Mean-flow measurements in the boundary layer and wake and wave field of a series 60 Cb = 0.6 ship model. Part 1: Froude Numbers 0.16 and 0.316. Attached Part 2: Scal effects on near-field wave patterns and comparisons with inviscid theory

Journal of Sfiip Research, Vol. 36, No. 4, Dec. 1992, pp. 3 6 0 - 3 7 7

Cieao-Flow Measurements in the Boundary Layer and Wake and

Wave Field ©f a Series SO = ©=i Ship Model=Parï 1: Froude

Numbers 0.16 and 0.316

Y. Toda,^ F. Stem,^ and J. Longo'

Part 1 of this two-part paper presents results from a towing-tank experiment conducted in order to explicate the influence of wavemaking by a surface-piercing body on its boundary layer and wake and provide detailed documentation of the complete flow field appropriate for validating computational meth-ods. Mean-velocity and pressure field measurements were performed for Froude numbers 0.16 and 0.316 for a 3.048 m Series 60 Cg = 0.6 hull form at numerous stations from the bow to the stern and into the near wake. For Froude number = 0.316, free-surface effects are very significant, whereas for Froude number = 0.16, they are negligible, except near the bow, such that comparison of the results enables the identification of the salient features of the wave-induced effects. Wave profiles and local and global elevations were also measured. In addition, resistance tests were conducted. The experi-mental equipment and procedures are described and the results are discussed to point out the essential differences between the flows at low and high Froude number. On the forebody, the differences are primarily in the outer (inviscid) flow, except at the bow, whereas on the afterbody and in the near wake, both the inner (viscous) and outer flows are altered. The results are discussed to assess the nature of the interaction between wavemaking and the boundary layer and wake. Most of the interaction can be explicated as a result of the wave elevations, wave-induced pressure gradients, and the displacement effects of the boundary layer. Part 2 concerns scale effects on near-field wave patterns and comparisons between the experimental results and inviscid theory.

Introduction

A L T H O U G H i t is generally recognized t h a t the w a v e m a k i n g of a surface-piercing body has a s i g n i f i c a n t i n f l u e n c e on i t s boundary layer and wake, detailed e x p e r i m e n t a l i n f o r m a -t i o n q u a n -t i f y i n g -t h i s i n f l u e n c e is v e r y l i m i -t e d , especially f o r p r a c t i c a l h u l l f o r m s . Interest i n t h i s p r o b l e m a n d i t s con-verse, t h a t is, t h e i n f l u e n c e o f boundary l a y e r and w a k e on w a v e m a k i n g , i n i t i a l l y was p r i m a r i l y w i t h viscous effects on wave resistance and propulsive performance due to l a c k of Reynolds n u m b e r (Re) s i m i l a r i t y i n model tests. M o r e re-cently, also of interest are the wave-boundaiy layer and wake i n t e r a c t i o n effects on the details of ship wakes and wave pat-terns due to the advent of satellite remote sensing.

The most extensive data a v a i l a b l e is f o r the u n i q u e , simple geometry of a foilplate model (Stern et a l . 1989). M e a n -velocity profiles i n the boundary layer and wave profiles were measured f o r three wave-steepness conditions. For m e d i u m and large steepness, the v a r i a t i o n s o f the e x t e r n a l - f l o w pres-sure gi-adients are shown to cause acceleration and decelera t i o n phdecelerases of the stredeceleramwise velocity component decelerand decelera l -t e r n a -t i n g d i r e c -t i o n of -the crossflow, w h i c h r e s u l -t i n large oscillations of t h e displacement thickness and wall-shear stress as compared to the zero-steepness condition. This w o r k is precursory to the present study. I n a contemporary study (Stern et a l . 1991), extensions were made f o r the wake re-gion. The trends are similar, however, interestingly, the near and i n t e r m e d i a t e w a k e display a bias such t h a t t h e w a k e is considerably more responsive to favorable as compared to

Wisiting research scientist, associate professor of mechanical engi-neering, and gj'aduate research assistant, respectively, Iowa Institute of Hydraulic Research, The University of Iowa, Iowa City, Iowa.

Manuscript received at S N A M E headquarters September 19, 1991; re-vised manuscript received March 11, 1992.

adverse pressure gradients, whereas t h e f a r w a k e e x h i b i t s a periodic nature.

For practical h u l l f o r m s , most e x p e r i m e n t a l i n f o r m a t i o n is f o r simple configurations such as deep-draft, t h i n struts ( K i n o s h i t a et a l . 1979, D o i 1986) and t h e W i g l e y h u l l (Shah-shahan 1985). Mean-velocity profiles i n t h e s t e r n r e g i o n and wave p r o f i l e s or patterns f o r several Froude n u m b e r s (Fr) were reported. The s i t u a t i o n is s i m i l a r f o r more realistic configurations, b u t t h e extent of the experiments is consid-erably reduced. Baba (1969) p e r f o r m e d mean-velocity mea-surements at f o u r stations—entrance, forebody and after-body shoulders, and s t e r n — a r o u n d a t a n k e r model a t F r = 0.22 i n his i m p o r t a n t study of w a v e b r e a k i n g resistance. K a -sahara (1983) performed mean-velocity measurements at f o u r stations near the stern a n d w a v e - p r o f i l e and pattern-resis-tance measurements f o r t w o ship models a t F r = 0.26 w i t h regard to wake resistance (that is, m o m e n t u m loss). Studies of b o t h k i n d s have been made a t t h e U n i v e r s i t y o f Tokyo (UT) w i t h reference to free-surface shock waves ( K a w a m u r a 1980). F r y and K i m (1988) reported mean-velocity measure-ments at stations near the bow f o r three ship models for the range 0.26 < F r s 0.41 and compared the results w i t h po-t e n po-t i a l - f l o w calculapo-tions. I n o n l y one case, po-t h a po-t is, po-t h e cir-c u l a t i n g - w a t e r cir-channel experiments of H o t t a and H a t a n o (1983,1985) have tui'bulence measurements been made. Note t h a t a l l of the other experiments referenced were p e r f o r m e d i n t o w i n g tanks. I n a d d i t i o n to the conventional research studies j u s t discussed, also of relevance are t w o large-scale research programs. The first is t h e experiments conducted under the Cooperative E x p e r i m e n t a l P r o g r a m (CEP) of t h e Resistance and F l o w C o m m i t t e e of the I n t e r n a t i o n a l T o w i n g T a n k Conference (1987). M e m b e r i n s t i t u t i o n s have reported detailed global (resistance tests, wave p a t t e r n analysis, a n d wake surveys) a n d local (surface-pressure a n d wall-shear stress d i s t r i b u t i o n s and boundary-layer traverses) measure-ments f o r the W i g l e y and Series 60 Cg = 0.6 h u l l forms. The

concern of the CEP is somewhat more w i t h the global t h a n the local measurements such t h a t the boundarylayer t r a -verses are l i m i t e d to the stern r e g i o n and, i n the case of the Series 60 Cg = 0.6 ship model, low Fr. The second is the experiments conducted very recently under the Advanced D y n a m i c E x p e r i m e n t a t i o n and A n a l y s i s f o r Signature Re-duction Progi-am (Hoekstra and L i g t e l i j n 1991). The goal of t h i s progi-am was to obtain a massive macro-wake database for a broad range of ship forms, w h i c h w o u l d be u s e f u l for g a i n i n g i n s i g h t i n t o the remote sensing of wakes as w e l l as how t h e y v a r y w i t h F r , t r i m , h u l l f o r m , n u m b e r of propel-lers, propeller r o t a t i o n , etc. The database includes mean ve-locities, Reynolds stresses, and wave elevations; however, the emphasis is on the detection of global structures as opposed to the f i n e details o f t h e complex f l o w fields. A l t h o u g h Hoek-stra and L i g t e l i j n (1991) provided a s u m m a r y of the m a i n findings extracted f r o m the data, i t is apparent t h a t the data is a r i c h source of f u r t h e r u s e f u l i n f o r m a t i o n .

I n general, these previous studies indicate s i g n i f i c a n t ef-fects due to the presence of t h e f r e e surface and a depen-dence on F r ; however, the extent of the measurements is l i m i t e d such t h a t general conclusions cannot be reached and t h e y are n o t s u f f i c i e n t l y detailed or documented to be u s e f u l as test cases f o r c o m p u t a t i o n a l methods. A l t h o u g h t h i s statement was w r i t t e n p r i o r to our knowledge of Hoekstra and L i g t e l i j n (1991), i t is s t i l l f e l t to be an accurate assess-m e n t such t h a t i t is apparent t h a t f u r t h e r e x p e r i assess-m e n t a l studies are r e q u i r e d b o t h to explicate the i n f l u e n c e of wave-m a k i n g by a surface-piercing body on its boundary layer and w a k e and provide detailed documentation of the complete flow field appropriate f o r v a l i d a t i n g c o m p u t a t i o n a l methods. The present study was u n d e r t a k e n f o r these purposes as p a r t of a larger project concerning free-surface effects on ship boundary layers and wakes. I n a d d i t i o n to the earlier men-tioned precursory and contemporary w o r k , some other re-lated studies under t h i s project w i l l be referenced later.

P a r t 1 of t h i s t w o - p a r t paper presents results f r o m mean-velocity and pressure field measurements f o r a 3.048 m Se-ries 60 CB = 0.6 ship model (Figs. 1 and 2) at numerous stations f r o m the bow to the stern and i n t o the near wake. The measurements are f o r t w o F r = 0.16 and 0.316. For F r = 0.316, free-surface effects are v e r y s i g n i f i c a n t , whereas f o r F r = 0.16, they are n e g l i g i b l e , except near the bow, such t h a t comparison of the results enables the i d e n t i f i c a t i o n of the salient features of the wave-induced effects. W a v e pro-files a n d local and global elevations were also measured. I n a d d i t i o n , resistance tests were conducted. The p r i n c i p a l d i -mensions of the model are g i v e n i n Table 1 and the loca-tions, extents, and conditions f o r the detailed measurements are summarized i n F i g . 3. The test conditions and results are documented i n s u f f i c i e n t d e t a i l to be u s e f u l as a test case for v a l i d a t i n g c o m p u t a t i o n a l methods. P a r t 2 (Longo et a l .

i

Fig. 1 Series 6 0 CB = 0.6 ship model

1991) concerns scale effects on n e a r - f i e l d wave patterns and comparisons between the e x p e r i m e n t a l results and i n v i s c i d theory. A l s o , f o r convenience c e r t a i n aspects of t h e P a r t 1 results are presented and f u r t h e r discussed.

The Series 60 CB = 0.6 ship model was selected f o r t h e experiments as a representative fine h u l l f o r m and to com-plement the m a n y previous and ongoing studies w i t h t h i s geometry [see Toda et a l . (1990) f o r comments concerning the h i s t o r y of the Series 60 geometry]. The m a n y experi-ments w i t h the Series 60 h u l l f o r m are f a r too numerous to review; however, of p a r t i c u l a r relevance is the f a c t t h a t i t is one of t h e f o u r h u l l f o r m s selected f o r t h e CEP and was used p r e v i o u s l y by the first t w o authors to study propeller-h u l l i n t e r a c t i o n (Toda et a l . 1990).

I n the f o l l o w i n g , an overview of the experiments is g i v e n . T h e n the most i m p o r t a n t aspects of the results are presented

A„„AT = ship-model midship and tow-ing-tank cross-sectional areas B = ship-model beam block coefficient C„ = midship coefficient pressure coefficient [= 2(p — P o) / p C / ' ] d = ship-model draft F r = Froude number ( = C Z / V g L ) g = gravitational acceleration H = total head [= (Cp + + v'^ +

Nomenclature

j , k = unit vectors i n directions of y and z axes

L = length between perpendiculars m = blockage coefficient ( = A „ / A j . )

P = dynamic pressure

Px,P, = axial and depthwise surface-pressure gi-adients

Po = uniform-stream pressure Re = Reynolds number (= UL/v)

U = carnage speed, uniform-stream

velocity

u,v,w = velocities in ix,y,z) directions

v-w = crossplane vector (= -I- lük) x,y,z = global C a r t e s i a n coordinates Greek

8 = boundary-layer thickness

V = kinematic viscosity l = wave elevation

l:,,ly = axial and transverse wave

slopes p = density

/ dw dv\

Ü), = axial vorticity = I

and discussed to p o i n t o u t t l i e essential features of the f l o w for b o t h low and h i g h F r . N e x t , a n assessment is made o f the n a t u r e o f t h e i n t e r a c t i o n between the w a v e m a k i n g o f t h e h u l l and i t s boundary l a y e r and wake. L a s t l y , some con-c l u d i n g r e m a r k s are made. The con-complete results and f u r t h e r details of the e x p e r i m e n t a l equipment and procedures are provided i n Toda et a l . (1991). I n the presentation o f the re-sults and the discussions to follow, a Cartesian coordinate system is adopted i n w h i c h the x-, y-, and z-axes are i n t h e direction o f the u n i f o r m f l o w , starboard side of the h u l l , a n d u p w a r d , respectively. The o r i g i n is at the intersection of the waterplane and t h e f o r w a r d perpendicular of t h e h u l l . The mean-velocity components i n the directions of the coordinate axes are denoted b y (u,u,w) and the carriage velocity by U. Unless otherwise indicated, a l l variables are nondimension-alized using the model l e n g t h between perpendiculars L , carriage velocity U, a n d f l u i d density p.

1.0 0.975 0.95 0.925 Q9 0.1

WITHOUT HUB WITH HUB

SERIES 60 C„=0.6 BODY PLAN

Fig. 2 Series 60 CB = 0.6 lines drawing: (a) profile plan (longitudinal section through centerplane), (b) body plan (transverse sections)

O v e r v i e w o f t h e e x p e r i m e n t s

The experiments were p e r f o r m e d i n t h e I o w a I n s t i t u t e o f H y d r a u l i c Research ( I I H R ) t o w i n g t a n k , w h i c h is 100 m l o n g and 3 m wide and deep. The lines o f the Series 60 CB = 0.6 ship model used i n the experiments are shown i n F i g . 2. These c o n f o r m to the standard offsets; however, the model is equipped w i t h a stern tube and a propeller hub, a l t h o u g h a l l o f t h e present experiments are f o r t h e w i t h o u t - p r o p e l l e r con-d i t i o n The con-details of the s t e r n a r r a n g e m e n t are basecon-d on t h e o r i g i n a l methodical series (Todd 1963). The b r o k e n lines i n F i g . 2 show the o r i g i n a l bare ( w i t h o u t - h u b ) h u l l , w h i c h was used, f o r example, i n the CEP, whereas t h e solid lines show the present m o d i f i e d ( w i t h h u b ) h u l l . The p r i n c i p a l d i -mensions of the model are g i v e n i n Table 1 [the offsets are provided i n Toda et a l . (1991)]. The model is 3.048 m long and constructed of fiber-reinforced Plexiglass. I n order to s t i m u l a t e t u r b u l e n t f l o w , a r o w of c y l i n d r i c a l studs of 1.6 m m h e i g h t and 3.2 m m diameter were f i t t e d w i t h 9.5 m m spacing on the model at x = 0.05.

Instrumentation, calibration, and data-acquisition system A one-component force transducer (0.9 N f u l l scale) was used w i t h the dynamometer to p e r f o r m t h e resistance tests. T h e global wave elevations were measured u s i n g a digi1;al-interface technique recently developed a t I I H R f o r m a k i n g h i g h - r e s o l u t i o n , low-noise, capacitance-wire wave-elevation measurements (Houser et a l . 1989). T h r e e capacitance-wire probes and d i g i t a l interfaces were used to p e r f o r m the mea-surements. A beam f i t t e d w i t h a slide was a f f i x e d perpen-d i c u l a r to the t o w i n g - t a n k w a l l . T h r e e c a l i b r a t i o n perpen-devices (one-dimensional vertical traverses) were m o u n t e d to the slide a t 30 cm i n t e r v a l s w i t h each s u p p o r t i n g a probe. W i t h t h i s a r r a n g e m e n t , the probes could be positioned a t any desired measurement p o i n t between the t o w i n g - t a n k w a l l and the ship model and could be calibrated at each point. The local wave elevations were measured u s i n g a Shinozuka 15 c m A C servo-mechanism wave probe. A n automated traverse was used to position the probe. The probe could be moved i n three directions o f a Cartesian coordinate system. The crossplane p o s i t i o n i n g iy-z planes) was d r i v e n b y t w o stepper motors w h i c h were controlled b y a m i c r o c o m p u t e r on the carriage. The a x i a l (xdirection) p o s i t i o n i n g was achieved b y m a n -u a l l y m o v i n g the y-z traverse system a l o n g 1.5 m r a i l s . For large distance a x i a l positioning, the r e l a t i v e position of the traverse and ship model were adjusted o n the t r a i l e r . A f i v e -hole p i t o t probe (modified N P L type) was used to measure the d i r e c t i o n and m a g n i t u d e o f t h e velocity i n the f l o w field a r o u n d the h u l l . The same a u t o m a t e d t r a v e r s e was used f o r p o s i t i o n i n g the probe. A static-pressure probe (the static pressure side of a conventional p i t o t probe) was used to mea-sure the u n i f o r m s t r e a m presmea-sure. T h i s also enables t h e

Table 1 Principal dimensions of the Series 6 0 CB = 0.6 ship model

Parameter Model Model Full-scale

Length, (m) Beam, (m) Draft, (m) Depth, (m) c,„ m Shaft center, m Wetted-surface area, m^ Displaced volume, m^ Entrance angle, deg L e n g t h / b e a m L e n g t h / d r a f t B e a m / d r a f t 3.048 0.406 0.163 0.244 0.60 0.977 0.0072 0.098 1.579 0.121 7 7.50 18.75 2.50 1.829 0.244 0.098 0.146 0.60 0.977 0.00226 0.059 0.569 0.026 7 7.50 18.75 2.50 121.920 16.256 6.502 9.758 0.60 0.977 3.'933 2526.400 7744.000 7 7.50 18.75 2.50

measurement of the h y d r o d y n a m i c pressure a n d e l i m i n a t e s the effects on the measurements of s m a l l deviations of the t o w i n g - t a n k r a i l s . I t was located at x = 0.1 or x = - 0 . 3 (de-p e n d i n g on the shi(de-p-model (de-position), y = - 0 . 4 ( t h a t is, o(de-p- op-posite side of the measurement region), a n d z = - 0 . 0 1 . T h i s position was selected so t h a t the probe was i n u n d i s t u r b e d f l o w and i t s wake and w a v e m a k i n g d i d not d i s t u r b the f l o w i n the measurement I'egion. The leads f r o m t h e fivehole p i -t o -t probe were connec-ted by v i n y l -t u b i n g -to one side of f i v e V a l i d y n e d i f f e r e n t i a l pressure transducers w i t h ± 0 . 3 psi diaphragms. The tube f r o m the static-pressure probe was connected b y v i n y l t u b i n g to a b r a n c h . F i v e pressure tubes were divided at the b r a n c h and connected to the other side of the transducers. A l l of the tubings between the sensor holes and the d i a p h r a g m were f i l l e d w i t h water.

T h e force transducer was calibrated w i t h deadweights and two pulleys. The capacitance-wire wave-elevation measure-m e n t systemeasure-m was c a l i b r a t e d before and a f t e r measure-measuremeasure-ment of each wave p a t t e r n . The c a l i b r a t i o n was accomplished by m a n u a l l y m o v i n g the probes up and down ( t h a t is, c h a n g i n g the i m m e r s i o n of the probe) w i t h the one-dimensional ver-t i c a l ver-traverses. The servo-mechanism wave probe was cali-b r a t e d cali-by a d j u s t i n g i t s r e l a t i v e position w i t h respect to the w a t e r surface u s i n g the automated traverse. T h i s was done each day before and a f t e r the measurements were per-f o r m e d . T h e d i per-f per-f e r e n t i a l pressure transducers were cali-b r a t e d u s i n g two w a t e r t a n k s . One was moved up and down by the automated traverse w h i l e the other was at a f i x e d elevation, t h a t is, the pressure was measured b y w a t e r head. The c a l i b r a t i o n was carried out before and a f t e r the mea-surements at a p a r t i c u l a r station. I n a l l three of the l a t t e r cases, the calibration results were linear and rep eatable (Toda et a l . 1991). The five-hole p i t o t probe was calibrated i n the I I H R 1.07 m octagonal, open-throat test section, closed-cir-c u i t w i n d t u n n e l . T h e d a t a were analyzed u s i n g a method s i m i l a r to F u j i t a (1979), w h i c h is described i n d e t a i l i n Toda et a l . (1991) along w i t h presentation of the c a l i b r a t i o n coef-f i c i e n t s . A computer p r o g r a m was used coef-f o r data analysis i n w h i c h values of the c a l i b r a t i o n coefficients at desired points are obtained by Lagrange i n t e r p o l a t i o n .

T h e data-acquisition system was an I B M P C - X T compat-ible microcomputer on the carriage w i t h an 8-channel data-acquisition board. A n RS-232C c o m m u n i c a t i o n p o r t (the se-r i a l pose-rt) was used to t se-r a n s m i t signals to the contse-rollese-rs of the stepper motors. For the steady measurements (resis-tance tests, local wave elevations, and m e a n - f l o w f i e l d ) , the force, wave elevation, or pressure sensed was converted to a voltage and t h e n filtered by a low-pass filter ( i n c l u d i n g a u n i t g a i n a m p l i f i e r ) and sampled t h r o u g h the A - D converter and averaged over the measurement period. A s a m p l i n g fre-quency of 50 Hz was used. For t h e unsteady measurements (global wave elevations), the wave elevation was converted to a voltage and t h e n sampled t h r o u g h the A - D converter. A s a m p l i n g frequency of 100 Hz was used.

Experimental procedures and uncertainty

Three types of measurements were made: resistance, wave profiles and elevations, and mean-velocity and pressure fields. A l l measurements are for the f u l l l o a d and w i t h o u t p r o p e l -ler or -rudder condition. F i r s t , resistance tests and wave pro-f i l e measurements were made. Based on these, the condi-tions for the subsequent detailed measurements were selected. The resistance tests were c a r r i e d out f o l l o w i n g standard t o w i n g - t a n k procedures. T h e tests were f o r t h e model-free condition ( t h a t is, the model was free to s i n k and t r i m ) . The force transducer was calibrated before and a f t e r the mea-surements. Force measurements were made f o r about 10 sec after the carriage attained steady speed. Measurements were performed f o r the range 0.1 < F r < 0.36. The wave profiles

were recorded for the model-fixed condition ( t h a t is, the model was fixed a t the design d r a f t ) . T h i s was done phototgi-aph-i c a l l y u s phototgi-aph-i n g both 35 m m and vphototgi-aph-ideo cameras. For the detaphototgi-aph-iled measurements, t w o F r were selected, 0.16 and 0.316. The F r = 0.316 value was chosen since for t h i s c o n d i t i o n free-sur-face effects are v e r y s i g n i f i c a n t and there is a p l a t e a u i n the resistance curves w h i c h imphes stable conditions f o r the measurements. I n a d d i t i o n , i t was decided to p e r f o r m a par-a l l e l set of mepar-asurements, i n the spar-ame t o w i n g t par-a n k under essentially i d e n t i c a l conditions, f o r F r = 0.16 since f o r t h i s condition free-surface effects are negligible, except near the bow, such t h a t comparisons w i t h the F r = 0.316 measure-ments w o u l d enable the i d e n t i f i c a t i o n o f the salient features of the wave-induced effects. Also, comparisons could be made w i t h the w i t h o u t - p r o p e l l e r condition measurements o f Toda et a l . (1990) w h i c h were also f o r F r = 0.16. A l l the mea-surements were made for the model-fixed condition. For the global wave-elevation measurements, the capacitance-wire system was positioned at about 55 m f r o m the south end of the t a n k such t h a t the carriage had a t t a i n e d a steady speed f o r about 25 m p r i o r to reaching the location o f the probes. The s a m p l i n g period was i n i t i a t e d by the carriage contact-i n g a swcontact-itch t h a t was mounted such t h a t w h e n contacted the probes were 1.12 m u p s t r e a m of the bow of t h e ship model. W i t h t h i s method, the t i m e could be converted to a l e n g t h -wise distance f r o m the bow of the ship model, thereby, en-a b l i n g the t r en-a n s f o r m en-a t i o n of the unsteen-ady wen-ave-eleven-ation measurements i n t o a steady wave p a t t e r n f o r coordinates m o v i n g w i t h the ship model. A t i m e i n t e r v a l of 8 sec was used f o r the measurements (800 data points per channel were obtained). Measurements were made for y positions of every 5 cm (18 l o n g i t u d i n a l cuts) and, i n t h i s case, f o r f o u r F r = 0.16, 0.25, 0.3, and 0.316. T h e closest measurement p o i n t to the ship model was y = 23 cm (2.7 cm f r o m t h e m a x i m u m beam). For the local wave-elevation measurements, t w o measurements were made per carriage r u n . A delay t i m e of 5 sec was used a f t e r the carriage a t t a i n e d a steady speed and before the first measurement was performed. Subsequently, data was t a k e n f o r a 5 sec period and t h e n the probe position was changed by the automated traverse. A second 5 sec mea-surement period was i n i t i a t e d a f t e r a 3.5 sec delay t i m e . Measurements were made at 19 a x i a l stations w i t h 8 to 20 data points t a k e n over the range 0 < y < 30 c m and, i n t h i s case, f o r o n l y one F r = 0.316. F o r the mean-velocity and pressure field measurements, t w o and three measurements were made per carriage r u n for F r = 0.316 a n d 0.16, re-spectively. The procedure was s i m i l a r to t h a t f o r the local wave-elevation measurements, except a 4.5 sec delay t i m e was used between the first and second or second and t h i r d measurements. I n m a n y cases, the probe was g i v e n a preset angle (around 5 deg) so t h a t measurements could be per-f o r m e d close to the h u l l . The per-flow angles were coiTected based on measurements i n u n i f o r m flow. Measurements were made f o r t e n a x i a l stations for b o t h F r = 0.16 and 0.316. Mea-surements a t about 2 0 0 - 3 5 0 points were made at each sta-tion. The measurement locations, extents, and conditions are s u m m a r i z e d i n F i g . 3. A t o t a l n u m b e r of about 4000 carriage r u n s were made i n p e r f o r m i n g the complete set of experi-ments.

For the resistance tests, the accuracy is estimated to be w i t h i n ± 7 X 10~* N . The error is a t t r i b u t e d to f r i c t i o n i n the dynamometer. T h i s corresponds to a n error of 5 percent at l o w F r ( = 0 . 1 ) and 0.5 percent a t h i g h F r ( = 0 . 3 ) . For the wave-profile measurements, the accuracy is estimated to be w i t h i n ± 2 m m . T h e error is a t t r i b u t e d to the thickness of the lines m a r k e d on the h u l l for t a k i n g the readings, t a k i n g the readings f r o m photographs, and the angle between the h u l l surface and the camera. N e a r the bow, t h e error is somewhat larger due to the presence of a t h i n l a y e r of w a t e r

Measurement stations for Mean-Velocity and Pressure

Wove Pattern (Fr = 0.316) — C r e s t Line — T r o u g f i Line •—Boundary-Loyer Ttiickness

Measurement Stations for _ Global ond Local Elevations

WT (°C) 10 10 9.8 9.2 8.4 26.5 10 14.9 19.6 10 Fr

Rex 10-6 2.04 2 0 4 2.03 1.99 1.95 3.09 2.04 2.33 2.63 2.04 0.16

Rex 10-6 4.02 4.02 4.01 3.93 3,85 6.11 4.02 4.61 5.19 4.02 0.316

Fig. 3 Measurement locations

w h i c h adhered to the h u l l surface and appeared t r a n s p a r e n t i n the photographs. For the global wave-elevation measure-ments, the noise and d r i f t of the d i g i t a l interface are s m a l l ; however, some error exists due to the probe and c a l i b r a t i o n device. The f o r m e r is r e l a t e d to the effects of surface tension etc. and the l a t t e r to u n c e r t a i n t y i n the i m m e r s i o n setting. Based on the r e p e a t a b i l i t y of b o t h the c a l i b r a t i o n and mea-surement results, the e x p e r i m e n t a l error is estimated to be w i t h i n ± 0 . 5 m m i n wave elevation. For the local wave-ele-v a t i o n measurements, the accuracy is estimated to be w i t h i n ± 0 . 5 m m i n wave elevation, except i n regions i n w h i c h the wave p a t t e r n was unsteady, where the error is somewhat larger. For the mean-velocity measurements, the accuracy is estimated to be w i t h i n 2.5 percent f o r the m a g n i t u d e and 1.5 deg for the d i r e c t i o n . The accuracy of the pressure coef-f i c i e n t is estimated to be w i t h i n ± 0 . 0 5 . A p p r o x i m a t e l y h a l coef-f of the error is a t t r i b u t e d to the pressure-measurement sys-t e m and i n sys-t e r p o l a sys-t i o n procedures and sys-t h e osys-ther h a l f sys-t o sys-the w i n d - t u n n e l c a l i b r a t i o n .

Results

I n the f o l l o w i n g , the most i m p o r t a n t aspects of the results [see Toda et a l . (1991) f o r the resistance-test results etc.] are presented and discussed to p o i n t o u t the essential features o f t h e f l o w f o r b o t h h i g h and low F r . A l t h o u g h n o t discussed i n t h e I n t r o d u c t i o n , i n comparison to the s i t u a t i o n f o r h i g h F r , a considerable a m o u n t of e x p e r i m e n t a l i n f o r m a t i o n is available f o r the m e a n - f l o w f o r bare ship h u l l s e i t h e r f o r double bodies or a t low Fr. M o s t of the experiments are f o r m e r c h a n t ships, f a i r l y s i m i l a r to the Series 60 CB = 0.6, b u t w i t h larger block coefficients (CE = 0.8) and p e r t a i n to the afterbody f l o w ( t h a t is, the f l o w over the stern and i n the near wake) w i t h p a r t i c u l a r reference to the propeller i n f l o w . However, some l i m i t e d studies have also been done f o r the forebody f l o w ( t h a t is, t h e f l o w over the bow and midbody), i n t h i s case, w i t h p a r t i c u l a r reference to bulbous bows and bilge keels. Several i n t e r p r e t a t i o n s have been g i v e n to the v o r t i c a l f l o w patterns (and a t t e n d a n t complicated velocity contours) associated w i t h the forebody and afterbody f l o w s f o r these h u l l f o r m s . T h i s is e x e m p l i f i e d by the range of ter-minology used to describe t h e m , f o r example, bilge vortices, l o n g i t u d i n a l vorticity, and three-dimensional separation. For a recent r e v i e w f o r the afterbody f l o w , see Patel (1988). N o reviews are available f o r the forebody f l o w . Generally, i t is believed t h a t , i n t h i s case, viscous effects are r e l a t i v e l y u n

-i m p o r t a n t . Below, we s h a l l s -i m p l y p o -i n t out these features w i t h the p r i m a r y emphasis on t h e i r m o d i f i c a t i o n due to the effects of w a v e m a k i n g .

Wave profiles and elevations

T h e wave p r o f i l e I, at the h u l l f o r F r = 0.316 is shown i n F i g . 4, i n c l u d i n g comparison w i t h one of t h e results f r o m the CEP, t h a t is, U T . Also shown are low F r wave p r o f i l e s f r o m U T and Toda et a l . (1990), a l t h o u g h present measurements were n o t performed. Note t h a t i n F i g . 4 t w o scales have been provided f o r ^: on the l e f t , I is n o r m a l i z e d b y the velocity head t 7 V 2 ^ ; and on the r i g h t , £ is n o r m a l i z e d i n t h e u s u a l m a n n e r by L. A comparison of t h e wave p r o f i l e s f o r low and h i g h F r clearly displays the f a c t t h a t , i n t h e f o r m e r cases, free-surface effects are negligible, except near the bow where, interestingly, the m a x i m u m 2Lg/U^ values ai-e, i n fact, larger. Also, the present a n d U T results show close agreement i n spite- of the differences i n model size a n d F r f o r t h e h i g h e r value. The overall wave-profile results o f t h e CEP also showed i n d i f f e r e n c e to model size f o r the f i x e d c o n d i t i o n , a l t h o u g h for the free condition, the expected scale effects were some-w h a t apparent near the stern.

I t is concluded t h a t , a l t h o u g h there are F r differences be-t w e e n be-the presenbe-t condibe-tions f o r be-the debe-tailed measuremenbe-ts a n d those of U T , t h a t is, F r = 0.316 versus 0.32 and F r = 0.16 versus 0.18 and there are differences i n the model sizes, t h e y are i n s u f f i c i e n t to cause s i g n i f i c a n t differences i n the wave p r o f i l e and t h u s the gi-oss features of the f l o w f i e l d . F u r t h e r m o r e , the differences between the F r = 0.316 and 0.3 wave profiles are r e l a t i v e l y s m a l l (Toda et a l . 1991). These facts were estabUshed to support t h e l a t e r use of U T surface-pressure measurements f o r F r = 0.18 a n d 0.3 as a n aid i n q u a l i t a t i v e l y e x p l i c a t i n g the present d e t a i l e d results. How-ever, i t should be recognized t h a t the i n t e n t i o n here is n o t to i m p l y t h a t such differences i n Re a n d F r are i n s u f f i c i e n t to cause s i g n i f i c a n t differences i n detailed features of the f l o w f i e l d , for example, i n P a r t 2, i t w i l l be shown t h a t such differences i n Re do, i n fact, cause differences i n n e a r - f i e l d wave patterns.

N e x t , the detailed wave-elevation results are considered. F i g u r e 5 shows the wave-elevation contours f o r F r = 0.316 a n d 0.16 and provides an overview of the results. F o r F r = 0.316, the contours were constructed using b o t h the local and global wave-elevation data. For F r = 0.316, the contours re-veal complex wave patterns consisting of both transverse and diverging wave systems. I n the local region (close to the h u l l ) ,

+ Wave

O Wave Fr = 0 . 1 6 0 - Wave

C o r t o u r intervol =

0.00164-Fig. 5 Wave-elevation contours

Contour interval = 0 . 0 3 2 0

TanU wall

- 0 . 2 0.0 0.2 0.4

Fig. 6 Wave-slope contours

the bow- and stern-wave systems are seen to i n i t i a t e w i t h crests and the shoulder systems w i t h troughs, w h i c h con-forms to the usual p a t t e r n described for this type of h u l l f o r m . The close-up views shown i n Figs. 4 and 5 of P a r t 2 of the f o r m e r t w o wave systems display t h e i r detailed character-istics. I n the global region ( t h a t is, away f r o m the h u l l ) , the bow-, shoulder-, and stern-wave systems i n t e r a c t i n a com-plex manner c r e a t i n g the o v e r a l l wave p a t t e r n . For F r = 0.16, t h e wave elevations ai-e v e r y s m a l l and the wave pat-t e r n is nondispat-tincpat-t, exceppat-t f o r pat-the effecpat-ts of pat-the bow wave.

A x i a l and transverse i,y wave-slope contours are pro-vided i n F i g . 6 for F r = 0.316, w h i c h are i n d i c a t i v e of the a x i a l a n d transverse wave-induced pressure gradients, re-spectively, i n the v i c i n i t y of the f r e e surface. Regions of pos-i t pos-i v e a n d negatpos-ive wave slopes correspond to regpos-ions of ad-verse and favorable pressure gi-adients, respectively, and C,y were obtained t h r o u g h n u m e r i c a l d i f f e r e n t i a t i o n of the wave-elevation data and w i l l be discussed l a t e r w i t h regard to the results f o r the mean-velocity and pressure fields. Note

t h a t the wave-slope and -elevation contours h a v e s i m i l a r patterns, except for the expected phase s h i f t .

T h e transverse and l o n g i t u d i n a l wave-elevation profiles for F r = 0.316 f r o m w h i c h the contours were constructed f o r t h i s F r are provided and discussed i n d e t a i l i n P a r t 2. The transverse profiles include b o t h the local and g l o b a l data. The data overlap and close agi-eement can be observed bet w e e n bet h e betwo measuremenbet sysbetems. The p r o f i l e s i n bet i -m a t e l y display the co-mplexity of the wave f i e l d , especially i n the bow and stern regions. Also shown are results f o r F r

= 0.16, w h i c h , here again, clearly e x h i b i t t h a t w a v e effects are n e g l i g i b l e f o r F r = 0.16 i n comparison to F r = 0.316. T h e transverse wave-elevation profiles m a i n l y display the detailed characteristics of the local-region wave system. The l o n g i t u d i n a l wave-elevation p r o f i l e s m a i n l y display t h e de-t a i l e d characde-terisde-tics of de-the global-region wave sysde-tem, how-ever, i n t h i s case, the intei-pretation of the wave p a t t e r n is more d i f f i c u l t due, as already noted, to the complex i n t e r -actions between the bow-, shoulder-, a n d stern-wave sys-tems.

x = 0

O W a v e Elevation (Local Measuremeni) a Wave Elevation (Global Measurement)

x = 0.6

o Wave Elevation (Local Measuremeni) fl Wave Elevation (GlotDai Measuremeni)

-z 0.025 0050 \ 0.9 0.925 0,95 0S6 -z 0025 0D50 Fn=0,316

r? (?tn o fti? nirtn n rti 4 ti—

fli 1 Li—

0 0025 0050 0D75 0,100 0,125 0 0D25 0050 0075 0,100 0,125

y y Fig. 7(a)

x = Q2 o W a v e Elevation {Local Measurement) a Wave Elevation (Global Measuremeni)

Fn = 0.16 Fn = 0316 -Z 0025 0.050 / • J 1 ft 1 A t H /rX).95 / u 1 l_A 1 0 0025 0D50 0.075 0.100 0J25 0 0025 0050 0.075 0.100 0125 y y Fig. 7(b) Fn = 0.16 OD50 - Z 0025 0050 '^X "x —k '-g '—^ i '• 20¬ 10— 5¬ 10-' in V 1 = - 5 i ^ , 0 1 0 " / 10z o -20^

i

Fig. 7 Total-liead and axial-velocity contours, crossplane vectors, and pressure and axial-vorticity contours

Mean-velocity and pressure fields

The total-head (H) and axial-velocity (u) contours, cross-plane vectors ( v - w ) , and pressure (p) and a x i a l - v o r t i c i t y M contours are shown i n F i g . 7; and the total-head, velocity

(u,v,w), and pressure profiles are s h o w n i n F i g . 8. I n most

cases, we s i m p l y r e f e r to Cp as p below a n d i n the f i g u r e s . Note t h a t p is the dynamic (that is, piezometric) pressure. The co^ contours were obtained b y n u m e r i c a l d i f f e r e n t i a t i o n of the mean-velocity data and are n o t p r o v i d e d f o r the fore-body since the present resolution was i n s u f f i c i e n t to accu-r a t e l y p e accu-r f o accu-r m the n u m e accu-r i c a l d i f f e accu-r e n t i a t i o n . T y p i c a l accu-results are provided a t f i v e stations, x = (0,0.2,0.6,0.9,1.1) and both F r = 0.16 a n d 0.316. The p r o f i l e s are f o r some selected z locations: at x = 0, z = -(0.0075,0.0275,0.0475); and a t a l l other X stations, z = -(0.01,0.03,0.05).

P r i o r to discussing the results, i t is u s e f u l to consider the n a t u r e o f the wave-induced pressure gi-adients, t h a t is, the wave-induced effects on the surface-pressure d i s t r i b u t i o n and t h e a d d i t i o n a l pressure gi-adients near t h e f r e e surface as-sociated w i t h the wave p a t t e r n . A s already discussed, F i g . 6 shows t h e a x i a l l:, and transverse wave-slope contours for F r = 0.316. Recall t h a t regions of positive and negative wave

O V/ave Elevation a Wave Elevation = 0.9 I {Local Measurement) 1 (Global Measurement) x=l.l

O Wave Elevation (Local Measurement) A Wave Elevation (Global Measurement)

slope correspon(i to regions of adverse and favorable wave-induced pressure gi-adients, respectively, i n t h e v i c i n i t y of the free surface. Note t h a t wave-slope contours are not pro-vided f o r F r = 0.16 since, as already pointed out, the ele-vations are v e r y s m a l l , except near the bow, such t h a t the wave slopes are negligible. U n f o r t u n a t e l y , the present pro-gi-am of experiments d i d n o t include surface-pressure mea-surements; however, as m e n t i o n e d earlier, such measure-ments were made at s i m i l a r F r i n the CEP, t h a t is, a t U T for F r = 0.18 and 0.3. Recall t h a t the wave profiles f r o m these experiments showed f a i r l y good agreement w i t h those corresponding to the present conditions; thus, i t was con-cluded t h a t the gi-oss features of the flow fields should also be s i m i l a r (see F i g . 4). The U T surface-pressure p r o f i l e s and contours and a x i a l and v e r t i c a l surface-pressure gradients are shown f o r both F r i n Figs. 9 t h r o u g h 12, respectively. Also included f o r comparison are i n v i s c i d - f l o w computa-t i o n a l resulcomputa-ts f o r F r = 0. S u r p r i s i n g l y , F r = 0 e x p e r i m e n computa-t a l data (double-model, w i n d - t u n n e l data) are u n a v a i l a b l e for the Series 60 CB = 0.6 ship model. The b a c k g r o u n d f o r the calculation method is described i n P a r t 2. Note t h a t the or-dinate i n Figs. 10 t h r o u g h 12 is z/d (where d is the d r a f t ) w h i c h is referenced to the keel (z = - 0 . 0 5 3 3 ) .

Considering the l o w F r = 0.18 s i t u a t i o n first: The data and F r = 0 calculations f o r t h e surface-pressure profiles are

quite s i m i l a r ; however, free-surface effects are evident i n the data, t h a t is, there are s i g n i f i c a n t differences between the F r = 0.18 wave p r o f i l e and the F r = 0 w a t e r l i n e pressure. S i m i l a r l y , f o r w a t e r l i n e s near the free surface, t h e data f o l -low the trends of the wave p r o f i l e , whereas the F r = 0 cal-culations f o l l o w the trends of the w a t e r l i n e pressure. Over-a l l , the p r o f i l e s displOver-ay the expected behOver-avior, t h Over-a t is, h i g h pressure at the bow and stern, w h i c h decreases f r o m the w a t e r l i n e to the keel, and, i n the m i d b o d y r e g i o n , l o w pres-sure (negative values), w i t h r e l a t i v e l y s m a l l v a r i a t i o n w i t h depth. T h e lowest pressure values are at t h e shoulders. The pressure recovery at the stern is considerably less f o r the data t h a n t h a t i n d i c a t e d by the i n v i s c i d calculations. The pressure behavior j u s t described is also displayed by the con-tours, t h a t is, t h e contours show h i g h pressure near the bow and stern and l o w pressure f o r the m i d b o d y r e g i o n and are n e a r l y v e r t i c a l , except near the bow, bilge, and stern. I n general, the distortions f r o m the vertical are related, no doubt, to the r a p i d changes i n h u l l geometry i n these regions; how-ever, i n the bilge region, the distortions coiTespond to a broad region of l o w pressure, w h i c h is r e l a t e d to the f o r m a t i o n of bow and sternbilge vortices, as w i l l be discussed later. I n t e r e s t i n g l y , the pressure is f a i r l y s y m m e t r i c about the m i d -body. The differences are a t t r i b u t a b l e to the a s y m m e t r y of the bow a n d s t e r n geometry and viscous effects. The

ex--z = O.OI 0.7 l.I 0,9 Q7 0 2 -Q2 0 2 -0,2 0 4 P 0 2 0 - 0 2 x=0 o E x p . (Fn.0.3f6) E x p . (Fn-0.160) S p l a s h Barebody (Fn=0.316) Splash Edbody (Fn»0.316) -z=0.03 -z=005 -• 1 1 1 1 1 1 ^ , 1 1 1 1 ^ ^ ^ ^ ^ «« -, 1 1 1 1 0.050 0100 0 y 0.050 0100 0 0.050 0100 Fig. 8(a)

0 9 0.7 l.I u 0.9 0.7 02 -02 02 -02 02 0 - 0 2 -z = 0.01 X=0.6 Exp. (Fn.0.316) Exp. (Fn=0.160) • Splash Barebody (Fn=0.316) Splash Edbody (Fn.0.316) -Z = O03 -z = 0.05 0.050 0.100 0 0 5 0 0.100 0.050 0.100 y Fig. 8(c) 1.0 Q6 -2 = 0.01 x = 0.9 Exp. (Fn=0.316) Exp. (Fn-0.160) Splash Barsbody (Fn=0.316) Splash Edbody (Fn.0.316) - 2 = 0.03 -2=0.05 — ^ 5 « ( « r « M 11 s 0 .a ; f 1 1 1 1 1 r_ 1 1 1 1 > . 1 1 1 1 1 i_ fefcL...,aaassrfi-a-iv-... , , • 0 6 0 2 0 2 0 2 0 0 5 0 0.100 0 y 0,050 a i o o 0 0,050 0,100 y Fig. 8(d)

-z=0.0 -0.2¬ 0.2 -0.2 0 2 O - 0 2 X = l.l Exp. (Fn.0.316) Exp. (Fn.0.160) . Splash Barebody (Fn.0.316) Splash Edbody (Fn.0.316) -z=0.03

^ ^ ^ ^ ^ ^

+ Pressure

(c) Fr = 0. (SPLASH) Fig. 10 Surface-pressure contours

p e r i m e n t a l a n d calculated a x i a l and v e r t i c a l surface-pres-sure gi-adients are also q u i t e s i m i l a r . H e r e again, free-sur-face effects are evident i n t h e data near the free surfree-sur-face. The a x i a l gradients indicate t h a t is favorable f o r 0 £ x < 0.4 a n d 0.55 < x < 0.7 (Fr = 0) a n d 0.65 (Fr = 0.18); and ad-verse f o r 0.4 £ X < 0.55 and 0.7 (Fr = 0) a n d 0.65 (Fr = 0.18) s X < 1. D i s t o r t i o n s are evident near the b i l g e a n d n e a r the waterplane at t h e stern. The v e r t i c a l giadients i n -dicate t h a t p^ is s l i g h t l y f a v o r a b l e ( t h a t is, = 0 ) for 0.3 s x s= 0.75; a n d adverse f o r 0 s x < 0.3 a n d 0.75 < x < 1. T h e contours are v e r y distorted, especially for F r = 0.18, w h i c h also show scatter and islands of negative a n d positive pres-sure gradients, p a r t i c u l a r l y i n t h e midbody region. I n con-clusion, the surface-pressure d i s t r i b u t i o n s f o r F r = 0.18 and 0 are q u a l i t a t i v e l y and, to a large degree, q u a n t i t a t i v e l y s i m i l a r , w h i c h f u r t h e r supports t h e c o n t e n t i o n t h a t the pres-ent low F r = 0.16 e x p e r i m e n t a l data are represpres-entative of t h e F r = 0 case. Note t h a t i n K a j i t a n i (1987) i t was shown t h a t even closer s i m i l a r i t y between measured and F r = 0 calculated surface-pressure d i s t r i b u t i o n s can be achieved b y f u r t h e r decreasing t h e F r f o r the measurements, t h a t is, f o r a 2.5 m model and F r = 0.13, t h e coincidence was v e r y good; a n d for a 6 m model and F r = 0 . 1 , t h e coincidence was ex-cellent. These are considered t h e l i m i t i n g l o w F r values f o r t h e respective model sizes i n order to o b t a i n accurate mea-surements.

N e x t , we consider t h e s i t u a t i o n for h i g h F r = 0.3. The ax-i a l wave-slope contours suggest t h a t the a x ax-i a l wave-ax-in- wave-in-duced pressure gi-adients are f a v o r a b l e f o r 0.2 s x < 0.4, 0.7 == x < 0.85, a n d 1.1 (local region) < x < 1.2 (local

re-+ dp/dK

1.0-1 0 dp/dx Contour Interval « 0.20

(c) Fr = 0 . (SPLASH) Fig. 11 Axial surface-pressure gradient contours

gion); a n d adverse f o r 0 s x < 0.2, 0.4 s x < 0.7, and 0.85 s x < 1.1 (global region). However, these i-egions are dif-f i c u l t to dedif-fine precisely since t h e contours are skewed a t an angle w h i c h is smaller t h a n t h a t for t h e d i v e r g i n g - w a v e sys-t e m . T h e sys-transverse sys-t,y wave-slope consys-tours suggessys-t sys-t h a sys-t sys-the transverse wave-induced pressure gi-adients are favorable for 0 s X < 0.2, 0.4 (local region) < x < 0.8 (global region), a n d 0.85 (local region) < x < 1.2; a n d adverse f o r 0.2 < x S 0.5 (global region) and 0.5 (local region) s x < 0.9 (global region). T h e contours are even more skewed t h a n the a x i a l contours. A l t h o u g h the general features of t h e surface-pres-sure p r o f i l e s a n d contours for h i g h F r are s i m i l a r to those f o r l o w F r [ t h a t is, h i g h Cp ( > 0 ) near t h e bow a n d s t e r n and low Cp ( < 0 ) i n t h e midbody region], there are pronounced wave-induced effects at a l l depths, w h i c h were o n l y h i n t e d a t i n t h e results f o r F r = 0.18. I n t h e bow r e g i o n , the max-i m u m Cp v a l u e max-is somewhat smaller t h a n t h a t f o r l o w F r , b u t covers a considerably broader region, a n d h i g h Cp values persist to l a r g e r depths due to the effects o f t h e bow wave. N o t e t h a t t h e f a c t t h a t the m a x i m u m Cp is l a r g e r f o r l o w t h a n h i g h F r is consistent w i t h the corresponding wave pro-f i l e s ( F i g . 4). I n t h e midbody region, t h e l o w Cp values a t the shoulders are reduced and cover a broader area. A l s o , the pressure rise between the shoulders is considerable i n com-p a r i s o n to l o w F r . These effects are a com-p com-p a r e n t l y due to the shoulder-wave system. I n the stern region, i n t e r e s t i n g l y , the pressure recovery is reduced, t h a t is, the zero p o i n t s h i f t s t o w a r d s the stern and the pressure values on t h e h u l l are reduced, a l t h o u g h , as w i l l be shown l a t e r , t h e pressure i n t h e near w a k e is a c t u a l l y l a r g e r for h i g h as compared to low

+ dp/dz O dp/dz - dp/dz Contour intarvol = 0.05 (a) Fr = 0.3 (b) Fr = 0.18 0.2 0.+ 0.6 0.8 X (c) Fr = 0. (SPLASH) Fig. 12 Vertical surface-pressure gradient contours

F r due to t h e effects o f the stern wave. The pressure de-creases (inde-creases) f r o m the w a t e r l i n e to the k e e l i n regions of h i g h (low) pressure, as was the case f o r low F r , however, t h e v a r i a t i o n s are considerably l a r g e r a n d more d r a m a t i c . The contours show no tendency of s y m m e t r y about t h e m i d -body. The a x i a l gradients indicate t h a t p., is f a v o r a b l e f o r

0 075 s; X < 0.4 and 0.65 s x < 0.8; and adverse f o r 0 s X < 0.075, 0.4 s X ss 0.65, and 0.8 s; x < 1. The v e r t i c a l gradients indicate t h a t is m o s t l y favorable f o r 0.3 s x s 0 6 except near t h e f r e e surface where i t is adverse; a n d mostly adverse f o r 0 ss x sS 0.3 and 0.6 s x ss 1, except near the f r e e surface where there are some s m a l l regions where i t is favorable. A comparison of the ranges of regions of favorable and adverse P;, and p, f o r low F r = 0.18 a n d h i g h F r = 0.3 indicates t h a t i n the l a t t e r case the regions and magnitudes of f a v o r a b l e p.^ on the forebody and adverse and favorable p^, on the m i d b o d y are a l l increased and the r e g i o n and m a g n i t u d e o f adverse p^ on the afterbody is reduced, whereas the regions a n d magnitudes of adverse p^ on the forebody and a f t e r b o d y are increased and the v a r i a t i o n s m the midbody r e g i o n appear more w e l l defined. Table 2 pro-vides a s u m m a r y of t h e surface-pressure gi-adients, wave slopes, and wave elevations a t the measurement locations.

I n v i e w of the above discussion, we now consider the pres-ent results, first f o r F r = 0.16, a n d t h e n for F r = 0.316, pro-vided i n Figs. 7 and 8. The discussion to f o l l o w proceeds f r o m the measurements at the bow {x = 0), to those at t h e s t e r n [x = 1), and finally the near w a k e (1 s; x s= 1.2) and is based on the complete results at a l l t e n stations and five z locations (Toda et a l . 1991), a l t h o u g h , as noted earlier, o n l y t y p

-i c a l results at f-ive stat-ions and three z locat-ions are prov-ided ^ ,„ i n Figs. 7 and 8. For each measurement s t a t i o n , the o v e r a l l ' ' flow p a t t e r n is discussed first w i t h reference to F i g . 7, f o l -lowed b y discussion o f t h e detailed p r o f i l e s w i t h reference t o ' F i g . 8. Recall t h a t the h u l l geometry and measurement lo-cations and extents are provided by Figs. 2 and 3, respec-t i v e l y . Also, shown i n F i g . 3 f o r reference are respec-the wave-sys-t e m creswave-sys-t and wave-sys-t r o u g h lines and boundary-layer wave-sys-thickness for F r = 0.316.

F o r F r = 0.16, at the first measurement s t a t i o n , x - 0 [Figs. 7(a) and 8(a)], the flow is d o m i n a t e d by stagnation effects associated w i t h the close p r o x i m i t y of the bow and, as is also the case f o r the other forebody stations, by dis-placement effects associated w i t h t h e i n c r e a s i n g cross sec-tions of the h u l l at the bow and associated divergence of the i n v i s c i d streamlines, w h i c h leads to the development of a t h i n boundary l a y e r on the h u l l , except near the keel where there is a t h i c k e n i n g due to t h e flow convergence towards the centei-plane. Note t h a t the underwater p o r t i o n of the bow is j u s t downstream of t h i s s t a t i o n (see F i g . 2). H is, of course, u n i f o r m l y 1. u < 1 t h r o u g h o u t the extent of the measure-ments, w i t h the lowest values near the centerplane, and gi-adually approaching 1 away f r o m t h e h u l l . N e a r the cen-tei-plane, the contours are nearly vertical, whereas away from the centei-plane the contours are displaced outwards near the f r e e surface such t h a t t h e y intersect the f r e e surface a t an angle o f about 45 deg, w h i c h correlates w i t h the fah-ly large w a t e r l i n e angles near the w a t e r p l a n e f o r the Series 60 CB = 0 6 ship model, v - w display the o u t w a r d displacement e f fects of the h u l l and, f u r t h e r m o r e , suggest t h a t there is a s t a g n a t i o n p o i n t at z - - 0 . 0 1 2 5 , t h a t is, t h e flow is gener-a l l y o u t w gener-a r d , b u t divides gener-at t h i s depth such t h gener-a t i t is curved u p w a r d s for - z < 0.0125 and downwards f o r - z > 0.0125. T h e largest v - w are near the fi-ee surface and keel. Note t h a t u s u a l l y f o r F r = 0 the s t a g n a t i o n p o i n t is a t z = 0. The f a c t t h a t i n the present case the s t a g n a t i o n p o i n t is at - z > 0 indicates free-smface eff'ects. However, F r y and K i m (1988) discuss the flow at the bow of the Series 60 CB = 0.6 ship model i n terms of a n a t t a c h m e n t l i n e based on t h e i r stream-wise plane vector measurements as opposed to a stagnation point as suggested by the present data. A l t h o u g h f u r t h e r more detailed data is r e q u i r e d to resolve t h i s issue, a stagnation-p o i n t flow at the bow of the Series 60 CB = 0.6 shistagnation-p model m a y be the r e s u l t o f t h e bow-stem c u r v a t u r e (see F i g . 2). As expected, the p contours are s i m i l a r to those f o r u, b u t w i t h reverse t r e n d i n m a g n i t u d e . The u p r o f i l e s display the ap-pearance of l a m i n a r stagnation-point flow. The i n n e r p a r t of t h e p r o f i l e s are s i m i l a r i n shape at a l l depths, whereas the outer p a r t indicate lower values near the free surface t h a n a t gi-eater depths, v is positive at a l l depths due, as already m e n t i o n e d , to the o u t w a r d displacement effects of the h u l l . A t z = - 0 . 0 0 7 5 , the p r o f i l e peaks s h a r p l y near the center-plane where the m a g n i t u d e is large. A t l a r g e r depths, the p r o f i l e s are rounded near the centerplane a n d of reduced and s i m i l a r m a g n i t u d e , iv is u p w a r d near t h e free surface and d o w n w a r d at larger depths due to t h e stagnation-point ef-fects described earlier. T h e p r o f i l e s are r e l a t i v e l y flat, b u t w i t h somewhat l a r g e r values near t h e centerplane. The i n -ner p a r t o f t h e p profiles are shai-ply peaked and display quite large values. The outer p a r t of the p r o f i l e s g r a d u a l l y ap-proach p = 0. The w i d t h of t h e i n n e r r e g i o n decreases w i t h depth. , , , 1

At X = 0 . 1 , the i n i t i a t i o n o f the h u l l b o u n d a r y l a y e r is displayed. B o t h the H contours a n d u contours close to t h e h u l l indicate t h a t the b o u n d a r y l a y e r is v e r y t h m and o f n e a r l y constant thickness, except near the keel where i t is r e l a t i v e l y t h i c k e r due to the a f o r e m e n t i o n e d convergence of the flow towards the keel. The w a v y character o f t h e H cont o u r s is due, no doubcont, conto conthe effecconts of conthe conturbulence s cont i m

Table 2 S u m m a r y of s u r f a c e - p r e s s u r e gradients, w a v e s l o p e s , w a v e elevations, and wave-Induced velocity a n d p r e s s u r e differences

x =

UTdata Fr = .316

x = F r = .18 Fr = .3 local global local global

Px Vz hi Pz _{Cx tx} All Av Aw Ap 0 Vz + + + + + .1 + •1- + near away + near away + + •2 + -^ •I-near away -1- + A .6 + •¥ •H + -H -I- + 4-outer + + .6 + •¥ •H + -H -I- +

+ = adverse pressure gradient, positive wave slope and elevation, and increased velocity or pressure difference - = favorable pressure gradient, negative wave slope and elevation, and decreased velocity or pressure difference

u l a t o r s a t x = 0.05. A w a y f r o m the h u l l , u < 1 due to the aforementioned displacement effects o f the h u l l , v - w are o u t w a r d near the free surface; however, at l a r g e r depths t h e crossplane f l o w t u r n s d o w n w a r d and converges towards the k e e l due to the r a p i d decrease of w a t e r p l a n e area i n the depthwise direction i n the v i c i n i t y of the bilge. The mag-n i t u d e imag-ncreases w i t h depth w i t h m a x i m u m values at the bilge, w h i c h appear to indicate the f o r m a t i o n of a bow-bilge vortex, however, the present r e s o l u t i o n is i n s u f f i c i e n t f o r a complete documentation. S i m i l a r vortex f o r m a t i o n s were p r e v i o u s l y observed f o r a f u l l - f o r m ship model i n O h (1977). The p contours are similar and consistent to those for u. Note the low p values i n the v i c i n i t y o f the bilge. The H profiles indicate a v e r y t h i n boundary l a y e r developing under f a -vorable pressure-gradient conditions. This is also t r u e for the

u p r o f i l e s , w h i c h also display t h e displacement effects near

t h e free surface and possibly the effects of the bow-bilge vor-tex near the bilge ( t h a t is, r e l a t i v e l y large values close to the h u l l surface). The i n n e r parts of both the H and u pro-files are very steep and appear t u r b u l e n t , w h i c h indicates t h a t the c y l i n d r i c a l studs f i t t e d atx = 0.05 to s t i m u l a t e t u r -b u l e n t flow were effective. A t a l l -b u t the largest depth, v is positive w i t h quite large values near the h u l l surface, here again, due to displacement effects. A t the largest depth, t h e i n n e r p a r t of the u p r o f i l e is negative and steep, w h i c h is a p p a r e n t l y related to the f o r m a t i o n of the bow-bilge vortex, and the outer p a r t is positive and flat. N e a r the free surface, the w p r o f i l e is r e l a t i v e l y flat w i t h s m a l l negative values. A t l a r g e r depths, the i n n e r p a r t o f the p r o f i l e becomes more negative w i t h depth such t h a t a t the largest depth large downward flow is displayed near the h u l l surface, w h i c h , here again, is apparently related to the f o r m a t i o n of the bow-bilge vortex. The p profiles show r e l a t i v e l y h i g h values near the

h u l l a t the free surface, and decrease w i t h depth. A t the largest depth, the pressure is negative i n t h e v i c i n i t y o f the bow-bilge vortex.

Atx = 0.2 [Figs. 7(6) a n d 8(5)] a n d 0.4, t h e g r o w t h of the b o u n d a r y layer and continued convergence of the flow to-wards the keel are evident. The H contours and u contours close to the h u l l display the t h i c k e n i n g of the boundary layer, w h i c h continues to be s t r o n g l y effected by the flow conver-gence towards the keel, t h a t is, 8 is q u i t e t h i c k near the keel, t h i n near the bilge, and somewhat t h i c k e r near the free sur-face, especially at x = 0.4. At x = 0.2, away f r o m the h u l l , t h e u contours continue to show some displacement effects near the free surface, w i t h increasing values at larger depths. Note the r a t h e r h i g h values i n the v i c i n i t y o f t h e bilge. A t

X = 0.4, away f r o m the h u l l , u = 1, except f o r a n i s l a n d of

h i g h velocity m i d w a y between the bilge a n d the w a t e r p l a n e . A t X = 0.2, v w is m o s t l y downwards w i t h r a t h e r large v a l -ues, w h i c h increase i n magnitude towards the bilge. The bow-bilge vortex appears to encompass a considerably larger area a n d induces u p w a r d flow near the centerplane. A t x = 0.4, v - w has decreased such t h a t i t is q u i t e s m a l l , except at the bilge where the r e m n a n t s of the bow-bilge v o r t e x appear to be evident. The p contours generally display decreasing v a l -ues f r o m x = 0.2 to 0.4, except i n the r e g i o n of the bow-bilge v o r t e x where the m i n i m u m pressure increases. The lowest values are close to the h u l l , especially i n t h e r e g i o n o f the bowbilge vortex. The H and u profiles indicate the t h i c k -e n i n g o f t h -e b o u n d a r y lay-er, as d-escrib-ed -earli-er. A t x = 0.2, t h e u p r o f i l e s show the influences of displacement and some wave effects and possibly the bow-bilge v o r t e x near the free surface and bilge, respectively. A t .r = 0.2, the v a n d w pro-files display s i m i l a r characteristics as at x = 0 . 1 , b u t w i t h increased magnitudes near the h u l l due to t h e large increase