c o r r e c t sail t r i m m i n g . The r e s u l t s f o r Ci u s i n g t h e RANS-based CFD s h o w t h e same t r e n d s w i t h t h e e x p e r i m e n t s , b u t are s l i g h t h i g h e r t h a n t h o s e f r o m t h e e x p e r i m e n t s f o r A W A b e t w e e n 2 0 ° a n d 3 0 ° a n d l o w e r f o r A W A greater t h a n 3 0 ° . I n p a r t i c u l a r , t h e decrease i n CL f o r A W A values greater t h a n 3 0 ° is c o n s i d e r a b l y large. This w i l l be discussed l a t e r w i t h t h e c a l c u l a t e d sail surface pressure a n d s t r e a m l i n e s . T h e c a l c u l a t e d results f o r Cp s l i g h t i y o v e r p r e d i c t t h o s e f r o m t h e e x p e r i m e n t s .
Fig. 4(c) shows t h e coordinates o f the center o f e f f o r t o f t h e sails. The X and z coordinates o f the geometric center o f e f f o r t (XCCE a n d ZGCE) are 0.63 m a f t and 4.80 m above the origin, w h i c h are i n d i c a t e d b y alternate l o n g a n d short dashed lines i n t h e figure. I t is seen t h a t b o t h the experimental a n d the calculated coordinates o f XCB are near XGCE
y. Masuyama / Ocean Engineering 90 (2014) 72-83 75
a
C L , C D 2 . 0 r ( 1 ) 1.5 1.0 ( 2 ) 0 . 0 1 1 ' 1 1 1 1 1 11
i C L C© I
Mt
©%
1 1 « - r i 1 0 2 0 3 0 4 0b
Cx,
C Y 2 . 0 1.5 1.0 0 . 5 0 . 0 1 0 2 0 3 0 4 0c
X O E , Z O E [m] I i I -Xs -a—E x p .
(Port)
#:C.
(Stbd)
^ : C DC a l .
(Port)
( V L M ) 0 : C L • : C D(RANS)
@ : C L 6 0 [ d e g ]E x p .
(Port)
#:Cx
i:Cv
(Stbd)
*:Cv
C a l .
(Port)
( V L M )0:Cx
• :Cy
(RANS)
@:Cx
5 0 [ d e g ] ft I : G e o m e j r i G e o m i t y i c XQOEE x p .
(Port)
(Stbd)
C a l .
(Port)
( V L M ) O ^ X C E IZl^ZCE(BANS)
@ : x o E 2 0 3 0 4 0 -yA 5 0 [ d e g ]Fig. 4 . Performance variation as a function of apparent wind angle (AWA) for mainsail and 130% jib.
a n d m o v e sliglitly f o r w a r d w i t f i increasing AWA. Unfortunately, tliere is a w i d e scatter i n the e x p e r i m e n t a l values o f ZCE- This is t h o u g h t t o be because the measured Ks m o m e n t contains a large c o m p o n e n t from
the mass o f the d y n a m o m e t e r f r a m e and r i g g i n g ( 6 5 9 leg). This m o m e n t was subtracted f r o m the measurement, t a l d n g i n t o account the measured heel angle. If there is a slight error i n t h e p o s i t i o n o f center o f gravity o f the d y n a m o m e t e r frame, or i n t h e measured heel angle, t h e eiTor i n the calculated m o m e n t w i l l be large. However, tiiough there is a scatter i n the measured data, i t can be seen t h a t ZCE is decreasing as A W A increases. The trends i n the m o v e m e n t o f b o t h XCE and ZCE as functions o f A W A m i g h t be caused b y the d e c r e m e n t o f force acting o n the a f t and upper parts o f the sails due to the loosening o f m a i n a n d j i b sheets w i t h increasing AWA, The calculated results f o r ZCE obtained using theRANS-based CFD s h o w the same t r e n d as the experiments. On the other hand, the calculated results using V L M are considerably higher tiian the experimental ones. This m i g h t be caused by over estimation o f the force acting o n the u p p e r p o r t i o n o f the mainsail. In this area, since the j i b is n o t overiapping, f l o w separation m a y occur easily. However, the V L M does n o t take f l o w separation i n t o account.
Fig. 5 ( 1 ) a n d ( 2 ) s h o w t h e c a l c u l a t e d results o f t h e sail surface pressure a n d s t r e a m l i n e s u s i n g RANS based CFD. Fig. 5 ( 1 ) i n d i -cates t h e case o f e x p e r i m e n t ID 9 6 0 9 2 3 3 5 ( A W A = 3 0 . 7 d e g ) , a n d 5 (2) i n d i c a t e s ID 9 6 0 8 0 2 4 8 ( A W A = 37,9 d e g ) . These d a t a c o r r e -s p o n d t o t h e p l o t t e d p o i n t -s o n t h e v e r t i c a l d o t t e d l i n e -s ( 1 ) a n d ( 2 ) i n Fig. 4. I n Fig. 5, t h e l e f t a n d r i g h t d i a g r a m s c o r r e s p o n d t o t h e p o r t a n d s t a r b o a r d sides, i.e., p r e s s u r e a n d s u c t i o n sides, respec-t i v e l y . I n 5 ( 1 ) , a l respec-t h o u g h s l i g h respec-t f l o w s e p a r a respec-t i o n o n respec-t h e s u c respec-t i o n side o f m a i n s a i l is seen, t h e s t r e a m l i n e s o f b o t h sides r u n s m o o t h l y . O n t h e o t h e r h a n d , i n 5 ( 2 ) , c o n s i d e r a b l e f l o w s e p a r a t i o n is o c c u r r i n g , i n p a r t i c u l a r , o n t h e s u c t i o n side o f j i b . T h i s is t h e m a i n r e a s o n f o r t h e r e d u c t i o n o f Ci value i n t h e RANS-based CFD c a l c u l a t i o n at ( 2 ) i n Fig. 4 ( a ) . T h e accurate p r e d i c t i o n o f t h e b o u n d a r y l a y e r f l o w s o n t h e sails a n d t h e t h r e e - d i m e n s i o n a l f l o w s e p a r a t i o n , associated w i t h t h e v o r t e x g e n e r a t i o n , are s t i l l b i g challenges f o r RANS based CFD.
T h e shapes a n d t h r e e - d i m e n s i o n a l c o o r d i n a t e s o f t h e sails are g i v e n i n Table 2. Table 2 ( 1 ) a n d 2 ( 2 ) s h o w t h e cases o f n u m b e r e d p o i n t s ( 1 ) a n d ( 2 ) i n Fig. 4, respectively. T h e figures d e s c r i b e d above t h e tables s h o w t h e sail s e c t i o n p r o f i l e s at 0, 2 0 , 4 0 , 60 a n d 80% o f t h e sail h e i g h t . The t h r e e - d i m e n s i o n a l c o o r d i n a t e s o f each section are g i v e n i n t h e tables. T h e o r i g i n o f t h e c o o r d i n a t e o f sail d y n a m o m e t e r s y s t e m is s h o w n i n Fig. 1. I n t h e tables, t h e p o s i t i v e d i r e c t i o n o f t h e x c o o r d i n a t e is a f t . T h e f o u r lines at t h e t o p o f t h e tables s h o w t h e m e a s u r e d values f o r t h e w i n d a n d s a i l t r i m c o n d i t i o n s , t h e b o a t a t t i t u d e a n d t h e sail p e r f o r m a n c e c o e f f i c i e n t s . I n r e f e r e n c e ( M a s u y a m a et al., 2 0 0 9 ) , t h e same tables are s h o w n w h i c h are m e a s u r e d at v a r i o u s sail t r i m c o n d i t i o n s . These t a b u -l a t e d d a t a m a y p r o v i d e a g o o d b e n c h m a r k f o r t h e v a -l i d a t i o n o f u p w i n d sail CFD i n f u l l scale l e v e l .
4. A e r o d y n a m i c f o r c e v a r i a t i o n d u r i n g t a c l d n g m a n e u v e r a n d t a c l d n g s i m u l a t i o n
4.1. Measurements of aerodynamic force variation during tacldng maneuvers
T a c k i n g o f a s a i l i n g y a c h t is a q u i c k m a n e u v e r i n g m o t i o n a c c o m p a n i e d b y large r o l l i n g angle changes i n a s h o r t p e r i o d o f time. To a n a l y z e t h i s t y p e o f large a m p l i t u d e m o t i o n , a m a t h e m a -t i c a l m o d e l f o r -t h e s i m u l a -t i o n w a s p r o p o s e d b y M a s u y a m a e -t a l . ( 1 9 9 3 , 1 9 9 5 ) . T h e c a l c u l a t i o n m e t h o d w a s a p p l i e d t o a 3 4 - f o o t s a i l i n g c r u i s e r a n d t h e s i m u l a t e d r e s u l t s h o w e d g o o d a g r e e m e n t w i t h t h e m e a s u r e d d a t a f r o m f u l l scale tests. H o w e v e r , i n t h e s e research, t h e m o d e l i n g o f a e r o d y n a m i c f o r c e v a r i a t i o n d u r i n g t a c k i n g w a s i n s u f f i c i e n t d u e t o l a c k o f i n f o r m a t i o n a b o u t t h e s a i l forces. I n o r d e r t o c l a r i f y t h e s a i l f o r c e v a r i a t i o n d u r i n g t a c k i n g
76 K Masuyama / Ocean Engineering 90 (2014) 72-83 cp
^
—
0.9—
0.8—
0.7 0.6—
0.5—
O./t 0.3 - - • 0.2—
0.1 •—
0—
•0.1—
•0.2—
-0.3—
-0.4 -0.6—
-0.6—
•0.7 .0.8 C|) 1 09 O.B 0,7 0.6 0.5 0.4 0.3 0.2 0.1 0 •0.1 -0.2 —]-0.3 — -0.4 •H-0.5 •0.6 -0.7 •0.8 •0,9 -1 (1) at E x p e r i m e n t a l I D 96092335 ( A W A = 3 0 . 7 deg.) cp -l—
0.9—
0.8—
0.7 0.6—
Q.6—
0.4 0.3 0.2 0,1 n u -0.1 -0.2 -0.3 -0.4 -D.6 -D.6 -0.7 -0.8E
r
(2) at E x p e r i m e n t a l I D 96080248 ( A W A = 3 7 . 9 deg.)Fig. 5. Surface pressure and streamlines obtained by RANS-based CFD (1) at Experimental ID 96092335 ( A W A = 3 0 . 7 ° ) (2) at Experimental ID 96080248 ( A W A = 3 7 . 9 ° ) .
m a n e u v e r , t h e m e a s u r e m e n t s w e r e c o n d u c t e d u s i n g fuixn ( M a s u y a m a a n d Fukasawa, 2 0 0 8 , 2010, 2011).
Fig. 6 s h o w s t w o examples o f t h e m e a s u r e d data i n t h e t i m e d o m a i n f o r X'sd, V"sd. K'si a n d d u r i n g t h e t a c k i n g o p e r a t i o n f o r 2 0 s, f r o m five seconds b e f o r e t o 15 s a f t e r t h e start o f t a c k i n g , w h e r e X'sd a n d Y'sd are t h e t h r u s t a n d side f o r c e c o e f f i c i e n t s a l o n g t h e axes o f sail d y n a m o m e t e r system, a n d K'sd a n d N'sd are t h e r o l l a n d y a w m o m e n t c o e f f i c i e n t s a r o u n d t h e same axes. Fig, 6(a) shows t h e case o f t a c k i n g f r o m s t a r b o a r d t o p o r t tack, a n d Fig. 6 ( b ) shows f r o m p o r t to s t a r b o a r d tack. The s c a t t e r i n g o f t h e data at t h e c r o s s i n g p o i n t s o f t h e curves is caused b y t h e c r e w a c t i o n o n t h e d y n a m o m e t e r f r a m e i n releasing a n d t r i m m i n g t h e j i b sheet d u r i n g
t a c k i n g . I n t h e m e a s u r e d data, t h e i n e r t i a forces and m o m e n t s d u e t o t h e mass o f t h e d y n a m o m e t e r f r a m e are i n c l u d e d . T h e s e e f f e c t s clearly appear at t h e s t a r t i n g a n d finishing stage o f t h e t a c k i n g m a n e u v e r , b u t are n o t so s i g n i f i c a n t a t t h e m i d d l e stage. H e n c e t h e m e a s u r e d data are i n d i c a t e d o n l y s u b t r a c t i n g t h e f o r c e s a n d m o m e n t s d u e t o t h e g r a v i t y force a c t i n g o n t h e d y n a m o m e t e r f r a m e u s i n g m e a s u r e d heel angle at e v e r y m o m e n t . Fig. 7 s h o w s t h e v a r i a t i o n o f sail f o r c e c o e f f i c i e n t s d u r i n g t a c k i n g as a f u n c t i o n o f t h e h e a d i n g angle o f t h e b o a t \ i f , w h e r e V / = 0 ° m e a n s h e a d i n g i n t h e t r u e w i n d d i r e c t i o n . D u r i n g t a c k i n g , t h e j i b sheet w a s released j u s t b e f o r e t h e j i b w a s b a c k w i n d e d o n t h e n e w t a c k i n o r d e r t o m i n i m i z e l u f f i n g o f t h e j i b a n d loss o f
Y, Masuyama / Ocean Engineering 90 (2014) 72-83
Table 2
Sail secl:ion profiles, measured experimental data and three-dimensional coordinates of the sails for the cases of numbered points (1) and (2) in Fig. 4, respectively.
(1) 96092335
30./ 15.E 8.E 6.5 15.- S.0 CL Cx CY XOEDTI] Z C E M 0.21 0.5C 1.3£ 0.41 4.17 %of 1 3 0 ^ i b M a i n s a i l heit X y z X y z -3.78C 0.00 0.00 0.046 O.OOO 1.320 -2.812 0.136 O.OOO 0.934 O.OOO 1.320 0 -1.843 0.272 O.OOO 1.822 O.OOO 1.320 % -0.875 0.408 0.000 2.710 0.000 1.320 0.094 0.544 0.000 3.598 O.OOO 1.320 1.062 0.681 0.000 4.486 0.000 1.320 -2.998 0.000 2.140 0,133 0.000 3.820 -2.305 0.429 2.140 0.888 0.176 3.820 20 -1.568 0.667 2.140 1.645 0.322 3.820 % -0.805 0.795 2.140 2.406 O.400 3.820 -0.027 0.861 2.140 3.173 0.363 3.820 0.760 0.886 2.140 3.947 0.222 3.820 -2.215 0.000 4.280 0.221 0.000 6.320 -1.771 0.442 4.280 0.834 0.227 6.320 40 -1.272 0.719 4,280 1.452 0.405 6.320 SS -0.723 0.850 4.280 2.081 0.483 6.320 -0.145 0.898 4.280 2.722 0.442 6.320 0.448 0.898 4.280 3.371 0.331 6.320 -1.433 0.000 6.420 0.308 0.000 8.820 -1.186 0.332 6.420 0.761 0.218 8.820 60 -0.893 0.570 6.420 1.222 0.389 8.820 % -0.552 0.715 6.420 1.699 0.470 8.820 -0.176 0.790 6.420 2.191 0.462 8.820 0.217 0.832 6.420 2.691 0.410 8.820 -0.650 0.000 8.560 0.396 0.000 11.320 -0.541 0.172 8.560 0.651 0.144 11.320 80 -0.414 0.318 8.560 0.914 0,261 11.320 X -0.255 0.419 8.560 1.190 0.330 11.320 -0.073 0.486 8.560 1.476 0.362 11.320 0.122 0.535 8.560 1.768 0.374 11.320 0.132 0.000 10.700 0.483 0.000 13.820 0.144 0.016 10.700 0.511 0.012 13.820 100 0.159 0.030 10.700 0.538 0.023 13.820 % 0.173 0.044 10.700 0.567 0.033 13.820 0.189 0.056 10.700 0.595 0.042 13.820 0.207 0.066 10.700 0.624 0.051 13.820(2) 96080248
K:,'ZjrjniiitMiri7;iji!jjit:iiü!^im^
37.£ 14.5 1.2 7.Ë 19.6 6,0 CL CD Cx Cy X O E D " ] Z O E N 1.58 0.45 0.62 1.52 0.34 4.17 !4of I S O K J i b M a i n s a i helt X y z X y z -3.780 O.OOO 0.000 0.046 0.000 1.320 -2.812 0.136 0.000 0.934 0.015 1.320 0 -1.843 0.272 0.000 1.822 0.031 1.320 % -0.875 0.408 0.000 2.710 0.046 1.320 0.094 0.544 0.000 3.597 0.062 1.320 1.062 0.681 0.000 4.485 0.077 1.320 -2.998 0.000 2.140 0.133 0.000 3.820 -2.314 0.461 2.140 0.891 0.150 3.820 20 -1.597 0.750 2.140 1.651 0.267 3.820 % -0.841 0.840 2.140 2.414 0.331 3.820 -0.062 0.810 2.140 3.182 0.333 3.820 0.728 0.724 2.140 3.954 0.262 3.820 -2.215 0.000 4.280 0.221 0.000 6.320 -1.769 0.437 4.280 0.829 0.239 6.320 40 -1.274 0.729 4.280 1.445 0.423 6.320 % -0.726 0.863 4.280 2.074 0.520 6.320 -0.145 0.899 4.280 2.717 0.511 6.320 0.450 0.892 4.280 3.368 0.442 6.320 -1.433 0.000 6.420 0.308 0.000 8.820 -1.218 0.362 6.420 0.757 0.230 8.820 60 -0.940 0.615 6.420 1.218 0.397 8.820 % -0.601 0.763 6.420 1.697 0.482 8.820 -0.230 0.854 6.420 2.187 0.504 8.820 0.157 0.918 6.420 2.687 0.481 8.820 -0.650 0.000 8.560 0.396 0.000 11.320 -0.565 0.191 8.560 0.656 0.128 11.320 80 -0.445 0.339 8.560 0.921 0.241 11.320 % -0.289 0.444 8.560 1.193 0.327 11.320 -0.113 0.527 8.560 1.478 0.368 11.320 0.071 0.597 8.560 1.771 0.377 11.320 0.132 0.000 10.700 0.483 0.000 13.820 0.142 0,018 10.700 0.511 0.011 13.820 100 0.154 0.034 10.700 0.539 0.022 13.820 % 0.167 0.049 10.700 0.567 0.032 13.820 0.181 0.064 10.700 0.596 0.041 13.820 0.196 0.077 10.700 0.625 0.049 13.82078 Y. Masuyama / Ocean Engineenng 90 (20J4) 72-83 e 1.0 0.5 k 0.0 -0.5 -1.0 0.5 è 0-0 3 0 2 0 10 -10 -20 -30 -0.5 j 1 1
s''—
— 1 p -60 -40 -20 2 0 4 0 3 0 2 0 10 0 -10 - 2 0 -30 3 0 2 0 10 0 -10 -20 -30(l)Tacking from starboard to port tack
6 0 <1> - * • TA
C
1.0 g 1.0 0.5 0.0 •0.5 •1.0 I p y ^s
i *\ -60 "40 ' 2 0 2 0 30 2 0 10 0 -10 -20 -30 4 0 6 0 </> -/A h O.E % 0.0 •0.5 i 1 1 S—
— \ P . 1 i n ... T -60 - 4 0 -20 2 0 4 0 3 0 2 0 1 0 10 - 2 0 -30 3 0 2 0 1 0 O -10 -20 -30 6 0 <l> — yK(2) Tacking from port to starboard tack
Fig. 7. Variation of sail force coefficients during tacl<ing operation as a ftinction of heading angle of boat (1 JTacking from starboard to port tack (2) Tacldng firom port to starboard tad<. w i n d p o w e r . I n Fig. 7 ( 1 ) , t h e curves s h o w t h e r e s u l t s o f 10 t a c k i n g m e t e r c o o r d i n a t e s y s t e m . The v a r i a t i o n s s t a r t f r o m close h a u l e d cases f r o m s t a r b o a r d t o p o r t tack. It s h o u l d be n o t e d a g a i n c o n d i t i o n o f s t a r b o a r d t a c k u n t i l t h e b o a t is o n p o r t tack, (i.e., t h a t forces a n d m o m e n t s are s h o w n u s i n g t h e sail d y n a m o - f r o m v / = - 4 5 ° t o 4 5 ° ) . T h e c o r r e s p o n d i n g A W A , f r o m ) ' / i = 3 0 °
V; Masuyama / Ocean Engineering 90 (2014) 72-83 79
t o - 3 0 ° , are also i n d i c a t e d i n t h e second abscissa i n t h e figure. Fig. 7 ( 1 )(a) s h o w s t h e v a r i a t i o n o f X'sd- W h e n t h e b o a t heads d i r e c t l y i n t o t h e w i n d , X'sd becomes a b o u t - 0 . 1 , (i.e., d r a g f o r c e c o e f f i c i e n t ) . Fig, 7 ( l ) ( b ) - ( l ) ( d ) s h o w s t h e forces a n d m o m e n t s b e c o m e zero n o t at 1 ^ = 0 ° , b u t a r o u n d )//-=10°, w h i c h indicates a d e l a y i n t h e v a r i a t i o n o f forces a n d m o m e n t s c o m p a r e d t o t h e c h a n g e o f h e a d i n g angle. This c o u l d be caused b y t h e sail filling w i t h w i n d due t o t h e y a w i n g m o t i o n f r o m t h e f o r m e r t a c k to y/ = 1 0 ° o n t h e n e w tack w h e n t h e j i b sheet w a s released. Fig. 7 ( 2 ) s h o w s t h e same v a r i a t i o n f o r t h e case o f p o r t t a c k t o s t a r b o a r d t a c k . I n t h i s case, t h e values o f Y'sd, K'sd a n d N'sd b e c o m e zero at a r o u n d y/= -10°, a n d t h e v a r i a t i o n o f forces a n d m o m e n t s are a l m o s t s y m m e t r i c a l t o Fig, 7 ( 1 ) , F r o m t h i s r e s u l t , i t can be c o n s i d e r e d t h a t t h e bias o f t h e zero crossing p o i n t o f t h e forces a n d m o m e n t s at t h e t a c k i n g m a n e u v e r is s y m m e t r i c a l .
assumed t o v a r y l i n e a r l y a l o n g t h e lines d e t e r m i n e d f r o m t h e results o f Fig, 7(a) a n d ( b ) . Stage C is t h e range o f ^ ^ = - 1 0 ° t o - 3 0 ° . I n t h i s r e g i o n , t h e basic p a t t e r n o f t h e c o e f f i c i e n t s is expressed as basic p e r f o r m a n c e curves. H o w e v e r , i t m a y t a k e several seconds t o recover t o t h e basic curves d u e t o t h e delay o f t r i m m i n g t h e sails f o r t h e n e w tack c o n d i t i o n . T h e r e f o r e , t h e coefficients are a s s u m e d to increase f r o m t h e l o w e s t values to t h e basic curve values w i t h elapsed t i m e . The r e c o v e r y t i m e w a s c h o s e n f r o m 5 t o 10 s b y t a k i n g t h e s i m u l a t e d heel angle c o r r e s p o n d i n g t o the measured one. Fig. 8 ( b ) s h o w s t h e case o f t a c k i n g from p o r t t o starboard tack. I n t h i s case, t h e v a r i a t i o n p a t t e r n proceeds i n t h e opposite d i r e c t i o n . The sail forces a n d m o m e n t s expressed i n eq. ( 1 ) are used f o r t h e equations o f m o t i o n i n t h e f o l l o w i n g chapter.
4.3. Equations of motion for tacking simulation
4.2. Model of sail force variation for taciiing simulation
Let us d e f i n e the m o d e l o f sail f o r c e v a r i a t i o n f o r t h e t a c k i n g s i m u l a t i o n as b o l d lines i n Fig. 8 r e f e r r i n g t o t h e m e a s u r e d data i n Fig. 7. Fig. 8(a) shows the case o f t a c k i n g f r o m s t a r b o a r d to p o r t tack. The abscissa indicates A W A (YA). I n t h e m o d e l , t h e basic sail p e r f o n m a n c e curves o f X'SQ a n d Y'SQ are d i v i d e d i n t o t h r e e stages. Stage A is t h e range o f YA t h a t is greater t h a n 2 0 ° . I n t h i s r e g i o n , the c o e f f i c i e n t s v a r y w i t h YA a c c o r d i n g t o t h e basic curves. Stage B is t h e range o f YA= 2 0 ° to - 1 0 ° . I n t h i s r e g i o n , t h e c o e f f i c i e n t s are
a
X ' s o , Y ' s o b w i t h X ' s o , Y ' E O I n o r d e r t o express t h e large a m p l i t u d e m o t i o n s u c h as a t a c k i n g m a n e u v e r o f a s a i l i n g yacht, t h e a u t h o r e m p l o y e d e q u a -t i o n s o f m o -t i o n expressed b y -t h e h o r i z o n -t a l b o d y axis s y s -t e m i n t r o d u c e d b y H a m a m o t o a n d A k i y o s h i ( 1 9 8 8 ) , T h e o r i g i n o f t h e c o o r d i n a t e s y s t e m is o n t h e C,G, o f t h e b o a t w h i c h is s h o w n i n Fig. 1. T h e x - a x i s lies a l o n g t h e c e n t e r i i n e o f t h e b o a t o n t h e s t i l l w a t e r p l a n e a n d is p o s i t i v e f o r w a r d . The y - a x i s is p o s i t i v e t o s t a r b o a r d i n t h e s t i l l w a t e r p l a n e . T h e zaxis is p o s i t i v e d o w n -w a r d s . I n t h i s c o o r d i n a t e s y s t e m , t h e m a n e u v e r i n g m o t i o n o f t h e b o a t a n d a e r o / h y d r o - d y n a m i c forces a c t i n g o n i t c a n be expressed i n t h e h o r i z o n t a l p l a n e e v e n t h o u g h t h e b o a t heels. B o t h a d d e d mass a n d a d d e d m o m e n t o f i n e r t i a , w h i c h are r e f e r e n c e d t o t h e b o d y axes fixed o n t h e boat, can be o b t a i n e d b y t h e c o o r d i n a t e t r a n s f o r m a t i o n . T h e n , t h e e q u a t i o n s o f m o t i o n expressed i n t h e h o r i z o n t a l b o d y axis s y s t e m f o r t h e m o t i o n s o f surge, sway, r o l l a n d y a w are d e r i v e d as f o l l o w s . T h e l e f t sides are forces a n d m o m e n t s d u e t o t h e mass a n d a d d e d masses o f t h e boat, a n d t h e r i g h t sides are fluid d y n a m i c forces a n d m o m e n t s a c t i n g o n t h e h u l l a n d sail w i t h r e f e r e n c e t o t h e h o r i z o n t a l b o d y axes. surge (m + mx) U-(m+myCos^(p+mzSin'^(p) Vyr = Xo+XH+Xvy,V\j/+XR+Xs ( 1 ) s w a y ( m - f m y C o s 2 ( / > - f - i n z S i n ^ < ^ ) V+ ( m + m x ) Uyr +2(jnz-my) sin (p cos(p- Vcj)
= YH + Y;i,4>+Yy,yf+YR + Ys r o l l Qxx+},«)'^-{{lyy+]yy)-{lzz+hz)} s i n (p COS (p'ljr^ = KH+Kx^+KR+Ks-mgGM s i n tp (2) (3)
Fig. 8. Model of sail force variation during tacking maneuver for tacking simulation (a) Tacking from starboard to port tack (b) Tacking from port to starboard tack.
y a w
iihy +Jyy) Sin^4> + (hz-l-Jzz) cos V ) 2 { ( / y y +Jyy)
-(Izz+Jzz)) s i n (p cos (p-y/^
==NH+N^y/+NR+Ns ( 4 ) The d e r i v a t i o n o f t h e s e e q u a t i o n s a n d c a l c u l a t i o n m e t h o d o f e a c h
t e r m are d e s c r i b e d i n d e t a i l i n references ( M a s u y a m a a n d Fukasawa, 2010, 2011),
4.4. Comparison between measured and simulated results
The s i m u l a t i o n m e t h o d was applied to several boats and t h e results s h o w e d g o o d agreement w i t h the measured data. I n t h i s report, the cases o f Fujin and Fair V are s h o w n i n t h e f o l l o w i n g sections, T l i e f a i r V i s a 3 4 - f b o t sailing cruiser, w h i c h w a s designed b y the a u t h o r a n d used f o r the first measurement o f tacldng maneuver.
80 Y. Masuyama / Ocean Engineering 90 (20M) 72-83
The principal dimensions and added masses o f Fujin a n d Fair V are s h o w n i n Table 3. The Runge-Kutta m e t h o d was e m p l o y e d to calculate t h e equations o f m o t i o n . The r o l l i n g a n d y a w i n g m o t i o n s were
Table 3
Principal dimensions and added masses of fujin and Fair V.
Boat name Fujin F a i r V
Class YR 10.3 KIT 34
LOA [mj 10.35 10.39
LWL (L) [ml 8.80 8.55
BiMAX [mj 3.37 3.04
BWL (B) [mj 2.64 2.42
Draft (Canoe body) [mj 0.44 0.41
Draft (Fin keel) (D) [mj 2.02 1.96
Displacement* [kgj 4410 3780
CM [mj 1.45 1.31
Xce (from IVIidsiiip) jm] - 0 . 6 0 - 0 . 1 0
IR (from C.G.) [mj 4.40 4.22 Sail area(lVIainsall) jm^j 33.2 30.2 Sail areaQib) jm^j 26.1 29.5 xgcE (from C.G.) [ml 0.67 0.87 zgcE (from C.G.) [ml - 6 1 3 - 6 . 2 0 m„ [kg] 160 140 my (Hull, Sail) [kg] 2130, 280 2410, 280 mj [kg] 12,000 10,400 / » [kg m^'j 17,700 12,500 ^yy [kg m^l 33,100 22,600 Izz [kg m^l 17,200 11,300 ] ^ (Hull, Sail) [kgm^l 7200, 8100 8600, 8100 Jyy [kg m^l 42400 34600 [kgm^j 6700 7600
* Including crew weight.
calculated a r o u n d the C,G, o f the boat. I n p u t data f o r the s i m u l a t i o n is t r u e w i n d velocity and the measured time history o f r u d d e r angle d u r i n g tacldng maneuver at increments o f 0,1 s.
4.4.1. Results of Fujin
Fig. 9 s h o w s t h e c o m p a r i s o n b e t w e e n m e a s u r e d a n d s i m u l a t e d results o f Fujin. Fig. 9 ( 1 ) s h o w s t a c k i n g f r o m s t a r b o a r d t o p o r t tack, a n d 9 ( 2 ) s h o w s t a c l d n g f r o m p o r t t o s t a r b o a r d tack. The s a i l f o r c e v a r i a t i o n s i n Fig. 6(a) a n d ( b ) c o r r e s p o n d t o these cases, respectively. The i n d i c a t e d results w e r e r e c o r d e d f o r 3 5 s, b e g i n -n i -n g 5 s b e f o r e t h e s t a r t o f t a c k i -n g . Fig. 9 ( 1 )(a) s h o w s t h e b o a t t r a j e c t o r i e s . S o l i d circles i n d i c a t e t h e p o s i t i o n s o f m e a s u r e d C.G. o f t h e b o a t a t each second, w h i l e o p e n circles i n d i c a t e t h e s i m u l a t e d p o s i t i o n s . The i l l u s t r a t i o n s o f t h e s m a l l b o a t s y m b o l i n d i c a t e t h e h e a d i n g angle i f f every t h r e e seconds. The w i n d b l o w s f r o m t h e right side o f t h e f i g u r e a n d t h e g r i d spacing is t a k e n as 15 m . Fig. 9 ( l ) ( b ) s h o w s t h e time h i s t o r i e s o f r u d d e r angle <5, h e a d i n g a n g l e ifr, h e e l angle q) a n d b o a t v e l o c i t y Vjj. T h e solid l i n e s are m e a s u r e d d a t a a n d t h e d o t t e d l i n e s are s i m u l a t e d data. I n Fig. 9 ( 1 )(b) a n d ( 2 ) ( b ) , t h e p a t t e r n s o f r u d d e r angle v a r i a t i o n can be c o n s i d e r e d as s t a n d a r d f o r t a c k i n g m a n e u v e r s . As s h o w n , t a c k i n g w i t h a y a w i n g m o t i o n o f 9 0 ° is c o m p l e t e d i n 7 - 8 s. T h e b o a t v e l o c i t y decreases a b o u t 30%, a n d t h e b o a t t a k e s a b o u t 15 s t o recover t o t h e p r e v i o u s v e l o c i t y a f t e r t h e y a w i n g m o t i o n is c o m p l e t e d . The m e a s u r e d t i m e h i s t o r i e s o f y/ a n d cp i n d i c a t e t h e d e l a y o f zero c r o s s i n g p o i n t o f ^ c o m p a r e d w i t h y/. This m i g h t b e caused b y t h e sail f i l l i n g w i t h w i n d d u e t o t h e y a w i n g m o t i o n u n t i l a r o u n d yf=W o n t h e o p p o s i t e t a c k as s h o w n i n Fig. 7. T h e s i m u l a t e d time h i s t o r i e s s h o w a s l i g h t d e l a y w h e n c o m p a r e d t o t h e m e a s u r e d data. I n p a r t i c u l a r , t h e delay o f t h e s i m u l a t e d h e e l
a
m e a s i s i m u l i r e d a t e d\
U T = 5 7 m / s\
\
start 0 t a c k i n j f ^ 4 * 15m start o f t a c k i n g C ï > meas\ simul ired atedr
Start 0 tackin/
f
U T = 5 4 m / sV f
U T = 5 4 m / s 15m [deg] 7 0 start o f t a c k i n g 35 S m/s] -5 -4 -3 V B -2 -1 0 - 3 5 - 7 0 (fy. H 0 : H Ö: R eading eel A n f udder h Angle le n g l e_±_
K I V B : Ï oat V e l o c i t y 8 y Wr' 8 " V B V B [m/s] 5 - 5 0 5 10 15 e l a p s e d time 2 0 2 5 V B 5 10 15 e l a p s e d time ( 1 ) F r o m s t a r b o a r d t o p o r t t a c k ( 2 ) F r o m p o r t t o s t a r b o a r d t a c kFig. 9. Measured and simulated results of tacking maneuver of Fujin (1) From starboard to port tack (2) From port to starboard taclc. 3 0 [ s e c ]
Y. Masuyama / Ocean Engineering 90 (2014) 72-83 81 m e a s i s i m u l ired i t e d U T = 4
A
-8r (l/s\
start 0 t a c k i n j r 8r 15m measT s i m u l i r e d i t e d4
o start 0 t a c k i n/
•f
U T = 4 9 E i / sV
r 9 E 1 5 m start o f t a c k i n g [deg] 7 0 start o f t a c k i n g 35 5 - 3 5 5 10 15 e l a p s e d time 2 0 2 5 3 0 [ s e c ] - 7 0 0 : H cp. H 5 : R e a d i n g e e l A n g udder A \ n g l e le n g l e V B : I ioat V e l o c i t y \ '^A \ '^A V B [m/s] 5 0 2 0 ( 1 ) F r o m s t a r b o a r d t o p o r t t a c k 5 10 15 e l a p s e d time ( 2 ) F r o m p o r t t o s t a r b o a r d t a c k 2 5 V B 3 0 [ s e c ]Fig. 10. IWeasured and simulated results of tacking maneuver of f a i r V (1) From starboard to port tack (2) from port to starboard tack
angle is r e l a t i v e l y large. T h i s m i g h t be caused b y t h e over-e s t i m a t i o n o f t h over-e d a m p i n g c o over-e f f i c i over-e n t f o r rolling./Cp. For t h i s p o i n t f u r t h e r i n v e s t i g a t i o n m i g h t be necessary. H o w e v e r , t h e s i m u l a t e d results o f v e l o c i t y d e c r e m e n t s h o w a g r e e m e n t w i t h t h e m e a s u r e d results. This suggests t h a t t h e m o d e l o f sail f o r c e v a r i a t i o n p r o p o s e d i n t h i s r e p o r t is adequate f o r t h e t a c k i n g s i m u l a t i o n . I n Fig. 9 ( 1 )(a) a n d ( 2 ) ( a ) , a l t h o u g h t h e s i m u l a t e d t r a j e c t o r i e s s h o w s l i g h t l y l a r g e r t u r n i n g radiuses t h a n t h e m e a s u r e d t r a j e c t o r i e s , t h e s i m u l a t e d results s h o w a g r e e m e n t w i t h t h e m e a s u r e d values o v e r a l l , 4.42. Results of Fair V Fig. 10 s h o w s t h e c o m p a r i s o n b e t w e e n m e a s u r e d a n d s i m u -l a t e d resu-lts o f Fair V. T h e c o n t e n t s o f these f i g u r e s are i d e n t i c a -l t o Fig. 9. I n t h e s e cases, t h e r u d d e r angle v a r i a t i o n s i n t h e f i r s t stage are r e l a t i v e l y s m a l l . These cause t h e delay o f y a w i n g m o t i o n o f t h e b o a t . Hence i t takes m o r e t h a n 10 s t o c o m p l e t e t h e t a c k i n g m a n e u v e r . O n t h e o t h e r h a n d , t h e s i m u l a t e d r e s u l t s s h o w a p r o m p t response t o t h e r u d d e r angle v a r i a t i o n . T h e r e f o r e t h e s i m u l a t e d t i m e h i s t o r i e s v a r y s l i g h t l y e a r l i e r c o m p a r e d w i t h t h e m e a s u r e d h i s t o r i e s . By t h e same r e a s o n i n g , t h e s i m u l a t e d t r a j e c -t o r i e s i n Fig. 1 0 ( 1 )(a) a n d ( 2 ) ( a ) s h o w s m a l l e r -t u r n i n g radiuses t h a n t h e m e a s u r e d t r a j e c t o r i e s . Overall, a l t h o u g h t h e t i m i n g o f b o a t m o t i o n i n d i c a t e d i n t h e s i m u l a t e d t i m e h i s t o r i e s s h o w s a s l i g h t discrepancy, t h e t e n d e n c y a n d a m o u n t o f v a r i a t i o n o f t h e b o a t m o t i o n i n d i c a t e g o o d agree-m e n t w i t h t h e agree-m e a s u r e d data, i n c l u d i n g t h e d e c r e agree-m e n t o f b o a t v e l o c i t y .
5. Role o f f u l l scale tests as the b r i d g e b e t w e e n m o d e l tests a n d C F D
W i n d T u n n e l tests using m o d e l sails are c o m m o n l y p e r f o r m e d at the Reynolds n u m b e r (Re) region o f a r o u n d 2 x 10^ to 5 x 10^. This region is referred t o as the critical Reynolds n u m b e r range, w h e r e t h e b o u n d a i y layer f l o w turns f r o m l a m i n a r t o t u r b u l e n t , causing the d r a g and l i f t coefficients change drastically. H o e m e r and Borst (1975) shows e x p e r i m e n t a l results o f w i n g sections i n t h i s region and indicates t h a t the m a x i m u m l i f t coefficient varies as a ftinction o f the Reynolds number, camber ratio and nose-radius ratio, and also can be v e r y sensitive to t h e test conditions. F r o m t h e author's experience o f w i n d t u n n e l tests (Tahara et al., 2012), the unexpected a n d unstable deviation o n measured data occurred i n particular i n the case o f d o w n w i n d sail. Normally, a spinnaker has a large camber and a sharp leading edge w h i c h w o r k s at a h i g h entrance angle. This causes the laminar-type separation at the suction side o f t h e leading edge at t h e l o w Reynolds n u m b e r region. W h e n this separation area spreads over the surface o f the suction side, t h e drag and l i f t coefficients change drastically. The author sometimes experienced t h a t the slight shape change o f a spinnaker by sheet t r i m m i n g caused serious d e v i a t i o n o n measured data. Therefore, i t should be considered t h a t the w i n d t u n n e l test i n this Reynolds n u m b e r r e g i o n has t o be p e r f o r m e d v e r y carefully. O n the other hand, f o r the f u l l scale boat, the sails w o r k i n the Reynolds n u m b e r o f almost greater t h a n 1 x 10^. I n this region, a l t h o u g h t h e effect o f critical Reynolds n u m b e r still remains, the effect o n the measured data m a y be less t h a n t h e case o f w i n d t u n n e l tests. Recently, Viola and Flay (2012) measured t h e pressure d i s t r i b u t i o n o n t h e surface o f f u l l scale d o w n w i n d sails d u r i n g sea tests using a
82 Y. Masuyama / Ocean Engineering 90 (2014) 72-83
Platu25-dass yacht. The results w e r e compared w i t h the measured data by w i n d t u n n e l tests, and showed very interesting differences i n the pressure distributions near the leading edge. The author t h i n k s this is the f i r s t report w h i c h points o u t the differences o f pressure d i s t r i b u t i o n o n the d o w n w i n d sails between f u l l scale a n d scale m o d e l . It can be considered that this fact indicates the importance o f f u l l scale measurements f o r t h e developments o f d o w n w i n d sails. A sail d y n a m o m e t e r boat m a y provide m o r e precise i n f o r m a t i o n n o t o n l y about pressure distribution, b u t also aerodynamic forces and sail shapes simultaneously i n f u l l scale level.
Investigation o f effect o n the sail aerodynamic forces by d y n a m i c m o t i o n o f the boat is another i m p o r t a n t research target o f the f u l l scale test using a sail d y n a m o m e t e r b o a t The research o f aerodynamic force v a r i a t i o n d u r i n g tacldng maneuver should be broadened to investigate t h e best tacldng procedure. The motions o f p i t c h i n g and rolling o f a boat also have a serious effect o n sail performance. For t h e research o f these effects, a sail d y n a m o m e t e r boat w i l l p r o v i d e essential i n f o r m a t i o n .
W h e n the sail tests w e r e p e r f o r m e d using Fujin, i t w a s d i f f i c u l t t o measure the shape o f sail such as balloon spinnaker s i m u l t a n e o u s l y w i t h aerodynamic forces. However, recently w e can easily e m p l o y h i g h p e r f o r m a n c e d i g i t a l cameras and 3 - d i m e n s i o n a l shape analyz-ing systems. Moreover, t h e developments o f measurement systems such as s m a l l gyroscope, GPS sensor, electronics transmitter, etc, can also p r o v i d e us good o p p o r t u n i t i e s f o r c a r r y i n g o u t sea tests easily. I t is w o r t h e m p h a s i z i n g t h a t the tests using a sail d y n a m o m e t e r boat can p r o v i d e t h e u l t i m a t e v a l i d a t i o n data f o r CFD i n f u l l scale level. Now, a n e w g e n e r a t i o n sail d y n a m o m e t e r boat is b e i n g prepared b y Professor Fabio Fossati at Politecnico d i M i l a n o (Fossati et al„ 2013). W e are l o o k i n g f o r w a r d to t h e results o f this boat f r o m tests at Lake Como i n Italy. 6. C o n c l u s i o n s T h e w o r k a c h i e v e d w i t h t h e s a i l d y n a m o m e t e r b o a t Fujin w a s r e p o r t e d . A t f i r s t , t h e s a i l shapes a n d p e r f o r m a n c e f o r u p w i n d c o n d i t i o n s w e r e m e a s u r e d i n s t e a d y s a i l i n g c o n d i t i o n s . T h e r e s u l t s w e r e c o m p a r e d w i t h t h e n u m e r i c a l c a l c u l a t i o n s u s i n g t h e m e a s u r e d s a i l shapes as t h e i n p u t data. T h e d a t a b a s e o f t h r e e - d i m e n s i o n a l c o o r d i n a t e s o f t h e sail shapes w a s also t a b u l a t e d w i t h t h e a e r o d y n a m i c c o e f f i c i e n t s . T h e s a i l s h a p e d a t a b a s e a n d t h e c o m p a r i s o n w i t h t h e n u m e r i c a l c a l c u l a t i o n s i n d i c a t e d i n t h i s r e s e a r c h p r o v i d e a g o o d b e n c h m a r k f o r t h e v a l i d a t i o n o f s a i l CFD i n f u l l scale l e v e l . T h e n , t h e a e r o d y n a m i c f o r c e v a r i a t i o n d u r i n g t a c k i n g m a n e u v e r s w a s m e a s u r e d b y Fujin, a n d a n e w s i m u l a t i o n m o d e l o f t a c k i n g m a n e u v e r w a s p r o p o s e d . T h e s i m u l a t e d r e s u l t s s h o w e d g o o d a g r e e m e n t w i t h t h e m e a s u r e d d a t a . F i n a l l y , t h e scale e f f e c t p r o b l e m o f w i n d t u n n e l t e s t s w a s discussed. W i n d t u n n e l t e s t s u s i n g m o d e l sails are p e r f o r m e d at t h e r e g i o n o f c r i t i c a l R e y n o l d s n u m b e r . T h e r e -f o r e , t h e w i n d t u n n e l t e s t i n t h i s R e y n o l d s n u m b e r r e g i o n h a d t o be p e r f o r m e d v e r y c a r e f u l l y . O n t h e o t h e r h a n d , t h e f u l l scale tests u s i n g a s a i l d y n a m o m e t e r b o a t are f r e e f r o m scale e f f e c t p r o b l e m s a n d a p p e a r m o r e p r o m i s i n g .
A c l m o w l e d g m e n t s
The a u t h o r wishes t o t h a n k Professor T. Fukasawa a t Osaka Prefecture University and Dr. Y. Tahara at N a t i o n a l M a r i t i m e Research Institute o f Japan f o r t h e i r c o n t r i b u t i o n s as co-researchers. The author also w o u l d like to t h a n k M r . H . M i t s u i , t h e f o r m e r h a r b o r master o f the A n a m i z u Bay Seminar House o f Kanazawa Institute o f Technology, f o r his assistance w i t h the sea trials. H e l p w i t h the sea trials g i v e n by graduate and undergraduate students o f t h e Kanazawa Institute o f Technology is also a c l m o w l e d g e d .
Appendb<. C a l c u l a t i o n o f v i s c o u s d r a g a c t i n g o n the sails a n d r i g g i n g
Since t h e v o r t e x l a t t i c e m e t h o d ( V L M ) can o n l y give i n d u c e d d r a g CD,-, t h e viscous d r a g a c t i n g o n t h e sails a n d rigging w a s c a l c u l a t e d a c c o r d i n g t o M i l g r a m et al, ( 1 9 9 3 ) .
For u p w i n d s a i l i n g c o n d i t i o n , t h e t o t a l d r a g c o e f f i c i e n t CD can be described as f o l l o w s :
CD=AXCI + CDP
(Al)
w h e r e t h e f i r s t t e r m i n d i c a t e s t h e i n d u c e d d r a g , CD,-, a n d t h e second t e r m indicates v i s c o s i t y a n d p a r a s i t i c d r a g . Cop, a c t i n g o n t h e sails a n d rigging. The v a l u e o f Cpp w a s o b t a i n e d as f o l l o w s :
( i ) Calculate t h e v a l u e o f Ce = Ca/cl u s i n g t h e c a l c u l a t e d results o f V L M .
( i i ) O b t a i n t h e m e a n v a l u e o f C^ at several ranges o f A W A .
( i n t h i s case, Ce = 0 . 0 8 1 f o r t h e A W A range f r o m 2 0 ° t o 3 0 ° , a n d 0.083 f r o m 3 0 ° t o 4 0 ° )
( i i i ) Plot t h e e x p e r i m e n t a l values o f Co vs.Cf f o r several ranges o f A W A as i n Fig. A l ( a ) a n d ( b ) .
( i v ) S u b s t i t u t i n g t h e value o f Ce f o r A i n Eq. ( A - 1 ) , calculate t h e v a l u e o f Cop b y a p p l y i n g a least square m e a n m e t h o d f o r t h e m e a s u r e d values o f CD a n d CL. The c a l c u l a t e d r e s u l t is s h o w n
b
e. Starboard tack o Port tack a Starboard tack o Port tack
Fig. A t . Relation between Co and CÏ for a 10° range of AWA. (a) AWA range; 2 0 - 3 0 ° and (b) AWA range; 3 0 - 4 0 °Masuyama / Ocean Engineering 30 (2014) 72-83 83
as a s t r a i g h t l i n e i n Fig. A l ( a ) a n d ( b ) , a n d t h e evaluated values o f Cpp are 0.070 a n d 0.096, respectively.
( v ) F r o m t h i s result, t h e value o f Cop was f o r m u l a t e d f o r t h e u p w i n d c o n d i t i o n as f o l l o w s ;
CBP = 0,0026 )'^ + 0 . 0 0 5 ( A 2 )
w h e r e is a p p a r e n t w i n d angle i n degrees.
( v i ) CD is calculated b y Co = Ca + Ccp u s i n g t h e results o f V L M .
R e f e r e n c e s
Fossati, F., Muggiasca, S., Bayati, I., Bertorello, C , 2013. Lecco innovation hub sailing yacht lab project - a sailing research infrastructure. In: Proceedings of the 3rd International Conference on Innovation in High Performance Sailing Yachts, Lorient, France, pp, 255-260.
Ful<asawa, T., 1993. Aeroelastic transient response of 3-dimensional flexible sail. In: Proceedings of the Aero-Hydroelasticity, ICAHE'93.
Hamamoto, M., Akiyoshi, T., 1988. Study on ship modons and capsizing in following seas (1st Report). J. Soc. Naval Archit. Jpn. No.l47, 173-180,
Hansen, H., Jackson, P„ Hochkirch, K., 2003, Comparison of wind tunnel and full-scale aerodynamic sail force. Int.J. Small Craft Technol. (IJSCT) 145 (Part B l ) , Hochkirch, K., Brandt, H„ 1999. Fullscale hydrodynamic force measurement on the
Berlin sailing dynamometer. In: Proceedings of the 14th Chesapeake Sailing Yacht Symposium, SNAME, pp. 33-44.
Hoerner, S.F., Borst, H.V., 1975. Fluid-dynamic lift, Hoerner Fluid Dyn., 4-12. Krebber, B., Hochkirch, K., 2006. Numerical invesUgation on the effects of trim for a
yacht r i g In: Proceedings of the 2nd High Performance Yacht Design Con-ference, Auckland, New Zealand,
Masuyama, Y , Nakamura, I., Tatano, H. and Takagi, IC, 1993. Dynamic performance of sailing cruiser by full-scale sea tests. In: Proceedings o f t h e 11th Chesapeake Sailing Yacht Symposium, SNAME, pp, 161-179.
Masuyama, Y , Fukasawa, X , Sasagawa, R , 1995. Tacking simulation of sailing yachts-numerical integration of equations of motion and application of neural
network technique. In: Proceedings of the 12th Chesapeake Sailing Yacht Symposium, SNAME, pp, 117-131,
Masuyama, Y , Fukasawa T., 1997 Full Scale measurement of sail force and the validation of numerical calculation method. In: Proceedings of the 13th Chesapeake Sailing Yacht Symposium, SNAME, pp. 23-36.
Masuyama, Y , Tahara, Y,Fukasawa, T , Maeda, N., 2 0 0 7 Database of sail shapes vs. sail performance and validation of numerical calculation for upwind condition. In: Proceedings of the 18th Chesapeake Sailing Yacht Symposium, SNAME, pp. 11-31.
Masuyama, Y and Fukasawa, T., 2008, Tacking simulation of sailing yachts with new model of aerodynamic force variadon. In: Proceedings of the 3rd High Performance Yacht Design Conference, Auckland, pp. 138-147
Masuyama, Y , Tahara, Y , Fukasawa, T , Maeda, N., 2009, Database of sail shapes versus sail performance and validation of numerical calculation for the upwind condition. J. Mar. Sci, Technol., JASNAOE vol. 14 (No. 2), 137-160.
Masuyama, Y , Fukasawa, T , 2010, Tacking simulation of sailing yachts with new model of aerodynamic force variation during tacking maneuver, J. Sailboat Technol,, SNAME, 2010 (-02).
Masuyama, Y , Fukasawa, T , 2011. Tacking simulation of sailing yachts with new model of aerodynamic force variation during tacking maneuver. Trans., SNAME VoL 119 (184-211), 2011,
Milgram, J. H., Peters, D, B., Eckhouse, D.N„ 1993, Modeling lACC sail forces by combining measurements with CFD. In: Proceedings of the 11th Chesapealce Sailing Yacht Symposium, SNAME, pp. 65-73.
Tahara, Y , 1996. Evaluation of a RaNS equation method for calculating ship boundary layers and wakes including wave effects, J. Soc. Naval Archit, Jpn, 180, 59-80.
Tahara, Y , Hayashi, G., 2003, Flow analyses around downwind-sail system of an lACC sailing boat by a multi-block NS/RaNS method. J, Soc. Naval Archit, Jpn. 194,1-12.
Tahara, Y , Masuyama, Y , Fukasawa, T , Katorl, M., 2012. CFD calculation of down-wind sail performance using flying shape measured by w i n d tunnel tests. In: Proceedings of the 4th High Performance Yacht Design Conference, Auckland, pp. 3 8 - 4 7
Viola, I.M., Flay, R,G., 2012. Sail aerodynamics: on-water pressure measurements on a downwind sail. J. Ship Res., SNAME 56 (4), 197-206,
