J M a r Sci Technol (2013) 18:339-348 D O I 10.1007/S00773-013-0211-8
O R I G I N A L A R T I C L E
Estimation and prediction of effective inflow velocity
to propeller in waves
Michio Ueno • Y o s h i a k i T s u k a d a • K a t s u j i T a n i z a w a
Received: 15 M a y 2012/Accepted: 14 January 2013/Published online: 7 February 2013 © J A S N A O E 2013
Abstract A free running test using a container ship m o d e l clarified properties o f effective i n f l o w velocity to propellers i n waves. The analysis assumes that thrust and torque vary keeping their relation to the e f f e c t i v e i n f l o w velocity as represented b y open-water characteristics o f a propeller i n a steady c a l m water condition. Measurement i n regular waves confirmed the variation o f average values o f the e f f e c t i v e wake coefficient and ship speed depending on wavelength and wave encounter angle. Comparison w i t h the longitudinal flow velocity measured at the sides o f the propeller using an onboard vane-wheel cuiTent meters c o n f i r m e d that one can estimate the e f f e c t i v e i n f l o w velocity based on thrust or torque data. Theoretical estimates i n regular waves based on a strip method are p r o -vided and compared w i t h the experimental data. A prediction model o f the future i n f l o w velocity is proposed to cope w i t h a time delay o f a propeller pitch controller f o r higher propeller efficiency i n waves.
K e y w o r d s E f f e c t i v e i n f l o w velocity i n waves • Free running model test i n waves • Thrust and torque i n waves • E f f e c t o f propeller load on wake coefficient • A R model • B u r g method
1 Introduction
Higher propulsive efficiency o f ships has become more important than ever as one o f the measures to prevent
M . Ueno ( E l ) • Y . Tsukada • K . Tanizawa
Fluids Engineering and Ship Performance Evaluation Department, National Maritime Research Institute, 6-38-1 Shinkawa, Mitaka, T o k y o 181-0004, Japan e-mail: ueno@nmri.go.jp
U R L : http://wvvw.nrm-i.go.jp/
global w a r m i n g . There are many measures to reduce the f u e l consumption such as development o f h u l l f o r m s hav-i n g small reshav-istance, h hav-i g h effhav-ichav-iency propellers, and devhav-ices to reuse heat or fluid energy otherwise discarded.
A m o n g them is a propeller pitch control based on a real time estimate o f e f f e c t i v e i n f l o w velocity to the propeller that depends on ship speed, ship motion, and waves. I n case there is a time delay caused by the estimation procedure or the mechanism i n the pitch controller, one must predict future i n f l o w velocity to the propeller.
Taniguchi [1] and M c C a r t h y et al. [2] reported open-water characteristics o f a propeller i n waves, where they fixed the propeller to the caniage. Nakamura et al. [3] studied open-water characteristics o f a propeller i n regular and iiTegular waves considering the effect o f heave, pitch and surge oscillations. They showed that the average p r o -peller characteristics i n waves are identical w i t h those i n calm water. T h e y also clarified the fluctuation o f thrust and torque i n waves trace o n open-water curves. Y a m a n o u c h i et al. [4] and Y o s h i n o et al. [5] reported experimental results on the thrust and torque fluctuation i n waves using free running models. Sluijs [6] and Nakamura et al. [7] used i n their experiments captive models i n w h i c h vertical motions were free. Nakamura et al. [ 8 ] , Tsukada et al. [ 9 ] , and Aalbers and Gent [10] reported the wake flow mea-surement i n waves at the propeller position using t o w e d model ships w i t h o u t a propeller. The f o r m e r t w o papers confirmed the average wake coefficient i n regular waves varies depending on wavelength. Nakamura et al. [8] pointed out the average wake coefficient i n irregular waves is the same i n general as that i n the c a l m water. Tasaki [11] discussed theoretically effects o f surge m o t i o n and orbital m o t i o n o f waves o n the effective i n f l o w velocity. Nakamura et al. [7] considered the effects o f heave and pitch m o t i o n . These are researches f o r m i n g a basis f o r this
340 J Mar Sci Teclinol (2013) 18:339-348
paper but no research intended to estimate the i n f l o w velocity i n real time using thi'ust or torque data and use i t to improve the propeller efficiency.
The authors carried out a free running model test f r o m the v i e w p o i n t o f estimating axial i n f l o w velocity o f a propeller i n waves. The thrust and torque data and open-water characteristics o f a propeller i n steady c a l m open-water provide direct estimates o f the i n f l o w velocity. This process assumes that a quasi-steady analysis works even i n unsteady conditions. A strip method provides theoretical estimates o f i n f l o w velocity and ship m o t i o n i n regular waves. The authors discuss whether the direct and the theoretical estimation are practical i n actual seas. Data o f relative l o n g i t u d i n a l flow velocity at the sides o f the pro-peller i n regular and irregular waves measured using vane-wheel cuiTent meters coiToborate the discussion. The authors propose a method to predict the i n f l o w velocity i n the near f u t u r e using past data to cope w i t h a possible t i m e delay o f a pitch controller.
2 Model test
2.1 M o d e l ship and test conditions
The test site is the A c t u a l Sea M o d e l Basin [ 1 2 ] , completed i n 2010, where 382 units o f flap type wave generators suiTound the whole periphery o f the tank except the adja-cent t r i m tank part. The caniage system consists o f a m a i n and a sub caniage w i t h a turntable that can tow or track a model ship.
The authors caixied out a free running test using a con-tainer ship model. Table 1 lists the principal dimensions o f the model ship compaied w i t h the actual one, i n which
L stands f o r the length between perpendiculars. The model
ship runs along designated courses by a self-steering control while the caniage system tracks i t using a C C D camera. Although cables connect the model ship to the carriage, they are loose enough not to restrain the ship's motion. Four wires clamp the model ship f o r acceleration and decelera-tion, w h i c h are also loose enough during measurement.
Table 2 shows the test conditions. A servomotor drove the propeller at two kinds o f constant revolutions n, 11.9 and
Table 1 Principal dimensions o f a container ship
Item Ship M o d e l Length between P. ( m ) , L Breadth (m) Draft (m) Block coefficient Prop, diameter (m) Expanded area ratio
300.0 40.0 14.0 9.0 0.65 0.775 4.000 0.533 0.187 0.120
16.6 ips. The wave encounter angle x vaiies f r o m 0 deg. f o l l o w i n g the wave condition, to a 180 deg. head wave condition, at intervals o f 45 deg. I n regular wave conditions, designated wave heights i ï ^ were 0.05 m and 0.075 m and the wavelength to ship length ratio UL vaiied f r o m 0.4 to 3.0. The spectra o f long crested irregular waves are the types o f the International Ship Stmcture Congress [13] o f which wave p e i i o d TQI are 1.0, 1.3 and 1.6 s, where their desig-nated significant wave heights were the same, 0.1 ni.
The authors also carried out conventional t o w i n g tests; resistance tests, self-propulsion tests, and propeller tests i n open water, to analyze the free running test data, though they do not appear e x p l i c i t l y i n this paper.
2.2 Measuring instruments
Table 3 shows measured items and measuring instruments i n the tank test. The model ship setup is shown i n F i g . 1.
T a b l e 2 Free running test conditions
Item Parameter
Propeller revolution, n (rps) 11.9 16.6 Ship speed i n calm water (m/s) 0.991 1.394 Froude number, f , „ i n calm water 0.158 0.223 Wave encounter angle, % (deg.)
0 ( f o l l o w i n g ) - 1 8 0 (head)
Regular wave Wave height, H.,y (m)
0.05, 0.075 Wave length ship length ratio, XIL
0.4-3.0 Irregular wave
Wave spectrum (long crested waves)
ISSC Wave period, T Q I ( S )
• 1.0, 1.3, 1.6 Significant wave height, H^n (m)
0.10
T a b l e 3 Measured items and devices in the free-running model test
Item Device
Ship position and speed Ship tnotion
Thrust and torque
Longitudinal flow velocity (314 m m right and 320 m m left o f f the propeller center)
Encounter wave
Relative wave height (fore-end centerline and A P both sides) Rudder angle
Tracking system Fiber optical gyro Dynamometer
Vane-wheel current meter (3 m m diameter)
Wave gauge (servo type, fixed to the sub-caiilage) Wave gauge (capacity type,
fixed to the model) Potentiometer
J Mar Sci Teclinol (2013) 18:339-348 341
F i g . 1 Model ship setup under the sub-carriage
A c c o r d i n g to t o w i n g test data [ 1 2 ] , m a x i m u m position eiTors o f the caniage are about Ö.003 m , 0.002 m , and 0.02 deg. f o r the m a i n and sub caniages and turntable, respectively. M a x i m u m speed eiTors are about 0.004 m/s, 0.004 m/s, and 0.1 deg./s. The C C D camera f i x e d to the turntable watches tracking targets onboard, t w o black cir-cles o f w h i c h the diameter is 0.08 m on a w h i t e board, located along the centerline, 0.4 m fore and a f t f r o m the center o f gravity o f the model ship. The image analysis tells position and heading o f the model ship relative to the caniages, on w h i c h data the model ship tracking is based. Resolutions o f an image are 640 x 480 pixels. Since the distance o f the circles is about 80 % o f 640 pixels, m a x i -m u -m position and direction enors are about 0.002 -m and 0.11 deg., respectively. Frequency o f analysis that depends on the size o f the circles is about 20 H z . The authors used 20 H z data o f position and speed stored i n files; on the other hand, they monitored these data i n real time w i t h other data measured at 20 Hz.
The fiber optical gyro measures pitch, r o l l , and y a w angles and rates together w i t h surge, sway, and heave accelerations.
The vane-wheel cuiTcnt meters fixed to the m o d e l ship are f o r comparison w i t h the estimated e f f e c t i v e i n f l o w v e l o c i t y converted f r o m the thrust and torque data. Fre-quency responses o f the current meters were tested sep-arately b y t o w i n g t h e m i n regular waves. The results t e l l the v a r i a t i o n o f a m p l i t u d e ratio and phase delay is not significant w i t h i n the frequency range o f f r e e r u n n i n g test.
2.3 Thrust and torque data corrections
The mass o f the propeller and shaft, 0.803 k g i n the model test, affects the thrust data i n p i t c h and surge oscillating motion. The effect was estimated using longitudinal acceleration data and subtracted f r o m measured thrust data. Since the accelerometer was fixed to the model ship, measured longitudinal acceleration involves surge and pitch effects combined. M a x i m u m thrust corrections i n i ? w = 0.05 m conditions were 1.8 and 1.0 % o f the steady thrust i n calm water w i t h n = 1 1 . 9 and n = 16.6 ips, respectively.
Suppose the added mass is h a l f the water sphere, o f w h i c h the diameter is equal to that o f the propeller, m u l -tiplied by the expanded area ratio, i t should be 0.351 k g . This implies the added mass e f f e c t o f the propeller disk should be smaller than h a l f the shaft and propeller mass effect, i f coiTected. Based on the rough estimate above, the authors did not take the effect into consideration.
The authors also conected torque data by subtracting propeller shaft f r i c t i o n calibrated depending on propeller revolution using a d u m m y boss. The f r i c t i o n component vaiies f r o m 1.2 to 2.3 % o f the measured torque.
3 Estimation using tlirust and torque data
3.1 Procedure f o r estimating e f f e c t i v e i n f l o w velocity
I n ordinary self-propulsion tests i n calm water, thrust or torque data tell the effective i n f l o w velocity using the open-water characteristics o f the propeller. These are the thrust or torque identification methods. A l t h o u g h the phenome-non i n waves, considered here, is unsteady, the authors applied the same procedure to every instantaneous mea-sured datum i n waves and discuss validity o f this procedure.
I n this paper, 'wake c o e f f i c i e n t ' and 'effective wake coefficient' mean 1 — vi'^ i n w h i c h Wp stands f o r an effective wake f r a c t i o n .
3.2 Average wake coefficient i n regular waves
Data i n regular waves are unsteady but periodic. I n this subsection, properties o f the average effective wake coef-ficient i n waves are discussed.
Ship speed decreases i n waves because o f the resistance increase i n , waves. Speed decrease is significant i n head wave conditions, as shown i n F i g . 2, especially where the wavelength to ship length ratio is around one. A p p l y i n g the thrust and torque identification methods and averaging after that provides average wake coefficients i n waves shown i n F i g . 3. The effective i n f l o w velocity analyzed
342 J M a r Sci Technol (2013) 18:339-348
using torque data is lai^ger than those using thrust data. I n general, the effective wake coefficient obtained by the thrust identification method is more reliable i n model tests. However, the torque identification m e t h o d should be more practical since torque data is more reliable than thrust f o r full-scale ships.
The average wake coefficient i n waves becomes larger than i n c a l m water admittedly i n head wave conditions
1.5 1.4 1.3 1.2 1.1 1^1.0 CO (;i=16.6rps, ft,=0.05m) X
+
0.9 r 0.8 (H=11.9rps,ffi.=0.05m) • 0.0 I.O 2.0 Wavelength/Ship length 3.0 X(deg.) - - C a l m O 45 + 180 • 0 X 135F i g . 2 Average model ship speed i n regular waves (;;, propeller revolution; designated wave height; x. wave encounter angle)
where the speed decrease is large. Figure 4 shows the average wake coefficient's dependency on Froude number i n head waves o f various wavelength and wave heights 0 . 0 5 and 0 . 0 7 5 m , w h i c h suggests that the larger the propeller load is the larger then is the average wake c o e f f i -cient. The authors think this is the same mechanism as wake coefficient's variation i n c a l m water measured i n a propeller load varying test by Hinatsu et al. [ 1 4 ] and A d a c h i [ 1 5 ] . The difference is that the change o f propeller load i n this free running test is caused by added resistance i n waves. Hinatsu et al. [ 1 4 ] , experimentally, and Toda [ 1 6 ] , theoretically and experimentally, explain this phe-nomenon i n c a l m water is a result of d e f o r m a t i o n o f boundary layer due to the propeller load. The wave and ship m o t i o n e f f e c t on the average nominal wake coefficient is discussed i n references [ 8 , 9 ] .
3 . 3 T i m e varying i n f l o w velocity i n iiTcgular waves
Figure 5 shows the time varying i n f l o w velocity o f t h e propeller converted f r o m thrust and torque data. Relative flow velocity measured b y the current meters and ship speed are also shown f o r comparison. The incident waves are long-crested iiTegular waves of w h i c h the wave encounter angle x is 1 8 0 deg., head wave c o n d i t i o n , wave period T Q I is 1.3 s and significant wave height is 0 . 1 m . The propeller r e v o l u t i o n is 1 1 . 9 ips. These data are typical examples i n its non-periodicity and unsteadiness.
F i g . 3 Average wake coefficient, 1 — u'p, i n regular waves obtained by thrust and torque identification method, dependency on wavelength to ship length ratio (;!, propeller revolution; H„, designated wave height; %, wave encounter angle) [;!=16.6rps,7ïu=0.05m] o 0.8 0.7 0.8 0.7 O.S ' 1 ' • • (X=180deg.)
• . . 1 .
V
• • 1 -8
8 ^ 9 1 O Q_ T. 1 (X=135deg.) ^ _ 2 _ o _ _ ^ QI
.£ 0.7 (X=45deg.) - c ^ - 6 ^ ^ I , I I 0.8 0.7 (X=Odeg.) . • - . - - ^ o_ _ a . J 1 - I-cr
0.0 1.0 2.0 Wavelength/Ship length [;i=n.9rps,fl'H=0.05m] 0.7 0.6 0.7 0.6 0.7 0.6 0.7 0.6 , o o B -Ö---W----0 _ Q _ 0 O (X=l • w^, 1 ^ (X=135deg.) - o - O (X=45deg.) —1 ' — - Q Q- _ _ l I r O - _ - ( ) (X=0deg.) O 3.0 0.0 1.0 2.0 3.0 Wavelength/Ship length In waves Calm Thrust ident. O Torque ident.•
SpringerJ M a r Sci Technol (2013) 18:339-348 343 0.8 0,7 (X=180d^,fl'„,=0.05m, 0.075m) < "iTn !•• (ffi QQM 0.6 1 0.10 [" ( i p s ) , T, thrust i d . Q, torque i d . ] 0.15 0.20 0.25 • C a l m t l 1.9T] • C a l m [ 1 6 . 6 T ] A C a l m [ 1 1 . 9 , Q ] • C a I m [ 1 6 . 6 , Q ] o I n w a v e [ 1 1 . 9 T ] ° I n wave[16.6,T] A I n wave [11.9,Q] O I n wave [ 16.6,Q]
F i g . 4 Average wake coefficient, 1 — ii'p, in regular waves obtained by thrust and torque identification method, dependency on Froude number, F,, (%, wave encounter angle; H „ , designated wave height; II, propeller revolution)
1.2 1.0 0.8 0.6 0.4 0.2 0.0 1.2 1.0 0.8 0.6 0.4 0.2 0.0 (T910;x=0deg., roi=1.3s,flin=0.10m, H=11.9rps) [ : > i 1 5 10 Tirae(s) 15 20
« [/(ship) »p[T] iip[Q] --—-i((stb) -- - - - »(port) *f/(ship), ship speed, longitudinal comp.;
i/pfT] &"p[Q], effective inflow velocity by thrust &torque idenl.; K(stb) & ii(porO, velocity by vane-wheel current meter.
F i g . 5 Time history o f longitudinal component o f ship speed, U (ship); effective i n f l o w velocity obtained using thrust and torque data, Up[T] and !(p[Q]; flow velocity measured b y vane-wheel current meter at starboard and port sides o f propeller, i((stb) and //(port) i n iiTegular head and f o l l o w i n g waves (%, wave encounter angle; Toi, primary wave period; Hy^, designated significant wave height; /!, propeller revolution)
T h e model ship speed varies due to surge m o t i o n i n waves. The relative f l o w velocities fluctuate around the m o d e l ship speed, w h i c h is a result o f a water particle's orbital m o t i o n due to waves. The reason w h y the averages o f these fluctuations are seen to be slightly smaller than the m o d e l ship speed is that the cuiTcnt meters are i n the wake flow near the model ship's side h u l l . The i n f l o w velocities converted f r o m thrust and torque data shows almost the same values. These time v a r y i n g characteristics resemble those o f the relative flow velocities though there are
quantitative differences . These quantitative differences should come f r o m those o f wakes at the center o f and the 314 or 320 m m o f f center o f the propeller position.
Figure 6 shows comparison o f an auto coiTclation coefficient and a cross correlation coefficient f o r c o n f i r m -ing the resemblance. The auto con-elation is o f the thrust converted i n f l o w velocity. The cross correlation coefficient is o f the thr-ust converted i n f l o w velocity and the starboard relative flow velocity. Some phase shift that c o u l d be partly attributed to phase delay o f the cuiTent meter is seen between these t w o coefficients, but the t w o coirelation coefficients agree w e l l . The authors consider that this result supports the fact that the thrust or torque converted i n f l o w velocity is reliable even i n unsteady conditions.
Based on the discussion above, the direct estimate o f i n f l o w velocity using thrust or torque is p r o m i s i n g f o r application to a propeller pitch control at actual seas though i t cannot t e l l future values.
4 E s t i m a t i o n using wave data
Average ship speed, ship m o t i o n i n waves, and orbital m o t i o n o f water particles due to waves determine the effective i n f l o w velocity to the propeller. Since theoretical calculations can estimate the ship m o t i o n i n waves, i t can also estimate the i n f l o w velocity i n waves based on i n c i -dent wave i n f o r m a t i o n . This section looks i n t o whether this procedure works or not.
L e t us consider the i n f l o w velocity i n regular waves o f w h i c h amplitude is h^, wave number k, and wave circular frequency ©. Figure 7 shows a coordinate system i n w h i c h positive directions f o r surge, heave, and p i t c h motions are f o r w a r d , d o w n w a r d , and bow up, respectively. T h e i r phase, measured f r o m w h e n wave trough is at m i d s h i p , takes a positive value f o r delay.
W a v e encounter circular frequency cOg, defined by the f o l l o w i n g equation, depends on wave encounter angle % and average ship speed U.
coe = CO - kU cos X. (1)
Suppose that surge, heave and p i t c h amplitudes are ^a, and 9a; their phase delays ej;, and Se; the propeller coordinates {xp, 0, zp). Then the f o l l o w i n g f o r m u l a is considered to estimate the i n f l o w velocity Mp, i n w h i c h t represents time.
Hp = ( 1 - Vi;p){;7 - ffle^a Sin(c0e? - E f ) }
+ coh^ e x p [ - / c { z p - I - Ca cos{cOet - £()
- X p 0 a COs(cL»e'^ " £ f l ) } ] COS X
X cos[cöer - /:cosx{a-p - ^^cos(cOet — fif)}]. (2)
I n E q . 2, the e f f e c t i v e wake coefficient (1 — Wp) is assumed to include its propeller l o a d dependency. Surge
344 J Mar Sci Teclinol (2013) 18:339-348
F i g . 6 Comparison o f auto con-elation coefficient of effective i n f l o w velocity obtained using thrust data, ;(p[T], and cross correlation coefficient o f !/p[T] and flow velocity measured by vane-wheel current meter at starboard side o f propeller, i((stb) i n in-egular head and f o l l o w i n g waves (x, wave encounter angle; TQI, primary wave period; Hy^, designated significant wave height; n, propeller revolution) 1.0 0.5 S 0.0 -0.5 -1.0 (T727; x=180deg,roi=1.3s, //i/3=0.10m, /!=11.9ips)
1
10 L a g ( s )Auto corr.(Hp[T], itp[T]) 15 0 (T910; x=Odeg,roi=1.3s, iïl/3=0.10m, )i=11.9ips)
ft A\
1 • MA A
\
v)
V
V
Ml
Lag (s) • Cross corr.(H(stb), iip[T])10 15
( » p [ T ] , Inflow vel. (thrust ident.), «(stb), Flow vel., stb side of prop.)
F i g . 7 Coordinate system ( O X Y , Earth fixed coordinate system; oxyz, ship fixed coordinate system; x, wave encounter angle; ^, surge; ^, heave; 9, pitch; 8, phase o f ship response)
m o t i o n affects ship velocity and the l o n g i t u d i n a l position o f the propeller. Heave and pitch motions affect the vertical position o f the propeller.
The authors confirmed tiirough trial calculations that the effects o f oscillation o f the propeller position or the effect of p i t c h and heave m o t i o n are negligible. Neglecting the effect and introducing a coefficient a representing the effect o f wave amplitude decrease at the stern, pointed out by Jinnaka [17, 18], lead to the f o l l o w i n g equation. Kp = (1 - Wp){U - cüe<^a sin(a;e/ - e^)}
- I - am /?a e x p ( - f e p ) cos x cos(cüe/ - kxp cos x ) . (3) Equation 3 consists o f the wake flow i n c l u d i n g the surge oscillation e f f e c t and the orbital m o t i o n o f water particles i n an attenuated wave at the stern. Nakamura et al. [7] adopted the e f f e c t o f wave amplitude decrease at the stern by introducing a coefficient i n their equations f o r head wave conditions. T a k i n g into account the e f f e c t o f encounter angle % i n Nakamura's coefficient, the authors assume a as f o l l o w s .
r
/ A \ X 0. 2 r 4 - 0 . 5 , f o r - ^ ^ < 2 . 5 ^ ^ 1 V ^ l c o s x i ; L\cosx\ 1, f o r 2.5 < , , ^ L | c o s x | . Figure 8 shows the calculated surge amplitude using thestrip method [ 1 9 ] , compared w i t h the experimental data o f
0.05 m wave height. A l t h o u g h the average model ship speed depends on the wavelength and the encounter angle, the calculations assume the ship speed is constant f o r each encounter angle. The average Froude numbers, measured and used i n the calculations, f o r the encounter angle 180, 135, 45, and 0 deg. are 0.149, 0.149, 0.155, and 0.158 for 11.9 rps and 0.212, 0.211, 0.217, and 0.233 f o r 16.6 rps, respectively. T h e calculations agree w e l l w i t h the experimental data, w h i c h confirms the v a l i d i t y of theoretical calculation.
Figure 9 presents the amplitude o f the effective i n f l o w velocity i n regular waves, calculated using Eqs. 3 and 4, and obtained experimentally using thrust and torque data. I n theoretical calculation, the e f f e c t i v e wake coefficient is assumed to be 0.7. The calculation seems to explain qualitatively the test data i n the l o n g wave region. D i f f e r -ences between the calculation and test results, however, are not small f o r a l l wave encounter angles. Since the estimates of surge m o t i o n are f a i r l y good as shown i n F i g . 8, the estimate o f wave amplitude attenuation, a i n Eq. 4, should be responsible mainly f o r these discrepancies.
Even i f a method c o u l d resolve this problem, one tra-ditional problem remains; the estimate o f wave field. I t is d i f f i c u l t to measure i n actual seas directional spectra including phase o f every elementary wave. Therefore, theoretical estimate o f i n f l o w v e l o c i t y is hard to apply to a propeller p i t c h control even though i t c o u l d tell f u t u r e values.
5 Prediction of effective inflow velocity
The direct estimate using thrust or torque data is practical and reasonable i n actual seas o n applying to a propeller pitch control. However, the direct estimate cannot tell the future i n f l o w velocity to cope w i t h a time delay o f a pitch controller. This is the reason w h y the direct estimate needs a prediction model.
J M a r Sci Technol (2013) 18:339-348 345
F i g . 8 Surge amplitude ratio to wave amplitude in regular waves, comparison o f experimental data with calculations ( H „ , designated wave height; n, propeller revolution; %, wave encounter angle) 2.0 1.5 1.0 ( H „ , = 0 . 0 5 m , H=11.9rps)
0
- " Q
( / / „ , = 0 . 0 5 m n =16.6ips) X(deg.) 2.0 3.0 0.0 1.0 Wavelength / Shiplength (Lines,cal.; Marks, exp.)•180 - - •135 -45 • 0 O 180 • 135 A 45 O 0
F i g . 9 Amplitude o f effective i n f l o w velocity obtained by thrust identification method {filled marks) and torque identification method {open marks), comparing w i t h calculation (lines)
( / / w . designated wave height; propeller revolution; X, wave encounter angle)
0.12 0.08 [m/s : 0.04 d a m 0.00 0.12 > £ in 0.08 a 0.04 1 1 1 1 1 i 1 1 . 1 1 J 1 J 1 i 1 1 1 1 1 1 (X=180d eg., ffii.=0.05m) •
/ • • • •
: # ^ O . 1 < > , 1 , , , 1 1 . . . . 0.00 1 1 1 1 1 ll n- .\
1 1 1 1 1 1 1 1 1 t 1 1 1 1 1 i 1 1 (X=Odeg 1 1 i i . 1 . 1 1 1 ., Hw=0.05m) • I 1 ƒ : , i^%
•
* a
A S . . .i
, . . 1 , , . . 1 . . . , 1.0 2.0 3.0 Wavelength/Ship length 0.0 1.0 2.0 Wavelength/Ship length 3.0 n (rps) 11.9 16.6 Calculation E x p . Thrust ident.•
O E x p . Torque ident. • AT i m e delay o f a propeller p i t c h c o n t r o l i n full-scale w o u l d be several seconds. T o predict several seconds' f u t u r e values, the authors applied the A R (Autoregression) model using the B u r g method [19] to the thrust or torque converted i n f l o w velocity data f o r the prediction.
The A R model is represented b y the f o l l o w i n g equation.
« p , / = fllMp,,-! - I - a 2 i ( p , i - 2 H 1- a » H p , , - M - (5)
I n E q . 5, Mp_/, ( a \ , a 2 , . . . , A M ) , and N, stand f o r the i n f l o w v e l o c i t y o f data number /, A R coefficients, and the number o f A R terms, respectively.
The procedure is as f o l l o w s . A t a point o f time, the analysis determines A R coefficients using the most recent data o f w h i c h number is A^^. The m i n i m u m Final Prediction Error determines the number o f A R terms, /V„ that is, though, l i m i t e d up to twice the square root o f /V^ [ 2 0 ] . The
A R calculation applying the most recent past /V, data pre-dicts a one-step f u t u r e value. The A R calculation a p p l y i n g to the predicted one step f u t u r e value and the most recent past /V, — 1 data predicts a two-step f u t u r e value. T h i s A R calculation procedure repeats until i t reaches designated A'p-step f u t u r e value. A t the next point o f time, on obtaining one new datum, the whole procedure above repeats.
F i g u r e 10 shows test number 727 ( T . 7 2 7 ) i n i r r e g u l a r head waves, the same measurement as F i g . 5; x = 180 deg., I] = 0.841 m/s, T Q I = 1.3 s, Hy-i = 0.10 m ,
n = 11.9 rps. T o t a l data number, N D , is 597 o f w h i c h
the f r e q u e n c y is 20 H z . Rudder angle varies s l o w l y between - 2 and 4 deg. d u r i n g this measurement. T h e r e f o r e , the r u d d e r blockage e f f e c t s h o u l d be n e g l i -g i b l y s m a l l . T h e p r e d i c t i o n procedure used filtered data, shown i n the top figure, to see p r e d i c t i o n errors c l e a r l y .
346 J M a r Sci Teclinol (2013) 18:339-348
[T727(filtered), thrust converted data]
[X=180deg., C/=Ö.841m/s, roi=1.3s, ffi/3=0.10m, H=11.9rps]
True, thiTJSt converted data
Predicted, steps to pred. point; o 1 (50% plot) •10 2 c 30 g 20 0 350 400 450 500 Data number (20Hz) 550
F i g . 10 Prediction o f effective i n f l o w velocity by A R model using the Burg method, compared w i t h true thrust converted data in head irregular waves (T. no. 727; 200-point A R analysis; x. wave encounter angle; U, ship speed; T Q I , primary wave period; Hm, designated significant wave height; n, propeller revolution)
[T910(filtered), thrust converted data]
[X=Odeg., C/=0.984m/s, 7oi=1.3s, //i/3=0.10m, /i=11.9ips]
400^ 450
Ü5
True, thrust converted data
Predicted, steps to pred. point; o 1 (33% p l o t ) 1 0 20
O w Ul Ö 30 (D n 20 10 z < 0 150 200 250 300 350 Data number (20Hz) 400
F i g . 11 Prediction o f effective i n f l o w velocity by A R model using the Burg method, compared w i t h true thrust converted data i n f o l l o w i n g irregular waves (T. no. 910; 100-point A R analysis; X, wave encounter angle; U, ship speed; Toi. primary wave period; H-iri, designated significant wave height; propeller revolution)
T h e authors had c o n f i r m e d beforehand that this filtering d i d not a f f e c t the outcome q u a l i t a t i v e l y . T h e second figure shows the c o m p a r i s o n o f p r e d i c t e d values w i t h true thrust converted i n f l o w v e l o c i t y data, f r o m data number 3 5 0 - 5 5 0 . A^^ is 200 and A^^ values are 1 , 5 , and
10. T h e p r e d i c t e d values o f Ap = 1 are almost i d e n t i c a l w i t h the true data. H o w e v e r , the larger Ap is, the larger the discrepancy between predicted values and true data becomes, w h i c h is s i g n i f i c a n t especially w h e n the data tendency changes f r o m the past. T h e b o t t o m figure is o f
N, f o r every A R analysis point. M o s t o f a l l , the A R t e r m
number is b e t w e e n 24 and 28, the l i m i t .
Figure 11 is another example o f a f o l l o w i n g iiTegulai' wave condition, test number 910 (T.910); X = 0 deg.,
U = 0.984 m/s, Toi = 1.3 s, H^i = 0.10 m , /z 11.9 ips,
N D = 427. is 100 and A'p values are 1, 10, and 20. Rudder angle varies between 0 and 4 deg. The discrepancy between predicted values and trae data is smaUer relatively f o r Np values than the head wave condition, F i g . 10. The reason is the true data are more periodic or monotonous and the A R model works w e l l f o r this f o l l o w i n g wave condition. Most o f all, the A R term number is 19 or 20, the l i m i t .
Figure 12 shows h o w the root mean square o f prediction eiTor grows w h e n the steps to the prediction point increase depending on the A R analysis number. Data ranges o f eiTor analysis are 221-578 f o r T.727 and 221-^08 f o r T.910, independent o f either the analysis point number or the number o f steps to prediction point. The difference between head and f o l l o w i n g wave conditions are clear. B o t h prediction eiTors seem to saturate f o r large but at d i f f e r e n t number o f steps to the prediction point.
0.15 I 1 • ^ X=180deg.(T727)
Numb, of steps to prediction point
F i g . 12 Root mean square o f prediction error depending on A R analysis data length and prediction point (comparison o f T. no. 727 w i t h T. no. 910; x, wave encounter angle)
I f we l o o k into a point o f the same prediction error, 0.04, f o r example, o f w h i c h the data number o f A R analysis is
100, the steps to prediction point are 6 and 15 f o r head and the f o l l o w i n g wave conditions, respectively. CoiTespond-i n g tCoiTespond-imes to the predCoiTespond-ictCoiTespond-ion poCoiTespond-int are 0.30 and 0.75 s f o r head and the f o l l o w i n g wave conditions. M o d a l wave encounter periods, on the other hand, are 0.92 and 2.52 s, respectively. The ratios o f these values then become comparable to 0.33 and 0.30 f o r head andthe f o l l o w i n g wave conditions. Based on an assumption that an aUowable time is one third the wave encounter period, i t w o u l d be, i n full-scale, 2.7 s i n head waves and 7.3 s i n f o l l o w i n g waves, respectively, f o r the above examples. For a cargo
J Mar Sci Teciinol (2013) 18:339-348 347
carrier w i t h a 4-blade controllable pitch propeller, o f w h i c h length, dead weight, propeller diameter, and m a x i m u m continuous output are 120 m , 11400 ton, 3.6 m , and 3.9 M W , respectively, the time delay o f p i t c h controller is around 1.7 s and the pitch control speed is 1 deg./s. These values seem to suggest this prediction model works w e l l as long as the time delay is concerned.
The encounter wave period, however, could be smaller than these examples above depending on wave period, ship speed, and encounter angle. I n case the allowable t i m e becomes smaller than the time delay o f a pitch controller, the prediction m o d e l may not w o r k w e l l . Therefore, ana-l y z i n g the wave encounter period w i ana-l ana-l heana-lp i n actuaana-l seas i n advising whether the model should be on or o f f .
The prediction model presented here is simple because i t employs only estimated i n f l o w velocity. The K a l m a n filter combined w i t h the A R model [21] or w i t h the principal component analysis [22] m i g h t i m p r o v e the prediction because they can use i n f o r m a t i o n such as ship speed or relative wave height, w h i c h the authors leave to future study.
6 Concluding r e m a r k s
T o realize a propeller pitch control that can respond to v a r y i n g i n f l o w velocity to propeller i n waves, its estimation and prediction are studied.
A free running model test was earned out to estimate the unsteady i n f l o w velocity to a propeller i n waves. The authors used an ordinary thrust and torque identification method to analyze the unsteady i n f l o w velocity though these direct methods w h i c h are originally f o r steady c a l m water conditions. The average e f f e c t i v e wake coefficient shows the propeller load dependencies, w h i c h are analo-gous to those observed i n propeller load v a r y i n g tests i n calm water. Relative longitudinal flow at the sides o f propeller show close coiTelation w i t h the estimated i n f l o w velocity, c o n f i r m i n g the direct method works w e l l even i n unsteady conditions. Theoretical estimates i n regular waves based on a strip method are also provided and compared w i t h the direct estimates. Differences between them i m p l i e d the need o f improvement i n evaluating wave amplitude's attenuation at stern.
T o cope w i t h a t i m e delay o f a propeller p i t c h con-troller, the authors proposed a p r e d i c t i o n m o d e l o f the i n f l o w v e l o c i t y using an A R m o d e l . A p p l i c a t i o n s o f the m e t h o d to the m o d e l ship data i n irregular waves con-firmed that i t could cope w i t h a possible t i m e delay o f the controller i n actual seas depending on a wave encounter p e r i o d .
A c k n o w l e d g m e n t s The authors thank M r . Yasushi Kitagawa at the National M a r i t i m e Research Institute f o r his providing the informa-tion about a propeller pitch controller of a cargo carrier. This study was supported by the Program for Promoting Fundamental Transport Technology Research f r o m the Japan Railway Construction, Trans-port and Technology Agency (JRTT).
Appendix
Reference test data including ship m o t i o n i n regular and iiTegular waves are shown i n Figs. 13 and 14.
1.2 .2 0.8 Q. 0.0 u 1.5
I
ffi 0.0 .a o S. -1.5 1.2I
I
0.4 0.0 >I
0.0 1.2 '5 S 0.8 •S 0.4 u I Z I 0.0 <D 1.5 M 0.0 o K -1.5(T.801; Wavelength/Ship length=2.0, ffli'm=0.053m )
1 ^
' 1
1
1
i
l
l
!
1 '
i I
' \ n 7!
\ 1 LA / \ 7 V / \ . / - ' i \ -M' \ -.j.'- \ \ / 1\ i /
1 \ 1T Y / j \ y j \
5 10 Time(s) 15(T.604; Wavelength/Ship length=1.0, ffii'm=0.040m )
. 1 1 1 1
. 1 . ^
' V
i ^ -
1 '
T
1 ;. i : .
1 1 " 1
i
1
1
Ar\ f \ \r\
A '
/ v
A / A
.'-\/-'-\ //'-\
/ • ' ' \ ' / • ' • \ M"> —1\~i V-l'
V'l V" U- JX/1 ; ^ 1 1 ^i
_X/1
v i — \
/ v '\j
v y ' \ /
5 10 Time(s) 15(T. 1009; Wavelength/Ship length=0.S5, ffii'm=0.046m)
I
1
J . . \^ . . . V ^ V \ ^ ' - ^ 1 ^ - V y ] ^ 1T ~
IN \1
1
1
!1 1 1
„ 1 „1
1 1 1 1i
10 Time(s) 15 [X=180deg., « = I 1 . 9 r p s ]Speed, Velocity: f/(ship) Up[T] « ( s t b ) ; (m/s) Pitch, Heave: Pitch ang.(deg.) - Heave acc.(m/s2) F i g . 13 T i m e history o f longitudinal component o f ship speed, (/(ship); effective i n f l o w velocity obtained using thrust data, t(p[T]; flow velocity measured by vane-wheel current meter at starboard, !((stb) in regular head waves (%, wave encounter angle; Hw^, measured wave height; u, propeller revolution)
348 J M a r Sci Technol (2013) 18:339-348 4,0 2,0 0,0 -2.0 -4,0 0.10 0.05 0.00 -0.05 -0.10 4,0 2.0 0,0 -2,0 -4,0 0.10
(T.727; x=180deg., roi=l,3s, //i/3=0.10m, »=11.9rps)
V
V
1/S2)
— p itch ang.(deg.) — tleave acc.(n 1/S2)
-rt »:
^
A 1h
A .V
^jt-APport(rn ) APstb(m)
15 20 Time(s) 25 30 (T910; x=Odeg., roi=1.3s, iïi/3=0.10m, /!=n.9rps)
^ —
r itch ang.(deg.) — Heave acc.(ni/s2)
F i g . 14 T i m e history o f pitch angle {bow-up positive), heave acceleration at center o f gravity {downward positive), and relative waves at aft peipendicular {upward positive) i n irregular waves, corresponding Fig. 5; ( / , wave encounter angle; TQU primary wave period; Hy^, designated significant wave height; n, propeller revolution)
References
1. Taniguchi K (1961) Propulsion performance i n waves. B u l l Soc Naval A r c h i t Japan 383:315-328 (in Japanese)
2. McCarthy JH, Norley W H , Ober G L (1961) The performance o f a f u l l y submerged propeller in regular waves. David Taylor M o d e l Basin, Report 1440
3. Nakamura S, Naito S, Inoue R (1975) Open-water characteristics and load fluctuations o f propeller i n waves. J Kansai Soc Naval A r c h i t Japan 159:41-55 ( i n Japanese)
4. Yamanouchi Y , Ando S (1966) Experiments on a Series 60, CB = 0.70 ship model i n obUque regular waves. Papers o f Ship Research Institute, No. 18
5. Yoshino T, Saruta T, Yoshino Y (1974) M o d e l tests on thr-ust and torque increase and fluctuations acting on the propeller shafts o f high-speed container ships w i t h single or t w i n screws i n oblique waves. Papers Ship Res Inst l l ( 4 ) : 2 1 7 - 2 3 2 (in Japanese)
6. Sluijs M F V (1972) Performance and propeller load fluctuations of a ship i n waves. Netherlands Ship Research Centre T N O , Report N o . 163S
7. Nakamura S, Hosoda R, Naito S (1975) Propulsive performance of a container ship i n waves (3rd Report). J Kansai Soc Naval A r c h i t Japan 158:37-46 (in Japanese)
8. Nakamura S, Hosoda R, Naito S, Inoue M (1975) Propulsive performance o f a container ship i n waves (4th Report). J Kansai Soc Naval A r c h i t Japan 159:29-39 (in Japanese)
9. Tsukada Y , Hinatsu M , Hasegawa J (1997) Measurement o f unsteady ship wakes i n waves. J Kansai Soc Naval A r c h i Japan 228:15-20 ( i n Japanese)
10. Aalbers A B , Gent W V (1985) Unsteady wake velocities due to waves and Motions measured on a ship model i n head waves. I n : Proceedings o f 15th symposium on naval hydrodynamics, v o l 15, pp 6 9 - 8 1
11. Tasaki R (1957) On the characteristics o f the d r i v i n g machine i n the self-propulsion test among waves. J Soc Naval A r c h i t Japan 101:25-32 (in Japanese)
12. Tanizawa K , Ueno M , Taguchi H , Fujiwara T, M i y a z a k i H , Sawada H , Tsukada Y (2010) The actual model ship basin. Papers Natl M a r i t Res Inst 10(4): 1-40 (in Japanese)
13. International Ship Structure Congress (1964) Report o f the committee 1, Environmental conditions. I n : Proceedings o f the 2nd ISSC
14. Hinatsu M , M o r i y a m a F, Tsukada Y , Adachi H (1982) On a con-elation between a propeller load and stern flow variation. I n : Proceedings o f the General Meeting o f Ship Research Institute v o l 40, pp 86-89 (in Japanese)
15. Adachi H (1983) On the theorehcal bases and application methods o f the propeller load vai-ying test method. J Soc N a v a l Ai-chit Japan 154:109-117 (in Japanese)
16. Toda Y , Tanaka I , Iwasaki Y (1982) Distortion o f axisymmetric boundary layer due to propeller suction. J Kansai Soc N a v a l A r c h i t Japan 1 8 5 : 3 9 ^ 8 (in Japanese)
17. Jinnaka T (1958) Some experiments on the exiting forces of waves acting on the fixed ship models. J Soc Naval Ai-chit Japan 103:47-57 (in Japanese)
18. Jinnaka T (1960) Periodic sources and its applications (contin-ued). J Soc N a v a l Ai-chit Japan 108:1-4 ( i n Japanese)
19. Salvesen N , T u c k EO, Faltinsen M (1970) Ship motions and sea loads. Trans Soc Naval Archit Marine Eng 78:250-287 20. Hino M (1977) Spectrum analysis. Asakura Shoten ( i n Japanese) 2 1 . Tanizawa K , M i n a m i Y (2006) Wave impact avoidance system
for ships. Japan Patent JP200844472A
-22. Hashimoto N , Nagai N , Shimizu K , Sugawara K (1996) On the Reliability o f the statistical wave forecasting through K a l m a n filtering combined w i t h principal component analysis. Report o f the Port and Harbour Research Institute, 35-1, pp 91-115 (in Japanese)
