Applied Ocean Research 60 (2016) 6 1 - 7 4 C o n t e n t s l i s t s a v a i l a b l e a t S c i e n c e D l r e c t
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Applied Ore^rrResearch
j o u r n a l h o m e p a g e : v v w w . e l s e v i e r . c o m / l o c a t e / a p o r O C E A NR E S E A R C H
Effect of waves on cavitation and pressure pulses
Bhushan Taskar-"'*, Sverre S t e e n R i c k a r d E. Bensow"^, Björn Schroder'
' Department of Marine Technology. Norwegian University of Science and Technology (NTNU), Trondheim, Nomay '' Chalmers University of Technology, Sweden' Rolls-Royce Hydrodynamlc Research Centre. Rolls-Royce AB, Krlstinehamn. Sweden
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A R T I C L E I N F O
Article history: Received 16 April 2016
Received in revised form 24 August 2016 Accepted 28 August 2016
Available online 13 September 2015
Keywords: Propulsion in waves Cavitation Pressure pulses Marine propeller
Propeller performance in waves Propeller design
A B S T R A C T
I n v i e w o f e n v i r o n m e n t a l c o n c e r n s , t h e r e is i n c r e a s i n g d e m a n d to o p d m i z e t h e ships f o r t h e a c t u a l o p e r -a t i n g c o n d i t i o n r -a t h e r t h -a n f o r c -a l m w -a t e r . N o w , i n o r d e r t o -a p p l y this f o r p r o p e l l e r d e s i g n , -a first s t e p w o u l d be t o s t u d y t h e effects o f w a v e s o n p r o p e l l e r o p e r a d o n . T h e r e f o r e , t h e a i m o f this p a p e r is t o i d e n t i f y a n d q u a n t i f y t h e effect o f v a r i o u s factors a f f e c t i n g t h e p r o p e l l e r i n w a v e s . The p e r f o r m a n c e o f KVLCC2 p r o p e l l e r i n t h e presence o f t h r e e d i f f e r e n t w a v e s has been c o m p a r e d w i t h c a l m w a t e r p e r f o r -m a n c e . Changes i n p e r f o r -m a n c e i n t e r -m s o f c a v i t a t i o n , p r e s s u r e pulses, a n d e f f i c i e n c y have been s t u d i e d . S i g n i f i c a n t increase i n pressure pulses has been obsei-ved d u e t o w a k e c h a n g e i n w a v e s e v e n t h o u g h c a v i t a d o n d i d n o t s h o w a n y s i g n i f i c a n t change. A n analysis u s i n g c a v i t a d o n b u c k e t d i a g r a m i n d i f f e r e n t w a v e c o n d i t i o n s i n d i c a t e s t h a t a p r o p e l l e r o p b m i z e d f o r c a l m w a t e r w a k e m a y p e r f o r m m u c h w o r s e i n t h e presence o f w a v e s . T h e r e f o r e , h a v i n g w a k e v a r i a t i o n a t least i n c r i t i c a l w a v e c o n d i t i o n s ( w h e r e t h e w a v e l e n g t h is close t o s h i p l e n g t h ) i n a d d i f i o n t o c a l m w a t e r w a k e c o u l d b e v e r y u s e f u l t o e n s u r e t h a t t h e p r o p e l l e r p e r f o r m s e q u a l l y w e l l i n t h e presence o f w a v e s . © 2 0 1 6 Elsevier L t d . A l l r i g h t s r e s e r v e d .
1. [ntroduction
T r a d i t i o n a l l y , propellers have been o p t i m i z e d for c a l m w a t e r conditions p a r t l y because one has n o t h a d the l<nowledge a n d tools to o p t i m i z e propellers f o r operations i n waves. However, w i t h increasing e n v i r o n m e n t a l concerns and emission regulations, there is g r o w i n g d e m a n d f o r the p r o p u l s i o n b e i n g o p t i m i z e d for the actual o p e r a t i n g conditions, w h i c h typically include waves.
Currently, propellers are designed using w a k e , t h r u s t deduction and relative r o t a t i v e efficiency o b t a i n e d i n c a l m w a t e r conditions. M o o r and M u r d e y [1 ] have s h o w n t h r o u g h m o d e l tests o f m u l t i p l e ship hulls i n c a l m w a t e r and i n waves that w a k e , t h r u s t deduction and propeller efficiency change i n t h e presence of waves. C i r c u m -ferentially averaged w a k e also changes due t o waves and ship m o t i o n s as d e m o n s t r a t e d by Nakamura a n d Naito (2). They also f o u n d that w a k e velocities increase i n waves, a n d i t is p r i m a r i l y caused due to p i t c h i n g m o t i o n of the ship. Similar results c o n f i r m -i n g s-ign-if-icant w a k e v a r -i a t -i o n -i n waves w e r e obta-ined -i n the RANS s i m u l a t i o n carried o u t b y Guo et al. [3] w h e r e t h e n o m i n a l w a k e field was obtained i n t h e presence o f waves. In these s i m u l a t i o n s ,
* Corresponding author.
E-mall address: bhushan.taskariSntnu.no (B. Taskar). http://dx.doi.Org/10.l 016/j.apor.2016.08.009 0141-1187/® 2016 Elsevier Ltd. All rights reserved.
the axial w a k e velocities increased w i t h u p to 35% o f ship speed in some regions. Such changes i n the w a k e d i s t r i b u t i o n o f a ship t r a v e l i n g i n waves w e r e e x p e r i m e n t a l l y c o n f i r m e d b y Hayashi [4]
using a m o d e l o f t h e KVLCC2 ship. Strong v a r i a t i o n o f w a k e w a s observed i n the presence o f waves t h r o u g h t h e PIV (Particle Induced V e l o c i m e t r y ) measurements.
Change i n w a k e d i s t r i b u t i o n changes t h e angle o f attack and the cavitation n u m b e r o f t h e propeller blades as s h o w n by Albers a n d Gent [ 5 ]. Chevalier a n d K i m [6], Jessup a n d W a n g [ 7 ] studied t h e cavitation o f a p r o p e l l e r operating i n waves by calculating w a k e velocities using p o t e n t i a l f l o w calculations a n d observed a d r o p i n the c a v i t a t i o n i n c e p t i o n speed o f the vessel i n waves.
Due t o increasing d e m a n d f o r efficiency, i t is no longer possi-ble t o design t h e propellers w i t h o u t c a v i t a t i o n . Cavitation can lead to erosion o n the propeller blades. Moreover, the pressure pulses can cause v i b r a t i o n i n t h e ship structure t h u s affecting passenger c o m f o r t and i n severe cases damage the s t r u c t u r a l i n t e g r i t y o f t h e h u l l . In m e r c h a n t ships, about 10% of p r o p e l l e r - i n d u c e d v i b r a t i o n velocities are caused by b e a r i n g forces, whereas a p p r o x i m a t e l y 90% are due t o pressure fluctuations, or h u l l surface forces |8). Survey of 47 ships w i t h v i b r a t i o n p r o b l e m has s h o w n that a r o u n d 80% o f the cases could be traced back to pressure pulses as a source of v i b r a -tion problems. Based o n r e p o r t e d cracks i n t h e aft peak o f 20 ships, s t r o n g correlation b e t w e e n fatigue damages i n the afterbody a n d
6 2 B. Taskar et a!./Applied Ocean Research 60 (2016) 61-74 Table 1 Propeller Geometry. Diameter ( D ) ( m ) 9 . 8 6 No of blades — 4— Hub diameter ( m ) 1.53 Rotational speed (RPM) 7 6 AelAo 0 . 4 3 1 (P/D)„,ea„ 0 . 6 9 0 Skew(°) 2 1 . 1 5 Rake(°) 0 Table 2 Ship Particulars.
Length between perpendiculars ( m ) 3 2 0 . 0 Length at water line ( m ) 3 2 5 . 5 Breadth at water line (m) 5 8 . 0
Depth (m) 3 0 . 0 Draft (m) 2 0 . 8 Displacement (m^) 3 1 2 , 6 2 2 Block coefficient (Cb) 0 . 8 0 9 8 Design Speed (knots) 1 5 . 5
K T ( M P U F ) Efficiency (fvlPUF) K Q ( M P U F ) Fig. 1. KT (Experiment) Efficiency (Experiment) KQ (Experiment) 0.6 0.5 0.4 0.3 ^ 0.2 g 0.1 Ü -0.1 0.1 0.3 0.5 0.7 Advance Coefficient J
Comparison of open water data of K V L C C 2 using MPUF-3A and model tests.
--the a m p l i t u d e o f pressure pulses at blade h a r m o n i c frequency was observed [9]. Therefore, i t is necessary to avoid cavitation erosion and h i g h pressure pulses even w h e n the c a v i t a t i o n is present. It is achieved by a d a p t i n g the propeller design t o c a l m w a t e r w a k e as cavitation and pressure pulses depend on the w a k e d i s t r i b u -t i o n [10,11]. However, given the significant w a k e v a r i a t i o n , i t is essential to investigate the performance of propeller in the pres-ence o f waves. Moreover, l o w e r i n g the pressure pulses comes at the expense of efficiency. Therefore, accurate e s t i m a t i o n o f pres-sure pulses in realistic operating c o n d i t i o n can help us m a x i m i z e the efficiency w h i l e still a v o i d i n g the u n w a n t e d consequences.
In this paper, w e have analyzed the performance o f the KVLCC2 propeller operating i n waves. T i m e - v a r y i n g w a k e data i n three dif-ferent head waves p r o v i d e d by Sadat-Hosseini et al. [ 12 ] have been used. Effect of various factors affecting propeller performance i n waves like w a k e change, ship m o t i o n s , w a v e d y n a m i c pressure, added resistance and RPM f l u c t u a t i o n has been studied separately to decide the order of i m p o r t a n c e o f each factor. Cavitation and pressure pulses have been calculated i n d i f f e r e n t w a v e c o n d i -tions and compared w i t h t h a t i n c a l m w a t e r w a k e . A n analysis o f propeller blade sections using a c a v i t a t i o n bucket d i a g r a m was per-f o r m e d to explore the possibility oper-f i m p r o v i n g propeller design to ensure o p t i m i z e d performance n o t j u s t i n c a l m w a t e r b u t also in the presence of waves.
2.
Methods and validation
2.1. Propeller analysis tools
The KVLCC2 propeller has been analyzed using the v o r t e x lattice m e t h o d i m p l e m e n t e d in MPUF-3A [13]. Details about the propeller geometry are given in Table 1 [14]. The fine g r i d has been used on the key blade w h i l e coarse g r i d has been used o n other blades. Open w a t e r curves obtained using MPUF-3A for the KVLCC2 propeller are compared w i t h e x p e r i m e n t a l l y obtained o p e n - w a t e r data [ 1 4 ] i n Fig. 1. W h e n the p r o p e l l e r was analyzed i n waves, the v a r i a t i o n i n
i n f l o w caused b y waves and ship m_otions is taken into account in a quasi-steady manner, m e a n i n g that for each t i m e instant, the f l o w field e n t e r i n g the propeller disk is treated as t i m e - i n v a r i a n t . The propeller is t h e n analyzed at each t i m e instance in t i m e - i n v a r i a n t w a k e using unsteady calculations. This approach is j u s t i f i e d by the fact t h a t the w a v e encounter frequency is m u c h l o w e r t h a n the propeller r o t a t i o n frequency.
For the analysis o f propeller blade section in calm w a t e r and in waves, the l i f t coefficient has been obtained for the propeller blade section at 0.7R f r o m MPUF-3A calculations. Cavitation bucket has been calculated by g i v i n g the blade section shape at 0.7R as an i n p u t to Xfoil [15]. W h i l e c a v i t a t i o n n u m b e r (Sigma) is calculated as f o l l o w s
-S i g m a : Po +
PSl^ - Py
0.5p[V^ +{0.7nnD)'^
w h e r e P q is atmospheric pressure, p is t h e density of w a t e r , g is acceleration due to gravity, h is the instantaneous submergence o f the blade section at 0.7R, P,, is the v a p o u r pressure o f w a t e r ,
Va is average p r o p e l l e r i n f l o w velocity, n is propeller rps and D is d i a m e t e r of the propeller. It should be kept i n m i n d that since b o t h /! a n d Va varies i n waves, the cavitation n u m b e r varies w i t h rime.
2.2. Wake data in the presence of waves
Experiments w e r e p e r f o r m e d by Sadat-Hosseini et al. [12] to o b t a i n w a k e data i n three d i f f e r e n t w a v e l e n g t h s i n head sea c o n d i -rion at design speed. A m o d e l of KVLCC2 was used for this purpose w i t h the m o d e l scale o f 1:100. Ship particulars are given in Table 2
[14]. I n these e x p e r i m e n t s , PIV (Particle Image V e l o c i m e t r y ) was used to o b t a i n t i m e - v a r y i n g n o m i n a l w a k e field in t h e propeller plane. CFD s i m u l a d o n s w e r e also p e r f o r m e d and results w e r e v a l i -dated using the data f r o m the PIV measurements. Since the CFD data are smoother and less noisy, w e have used t h e m in our calculations. These results w e r e available f o r waves \ / L = 0.6,1.1 a n d 1.6 at 8 , 1 2 and 6 time intervals respectively in one w a v e encounter p e r i o d . Wakes at d i f f e r e n t t i m e intervals have been denoted by t/T, w h i c h is a fraction o f time't' i n one w a v e encounter p e r i o d ' T ' . Note t h a t ' T ' is d i f f e r e n t i n each w a v e case. A t t/T = 0 the w a v e crest is located at the f o r w a r d perpendicular of the ship. W a v e h e i g h t o f these waves corresponds to a full-scale w a v e a m p l i t u d e o f 3 m . W a k e fields i n catm w a t e r and at four instances i n \ / L = 1.1 can be seen in Fig. 2.
Due to the higher f r i c t i o n coefficient o f the m o d e l scale ship, the w a k e field calculated i n m o d e l scale s h o u l d be contracted (scaled) f o r analyzing the p r o p u l s i o n performance i n f u l l scale. H o w e v e r , i t is n o t u n c o m m o n t h a t propellers are evaluated i n m o d e l scale w a k e as far as pressure pulses are concerned. It is p a r t l y because t h e m o d e l scale h u l l is used i n the tests carried o u t i n t h e cavita-tion t u n n e l for t h e m e a s u r e m e n t of pressure pulses, w h i c h means t h a t the p r o p e l l e r is analyzed in model scale w a k e to p r o v e t h a t the pressure pulses in full scale are w i t h i n the contractual r e q u i r e -m e n t s . The general experience is t h a t analyzing the p r o p e l l e r i n m o d e l scale w a k e gives a conservative estimate of cavitation and pressure pulses.
B. Taskar et al/Applied Ocean Reseatcli 60 (2016) 61-74 63
t/T = 053588 t/T = 0.80383
Fig. 2. Wal<e in calm water compared to tlie wake in the presence of wave having wavelength ratio X/L=1.1.The analysis in m o d e l scale w a k e also avoids the c o m p l e x i t y and u n c e r t a i n t y of the w a k e scaling procedure. Moreover, f o r this study, i t is m o r e i m p o r t a n t to compare the propeller cavitation and pressure pulses i n c a l m w a t e r w i t h that in waves t h a n p r e d i c t i n g t h e exact a m o u n t o f cavitation and pressure pulses in full scale. W e t h i n k t h a t the use o f m o d e l scale w a k e is sufficient for the q u a l i t a t i v e study of the effect o f waves o n p r o p e l l e r performance.
T i m e - v a r y i n g p o t e n t i a l w a k e i n the presence of waves has been calculated using S h i p f l o w M o t i o n s [16]. Simulations w e r e per-f o r m e d at design speed i n three d i per-f per-f e r e n t w a v e l e n g t h s ( X / L = 0 . 6 , 1.1, 1.6), free to heave and p i t c h . W a k e v a r i a t i o n o b t a i n e d using t h e p o t e n t i a l flow calculation has been c o m p a r e d w i t h the w a k e data o b t a i n e d f r o m CFD to investigate the appropriateness o f c o m -p u t i n g the w a k e v a r i a t i o n i n waves using -p o t e n t i a l flow theory. The m o t i v a t i o n for this being the excessive c o m p u t a t i o n a l expense of seakeeping calculations w i t h CFD.
2.3. Calculation of ship motions and added resistance
Ship m o t i o n RAOs (Response a m p l i t u d e operators) w e r e c a l -culated using linear strip theory, u t i l i z i n g p o t e n t i a l t h e o r y and pressure i n t e g r a t i o n , i m p l e m e n t e d in t h e ShipX Veres s o f t w a r e . Using the m o t i o n response of the vessel, added resistance coef-ficients have been calculated using the m e t h o d b y Loukakis a n d Sclavounos [17] ( w h i c h is an extension o f the classical Gerritsma a n d Beukelman's m e t h o d ) also i m p l e m e n t e d in ShipX Veres. Heave RAO, p i t c h RAO and added resistance calculations have been c o m -pared w i t h t h e e x p e r i m e n t a l investigations p e r f o r m e d by W u [18].
These comparisons can be seen i n Fig. 3. A d d e d resistance was t h e n c o m p u t e d i n irregular waves f o r d i f f e r e n t peak frequencies u s i n g t h e P i e r s o n M o s k o w i t z w a v e s p e c t r u m . Speed loss for a p a r t i c u -lar w a v e c o n d i t i o n (e.g. \ / L = l . l , w a v e a m p l i t u d e = 3 m ) has been calculated i n irregular waves h a v i n g a peak frequency equal t o the regular w a v e frequency and significant w a v e h e i g h t equal t o the
height o f t h e regular wave. The reason b e h i n d using irregular waves for the c o m p u t a t i o n of speed loss is to avoid g e t t i n g unreasonably l o w ship speeds as a results o f added resistance i n regular waves w h i c h is often m u c h larger t h a n the added resistance in c o r r e s p o n d -i n g -irregular waves.
2.4. Calculation of propeller RPM fluctuation
I n order to calculate the RPM fluctuation, a coupled e n g i n e -propeller m o d e l of Taskar et al. [ 19,20] has been u t i l i z e d . The study analyzes t h e engine-propeller i n t e r a c t i o n i n the presence o f waves considering a fluctuating w a k e field, p r o p e l l e r emergence, and free surface effects. Simulations i n regular head waves o f 3 m w a v e a m p l i t u d e s h o w e d a r o u n d 3% f l u c t u a t i o n i n RPM. Hence, p r o p e l l e r c a v i t a t i o n has been analyzed i n 3% h i g h e r RPM to calculate the possible change i n pressure pulses and cavitation.
2.5. Pressure pulse calculation
Pressure pulses have been c o m p u t e d u s i n g HULLFPP [21] w h i c h calculates field p o i n t p o t e n t i a l induced by a c a v i t a t i n g p r o p e l l e r using a p o t e n t i a l based b o u n d a r y e l e m e n t m e t h o d . T i m e series o f cavity shapes, cavity v o l u m e s a n d pressure d i s t r i b u t i o n o n blades calculated by MPUF-3A are used as an i n p u t t o t h i s code. I n the c o m p u t a t i o n s , the h u l l was assumed t o be a flat plate at a distance o f 30% o f t h e p r o p e l l e r d i a m e t e r f r o m the blade t i p . Tip clearance o f 30% is c o m m o n l y seen o n ships.
I n the p r o p e l l e r design m e t h o d o l o g y , p r e d i c t i o n o f pressure pulses plays an i m p o r t a n t role. The p r o p e l l e r g e o m e t r y should be such that the level o f pressure pulses is b e l o w the specified t h r e s h -o l d . The m e t h -o d pr-op-osed by H-olden et al. [22] is o f t e n used to analyze pressure pulses in t h e i n i t i a l design stage. This m e t h o d is based o n n u m e r o u s e x p e r i m e n t a l studies and experiences w i t h full-scale pressure pulses. The a p p l i c a b i l i t y of Holden's m e t h o d for
6 4 B. Tasknr et al. /Applied Ocean Research 60 (2016) 61-74
wavelength/ship length
Fig. 3. Added resistance and sliip motions calculation compared w i t h the expenmental measurements.
_ 7
I s
0
^ X / L = l . l H u l l F P P calm water HullFPP X V L = 1.1 Holden
calm water Holden 0.0 0.2 0.4 0.6
Time t/T
0.8 1.0
Fig. 4 . Companson of pressure pulses calculated using Holden method and HULLFPP code.
the analysis o f propeller i n waves has been tested by c o m p a r i n g the results w i t h more accurate HULLFPP calculations. A c o m p a r i s o n of pressure pulses predicted by b o t h methods has been presented in Fig. 4.
In Fig. 4, i t is e v i d e n t that pressure pulses p r e d i c t e d by Holden's m e t h o d are m u c h higher t h a n those predicted by HULLFPP. M o r e -over, the t r e n d o f v a r i a t i o n in pressure pulses in d i f f e r e n t w a k e fields is d i f f e r e n t i n t w o cases, as seen for X/L = 1.1. Therefore, anal-ysis using a simple m e t h o d like Holden's m i g h t n o t be a g o o d idea. A more detailed analysis like the one using HULLFPP is r e q u i r e d to capture the effects o f m i n o r variations in w a k e structure. An e x p l a -n a t i o -n f o r the large o v e r - p r e d i c t i o -n by Holde-n's m e t h o d c o m p a r e d to HULLFPP m i g h t be t h a t i t is based on data f r o m old propellers, t y p i c a l l y w i t h l i t t l e skew.
2.6. Calculation of unsteady wave pressure
Propeller c a v i t a t i o n can get affected by the change in c a v i t a t i o n n u m b e r caused by ship motions as w e l l as d y n a m i c w a v e pres-sure. To study this effect, the t o t a l pressure w a s calculated at the location o f the propeller shaft, considering the instantaneous d e p t h o f propeller and the phase of the passing w a v e . The total pressure was t h e n used in the calculation o f cavitation n u m b e r for a n a l y z i n g t i m e - v a r y i n g c a v i t a t i o n and pressure pulses i n waves.
3. Analysis
I n i t i a l l y , the p r o p e l l e r was analyzed i n t h e c a l m w a t e r w a k e field to observe the cavitation p a t t e r n and pressure pulses i n c a l m w a t e r c o n d i t i o n . The influence of the factors affecting propeller i n waves (i.e. w a k e v a r i a t i o n , ship m o t i o n s , d y n a m i c w a v e pressure, speed loss and RPM fluctuations) o n cavitation a n d pressure pulses has been studied. Cavitation bucket diagram has been studied to observe the effect o f these factors o n l i f t coefficient and c a v i t a t i o n
number. The analysis has been d i v i d e d i n t o three parts w h e r e the influence o f each factor has been considered separately.
1. W a k e v a r i a t i o n and change in c a v i t a t i o n n u m b e r due to ship m o t i o n s and waves
2. Increased l o a d i n g due to speed loss
3. RPM fluctuations due to engine propeller interactions and aver-age w a k e v a r i a t i o n
3. J. Effect of wake variation and change in cavitation number
The KVLCC2 propeller has been analyzed using MPUF at m u l t i p l e t i m e intervals i n the presence of three d i f f e r e n t regular waves. I n order to observe the effect o f w a k e v a r i a t i o n alone, the propeller i m m e r s i o n was assumed constant at 15.1 m d e p t h , equal to that i n cal m w a t e r . The m a x i m u m a m o u n t o f c a v i t a t i o n in each case can be seen i n Fig. 5. In calm w a t e r , the blade p o s i t i o n at w h i c h m a x i m u m cavitation occurs has been p l o t t e d . H o w e v e r , i n the presence o f waves, cavitation depends n o t only on the location o f t h e blade but also o n the phase o f the passing w a v e . M a x i m u m cavitation w i t h respect to blade position as w e l l as t i m e i n s t a n t (or w a v e phase) can be seen in Fig. 5.
It can be seen f r o m Fig. 5 t h a t for three w a v e l e n g t h s , m a x i m u m cavitation occurred at d i f f e r e n t blade positions a l t h o u g h the loca-t i o n o f c a v i loca-t a loca-t i o n on loca-the blade was similar. M a x i m u m caviloca-taloca-tion is observed i n t h e case o f X . / L = l . l (Le. w h e n the w a v e l e n g t h is close to ship length) at the i n s t a n t w h e n the stern of t h e ship is m o v i n g d o w n causing l o w w a k e velocities in the upper p a r t of the p r o p e l l e r disc close to the centerline. Here, i t is i m p o r t a n t t o note t h a t the m a x i m u m cavitation i n the presence of waves is occur-r i n g at one blade location at one instant i n a single w a v e encounteoccur-r p e r i o d . The m a x i m u m cavitation seen i n one f u l l r o t a t i o n of the blade varies as the w a v e passes, i t can be as l o w as t h a t s h o w n i n
Fig. 6. It was also observed t h a t i n c a l m w a t e r , cavity is present o n a couple o f blades simultaneously for a signiflcant a m o u n t o f t i m e whereas i n o t h e r cases, as the cavity o n one blade vanishes, the next blade starts cavitating. This m a y have an effect o n the behavior o f pressure pulses.
In a d d i t i o n to the effect o f w a k e v a r i a t i o n , change i n cavitation n u m b e r can also affect propeller c a v i t a t i o n and pressure pulses. In the presence o f waves, v a r y i n g propeller i m m e r s i o n due t o ship m o t i o n s and d y n a m i c w a v e pressure lead t o a change i n cavitation n u m b e r . Therefore, the propeller has been analyzed to see the c o m -b i n e d effect of v a r i a t i o n i n cavitation n u m -b e r and w a k e v a r i a t i o n o n the cavitation and pressure pulses.
The t o t a l pressure, i n c l u d i n g the d y n a m i c pressure, at the loca-t i o n o f loca-the propeller, was expressed i n loca-t e r m s of an equivalenloca-t heighloca-t of w a t e r c o l u m n . The propeller was analyzed in wakes at d i f f e r e n t t i m e instances at calculated e q u i v a l e n t propeller d e p t h . Therefore,
B. Taskar et al./Applied Ocean Research 60 (2016) 61-74 65
Calm water A/L= 1.6, t/T = 0.41445
Fig. 6. M i n i m u m suction side cavitation seen in the presence of wave among all three waves considering only wake change.
c o m p a r i n g the c a v i t a t i o n and pressure pulses using f i x e d c a v i t a t i o n n u m b e r w i t h that using v a r y i n g c a v i t a t i o n n u m b e r w i l l s h o w t h e effect o f a change i n c a v i t a t i o n n u m b e r i n waves.
As i n the earlier case, the c a v i t a t i n g propeller has been presented at the angle and t i m e i n s t a n t o f m a x i m u m cavitation in each w a v e
Calm water A/L = 1.6, t/T = 0.23379
Fig. 8. M i n i m u m suction side cavitation seen in the presence of wave among all three waves considering wake change, ship motions and dynamic wave pressure.
in Fig. 7. C o m p a r i n g m a x i m u m cavitation in \ / L = l . l a n d 1.6 i n Fig. 7 w i t h Fig. 5, i t seems t h a t i n c l u d i n g the v a r i a t i o n i n c a v i t a t i o n n u m b e r reduces the m a x i m u m v o l u m e of cavitation. This is because the v a r i a t i o n i n cavitation n u m b e r is favourable for the instances of unfavorable w a k e v a r i a t i o n . In o t h e r w o r d s , t h e w o r s t possible w a k e i n waves occurs at a cavitation n u m b e r h i g h e r t h a n t h a t i n calm w a t e r . Whereas, i n X./L=0.6, the a m o u n t o f c a v i t a t i o n is h i g h e r w h e n the v a r i a t i o n of c a v i t a t i o n n u m b e r is taken i n t o account. The a m o u n t o f c a v i t a t i o n varies as the w a v e passes, the m i n i m u m cav-i t a t cav-i o n a m o n g three w a v e condcav-itcav-ions can be observed cav-i n Fig. 8. I n this case, a l t h o u g h the blade at 12 O'clock p o s i t i o n shows m i n i m u m cavitation, blade at 6 O'clock p o s i t i o n has h i g h e r c a v i t a t i o n . This
Calm water A/L = 0.6, t/T = 0.01977 A/L= 1.1, t/T = 0.30813 A/L= 1.5, t/T = 0.92454
Fig. 7. M a x i m u m suction side cavitation seen i n each wave considering wake change, ship motions and dynamic wave pressure.66 a Taskar etal./ Applied Ocean Research 60(2016)61-74
0 0.2 0.4 0.6 0.8 1
Time t/T
Fig. 9. Variation of propeller immersion in waves measured from calm water line {Propeller immersion i n calm water is 15.1 m).
happens w h e n the stern o f t h e ship is m o v i n g u p ( n o t e Fig. 9), caus-i n g l o w wal<e veloccaus-itcaus-ies caus-i n t h e l o w e r p a r t o f p r o p e l l e r dcaus-isc close to t h e c e n t e r l i n e . Hence, p r o p e l l e r blade starts c a v i t a t i n g even w h e n i t is at 6 O'clock p o s i t i o n .
To c o m p a r e t h e c a v i t a t i o n i n c a l m w a t e r w i t h t h a t i n waves, i t w o u l d be m o r e a p p r o p r i a t e to c o m p a r e t h e t i m e h i s t o r y o f c a v i t a t i o n v o l u m e i n c a l m w a t e r w i t h t h a t i n waves. Therefore, c a v i t a t i o n v o l u m e o n a single blade has been p l o t t e d as a f u n c -t i o n o f blade p o s i -t i o n i n -t h e c a l m w a -t e r a n d d i f f e r e n -t -t i m e s i n each w a v e c o n d i t i o n . Cavitation v o l u m e s w i t h constant c a v i t a t i o n n u m b e r have been presented i n Figs. 1 0 1 2 and those c o n s i d -e r i n g t h -e v a r i a t i o n i n c a v i t a t i o n n u m b -e r hav-e b-e-en p l o t t -e d i n Figs. 1 3 - 1 5. First, c o m i n g to t h e c o m p u t a t i o n s a t f i x e d c a v i t a t i o n n u m b e r . I n X/L = 0.6, a t all t i m e s , m a x i m u m c a v i t a t i o n is l o w e r t h a n t h e a m o u n t o f c a v i t a t i o n i n c a l m w a t e r . Whereas, in X / L = l . l a n d X / L = 1 . 6 m a x i m u m c a v i t a t i o n v o l u m e is as h i g h as t w i c e the a m o u n t o f m a x i m u m c a v i t a t i o n i n c a l m w a t e r . H o w e v e r , this happens o n l y f o r one t i m e instance. In m o s t o t h e r cases, t h e a m o u n t o f c a v i t a -tion is e i t h e r c o m p a r a b l e or l o w e r t h a n the c a l m w a t e r c a v i t a t i o n . I n cases X / L = l . l a n d X / L = 1 . 6 c a v i t a t i o n s o m e t i m e s appears o n t h e blade at 6 O'clock p o s i t i o n w h i c h is n o t seen i n t h e c a l m w a t e r a n d t h e X/L = 0.6 case. In cases of X / L = l . l , t/T = 0.46890 l.E-03 Q 8.E-04 6.E-04 4.E-04 O.E+00
A/L = 0.6
-180 -120 -60 0 60 120 Blade A n g l e ( D e g ) 180 •calm water -t/T=0.01977 t/T=0.27676 -t/T=0.39537 -t/T=0.65235 -t/T=0.77098 -t/T=0.90936Fig. 10. Cavitation volume variation i n \ / L = 0 . 6 at different times as wave passes considering only wake change.
l.E-03 o 8.E-04 E 6.E-04 O
>
>. 4.E-04 • > ra U 2.E-04 O.E+OOA/L = 0.6
-180 -120 -60 0 60 120 Blade A n g l e ( D e g ) 180 - c a l m water -tA=0.01977 t/T=0.27676 -t/r=0.39537 -t/r=0.65236 -t/r=0.77098 -tA=0.90936Fig. 13. Cavitadon volume variation in \ / L = 0 . 6 at different times as wave passes, considering wake change, ship motions and dynamic wave pressure.
l.E-03 8.E 04 Q a 6.E-04 E O 4.E-04 > >. 2.E-04 • >
TO
u O.E+00A/L =
1.14
I
-180 -120 -60 0 60 120 180 Blade Angle (Deg)calm water tA=0.13397 t/T=0.30813 t/T=0.46890 t/T=0.62966 1^=0.80383 t/T=0.96459
Fig. 11. Cavitation volume variadon in \ / L = l . l at different rimes as wave passes considering only wake change.
O.E+OO -180 -120 -60 0 60 120 Blade A n g l e ( D e g ) 180 • c a l m water -t/T=0.04019 't/T=0.21435 t/T=0.37512 -t/T=0.53588 -tA=0.72344 -t/T=0.88421
Fig. 14. Cavitation volume variation in \ / L = 1.1 at different times as wave passes, considering wake change, ship motions and dynamic wave pressure.
O.E+00 -180 -120 -60 0 60 120 180 B l a d e A n g l e ( D e g ) - c a l m water -t/T=0.07439 -tA=0.23379 t/r=0.41445 -t/r=0.57385 -t/T=0.72263 -t/T=0.92454 O.E+OO -180 -120 -60 0 60 120 180 Blade A n g l e ( D e g ) - c a l m water -t/T=0.07439 - t / T = 0 . 2 3 3 7 9 t/T=0.41445 -tA=0.57385 -t/T=0.72263 - t / T = 0 . 9 2 4 5 4
Fig. 12. Cavitarion volume variarion i n X/L=1.6 at different times as wave passes, considering only wake change.
Fig. 15. Cavitation volume variation in X/L=1.6 at different rimes as wave passes, considering wake change, ship morions and dynamic wave pressure.
B. Taskar etal./Applied Ocean Research 60(2016)61-74 67
First Harmonic
First Harmonic
0.2 0.4 0.6 0.8
Time t/T
Fig. 16. First harmonic amplitude of pressure pulses in wavesconsidering only wake change.
0.2 0.4 0.6 0.8
Time t/T
Fig. 19. First harmonic amplitude of pressure pulses in waves considering wake change, ship motions and wave dynamic pressure.
Second Harmonic
C/l0.0
0.2 0.4 0.6 0.8
Time t/T
1.0
-*—A/L = 0.6
-•—
X/L = 1.1
X/L =1.6
calm water
Fig. 17. Second harmonic amplitude of pressure pulses in waves considering only wake change.
Second Harmonic
0.2 0.4 0.6 0.8
Time t/T
1.0
-X/L = 0.6
X/L =1.1
•X/L = 1.6
•calm water
Fig. 20. Second harmonic amplitude of pressure pulses in waves considering wake change, ship motions and wave dynamic pressure.
Third Harmonic
0.0 0.2 0.4 0.6 0.8 1.0
Time t/T
X/L = 0.6
X/L =1.1
-•—
X/L =1.6
calm water
Fig. 18. Third harmonic amplitude of pressure pulses in waves considering only wake change. _
0-6
raef.0.4
5 0.2
^ 0
Third Harmonic
0.0 0.2 0.4 0.6
Time t/T
0.8 1.0
-X/L = 0.6
X/L =1.1
-
X/L =1.6
•calm water
Fig. 2 1 . Third harmonic amplitude of pressure pulses in waves considering wake change, ship motions and wave dynamic pressure.
and X/L = 1.6, t/T = 0.23379, the v o l u m e o f cavitation is higher at 6 O'clock position t h a n at 12 O'clock p o s i t i o n . These are the instances w h e n the stern o f t h e ship is m o v i n g u p w a r d s as noted earlier.
Cavity v o l u m e v a r i a t i o n considering v a r i a t i o n i n cavitation n u m b e r has been p l o t t e d i n Figs. 1 3 - 1 5. C o m p a r i n g these plots w i t h Figs. 1 0 - 1 2, i t can be observed t h a t m a x i m u m cavitation v o l u m e is l o w e r b y about 45% i n X/L = 1.1 and by a b o u t 38% i n X/L = 1.6 w h e n the effect o f v a r i a t i o n i n cavitation n u m b e r is included. Therefore, the change i n c a v i t a t i o n n u m b e r d u e to w a v e s and ship m o t i o n s seems t o favor the propeller p e r f o r m a n c e f o r these w a v e l e n g t h s . Whereas, for X/L = 0.6, the m a x i m u m c a v i t a t i o n v o l u m e is 18% higher w h e n the c a v i t a t i o n n u m b e r v a r i a t i o n is i n c l u d e d . Consid-ering all the factors affecting propeller i n waves, o n l y i n a few t i m e instances, the cavitation v o l u m e is larger t h a n the m a x i m u m c a v i -t a -t i o n v o l u m e in c a l m w a -t e r . Thus, waves d o n o -t s i g n i f i c a n -t l y affec-t average cavitation v o l u m e .
In all the cases, the p a t t e r n o f the cavity v o l u m e varies i n a m u c h d i f f e r e n t w a y t h a n i n the c a l m w a t e r case. In c a l m water, the cavity v o l u m e v a r i a t i o n shows double peaks whereas, i n the presence o f waves, cavity v o l u m e has j u s t a single m a x i m u m i n m o s t o f t h e cases. This, as explained earher, is due to l o w - s p e e d area developed close t o p r o p e l l e r centerline due t o t h e m o t i o n o f the stern. This behavior suggests t h a t pressure pulses are affected by o p e r a t i o n in waves as t h e y p r i m a r i l y d e p e n d on cavity v o l u m e v a r i a t i o n and distance to the h u l l . Therefore, i t is i m p o r t a n t t o see h o w pressure pulses are affected i n the presence of waves.
Pressure pulses w e r e analyzed i n waves and in c a l m w a t e r using HULLFPP as already m e n t i o n e d . V a r i a t i o n o f the first, second and t h i r d h a r m o n i c s i n waves has been compared w i t h those i n calm w a t e r . Usually, the a m p l i t u d e o f the first h a r m o n i c i.e. pressure pulses o f blade pass frequency is highest and m o s t significant f r o m the h u l l v i b r a t i o n p o i n t of v i e w . Pressure pulses i n calm w a t e r
6S a Taskar et al. /Applied Ocean Research 60 (2016) 61-74 — 4 — X / L = 0.6 - —X / L = 1.1 - • -X / L = 1 . 6 —X—calm water 12.0 14.0 16.0 18.0
Propeller Immersion (m)
A/L = 0.6
0.45Fig. 22. Variation of pressure pulses w i t h change in propeller immersion (Propeller immersion in calm water is 15.1 m).
0) Ü 0.35 iE <u
3
0.25 0.15 0.3 0.4 • t/r=0.01977 • t/r=0.27676 t/r=0.39537 t/r=0.65236 t/r=0.77098 tA=0.90936 calm water cavitation bucketFig. 25. Variation in lift coefficient of blade section at 0.7R at different times as wave passes in X/L=0.6 considering wake change, ship motions and dynamic wave pressure.
0.45
c <u:0 0.35
%
8
0.25
0.15
r '/
I0.3 0.4 0.5 0.6
Sigma
0.7 0.8
•A/L=0.6,
t/T=0.90936
A/L=l.l,
t/T=0.30813
•
VL=1.6,
t/T=0.92454
— calm water
Fig. 23. Variation in lift coefficient of blade section at 0.7R at the instance of maxi-m u maxi-m cavitation i n each wave considering only wake change.
0.45 • 0.35 E u 0.25 0.15
A/L = 1.1
0.3 0.4 0.5 0.6 Sigma 0.7 0.8 t/T=0.04019 t,Ar=0.21435 t/r=0.37512 t/T=0.53588 t/T=0.72344 t/T=0.88421 calm water cavitation bucketFig. 26. Variation in lift coefficient of blade section at 0.7R at different times as wave passes in \ / L = l . l considering wake change, ship motions and dynamic wave pressure.
0.45
0.35
c u5 0.25
0.15
f ' t 1 I0.3 0.4 0.5 0.6
Sigma
0.7 0.8
•X/L=0.6,
t/T=0.01977
X/L =1.1,
t/T=0.30813
•X/L =1.6,
t/T=0.92454
— calm water
Fig. 24. Variation i n lift coefficient of blade secUon at 0.7R at the instance of maxi-m u maxi-m cavitation i n each wave considering wake change, ship maxi-motions and dynamaxi-mic wave pressure.
A/L = 1.6
0.45 0) O 0.35 iE OJ 5 0.25/
0.15 0.3 0.4 0.5 0.6 Sigma 0.7 0.8 — t/T=0.07439 t/T=0.23379 t/T=0.41445 t/T=0.57385 t/T=0.72253 t/T=0.92454 calm water cavitation bucketFig. 27. Variation in lift coefficient of blade section at 0.7R at different times as wave passes in \ / L = 1.6 considering wake change, ship motions and dynamic wave pressure.
and i n waves considering constant c a v i t a t i o n n u m b e r have been c o m p a r e d i n Fig. 16. For X/L =1.1 a n d 1.6, t h e first h a r m o n i c o f pressure pulses is higher t h a n i n c a l m w a t e r f o r a l m o s t all t i m e instances. M a x i m u m pressure pulses i n these w a v e conditions are m o r e t h a n double o f those i n c a l m w a t e r . In t h e case o f X/L = 0.6, pressure pulses are higher t h a n c a l m w a t e r for 50% of the t i m e . Thus, i t is clear t h a t w a k e v a r i a t i o n does significantly affect pressure pulses.
C o m i n g to second a n d t h i r d h a r m o n i c of pressure pulses, they are considerably higher than c a l m w a t e r value o n l y for X/L = 1.1 as seen i n Figs. 17 and 18. Moreover, f o r X/L = 1.1 t h e m a x i m u m value of t h e second h a r m o n i c is close t o the first h a r m o n i c a m p l i t u d e o f pressure pulses i n calm w a t e r . For the o t h e r waves, t h e second
and t h i r d h a r m o n i c pressure pulses are either comparable or l o w e r t h a n t h e c a l m w a t e r value.
I n Figs. 1 9 - 2 1, pressure pulses considering t h e effect o f w a k e v a r i a t i o n , ship m o t i o n s , a n d d y n a m i c w a v e pressure have been p l o t t e d . In t h e case o f waves w i t h X/L = 1.1 a n d 1.6 m a x i m u m v a l -ues o f first h a r m o n i c o f pressure pulses is l o w e r t h a n that observed using w a k e change alone, w h i c h is i n line w i t h t h e change i n cavitation v o l u m e as discussed above. However, pressure pulses i n Fig. 19 are h i g h e r t h a n t h a t i n Fig. 16 for a p p r o x i m a t e l y 50% of the times i n all three waves. The m a x i m u m 0.4 kPa increase in the first h a r m o n i c of pressure pulses is observed d u e t o the effect o f v a r i a t i o n i n t h e cavitation n u m b e r ( i n the case o f X/L = 1.6, t/T = 0.57385).
B. Taskar et al./Applied Ocean Researcli 60 (20)6) 61-74 69
The second h a r m o n i c of the pressure pulses is higher than the calm w a t e r value only for X./L= 1.1 w h i l e i n other waves, i t is l o w e r than i n c a l m w a t e r . For t h i r d h a r m o n i c , hardly any t i m e instances — s h o w higher pressure pulses t h a n c a l m w a t e n ^ i u S i - e o n s i d e r i n g first, second a n d t h i r d h a r m o n i c o f pressure pulses i n waves, w a v e c o n d i t i o n X/L =1.1 seems critical f o r the analysis of propeller in the presence of waves.
To separate the effect o f v a r i a t i o n in cavitation n u m b e r f r o m the effect of w a k e change, change i n the first h a r m o n i c o f pres-sure pulses are p l o t t e d i n Fig. 22 against equivalent propeller i m m e r s i o n . Change in pressure pulses has been calculated as the difference b e t w e e n the pressure pulses c o m p u t e d w i t h fixed and w i t h v a r y i n g c a v i t a t i o n n u m b e r i.e. difference b e t w e e n the level of pressure pulses in Figs. 16 a n d 19. The m a x i m u m increase o f about 0.4 kPa is observed due to the effect of variation i n cavitation number.
The propeller was analyzed i n c a l m w a t e r w a k e at d i f f e r e n t immersions to compare the rate o f change o f pressure pulses w i t h respect to propeller i m m e r s i o n i n c a l m w a t e r w i t h t h a t in waves. From Fig. 22 i t is seen t h a t increase i n pressure pulses due to change in propeller i m m e r s i o n is similar i n calm w a t e r w a k e as w e l l as in w a k e i n the presence of waves. Therefore, possible increase in pres-sure pulses due to c o m b i n e d effect of waves and ship m o t i o n s can be a p p r o x i m a t e d by analyzing the propeller in calm w a t e r w a k e by v a r y i n g the propeller i m m e r s i o n .
The l i f t coefficient obtained f r o m MPUF-3A calculations has been p l o t t e d against cavitation n u m b e r (sigma) for one f u l l r o t a -t i o n of -the blade sec-tion a-t 0.7R, -thus f o r m i n g a loop. Cavi-ta-tion bucket obtained f r o m X f o i l calculations has also been p l o t t e d for this propeller blade section. Operating loops in c a l m w a t e r as w e l l as at the i n s t a n t of m a x i m u m cavitation in each w a v e l e n g t h can be seen i n Fig. 23 along w i t h the cavitation buckeL Comparing the o p e r a t i n g loops and X f o i l calculations w i t h MPUF results, there is a slight discrepancy since c a l m w a t e r operating loop is w e l l inside the cavitation bucket predicted by X f o i l hence the section at 0.7R should be free o f any c a v i t a t i o n i n c a l m w a t e r whereas MPUF c o m p u t a t i o n s s h o w the presence of cavitation at that sec-t i o n . This can be due sec-to calculasec-tions being for 2D fiow i n X f o i l and 3D flow in MPUF. Therefore, t h e cavitation bucket should o n l y be considered for the a p p r o x i m a t e e s t i m a t i o n o f the c a v i t a t i o n -free zone. The a i m o f p l o t t i n g the operating loops is t o compare the v a r i a t i o n i n c a v i t a t i o n n u m b e r and l i f t coefficient i n d i f f e r e n t wakes.
I n this case, the propeller d e p t h was assumed constant, so the change i n sigma is o n l y due to change i n instantaneous d e p t h of the propeller blade as i t rotates. Therefore, v a r i a t i o n i n sigma is s i m i l a r i n all the cases. However, the v a r i a t i o n o f l i f t coef-ficient changes drastically i n the presence of waves, also the v a r i a t i o n is m u c h larger i n X/L = 1 . 1 and 1.6 t h a n i n c a l m water. Hence, i f p r o p e l l e r sections are designed considering o n l y the calm w a t e r w a k e , performance could become m u c h worse i n waves.
Similar X f o i l analysis considering the v a r i a t i o n i n cavitation n u m b e r (due to v a r y i n g propeller i m m e r s i o n ) i n a d d i t i o n to w a k e change (=angle of attack v a r i a t i o n ) at the instance o f m a x i m u m c a v i t a t i o n has been presented i n Fig. 24. Comparing i t w i t h Fig. 23, v a r i a t i o n i n sigma can be seen in a d d i t i o n to v a r i a t i o n i n l i f t coeffi-cient. It can be observed t h a t o p e r a t i n g loops for w a v e l e n g t h ratios 1.1 and 1.6 have s h i f t e d t o w a r d s higher sigma. This leads to a slight r e d u c t i o n in c a v i t a t i o n and pressure pulses (observed earlier) as cavitation bucket is s l i g h t l y w i d e r at higher sigma.
In a d d i t i o n t o the i n s t a n t of m a x i m u m cavitation, t h e behavior of operation loops should be e x a m i n e d at other t i m e instances t o k n o w the behavior o f the o p e r a t i n g loop as the w a v e passes. There-fore, X f o i l analysis has been carried o u t at d i f f e r e n t t i m e instances i n each w a v e as seen i n Figs. 2 5 - 2 7 . W a k e v a r i a t i o n , as w e l l
First Harmonic
-X/L = 0.6 X/L = 1.1 -X/L = 1.6 0.0 0.2 0.4 0.6 0.8TimetA
1.0Fig. 28. Increase in pressure pulses as a result of increased load on the propeller caused by the added resistance.
A/L = l . l
0.45 <u G 0.351
0.15 [/
/
/
— t/r=0.04019
t/r=0.04019
with speed loss 0.3 0.4 0.5 0.6 0.7 0.8 Sigma t/T=0.72344 t/T=0.72344 with speed loss Fig. 29. Comparison of variation in lift coefficient of blade section at 0.7R w i t h and w i t h o u t speed loss.as v a r i a t i o n in propeller i m m e r s i o n , has been considered i n this analysis.
C o m p a r i n g Fig. 24 w i t h Fig. 26, i t can be observed that the instance of m a x i m u m cavitation v o l u m e is n o t necessarily the w o r s t c o n d i t i o n for the propeller blade. Even t h o u g h pressure side cavitation is n o t seen i n the MPUF analysis at any t i m e instance, X f o i l analysis tells us t h a t the propeller operates v e r y close to h a v i n g pressure side sheet cavitation at some time-instances. (Cav-i t a t (Cav-i o n bucket (Cav-is o n l y a p p r o x (Cav-i m a t e as n o t e d earl(Cav-ier. I t has been p r o v i d e d as a reference to the c o m p a r i s o n o f d i f f e r e n t o p e r a t i n g loops.) The m a x i m u m deviation f r o m the c a l m w a t e r o p e r a t i n g loop is seen i n X/L = 1 . 1 . In this w a v e , m a x i m u m increase i n suc-t i o n side cavisuc-tasuc-tion has been observed. Moreover, suc-the propeller is m o r e prone to pressure side cavitation as w e l l as b u b b l e cavitation at certain t i m e instances i n this w a v e as c o m p a r e d to calm w a t e r c o n d i t i o n .
For the studied propeller, m o s t of the o p e r a t i n g points lie w i t h i n the cavitation bucket, even in the presence of waves. This could be due to the general experience o f the p r o p e l l e r designers about r e q u i r e d margins for o p e r a t i o n i n waves a n d o f f design c o n d i -tions, as t h e y d i d n o t have the i n f o r m a t i o n about w a k e field i n waves at the t i m e o f designing the propeller. H o w e v e r , there are no clear guidelines regarding cavitarion m a r g i n s to avoid p e r f o r -mance drop i n waves, and w h e n designing a n o t h e r propeller for another ship, the r e s u l t i n g propeller p e r f o r m a n c e in waves m i g h t be less favourable.
3.2. Effect of increased loading
A d d e d resistance due to waves leads to increased propeller load. This is likely to increase the a m o u n t of cavitarion on the propeller.
70 B. Taskar etal. /Applied Ocean Research 60 (2016) 61-74
First Harmonic
0.4
0.7 0.6 •p 0.5 a! 0.3 tn0.2
QJ u ! .0.0
. I.
X/L = 0.6 X/L =1.1 X/L = 1.6
Fig. 30. Increase in pressure pulses due to RPM fluctuations in waves.2.5 1,5 0.5 2.1 U.i Q 2 • Wake variation n S h i p motions, wave pressure RPM variation Speed loss
Fig. 3 1 . Comparison of m a x i m u m increase in ttie first harmonic of pressure pulses due to different factors in the presence of waves.
Moreover, pressure pulses are l i k e l y to change i f there is a sig-n i f i c a sig-n t v a r i a t i o sig-n isig-n the c a v i t a t i o sig-n p a t t e r sig-n . Hesig-nce, the sesig-nsitivity o f cavitation a n d pressure pulses t o w a r d s the increased propeller loading has been studied.
As ship m o t i o n s depend on ship speed, w a k e v a r i a t i o n w i l l also change for d i f f e r e n t ship speed. However, i n the absence o f w a k e data at reduced speed, w a k e v a r i a t i o n a t design speed has also been used at reduced ship speed. The ship speed has been calculated i n i r r e g u l a r waves of peak frequency 0.090, 0.067 and 0.055Hz, c o r r e s p o n d i n g to X/L = 0.6, 1.1 and 1.6 respectively w i t h significant w a v e a m p l i t u d e o f 3 m . Ship speed obtained u s i n g constant p r o p e l l e r RPM is 11.9, 11.3 and 11.6 knots for the three w a v e c o n d i t i o n s . The p r o p e l l e r has been analyzed i n each w a v e c o n d i t i o n u s i n g the corresponding w a k e v a r i a t i o n and ship speed. Propeller d e p t h was assumed constant. The o n l y
dif-& 0.4
S
-I
0.3 " ^ 0 . 2 0.1 I 0.2 0.2 0.25 0.3 0.35 0.4 Advance Coefficient J 0.45Fig. 33. Propeller efficiency, KT and KQ in the presence of waves along w i t h pro-peller open water data. Propro-peller open-water efficiency, KT and have been shown using solid, dash-dot and dashed lines respectively. Efficiency, KT and KQ in waves has been denoted by square, circle and triangle respectively. (X/L=0.6-Green; X/L=1.1-0range; X/L= 1.6-Blue). Performance in calm water wake has been denoted by cross mark.
ference b e t w e e n the c o m p u t a t i o n s i n section 3.1 ( w i t h constant cavitation n u m b e r ) and these c o m p u t a t i o n s is the speed o f t h e ship.
Increase in pressure pulses has been c o m p u t e d by c o m p a r i n g the pressure pulses i n this analysis w i t h those calculated c o n -sidering w a k e change only (Fig. 16). As seen i n Fig. 28, pressure pulses increased at m a x i m u m about 0.2 kPa due to increased load. The m a x i m u m c a v i t a t i o n v o l u m e increased by about 10%. H o w -ever, in some cases, m a x i m u m c a v i t a t i o n v o l u m e and pressure pulses decreased even after increasing the propeller load. This was observed in the instances of w a k e v a r i a t i o n that caused h i g h pres-sure pulses ( X / L = l . l , t/T = 0.30813and X/L = 1.6, t/T = 0.92454). I t was observed that the cavity is present for larger range of blade angles in the presence o f speed loss or increased loading, b u t m a x i m u m cavitation v o l u m e is lower. H o w e v e r , decrease in the m a x i m u m cavitation v o l u m e is very small.
V a r i a t i o n i n l i f t coefficient and c a v i t a t i o n n u m b e r w e r e also p l o t t e d to observe the effect o f speed loss o n o p e r a t i n g loops. As seen i n Fig. 29 o p e r a t i n g loops shift t o w a r d s higher l i f t coefficient due t o speed loss, w h i c h is expected since blade angle o f attack increases due to decreased advance coefficient o f the propeller as the ship speed reduces. The increased angle of attack leads to higher propeller loading. Note t h a t the increase i n l i f t coefficient is greater for the points at l o w e r l i f t coefficient. Also, the o p e r a t i n g loops s h i f t t o w a r d s higher sigma as the ship speed is reduced. Therefore, due to speed loss, t h e p r o b a b i l i t y of pressure side c a v i t a t i o n reduces. The presence o f waves w i l l often be accompanied b y speed loss thus, l o w e r i n g the risk of pressure side cavitation, w h i c h looks i m m i n e n t i n Fig. 26.
0.2 0.4 0.6 0.8
Time t/T
o
>- 0.3
^ 0.0 0.2 0.4 0.6 0.8 1.0
-*^X/L=0.6
X/L =1.1
-•-
X/L=1.6
calm water
Time t/T
B. Taskar et al./Applied Ocean Research 60 (2016) 61-74 71
33. Effect of RPM fluctuations
As the ship travels i n waves, w a k e fluctuates d u e to c o m b i n e d effect o f waves and ship m o t i o n s . This leads to v a r y i n g p r o p e l l e r t o r q u e a n d therefore v a r y i n g loads on t h e engine. Propeller RPM fluctuations depend on the engine c o n t r o l system, system inertia, and load variations. This RPM f l u c t u a t i o n m i g h t alter the c a v i t a t i o n p a t t e r n a n d pressure pulses. It was observed that RPM f l u c t u a t i o n is i n phase w i t h v a r i a t i o n i n t h e average w a k e . Whereas v a r i a t i o n i n pressure pulses is a f u n c t i o n of w a k e d i s t r i b u r i o n rather t h a n t h e average w a k e .
RPM f l u c t u a t i o n w a s calculated using e n g i n e - p r o p e l l e r coupled s i m u l a t i o n s , as described i n section 2.4. I n t h e presence o f waves, the p r o p e l l e r speed w a s seen t o fluctuate b e t w e e n 7 4 to 78 RPM at a constant ship speed o f 15.5 knots. The p r o p e l l e r has been analyzed at the i n s t a n t o f 78 RPM i n the corresponding w a k e . The instances o f m a x i m u m propeller speed occur at t/T = 0.39537, 0.46890 a n d 0.72263 i n \ / L = 0.6, 1.1 and 1.6 respectively. Pressure pulses i n these conditions w e r e compared w i t h those i n t h e same instance o f the w a k e b u t at 76 RPM, w h i c h is design RPM. A b o u t 0.3 kPa increase i n t h e first h a r m o n i c o f pressure pulses can be observed i n Fig. 30. However, this increase is small as c o m p a r e d to increase i n pressure pulses due t o w a k e change in waves.
3.4. Summary of tlie factors affecting the pressure pulses in waves
The effect o f w a k e change, ship m o r i o n s , w a v e d y n a m i c pres-sure, speed loss and RPM v a r i a t i o n has been observed on cavitation a n d pressure pulses. A l l these effects have been considered i n t h e
presence o f waves o f 3 m w a v e a m p l i t u d e to be able to compare t h e influence of these effects. Fig. 3 1 compares the m a x i m u m increase i n t h e first h a r m o n i c o f pressure pulse due to all four effects. The largest increase i n pressure pulses is due to w a k e v a r i a t i o n i n waves. Effects of ship m o t i o n s , RPM fluctuation, and speed loss are rela-tively small. Since w a k e v a r i a t i o n is h a v i n g a significant i m p a c t o n the p r o p e l l e r performance, i t should be taken i n t o account w h i l e designing the propeller.
Also, note t h a t c o n s i d e r i n g the effect of w a k e v a r i a t i o n i n p r o -peller design procedure is m u c h m o r e d i f f i c u l t t h a n considering the effect of ship m o t i o n s , added resistance and RPM fluctuations. Since o b t a i n i n g reliable w a k e i n waves is a challenging task i n itself.
3.5. Efficiency variation in waves
As w a k e varies significantiy i n waves, propeller efficiency also varies w i t h time. The propeller has been analyzed i n d i f f e r e n t wakes in waves a t design RPM, constant c a v i t a t i o n n u m b e r , a n d design ship speed. V a r i a t i o n i n p r o p e l l e r efficiency due to w a k e v a r i a -tion has been p l o t t e d i n Fig. 3 2. W h e n Kx, K Q and efficiency i n t h e presence o f waves is p l o t t e d against t h e corresponding advance coefficients, data-points f o l l o w propeller open w a t e r curves as observed i n Fig. 3 3. F r o m this, w e can conclude t h a t the efficiency is p r i m a r i l y affected by the average change i n w a k e f r a c t i o n and n o t m u c h b y w a k e d i s t r i b u t i o n . Whereas c a v i t a t i o n a n d pressure pulses are d i r e c t l y related to w a k e d i s t r i b u t i o n , a n d t h e y d e p e n d less on average w a k e at least i n the v i c i n i t y of operating p o i n t , as w e have argued eariier.
t/T = 0.53588 t/T = 0.04019 Calm water
Fig. 35. Wakes i n wave \ / L = 1 . 1 obtained using potential flow calculations at a couple of instances.B. Taskar et al. / Applied Ocean Research 60(2016)61-74
I n a d d i t i o n to the w a k e v a r i a t i o n i n waves, w a k e fraction aver-aged over one w a v e encounter period is l o w e r t h a n the calm w a t e r Taylor w a k e fraction due to t h e p i t c h i n g m o t i o n of ship leading to increased propeller i n f l o w as described b y Faltinsen e t a l . [ 2 3 ] .
Since average w a k e is d i f f e r e n t i n the presence of waves, this can affect the choice of o p t i m u m propeller d i a m e t e r and RPM. Choosing the o p t i m u m diameter for the w a k e i n waves can lead to better p r o -peller efficiency i n realistic o p e r a t i n g c o n d i t i o n rather than i n c a l m w a t e r . D o i n g so, propeller efficiency m a y reduce i n calm w a t e r b u t the vessel w i l l p e r f o r m better i n waves. A f u r t h e r study is r e q u i r e d to q u a n t i f y total gain i n efficiency considering d i f f e r e n t w e a t h e r c o n d i t i o n s .
3.6. Coniputation of wake in waves
F r o m the presented analysis, i t is e v i d e n t that t h e p r o p e l l e r s h o u l d be analyzed n o t j u s t i n c a l m w a t e r b u t also i n waves. M o r e o v e r , propeller o p t i m i z a t i o n should also consider t h e oper-a t i o n i n reoper-alistic w e oper-a t h e r conditions, since c oper-a l m w oper-a t e r is roper-ather oper-an e x c e p t i o n at sea. However, to achieve this, t h e first step w o u l d be t o o b t a i n t h e w a k e d i s t r i b u t i o n i n waves, as w a k e v a r i a t i o n has m o r e i m p a c t t h a n the o t h e r effects of waves o n t h e p r o -peller. Currently, i t is n o t a standard practice to o b t a i n w a k e i n waves. Thus, to analyze and o p t i m i z e a propeller i n the presence of waves, w e need to have a tool or a m e t h o d t o calculate w a k e i n waves.
The v a r i a t i o n of spatially averaged w a k e i n waves can be d i v i d e d i n t o t w o factors: (a) M e a n change i n w a k e due t o p i t c h i n g m o t i o n o f ship, as explained b y Faltinsen et al. [23] and (b) Wake fiuctuation due t o induced particle velocities caused by i n c o m i n g waves and surge m o t i o n of ship, as discussed b y Ueno et al. [24]. Both these factors are caused b y p o t e n t i a l effects. Therefore, a l t h o u g h w a k e itself is a viscous p h e n o m e n o n , w a k e change could be p r i m a r i l y due t o p o t e n t i a l effects. Chevalier and K i m [6], Jessup and Boswell [25] have studied cavitation of a propeller o p e r a t i n g i n waves by calculating w a k e velocities using p o t e n t i a l flow calculations. Thus, w e w i l l proceed to check i f p o t e n t i a l flow calculations are suitable for finding t h e change i n w a k e d i s t r i b u t i o n due to waves f o r o u r c u r r e n t case vessel.
W e checked i f p o t e n t i a l flow calculations can be used t o esti-m a t e the change o f w a k e d i s t r i b u t i o n due t o waves using the S h i p f l o w software. First, the KVLCC2 h u l l was s i m u l a t e d i n c a l m w a t e r t o o b t a i n the p o t e n t i a l w a k e . The h u l l w a s t h e n analyzed u s i n g S h i p f l o w M o t i o n s to get t h e p o t e n t i a l w a k e i n waves. P o t e n -tial wakes i n c a l m w a t e r and i n waves can be seen i n Fig. 34. The p o t e n t i a l calm w a t e r w a k e has been subtracted f r o m t h e calm w a t e r w a k e d i s t r i b u t i o n and p o t e n t i a l w a k e i n a particular w a v e has been added t o i t to get total w a k e i n a w a v e . W a k e d i s t r i b u t i o n o b t a i n e d using this procedure can be seen i n Fig. 35 at a couple of instances in w a v e \ / L = 1.1. It can be observed t h a t w a k e obtained using this m e t h o d does n o t resemble t h e w a k e d i s t r i b u t i o n obtained f r o m CFD c o m p u t a t i o n s as seen i n Fig. 1. One of the reasons is t h a t t h e difference b e t w e e n p o t e n t i a l w a k e i n waves and i n c a l m w a t e r is a l m o s t constant over t h e plane of propeller disc. Hence, w a k e v a r i a t i o n obtained using this m e t h o d o l o g y adds or subtracts a c o n -stant value f r o m the c a l m w a t e r w a k e . Therefore, contours o f w a k e plots r e m a i n a l m o s t unaltered w h i l e j u s t t h e level of contours changes.
Thus, i t seems t h a t viscous effects play a m o r e signiflcant role i n w a k e v a r i a t i o n than previously t h o u g h t ; p a r t l y due to the relatively h i g h block coefficient o f KVLCC2 h u l l . Therefore, any p o t e n t i a l fiow calculation m e t h o d m u s t be expected to fail to capture these effects, and therefore w o u l d fail to capture i m p o r t a n t w a k e features like w a k e peak. Hence, p o t e n t i a l flow m e t h o d s do n o t seem to be suited
for calculation o f the change o f w a k e d i s t r i b u t i o n due to waves, at least i n the case o f high block coefficient singlescrew ships. H o w -ever, i t w o u l d be i n t e r e s t i n g t o p e r f o r m similar investigations for slender ships and t w i n - s c r e w vessels.
4.
Discussion
The analysis shows that t h e average a m o u n t of c a v i t a t i o n seen i n t h e presence o f waves is n o t significantly d i f f e r e n t f r o m that i n the calm water, even t h o u g h t h e d i s t r i b u t i o n of w a k e is v e r y d i f f e r -ent. However, pressure pulses show a significant increase. Pressure pulses are p r o p o r t i o n a l to t h e second derivative of the cavity v o l -u m e . Therefore, higher cavity v o l -u m e variations i n the presence o f waves lead to higher pressure pulses.
It was observed that average w a k e and w a k e d i s t r i b u t i o n b o t h change i n the presence o f waves. Littie or no correlation is observed b e t w e e n the v a r i a t i o n o f Taylor w a k e f r a c t i o n i n Fig. 32 a n d the v a r i -a t i o n of pressure pulses i n Fig. 16. Therefore, pressure pulses v a r y p r i m a r i l y due to change i n w a k e d i s t r i b u t i o n rather t h a n v a r i a t i o n i n t h e average w a k e .
The X f o i l analysis gives a clear picture o f w o r s t possible oper-a t i n g conditions i n woper-aves. However, these conditions w o u l d v oper-a r y d e p e n d i n g o n vessel design. Hence, instead of solely r e l y i n g o n t h e experience o f propeller designers f o r t h e cavitation margins, i t w o u l d be beneficial to have data of w a k e v a r i a t i o n i n at least one w a v e l e n g t h . H a v i n g w a k e data at least i n one w a v e l e n g t h w o u l d be very useful, especially i n the case of a u t o m a t e d p r o p e l l e r o p t i -m i z a t i o n as described by Vesting [26], w h e r e the experience o f the propeller designers is often missing.
I n this study, t h e cavitation i n d i f f e r e n t cases has been c o m p a r e d i n t e r m s of its v o l u m e . It is i m p o r t a n t also to look at t h e erosive-ness of cavitation i n waves c o m p a r e d to c a l m water. Since smaller v o l u m e s of c a v i t a t i o n can still be m o r e erosive and therefore create m o r e damage to t h e propeller.
Investigations i n this paper are based on one h u l l and p r o -peller design. W e k n o w t h a t w h e n i t comes to pro-peller design and w a k e v a r i a t i o n , each ship w i l l have a d i f f e r e n t propeller and w a k e v a r i a t i o n . Hence, i n order to d r a w any generalized conclusions, m o r e ships s h o u l d be studied to check t h e general v a l i d i t y o f o u r findings. Also, o t h e r w a v e conditions should also be analyzed e.g. irregular waves and f o l l o w i n g waves. Moreover, fullscale e x p e r i -m e n t a l -measure-ments o f pressure pulses i n waves are r e q u i r e d to c o n f i r m w h a t is seen i n t h e simulations, since there are c o m p l e x -ities i n v o l v e d w h i l e g o i n g f r o m m o d e l scale to f u l l scale, like scale effects f o r w a k e v a r i a t i o n a n d for the p r o p e l l e r itself. I n spite o f all this, t h e analysis i n this paper strongly suggests t h a t t h e c o n -d i t i o n s coul-d become m u c h w o r s e i n waves an-d m u c h -d i f f e r e n t f r o m w h a t is seen i n c a l m w a t e r . W h e n these conditions become clearer, i t w o u l d be possible to e x t e n d t h e boundaries of p r o -peller o p t i m i z a t i o n b y considering the conditions i n t h e presence of waves.
5.
Conclusions
The infiuence of o p e r a t i o n i n waves o n the propeller p e r f o r -mance, i n terms o f efficiency, cavitation e x t e n t and pressure pulses, has been investigated i n this paper, using KVLCC2 as a case. The effect of w a k e change, ship m o t i o n s , w a v e d y n a m i c pressure, speed loss and RPM v a r i a t i o n has been considered. It is f o u n d t h a t t h e v a r i -a t i o n o f w -a k e d i s t r i b u t i o n i n w-aves h-as b y f-ar the l-argest i m p -a c t o n the propeller p e r f o r m a n c e and the greatest change occurs for waves t h a t have a l e n g t h a p p r o x i m a t e l y equal to the ship l e n g t h . H o w e v e r , g e t t i n g w a k e data for operation i n waves is h a r d . Also, t h e n u m b e r of w a k e fields t o be considered i n a p r o p e l l e r design
B. Taskar et al/Applied Ocean Research 60 (2016) 61-74 73
m u s t be v e r y l i m i t e d - c u r r e n t p r a c t i c e is t o consider o n l y t h e c a l m w a t e r w a k e f i e l d at the design speed. Thus, w e r e c o m m e n d t h a t the w a k e field i n a regular w a v e o f w a v e l e n g t h to ship l e n g t h r a t i o X/L = 1.1 is taken i n t o a c c o u n t i n the design, i n a d d i t i o n t o t h e c a l m w a t e r w a k e field. K n o w i n g the w a k e d i s t r i b u t i o n i n w o r s t i n t e n d e d o p e r a t i n g c o n d i t i o n can help us m a x i m i z e the p r o p e l l e r e f f i c i e n c y w h i l e s t i l l a v o i d i n g t h e u n w a n t e d effects o f c a v i t a t i o n and pressure pulses.
As o u r study has considered o n l y one ship and p r o p e l l e r design, w e r e c o m m e n d e x t e n d i n g t h e s t u d y t o m o r e ship designs. Also, the effect o f i r r e g u l a r waves and d i f f e r e n t w a v e headings o n t h e w a k e d i s t r i b u t i o n s h o u l d be i n v e s t i g a t e d .
A c k n o w l e d g e m e n t s
The a u t h o r s w o u l d l i k e t o t h a n k Professor Frederick Stern f r o m the U n i v e r s i t y o f I o w a for p r o v i d i n g the w a k e data i n waves used to analyze p r o p e l l e r i n d i f f e r e n t c o n d i t i o n s . W e also t h a n k Professor B j o r n a r Pettersen f o r h e l p i n g us o b t a i n the w a k e data. This w o r k is f u n d e d by the p r o j e c t ' L o w Energy a n d Emission Design o f Ships' (LEEDS, NFR 2 1 6 4 3 2 / 0 7 0 ) w h e r e the Research Council o f N o r w a y is the m a i n sponsor. W e are g r a t e f u l to Rolls-Royce H y d r o d y n a m l c Research Centre a l o n g w i t h the U n i v e r s i t y T e c h n o l o g y centers o f Rolls Royce at N T N U a n d Chalmers U n i v e r s i t y o f T e c h n o l o g y for t h e i r s u p p o r t . W e w o u l d also l i k e t o s h o w o u r g r a t i t u d e to Profes-sor Carl-Eric Janson f r o m Chalmers U n i v e r s i t y o f T e c h n o l o g y for h e l p i n g us w i t h t h e S h i p f l o w c o m p u t a t i o n s .
Appendix A.
See Fig. A l and A2.
t/T = 0.15815 t/T = 0.39537 t/T = 0.65236 t/r = 0.90936 .0015 -0 01 fli t/T = 0.23379 t/T = 0.41445
K
K
lOIS .001 <10OS D OSXS DOI OOIS
t/J = 0.72263
• £D5 QUI OOtS
Fig. A l . Wake in the presence of wave having wavelength ratio X/L=0.6.
tfT = 0.92454
Fig. A2. Wake in the presence of wave having wavelength ratio X/L=1.6.
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