Experimental analysis on the risk of vortex ventilation and the free surface ventilation of marine propellers

Applied Ocean Research 67 (2017) 201-212

E f c S E V i B E ^

Contents lists available at ScienceDirect

Applied Ocean Research

A 1. F L I r D • O C E A n I

researchI

Experimental analysis on the risk of vortex ventilation and the free

surface ventilation of marine propellers

Anna Maria Kozlowska

^

'

*'

'

*

, Sverre Steen

' Department o/Marine Technology, NTNU, 7491 Trondheim, Trondheim, Norway Rolls Royce University Technology Centre "Performance in a Seaway", Trondheim, Norway

CiDssMark

A R T I C L E I N F O A B S T R A C T

Arricle history: Received 21 January 2017 Received in revised form 9 June 2017 Accepted 12July 2017

Keywords: Vortex ventilation

Propeller hull vortex cavitation Boundaries

Empirical relations Ventilation inception Model tests

The paper presents a discussion o f t h e ventilation inception a n d air d r a w i n g prediction of ships propellers, aiming to predict under w h a t conditions ventilation w i l l happen, and the actual physical m e c h a n i s m of the ventilation.

T h r e e different types of ventilation inception m e c h a n i s m s are included in our discussion: free surface vortex ventilation, ventilation by sucking d o w n the free surface w i t h o u t forming a vortex as w e l l as ventilation b y propeller c o m i n g out of the water. Ventilation prediction is based on a series o f model tests, w h e r e the propeller is tested i n different levels of intermittent ventilation. T h e use of u n d e r w a t e r video gives a visual understanding o f the ventilation phenomena.

Ventilation by vortex formation has analogies w i t h other p h e n o m e n a , s u c h as the inlet vortex in p u m p sumps, ground vortex at the inlet of the aircraft engines and the Propeller Hull Vortex Cavitation (PHVC). The paper includes comparison b e t w e e n Propeller Hull Vortex Cavitation (PHVC) and Propeller Free Surface Vortex Ventilation ( P F S W ) as w e l l as comparison b e t w e e n P F S W and vortex formations of aero engines during high p o w e r operation near a solid surface.

E x p e r i m e n t a l data based on several different model tests s h o w s the b o u n d a i y b e t w e e n t h e vortex forming, non-vortex forming and free surface ventilation flow regimes. For comparison the following parameters, w h i c h determined the intensity of the h y d r o d y n a m i c interaction b e t w e e n the propeller and free surface have been used: propeller load coefficient Cr, tip clearance ratio c/D, propeller submergence ratio h/R, ambient velocity V,- and f l o w cavitation/ventilation n u m b e r o-cav/o'vEnt.

® 2 0 1 7 Elsevier Ltd. A l l rights reserved.

1. I n t r o d u c t i o n

W h e n a ship p r o p e l l e r operates u n d e r h i g h l y loaded c o n d i t i o n , u n s t e a d y l i n e v o r t e x c a v i t a t i o n m a y occur b e t w e e n t h e p r o p e l l e r t i p a n d t h e h u l l . This t y p e o f c a v i t a t i o n is k n o w n as p r o p e l l e r - h u l l v o r t e x c a v i t a t i o n (PHVC) and, i f i t occurs, i t causes s t r o n g v i b r a t i o n s a n d noise i n t h e s t e r n o f t h e ship. W h e n a p r o p e l l e r is o p e r a t i n g close t o t h e f r e e w a t e r surface, a v o r t e x m i g h t f o r m b e t w e e n t h e p r o p e l l e r a n d t h e f r e e surface t h r o u g h w h i c h air can be d r a w n d o w n t o t h e p r o p e l l e r , so t h a t i t ventilates - a p h e n o m e n o n w e call Pro-p e l l e r Free Surface V o r t e x V e n t i l a t i o n ( P F S W ) . V e n t i l a t i o n t y Pro-p i c a l l y occurs w h e n the p r o p e l l e r l o a d i n g is h i g h and t h e p r o p e l l e r s u b m e r -gence is l i m i t e d , a n d w h e n t h e r e l a t i v e m o t i o n s at t h e p r o p e l l e r are

* Corresponding author at: Department of Marine Technology, NTNU, Trondheim 7491, Norway.

E-mail addresses: anna.kozlowska®ntnu.no (A.M. Kozlowska), sverre.steen@ntnu.no (S. Steen).

http://dxdoi.Org/10.1016/J.apor.2017.07.006 0 1 4 1 - 1 1 8 7 / © 2017 Elsevier Ltd. All rights reserved.

large d u e t o heavy seas. P r o p e l l e r v e n t i l a t i o n i n c e p t i o n depends o n d i f f e r e n t p a r a m e t e r s i.e. p r o p e l l e r l o a d i n g , f o r w a r d speed a n d t h e distance f r o m t h e p r o p e l l e r t o t h e f r e e surface, see f o r instance Cal-i f a n o [ 2 ], K o z l o w s k a et al. [ 9 ] a n d K o z l o w s k a a n d Steen [ 1 0 ]. I t is l i k e l y t h a t t h e physical p h e n o m e n a causing v o r t e x f o r m i n g o f PHVC a n d v o r t e x v e n t i l a t i o n are closely related, seeHuse [ 5 ]. I n t h i s paper, P F S W w i l l be c o m p a r e d t o PHVC w i t h t h e a i m o f g e t t i n g a b e t t e r u n d e r s t a n d i n g o f t h e physical m e c h a n i s m s causing PFSW, a n d o n t h a t basis enable t h e m a k i n g o f b e t t e r s i m u l a t i o n and p r e d i c t i o n m e t h o d s f o r PFSW.

V e n t i l a t i o n b y v o r t e x f o r m a t i o n ( P F S W ) has been s t u d i e d b y several researchers see f o r instance Koushan ( 2 0 0 6 1, I I a n d 111), K o z l o w s k a et al. [ 9 ], K o z l o w s k a a n d Steen [ 1 0 ], Califano [ 2 ], Koushan et al. [ 8 ] and K o z l o w s k a et al. [ 1 1 ].

K o z l o w s k a et al. [ 9 ] focused o n v e n t i l a t i o n i n c e p t i o n m e c h a -nisms, classification o f d i f f e r e n t types o f v e n t i l a t i o n , t h r u s t loss r e l a t e d t o each t y p e o f v e n t i l a t i o n , a n d p r o v i d e d a s i m p l e c a l c u -l a t i o n m e t h o d f o r p r e d i c t i n g t h r u s t -loss.

202 A.M. Kozlowska, S. Steen / Applied Ocean Research 67(2017)201-212

Nomenclature

Symbols index

Ov Vortex radius [ m ]

c T i p clearance, distance f r o m the t o p o f propeller disk to the surface ( h u l l ) [ m ]

c/D Tip clearance r a t i o [ - ]

Cp Propeller load c o e f f i c i e n t [ - ]

cjn Propeller load c o e f f i c i e n t f o r n o n - v e n t i l a t e d deeply submerged propeller [ - ]

co.7 Chord l e n g t h at 0.7R [ m ]

Cio,7 L i f t coefficient at 0 . 7 R [ m ]

D, R Propeller diameter, propeller radius [ m ]

h Propeller submergence f r o m the propeller axis to

the free surface [ m ]

h/R Propeller submergence f r o m the propeller axis to t h e free surface [ - ]

] Advance n u m b e r [ - ]

]c Critical advance c o e f f i c i e n t [ - ] Jsc Super critical advance c o e f f i c i e n t [ - ]

Kt T h r u s t c o e f f i c i e n t [ - ]

Kjn Time-averaged m e a n value o f the t h r u s t c o e f f i c i e n t

f o r deeply submerged n o n - v e n t i l a t e d propeller [ - ] n Propeller revolutions [Hz]

P/D Propeller p i t c h r a t i o [ - ]

P F S W Propeller free surface v o r t e x v e n t i l a t i o n [ - ] PHVC Propeller h u l l v o r t e x c a v i t a t i o n [ - ] r Span-wise c i r c u l a t i o n [ m ^ / s ] Pv Vapor pressure [Pa] Po A t m o s p h e r i c pressure [Pa] S Surface tension o f the w a t e r [ N / m ] r Propeller t h r u s t [ N ]

Speed o f advance [ m / s ]

Vj Velocity t h r o u g h t h e p r o p e l l e r disk [ m / s ]

Vo Free stream velocity [ m / s ]

z N u m b e r o f blades [ - ] Pr Total t h r u s t loss f a c t o r [ - ] ffcav Cavitation n u m b e r [ - ] (Tvent V e n t i l a t i o n n u m b e r [ - ] p Density o f w a t e r [ k g / m ^ ] V K i n e m a t i c viscosity [m^/s] J=VA/n D Advance c o e f f i c i e n t pn^D^ T h r u s t coefficient CT c = ( f i I • ^ Propeller load c o e f f i c i e n t

R) T i p clearance, distance f r o m the t o p o f p r o p e l l e r disk to the free surface ( h u l l )

Ocav = J Cavitation n u m b e r ( p r o p e l l e r axis is t h e r e f

-0-5p{Vf,)

erence pressure f o r the c a v i t a t i o n n u m b e r ) o'vent=2gh/(Voo)^ V e n t i l a t i o n n u m b e r

We = nD^/pD/S W e b e r n u m b e r

K o z l o w s k a and Steen [ 10] focused o n c o m p a r i s o n b e t w e e n v e n -t i l a -t i o n i n s-ta-tic and d y n a m i c condi-tions (heave m o -t i o n ) b o -t h f o r o p e n and ducted propeller, and discussed h o w t o estimate t h r u s t loss. As a conclusion, a n e w f o r m u l a t i o n o f the relations b e t w e e n v e n t i l a t i o n and t h r u s t loss w a s developed.

Kozlowska et al. [ 1 1 | presented c o m p a r i s o n b e t w e e n m o d e l tests and n u m e r i c a l calculations o f t h r u s t loss due to v e n t i l a t i o n . The c o m p a r i s o n contains t w o m a i n aspects: c o m p a r i s o n b e t w e e n blade forces and m o m e n t s d u r i n g n o n - v e n t i l a t i n g and v e n t i l a t i n g phase and c o m p a r i s o n o f results o f f l o w v i s u a l i z a t i o n u s i n g h i g h speed v i d e o ( e x p e r i m e n t s ) w i t h CFD s i m u l a t i o n results. The c o m

-Free surface

P F S V V ^

axis

h/R=1.2, n=14Hz. J^O

PFSW

Propeller,

axis. „ ^

Fig. 1. Impact of ttie free surface ventilation (PFSW) for complete submerged pro-pellers.

parisons a i m at i d e n t i f y i n g the degree o f c o r r e l a t i o n and discuss reasons f o r deviations.

P F S W occurs f o r c o m p l e t e l y submerged, h i g h l y loaded p r o -pellers at l o w advance speed. The v o r t e x f u n n e l can reach t h e surface quite f a r f r o m t h e p r o p e l l e r disc, especially f o r large sub-mergence ratios. Fig. 1 shows t w o examples o f PFSW. Note t h a t submergence fi is the distance f r o m the u n d i s t u r b e d f r e e surface t o the p r o p e l l e r axis.

The PHVC p h e n o m e n o n was f i r s t r e p o r t e d by Huse [ 5 ]. System-atic observations had been carried o u t t o investigate the effect o f t h e a f t e r b o d y f o r m , t i p clearance c/D, p r o p e l l e r l o a d i n g cj and cavita-t i o n n u m b e r ffcav E x p e r i m e n cavita-t a l observacavita-tion w i cavita-t h a flacavita-t, h o r i z o n cavita-t a l plate above the p r o p e l l e r i n a c a v i t a t i o n t u n n e l s h o w e d t h a t PHVC is m o r e l i k e l y to occur f o r s m a l l t i p clearances ( u p t o 20% o f propeller diameter, c=0.2D) f o r l o w advance c o e f f i c i e n t ; .

Based o n e x p e r i m e n t a l investigations f o u r hypotheses have been suggested f o r c r i t e r i a leading to PHVC: a so called " s t a r t i n g vortex", "vortices created b y the shear f l o w i n the w a k e f i e l d " , "vor-tices created i n other regions o f t h e f l o w f i e l d " as w e l l as "the p i r o u e t t e effect", see Fig. 2. The "Starting v o r t e x " hypothesis is based o n H e l m h o l t z ' s second t h e o r e m , w h i c h states t h a t a v o r t e x m u s t be either closed or t e r m i n a t e o n the b o u n d a r y o f the f l u i d .

Fig. 2 b e l o w shows the c o r r e s p o n d i n g v o r t e x line representation o f a p r o p e l l e r blade. Circulation w i l l also be closed o n the shortest pos-sible w a y . This means t h a t t h e t i p clearance m u s t be less t h a n t h e blade l e n g t h and axial f l o w v e l o c i t y i n the r e g i o n b e t w e e n h u l l and blade t i p should be close t o zero. Hypothesis based o n "vortices cre-ated b y shear f l o w i n t h e w a k e field" means t h a t a h i g h w a k e peak i n the u p p e r part o f the p r o p e l l e r disk gives rise t o intense shear flow i n the region o f highest velocity gradient. This represents a v o r t i c -i t y -i n t h e flow f-ield t h a t m a y "curl u p " t o f o r m the concentrated vortices necessary to create PHVC.

The basic idea f o r the hypothesis based o n "vortices created i n other regions o f the flow field" is t h a t the cores o f vortices w i l l cavitate w h e n e n t e r i n g t h e l o w pressure r e g i o n b e t w e e n p r o p e l l e r and h u l l .

Huse [5] concluded t h a t the hypothesis based o f t h e " p i r o u e t t e effect" is p r o b a b l y the m o s t correct. By this hypothesis the e f f e c t o f t i p clearance, randomness, e f f e c t o f blade angular p o s i r i o n a n d effect o f v e r t i c a l fins can be satisfactory explained. The basic phe-n o m e phe-n a related to " p i r o u e t t e e f f e c t " w e r e f u r t h e r e x p l a i phe-n later b y M a r t i o et al. [12]. As the gap b e t w e e n the p r o p e l l e r blade t i p a n d the w a l l is decreased, the blade s u c d o n side does n o t o b t a i n enough w a t e r f r o m t h e i n l e t side, so w a t e r is also sucked f r o m d o w n s t r e a m , causing a r o t a t i o n o f the flow, w h i c h is concentrated i n t o a v o r t e x by the so-caUed p i r o u e t t e effect ( r o t a t i o n a l v e l o c i t y has t o increase considerably i n order to keep the angular m o m e n t u m constant,

AM. Kozlowska, S. Steen / Applied Ocean Research 67 (2017)201-212 2 0 3

PHVC

Fluctuating part

of bound vortex

Imaginary part

of closed vortex loop

3 0 :

Inflow direction

Voiticity due to

velocity gradient

Stagnation point

_{Flat plate}

ï ^ \

v o l u m e A

Inflow diiection

Fig. 2. "starting vortex" (top), "vortices created by the shear flow in the wake field (middle) and "pirouette effect (bottom) hypothesis illustration, Huse [5],

w h e n the radius is reduced, t h u s f o r m i n g a marl<ed v o r t e x ) and f i n a l l y causing the PHVC i n c e p t i o n .

A m o r e systematic i n v e s t i g a t i o n o f the PHVC phenomena has been carried out by Sato et al. [ 1 7 ] and N i s h i y a m a [ 1 4 ]. Sato et al.

[17] presented observadon o f f l o w on h o r i z o n t a l flat plate above a w o r k i n g p r o p e l l e r to understand p r o p e l l e r h u l l v o r t e x cavitadon. A i r bubbles w e r e i n j e c t e d i n t o the f l o w f i e l d i n o r d e r t o visualize streamlines o f the plate. As a c o n d n u a t i o n o f his w o r k the f l o w pat-terns w e r e s i m u l a t e d by a RANS m e t h o d s b y M a r d o et al. [12]. The agreement b e t w e e n the observations and c o m p u t a d o n a l results was considered to be sadsfactory.

A n o t h e r p h e n o m e n o n w i t h s i m i l a r i t i e s to P F S W is the occur-rence o f g r o u n d vordces f o r aero engines, and i t is o f interest to see i f the k n o w l e d g e o n g r o u n d vortices can be a p p l i e d to PFSW. The t h r e s h o l d o f f o r m a t i o n of so-called g r o u n d vortices f o r aero engines d u r i n g h i g h p o w e r o p e r a d o n near a solid surface has been i n v e s t i -gated since 1985 i.e., see f o r instance Nakayama a n d Jones [13] and Jermy and Ho [7]. The factors d e t e r m i n i n g t h e f o r m a t i o n o f v o r t e x include engine thrust, distance f r o m the g r o u n d and the a m b i e n t velocity are presented i n Fig. 3. The t h r e s h o l d o f v o r t e x f o r m a t i o n n u m e r i c a l l y predicted agrees w i t h previous w i n d t u n n e l studies

This paper focuses on the b o u n d a r y b e t w e e n v o r t e x f o r m i n g , n o n - v o r t e x f o r m i n g , and the f r e e surface v e n t i l a t i o n o f m a r i n e propellers. Results o f f o u r d i f f e r e n t e x p e r i m e n t a l campaigns are applied i n t h i s paper. The n a m i n g c o n v e n t i o n g i v e n i n Table 1 is used.

The m a j o r i t y o f the results presented w e r e o b t a i n e d d u r i n g the test c a m p a i g n Koz16. Some cases f r o m the o t h e r three test

cam-& GSmylUl.lKKlS

113i W M f l m ^ a»CfMtiwO:

1.6 2 . 0 3 . 2 .1.6 4 . 0 4 . 4 4 . 8 5 J

Fig. 3. Experimental data showing the boundary between the vortex forming and non-vortex forming flow regimes, Jermy and Ho (7) as the function ofthe distance from the inlet center to the ground divided by inlet radius (h/R) and the inlet velocity divided by ambient velocity(f,/V„).

Table 1 Test campaigns.

Author Year Acronym Publications

Kozlowska and Califano Kozlowska

Kourosh and Spence Kozlowska 2009 2010 2010 2016 Koz09 KozlO KoulO Kozie Califano [2] Kozlowska etal. [11] Koushan et al. [8] Presented in this paper

paigns w e r e used f o r c o m p a r i s o n or t o invesdgate missing cases relevant to t h i s study. The /<ozI6 test c a m p a i g n is described i n

Chapter! b e l o w .

Test campaign (KozOB), p r e v i o u s l y p u b l i s h e d by Califano [ 2 ], w e r e conducted at submergence ratios 1.0 < h/K < 2.9 i n the M a r i n e Cybernetics Laboratory at t h e M a r i n e Technology Centre, h a v i n g dimensions ( l e n g t h x b r e a d t h x d e p t h ) o f 4 0 m x 6.45 m x 1.5 m . The carriage speed U and t h e propeller shaft f r e q u e n c y n w e r e varied i n o r d e r to o b t a i n advance ratios J a r o u n d 0 . 1 . The p r o -peller (P1374) had a d i a m e t e r o f 2 5 0 m m , blade area rado equal to 0.6 design p i t h rado P/D = 1.1, t h e p r o p e l l e r h u b diameter w a s 65 m m . D u r i n g measurements images w e r e acquired w i t h a h i g h speed camera at s a m p l i n g frequencies i n the range b e t w e e n 6 0 and 480 Hz, depending o n the test condidons. The test campaign

{KozlO], p u b l i s h e d b y K o z l o w s k a et al. [11] w e r e conducted i n the large t o w i n g t a n k at the M a r i n e Technology Centre, h a v i n g dimensions ( l e n g t h x b r e a d t h x d e p t h ) o f 260 m x 10.5 m x 5.6 m . Tests w e r e conducted f o r f o u r submergence ratios h/R'-2.5, 1.5,

1.0, 0. For all f o u r submergences t h e carriage speed was v a r i e d i n

order t o o b t a i n the f o l l o w i n g advance ratios / = 0 , 0.35, 0.3, 0.45,

0.6, 0.75,0.9,1.05,1.2. Propeller r e v o l u d o n speed was constant and

equal t o 18 Hz. The p r o p e l l e r (P1440) had a d i a m e t e r o f 2 0 0 m m , design p i t c h r a d o o f 1.2 and expanded area rado o f 0.447. The test campaign {KoulO) was p u b l i s h e d b y Koushan et al. [8]. The same propeller m o d e l as f o r test c a m p a i g n {KozlO) w a s used f o r e x p e r i -ments. Test w e r e conducted i n t h e large t o w i n g t a n k at the M a r i n e Technology Centre i n c a l m w a t e r and t w o d i f f e r e n t propeller sub-mergences h/R=2.5 and h/R^l.O. Propeller r e v o l u d o n speed was constant and equal to 18 Hz. For all f o u r submergences, the car-riage speed w a s v a r i e d i n o r d e r t o o b t a i n the advance rados i n the range 0 < J < 1.2.

2. Test set u p a n d i n s t r u m e n t a t i o n

The Kozl6 test was p e r f o r m e d i n the large t o w i n g t a n k at t h e M a r i n e Technology Centre. A f o u r - b l a d e d , right handed p r o p e l l e r m o d e l (P1374) was used. The p r o p e l l e r has a d i a m e t e r o f 250 m m .

204 AM. Kozlowska, S. Steen / Applied Ocean Research 67(2017)201-212 Table 2

Lower limits of advance number J due to the torque and thrust limits of the dynamometer. The max thrust and torque values are the maximum values measured during the experiments.

Vo

nlrpsl 9 rps 12rps 14 rps 16rps

Max Virus f . UN] 194N 345 N 368 N 335 N

•t A "2 Mm Max Torque: QINM)

Jl-\ 7.1 Nm 0 12.7 Nm 0 14.2 Nm 0 3 l*t.J ViiU 0.6 ^ V i . J R SuUion Inlet

i

Fig. 5. A sketch showing principal parameters, (Vi/Vo) and (h/R).

Weber number <180, surface tension related scale effects

Fig. 4. Test set up (left) and propeller view from underwater (bottom right) and above water camera (top right).

blade area r a t i o equal t o 0.6 design p i t h r a t i o P/D ^1.1 and the p r o -p e l l e r h u b d i a m e t e r is 65 m m .

A c o n v e n t i o n a l K e m p f a n d Remmers t w o - c o m p o n e n t s p r o p e l l e r o p e n w a t e r d y n a m o m e t e r w a s used t o measure p r o p e l l e r t h r u s t a n d t o r q u e . Due t o t h e torque ( 1 5 N m ) a n d force ( 4 0 0 N ) l i m i t s o f t h e d y n a m o m e t e r t h e range o f J values f o r t h e h i g h e r r e v o l u t i o n s speeds had t o be l i m i t e d , t h e l i m i t s are g i v e n i n Table 2 b e l o w .

D u r i n g measurements, images are acquired w i t h t w o h i g h speed cameras ( t o p and suction side v i e w o f the p r o p e l l e r ) at a s a m p l i n g f r e q u e n c y o f 200 Hz. The cameras w e r e c o n t r o l l e d b y a dedicated c o m p u t e r p r o v i d i n g trigger pulses i n order t o e x t r a c t t i m e stamps f o r the acquired images. Fig. 4 shows a p i c t u r e o f t h e test set-up and a sample o f the pictures f r o m above-and u n d e r w a t e r videos.

The necessary l i g h t f o r the camera a c q u i s i t i o n system is p r o -v i d e d b y t w o l a m p s : one abo-ve the w a t e r surface and one u n d e r w a t e r . The signals w e r e acquired at a s a m p l i n g f r e q u e n c y o f 200 Hz using a 20 Hz low-pass B u t t e r w o r t h f i l t e r . Test w e r e per-f o r m e d at d i per-f per-f e r e n t draughts and p r o p e l l e r speeds. The d r a u g h t is d e f i n e d as submergence o f the p r o p e l l e r center h d i v i d e d b y p r o -peller radius R. For each d r a u g h t and pro-peller speed the p r o p e l l e r w a s tested at d i f f e r e n t advance numbers, ranging f r o m the l o w e r l i m i t specified i n Table 2 t o J = 1.0. The d i f f e r e n t advance numbers w e r e obtained at various propeller speeds so t h a t f o r the same advance numbers d i f f e r e n t p r o p e l l e r t h r u s t w e r e obtained, t h u s v a r y i n g the W e b e r n u m b e r . W e b e r n u m b e r (We) is square root r a t i o o f t h e i n e r t i a force to the force o f surface tension a n d is d e f i n e d as We = n D y ^ p D / S , w h e r e n is n u m b e r o f p r o p e l l e r r e v o l u t i o n s , D is propeller diameter, p is density o f the w a t e r and S is surface t e n -sion o f t h e w a t e r . According to Shiba [18] the i n f l u e n c e o f Weber's n u m b e r disappears above the so-called m i n i m u m Weber's n u m b e r , w h i c h is about 180. Full scale propellers operate w e l l above Weber's n u m b e r 180 b u t f o r m o d e l scale tests Weber's n u m b e r c o u l d be l o w e r t h a n m i n i m u m values. I n our case o n l y f o r p r o p e l l e r r e v o l u -t i o n speeds over n = 13Hz, -the i n f l u e n c e o f Weber's n u m b e r can be neglected, w h e n f o l l o w i n g the advice b y Shiba [ 1 8 ]. The complete test m a t r i x is g i v e n i n Table 3 b e l o w . FSVentilaÜon 1 0 ' jVortex •-Ventilation No Ventilation > K0209,VV. P13r4 Kq zI) 9 .F S V , P I 374 KO209.NV. P1374 K o z l O . W . P14J0 K a z l O. F S V , P U 4 0 Kq z 1 0 ,N V , P H4 0 K o u l O . W . P1440 K o u l O. F S V , P 1 4 4 0 KoulO.NV, P I 4 4 0 K o z i e. V V . P1374 Koz16,FSV.P1374 ' Kozie.tiV. P1374 .•I I Ï I I • I • • • •

./

i l l

Fig. 6. Experimental data showing the boundary between the vortex forming and no vortex forming flow regimes for marine propellers operating in transient condi-rion(from low to high advance speed), propeller revolutions: (n>9Hz,We>132), Acronyms included in the legend: W means ventilation by vortex formation, FSV means free surface ventilation, NV means no ventilation, P1374; propeller model (D = 250 mm, P/D = l . l , E A R = 0.6,z=4),P1440: propeller model ( D - 2 0 0 mm, P/D = 1.2,EAR = 0.447,z = 4).

3. C o m p a r i s o n b e t w e e n g r o u n d vortex inlet f o r m a t i o n a n d

propeller ventilation

3.1. Propeller ventilation

Propeller v e n t i l a t i o n by v o r t e x f o r m a t i o n has analogies to the i n l e t v o r t e x . Using t h e same parameters f o r propeller and s u c t i o n inlet, see Fig. 3, the b o r d e r l i n e b e t w e e n t h e v o r t e x f o r m i n g , n o n -v o r t e x f o r m i n g and f r e e surface -v e n t i l a t i o n f l o w regimes f o r m a r i n e propellers can be d r a w n .

F o l l o w i n g the w o r k f o r i n l e t vortices, t h e e x p e r i m e n t a l results f o r m o d e l propellers are c o m p a r e d i n order t o compare the c r i t e r i a b e t w e e n v o r t e x f o r m i n g , n o n - v o r t e x f o r m i n g a n d free surface v e n t i l a t i o n f l o w regimes o f m a r i n e propellers.

T w o factors, w h i c h d e t e r m i n e d the f o r m a t i o n o f the v o r t e x , w e r e investigated as f o r t h e i n l e t v o r t e x : p r o p e l l e r radius d i v i d e d by the distance f r o m t h e p r o p e l l e r center t o the free surface h/R and the v e l o c i t y t h r o u g h t h e p r o p e l l e r disk V,- d i v i d e d b y t h e free stream

v e l o c i t y Vo, Vj = Vo + 0.5 ^-Vq + ^V^ + , see Fig. 5. E x p e r i m e n t a l data based o n the d i f f e r e n t m o d e l tests l i s t e d i n Table 1 s h o w the b o u n d a r y b e t w e e n t h e v o r t e x f o r m i n g , n o n -v o r t e x f o r m i n g and f r e e surface -v e n t i l a t i o n f l o w regimes. The t y p e o f v e n t i l a t i o n is i d e n t i f i e d visually, either d i r e c t l y or f r o m the v i d e o recordings. The e f f e c t o f t h e v o r t e x f o r m a t i o n f o r m a r i n e p r o -pellers d u r i n g transient o p e r a t i o n near f r e e surface is presented i n Fig. 6 b e l o w . The factors d e t e r m i n i n g t h e f o r m a t i o n o f a v o r t e x include t h e distance f r o m the propeller center t o the free sur-face d i v i d e d b y t h e p r o p e l l e r radius and the axial velocity at t h e p r o p e l l e r plane d i v i d e d b y the free stream velocity. The color o f t h e data p o i n t s specifies i f v e n t i l a t i o n is observed or n o t . Fig. 6

include the w h o l e range o f tested propeller r e v o l u t i o n s i.e. n > 9 rps. A c c o r d i n g t o Shiba [ 1 8 ] the i n f i u e n c e o f t h e Weber's n u m b e r

dis-Table 3 Test Matrix.

A.M. Kozlowska, S. Steen/Applied Ocean Research 67 (2017) 201-212 205

n | r p s ] 9rps 12rps 14rps TSips i l - l 0 - 1 0 0 - 1 . 0 0 3 - 1 . 0 / o r V R > 1.4 0.6-1.0/or/VR> 1.2 0 - 1 . 0 / o r f v « < 1 . 4 0 - 1 . 0 / o r V R < 1 . 2 Y/i[-\ 0 - 2 . 2 5 0 - 3 . 0 1.05-3.5/or/VR>1.4 2 . 4 - 4 . 0 / o r ( i / R > i a 0-3.5/orh/R<1.4 0-4.0/orh/R<1.2 hlR [-1 -0.5,0.03.1.0,1.2,1.4.13.1.6.1.8 -0.5,0,0.5.1.0.1.2.1.4,1.5,1.6,2.0 -03.0.0.5.1.0,1^1.4.1.5,1.6.2.0 -0.5,0,0.5,1.0,12,1.4.1.5.1.6,2.0 10 8

5

Weber number fel 80

\ fvorlex Ventilation NoVenUlalion

• Koz09.W.P1374 ; ' Koz09,FSV.P13r4' ' Koz09.NV. P1374 \ KozlO.W. P144t) \ KozlO.FSV, P1440i KOZ10.NV.P1440 ! KoulO.W, PI440 KoulO.FSV, P1440f KoulO.NV,PI440 j Kozie.VV. P I 374 f K o z 1 6 f S V , P l 3 H i . K o z i e . N V . e . l 3 7 4 - r " U I I t t I I I . ! I - I s 0.2 0.4 0.6 0,8 1 1.4 1.6 1.8 2 2,2 2,4 2,6 2,8 3 h / R H

Fig. 7. Experimental data showing the boundary between the vortex forming and no vortex forming flow regimes for marine propellers operating in transient condi-tion (from low to high advance speed), propeller revolucondi-tions (n > 13 Hz, W e > 180) Acronyms included in the legend: W means ventilation by vortex formation. FSV means free surface ventilation, NV means no ventilation. P1374; propeller model ( D - 250 mm, P/D = 1.1. EAR - 0.6, z=4), P1440: propeller model (D=200 mm, P/D = 1.2, EAR=0.447, z=4).

appears above t h e so-called m i n i m u n i W e b e r n u m b e r , w h i c h is a p p r o x i m a t e l y 180. For o u r e x p e r i m e n t s a W e b e r n u m b e r larger t h a n 180 corresponds t o a p r o p e l l e r speed n > 13 rps, m e a n i n g t h a t f o r t h e 9 and 12 rps tests, surface t e n s i o n related scale effects m i g h t i n f l u e n c e t h e results. Fig. 7 presents t h e results o n l y f o r tests w i t h p r o p e l l e r r e v o l u t i o n s n > 13 rps, hence t h e i n f l u e n c e o f Weber's n u m b e r can be neglected. I n b o t h figures, lines t o divide the d o m a i n i n t o d i f f e r e n t v e n t i l a t i o n categories are t e n t a t i v e l y i n c l u d e d . These lines m i g h t be used ( w i t h care) to p r e d i c t w h a t t y p e o f v e n t i l a t i o n t h a t m i g h t appear i n a g i v e n o p e r a t i o n a l con-d i t i o n . Both plots are basecon-d o n tests w i t h t w o con-d i f f e r e n t m o con-d e l

ncv«-n«nt ol bl4d«s

Fig. 9. Two PHVC, C7 = l l , 8 , c/D = 0,2, Nishiyama [14],

propellers; P1374: D = 2 5 0 m m , P/D= Ï. J, EAR = 0.6,z=4, and P I 4 4 0 : D = 2 0 0 m m , P/D = 1.2, EAR = 0.447, z = 4.

4. C o m p a r i s o n b e t w e e n cavitation a n d v e n t i l a t i o n

p h e n o m e n o n

Comparison b e t w e e n PHVC, and P F S W occurrence and f l o w f i e l d Sato et al. [ 1 7 ] classified flow patterns f o r three d i f f e r e n t cat-egories: d o w n s t r e a m v o r t e x , double v o r t e x and u p s t r e a m v o r t e x flow, see Fig. 8. D o w n s t r e a m v o r t e x flow s i t u a t i o n occurs w h e n t h e reverse flow become stable and a v o r t e x p a t t e r n can be detected j u s t above the propeller. For r i g h t - h a n d e d propellers t h i s v o r t e x

U h il h b

Vortex system in the Vortex system in the Vortex system m the

aft vortex flow region double vortex flow fore vor-tex flow region

region

A.M. Kozlowska, S. Steen /Applied Ocean Research 67 (2017) 201-212

•4

ft

^ ^ ^ ^ ^

i

V

(a) Impact of the (b) Impact of the (c) Impact of both

port side vortex on starboard side vortex vortices on the

the blade, t=5.497s. on the blade, blade, t= 10.649s.

t=10.307s.

Fig. 10. PFSW, h/R = 2.04,J= 0,075 (CT = 253, C/ D = 0.52), Califano |2].

J=0.249 J=0.326 J=0.433

is r o t a t i n g i n a c l o d t w i s e d i r e c t i o n . Double v o r t e x f l o w occurs f o r small clearance/Diameter c/D ratios {c/D < 0.11). A counter clock-w i s e v o r t e x is located o n the portside o f the clockclock-wise r o t a t i n g v o r t e x . U p s t r e a m v o r t e x f l o w s occur w h e n t h e counter clocl<wise v o r t e x m o v e close a n d hence absorbs the clockwise v o r t e x . As w e can see f r o m Figs. 9 and 10 t h e v e n t i l a t i o n v o r t e x f o r m a t i o n is very s i m i l a r t o the p r o p e l l e r h u l l v o r t e x c a v i t a t i o n p h e n o m e n o n . W e can also observe three types o f the v e n t i l a t i n g v o r t e x i m p a c t o n the propeller blades: i m p a c t o n the p o r t side, starboard side o f t h e p r o p e l l e r blade as w e l l as i m p a c t o f b o t h vortices o n the blade, see

Fig. 10.

N u m e r i c a l RANS s i m u l a t i o n p e r f o r m e d by M a r t i o et al. [12]

shows reasonably good agreement b e t w e e n the v o r t e x f l o w obser-vations and calculations, see Fig. 1 1. I t was observed b y M a r t i o et al. [ 1 2 ] t h a t the o s c i l l a t i o n a m p l i t u d e o f Kp reduced s i g n i f i c a n t l y

b e t w e e n advance n u m b e r s 0.249 and 0.326. Still b o t h situations produce d o u b l e v o r t e x f l o w c o n d i t i o n as s h o w n on Fig. 1 1. The traced streamlines a t J ^ O . 3 2 6 a n d ] = 0 . 4 3 3 i l l u s t r a t e t h a t f o r these cases the generated vortices o n the f r e e surface do n o t i n t e r a c t w i t h a blade at any p o s i t i o n . This is probably e x p l a i n i n g w h y the f l u c t u a -tions o f t h e t h r u s t c o e f f i c i e n t is s t r o n g l y reduced b e t w e e n ; = 0 . 2 4 9 a n d j = 0 . 3 2 6 . W e observe the s i m i l a r c o r r e l a t i o n f o r v e n t i l a t i o n v o r -tex p h e n o m e n a . Above the so-called critical advance c o e f f i c i e n t (Jc) w e observe t h a t t h r u s t loss due to v e n t i l a t i o n is m u c h smaller t h a n f o r advance ratios b e l o w t h i s critical advance c o e f f i c i e n t . This is p r o b a b l y because t h a t f o r higher advanced ratios the generated vortices o n t h e f r e e surface do n o t interact w i t h t h e propeller, so the v e n t i l a t i o n does n o t reach the p r o p e l l e r blades, see Fig. 12. The other reason f o r this is t h a t the suction (described as propeller load

A.M. Kozlowska, S. Steen /Applied Ocean Research 67(2017)201-212 7.01

port side vortex

vortex doesjiot interact

with propeller blades

J=0, n=12, c/D=0,3

J=0.2, n=12, c/D=0.3

_{J=0.4, n=12, c/D=0.3}

J=0, n=12, c/D=0.25

J=0.2, n=12, c/D=0.25

vortex does not interact

with propeller blades

J=0.4, n=12, c/D=0.25

Fig. 12. Appearance of ventilation for different advance ratios, c/D = 0.25,0.3 and n = 12 rps, (Kozl6).

= 0)

I I

\

Fig. 14. Ventilation flow regimes for a conventional propeller based on experiments that are listed in Tablet.

Fig. 13. Vendlation flow regimes Olofsson [ 15|, surface piercing propellers.

f a c t o r Cp) w h i c h is generated b y the p r o p e l l e r is smaller f o r h i g h e r advance ratios.

4.1. Ventilation regimes anti critical advance ratios

The p r o p e l l e r m i g h t be n o n v e n t i l a t e d , p a r t i a l l y or f u l l y v e n -t i l a -t e d , d e p e n d i n g o n several fac-tors, w h e r e submergence and advance n u m b e r are clearly i m p o r t a n t . Olofsson [15] d i v i d e d these v e n t i l a t i o n states i n t o regimes i l l u s t r a t e d i n Fig. 13. The p a r t i a l l y v e n t i l a t i n g r e g i m e is characterized b y h a v i n g v a r y i n g p a r t o f the p r o p e l l e r blade covered by air. I n t h i s regime p r o p e l l e r t h r u s t fluctuates r a p i d l y . The regime is q u i t e stable i n t i m e and lead t o considerably reduced t h r u s t . The p r o p e l l e r m i g h t also e x p e r i -ence t r a n s i t i o n b e t w e e n f u l l y a n d p a r t i a l l y v e n t i l a t e d f l o w regimes. The range o f advance numbers w h e r e this happens is called the

unstable regime or t r a n s i t i o n regime. The sketch i n Fig. 13 o r i g -i n a l l y p u b l -i s h e d -i n Olofsson [ 1 5 ] is based o n e x p e r i m e n t s w i t h surface-piercing propellers ( m e a n i n g propellers designed t o oper-ate submerged t o t h e p r o p e l l e r center). Thus, i t is o f i n t e r e s t t o make a s i m i l a r p l o t based o n e x p e r i m e n t s w i t h n o r m a l , n o n - v e n t i l a t i n g propellers t h a t are v e n t i l a t i n g due to i n s u f f i c i e n t submergence. Such a p l o t has been made based o n the f o u r e x p e r i m e n t a l c a m -paigns listed i n Table 1 and is s h o w n i n Fig. 14. The m a i n d i f f e r e n c e b e t w e e n these t w o plots is f o r n o n v e n t i l a t e d a n d p a r t i a l l y v e n -t i l a -t e d fiow regimes. For submergences h/R&g-t;1.4 w e observe o n l y t w o d i f f e r e n t flow regimes. V e n t i l a t i o n starts f r o m t h e unstable r e g i m e (thus i t is p a r t i a l l y v e n t i l a t e d ) and w e do n o t observe the f u l l y v e n t i l a t e d flow regime w h e r e t h e t h r u s t loss is s i g n i f i c a n t and stable.

W h i c h o f t h e three d i f f e r e n t flow regimes the p r o p e l l e r is oper-a t i n g i n hoper-as oper-a significoper-ant i m p oper-a c t on the p r o p e l l e r t h r u s t , oper-as one coper-an see f r o m Fig. 16 and Fig. 17. The o p e n w a t e r curve f o r t h e deeply

208 A.M. Kozlowska, S. Steen / Applied Ocean Research 67(2017)201-212

Fig. 15. Open water curve for deeply submerged (KT„ , KQ», eta„) and ventilated {Kj, Kd, eta) propeller.

D=250mm, EAR=0.6, z=4. P(D=1.1

Fig. 16. Super critical, unstable and sub critical ventilation regime presented for h/R = 1.0 and1.2,(Kozl6),

D=250mm, EAR=0.6. Z'A, P/D=1.1

Fig. 17. Unstable and sub critical ventilation regime presented for h/R=1.6 and 1.5, (KozlB).

submerged (Kpn, Kqj,, eta„) a n d v e n t i l a t e d (Kp. % eta) p r o p e l l e r is presented i n Fig. 15.

In the f u l l y v e n t i l a t e d r e g i m e w h e n the p r o p e l l e r is h i g h l y loaded and f u l l y v e n t i l a t e d , t h r u s t loss is s i g n i f i c a n t and q u i t e sta-ble, b o t h i n t i m e and i n the sense t h a t a f u r t h e r r e d u c t i o n o f the advance n u m b e r does n o t change the propeller t h r u s t c o e f f i c i e n t

Kp^Tjpn^D'^. The advance c o e f f i c i e n t is b e l o w t h e super critical

advance c o e f f i c i e n t jsc A b o v e the super c r i t i c a l advance c o e f f i -cient Jsc a n d b e l o w t h e critical advance c o e f f i c i e n t Jc is the unstable regime, w h e r e the p r o p e l l e r is p a r t i a l l y v e n t i l a t e d . This r e g i m e is characterized b y large v a r i a t i o n i n t i m e o f the a m o u n t o f v e n t i -l a t i o n and the a m o u n t o f t h r u s t -loss. Above jc is the sub critica-l regime, w h e r e the p r o p e l l e r is n o n v e n t i l a t e d or e x p e r i e n c i n g l i m -i t e d v e n t -i l a t -i o n . For deeper submergences (h/R = 1.5, h/R^I.e) w e observe o n l y t w o d i f f e r e n t v e n t i l a t i o n regimes, v e n t i l a t i o n starts f r o m the unstable r e g i m e at J = 0 and w e do n o t observe t h e super critical v e n t i l a t i o n r e g i m e , see Fig. 17. Test results are presented

i n the f o r m o f t o t a l t h r u s t loss f a c t o r P^-KplKpn w h e r e Kpn is t h e time-averaged m e a n value o f the t h r u s t c o e f f i c i e n t at t h e relevant advance c o e f f i c i e n t } obtained f r o m the c a l m water, deeply sub-m e r g e d n o n - v e n t i l a t e d propeller. Due t o t h e torque (15 N sub-m ) and force (400 N ) l i m i t s o f t h e d y n a m o m e t e r the range of J values f o r the higher revolutions speeds ( n > 1 4 H z ) had t o be l i m i t e d espe-cially f o r larger submergences {hjR>\ .2). This is the reason w h y w e present super critical, unstable and sub critical v e n t i l a t i o n r e g i m e for d i f f e r e n t propeller r e v o l u t i o n s ( n = J6Hz f o r h/R = 1.0, 1.2 p r e -sented i n Fig. 16 and n = 12Hz f o r h/R = 1.6,1.5 presented i n Fig. 1 7j . As the result the surface tension scale effects m i g h t i n f l u e n c e t h e results. A c c o r d i n g t o Shiba [ 18] the i n f l u e n c e o f t h e Weber's n u m b e r disappears above the so-called m i n i m u m W e b e r number, w h i c h is a p p r o x i m a t e l y 180. For o u r experiments a W e b e r n u m b e r larger t h a n 180 corresponds to a propeller speed n > 13 rps, m e a n i n g t h a t for t h e 9 and 12 rps tests, surface tension related scale effects m i g h t i n f l u e n c e the results.

4.2. Inception of cavitating/ventilating vortex

I n c e p t i o n o f v o r t e x c a v i t a t i o n is a c o m p l i c a t e d issue because i t involves a v o r t e x w i t h a l o w pressure r e g i o n i n the core, b u t also nuclei t o expand i n t h a t v o r t e x core. W h e n a c a v i t a t i o n n u c l e i reach a c r i t i c a l l y l o w pressure i t w i l l r a p i d l y expand so t h a t t h e c a v i t a t i o n is f o r m e d .

Cavitation i n c e p t i o n depends o n the m i n i m u m pressure i n the v o r t e x core. The v e l o c i t y d i s t r i b u t i o n o f a 2 D v o r t e x f l o w as g i v e n by t w o d i f f e r e n t v o r t e x models is s h o w n i n Fig. 18 b e l o w .

The pressure d i s t r i b u t i o n i n the center o f a v o r t e x is l o w e r t h a n i n the s u r r o u n d i n g f l u i d because o f the c e n t r i f u g a l effects o f the r o t a t i n g f l u i d . I n a c y l i n d r i c a l v o r t e x this can be easily d e r i v e d f r o m the f o r c e e q u i l i b r i u m on a f l u i d particle i n r o t a t i n g f l o w . A r o t a t i n g particle w h i c h f o l l o w s a c y l i n d r i c a l p a t h a r o u n d the v o r t e x core is subjected to a c e n t r i f u g a l force, w h i c h has to be compensated b y a pressure force i n the r a d i a l d i r e c t i o n

dp_ vOf dr ^ r

(1)

In the case o f a Rankine vortex, the pressure i n t e g r a t i o n over radius r f r o m a to oo results i n

• p ( a ) :

4;r2a„2 (2)

W h e r e Ov is the radius o f t h e c a v i t a t i n g / v e n t i l a t i n g v o r t e x and T is the c i r c u l a t i o n s t r e n g t h .

For a v e n t i l a t i n g vortex, the pressure i n t h e center o f t h e v o r t e x is t y p i c a l l y assumed t o be equal t o the a t m o s p h e r i c pressure, pat w h i l e the pressure f a r a w a y f r o m t h e v o r t e x , Poo =Par + pgh so w e can express Eq. (2) as:

Vat + PSh - Vat =

47r2a„2 (3)

The p r o b l e m n o w is t o estimate the radius o f t h e viscous core at w h i c h v e n t i l a t i o n i n c e p t i o n starts. To t h i s end, w e f i r s t need to f i n d t h e s t r e n g t h o f t h e c i r c u l a t i o n T. This is d i f f i c u l t , and a s i m -p l i f i e d a-p-proach is taken. The c i r c u l a t i o n should increase w i t h the p r o p e l l e r loading, and i t seems reasonable t o l i n k i t t o the circula-t i o n o f a p r o p e l l e r blade. Therefore, w e scircula-tarcircula-t w i circula-t h u s i n g circula-the k n o w n a p p r o x i m a t e r e l a t i o n b e t w e e n p r o p e l l e r blade l i f t c o e f f i c i e n t at 70% radius ci.0,7, t h r u s t c o e f f i c i e n t f o r n o n - v e n t i l a t e d , deeply s u b m e r g e d p r o p e l l e r Km and blade area ratio EAR, w h i c h is v a l i d as an a p p r o x -i m a t -i o n f o r t y p -i c a l c o n v e n t -i o n a l propellers Gutsche [ 4 ]:

Cl0,7 = Kpn 1.5E4R

A.M. Kozlowska, S. Steen /Applied Ocean Research 67(2017)201-212 2 0 9

>•

The veiocity distribution in

\ a vortex with a

01

>

\solid core rotation

Potential flow

4 Vortex core radius radius

.5¬

1

The veiocity

distribution in a

cylindrical vortex

Viscous core radius

Fig. 18. The velocity distribution on the vortex flow.

Fig. 19. Minimum vortex radius for ventilation to occur for n = 16 Hz.

Using the K u t t a Joul<owsl<i t h e o r e m , the l i f t c o e f f i c i e n t can be linl<ed to the c i r c u l a t i o n at the same blade section:

Table 4

Clü.7

P-r-Vc

0.5.p.V}.Coj ( 5 )

W h e r e Vc is t h e local r e l a t i v e v e l o c i t y at t h e blade section, w h i c h , w h e n i g n o r i n g i n d u c e d velocities can be calculated as Vc =

\Jv^ + {0.7ÏMDf w h e r e n is the p r o p e l l e r speed. By c o m b i n i n g

the t w o expressions f o r t h e l i f t c o e f f i c i e n t , the expression f o r the c i r c u l a t i o n s t r e n g t h is o b t a i n e d :

•-, Vc • Co.7 • Kjn

3-EAR ( 6 )

By using the Eq. (6) to express the c i r c u l a t i o n w e o b t a i n a f o r -m u l a f o r the radius o f v e n t i l a t i n g v o r t e x

(Vc-Co.7-Km) 7 ( 3 2 7 r y ^

(7)

A question t h a t remains is h o w large the radius a„ needs t o be for v e n t i l a t i o n t o occur. For v e r y small radii, the air f l o w v e l o c i t y increases, l e a d i n g to decreasing air pressure, so t h a t the assump-tions about atmospheric pressure used f o r d e r i v i n g Eq. (3) is no longer v a l i d . Decreasing a i r pressure means reduced radius, so assuming atmospheric pressure means t h a t w e o v e r - p r e d i c t the v o r t e x core radius, especially f o r s m a l l r a d i i . To correct f o r t h i s effect, w e need t o k n o w the a i r f l o w rate, s o m e t h i n g w h i c h is r e a l l y

Maximum advance ratio C/max) for ventilation to occur based on minimum radius of the vortex core a„.

a„ h/R Jnax V, VilVo Crn Kt„

jnun] I - l 1-1 |m/s] _{[-1 l - I I - l} 3.3 3.4 0.000 2.51 _ _ _0.62 3 3 2.0 0.195 2.74 3.52 3 5 3 9 0.53 3.3 l.B 0.260 2.83 2.72 18.77 0.50 3 3 1 . 6 0300 2.89 2.41 13.57 0.48 3 3 1.4 0360 2.98 2.07 8.87 0.45 3 3 1.2 0.440 3.11 1.77 5.44 0.41

q u i t e h a r d t o calculate, since i t involves h o w t h e air is s w e p t f r o m t h e p r o p e l l e r i n t o t h e f r e e stream.

F r o m t h e e x p e r i m e n t s , presented i n Table 1, i t is f o u n d t h a t v e n t i l a t i o n does n o t occur f o r b o l l a r d c o n d i t i o n ]=0 f o r p r o p e l l e r submergences over3.4, see K o z l o w s k a e t a l . [9]. Based o n this obser-v a t i o n w e calculated, according to Eq. (7), t h a t t h e m i n i m u m v o r t e x core f o r v e n t i l a t i o n t o occur is equal t o 3.3 m m f o r n = 3 6 Hz. Fig. 19

presents the calculation f o r t h e radius o f v e n t i l a t i n g v o r t e x f o r d i f -f e r e n t submergences {h/R=2.0, 1.8, 1.6, 1.4, 1.2) and advance ratio f r o m 0 t o 0.7, based o n Eq. (7). I f w e assumed t h a t the m i n i m u m v o r t e x radius f o r the p r o p e l l e r t o v e n t i l a t e is 3.3 m m w e can t h e n calculate the m a x i m u m advance r a t i o f o r d i f f e r e n t submergences f o r a p r o p e l l e r to v e n t i l a t e , see Table 4. W h e n w e k n o w the advance r a t i o and the p r o p e l l e r characteristics, i t is s t r a i g h t

210 AM. Kozlowska, S. Steen/Applied Ocean Research 67 (2017)201-212

Kozlowska tV. af (2009)

J=0, n=12Hz, h/R=S.4 J=0.J3S. n=12Hz, h/R=2.04

Kozlowska ei.aL (2009} Califano f2011)

3

J=0,n=14Hz,hm^2.6

(2009)

J=0, ti=J4m, fi^R^I.S

Kozhwska et.ak {2009)

J=O.I, n=l6Hz, h/n^2-04

Califam (2011)

Fig. 20. Ventilation inception by vortex formation based on experiments presented in Table 1.

f o r w a r d t o calculate also o t h e r parameters l i k e the v e l o c i t y t h r o u g h t h e p r o p e l l e r V,-, a n d the t w o f o r m u l a t i o n s f o r p r o p e l l e r t h r u s t c o e f f i c i e n t Cm and Km- I f one w a n t s to use the data i n Table 4

t o estimate w h e n v o r t e x v e n t i l a t i o n m i g h t occur f o r o t h e r p r o -pellers t h a n t h e ones s t u d i e d here, i t is r e c o m m e n d e d t o use a p i t c h - i n d e p e n d e n t parameter like V,-. The m i n i m u m v o r t e x radius w i l l p r o b a b l y depend o n the a m o u n t o f air sucked t h r o u g h i t , since a stronger air f l o w w i l l reduce the pressure b e l o w atmospheric ( w h i c h is the c u r r e n t a p p r o x i m a t i o n ) . Thus, t h e stronger the v e n t i -l a t i o n air f -l o w , the -larger the ca-lcu-lated m i n i m u m radius needs t o be. A n i m p l i c a t i o n of t h i s is t h a t the calculated m i n i m u m radius w i l l need to be bigger f o r f u l l scale. H o w m u c h is h a r d t o say w i t h o u t q u a n t i f y i n g t h e a m o u n t o f air sucked t h r o u g h the v o r t e x .

C o m p a r i s o n b e t w e e n the calculation o f the m a x i m u m advance ratio f o r v e n t i l a t i o n t o occur f o r d i f f e r e n t submergence ratios p r e -sented i n Table 4 based on t h e m i n i m u m radius o f t h e v o r t e x core correspond q u i t e w e l l w i t h e x p e r i m e n t s , see Figs. 2 0 and 2 1. For deeply submerged p r o p e l l e r h/R'=2.04 w e observe v e n t i l a t i o n f o r

J = 0 . I a n d j = 0 . 1 3 3 , w h i c h correspond w i t h t h e m a x i m u m advance

r a t i o Jn,ax = 0.195. For h/R=L6 w e observe t h a n v e n t i l a t i o n stops above the J=0.2, w h i c h correspond w i t h t h e m a x i m u m advance ratio Jmax = 0.3. For p r o p e l l e r submergence h/R = 3.2 w e observe v e r y l i t t l e a m o u n t o f v e n t i l a t i o n f o r J > 0.4.

I f is o f i n t e r e s t t o compare t h e o u t c o m e o f Eq. (7), g i v e n i n

Table 4, w i t h the b o u n d a r y lines i n Fig. 7. Such a c o m p a r i s o n is g i v e n i n Fig. 22. I t can be seen t h a t the agreement b e t w e e n the t w o m e t h -ods is good, g i v e n t h e i n h e r e n t u n c e r t a i n t i e s i n t h e observations t h a t these m e t h o d s are based on. The agreement is p a r t i c u l a r l y good f o r h/R < 3.8. For deeply submerged propellers the alternative m e t h o d seems to o v e r p r e d i c t the m a x i m u m advance r a t i o f o r v e n -t i l a -t i o n , w h i c h m i g h -t be caused by neglec-ting -the e f f e c -t o f -t h e air f l o w o n the v o r t e x core radius, as p r e v i o u s l y m e n t i o n e d .

5 . C o n c l u s i o n s

A n analysis o f t h e e x p e r i m e n t a l data a l l o w s to d e f i n e the b o u n d -aries b e t w e e n appearance or absence o f v e n t i l a t i o n b y v o r t e x f o r m a t i o n f o r m a r i n e propellers w o r k i n g near t h e free surface. The factors d e t e r m i n i n g the f o r m a t i o n o f v o r t e x i n c l u d e p r o p e l l e r radius d i v i d e d b y the distance f r o m the p r o p e l l e r t o the f r e e sur-face and t h e axial v e l o c i t y at the p r o p e l l e r plane d i v i d e d b y the free s t r e a m v e l o c i t y .

It has been s h o w n t h a t t h e v o r t e x f o r m i n g m e c h a n i s m o f Pro-peller H u l l V o r t e x C a v i t a t i o n (PHVC) is closely r e l a t e d to t h e m e c h a n i s m of Propeller Free Surface V o r t e x V e n t i l a t i o n (PFSV) v e n -t i l a -t i o n . The v o r -t i c i -t y is f o r m e d by s -t r o n g h y d r o d y n a m i c i n -t e r a c -t i o n

A.M. Kozlowska, S. Steen I Applied Ocean Research 67(2017)201-272 2 1 1

J=0, n=I2H: J=0.2, n==12Hz J=0.4, n-'14H: J=0.6. n^l6H: J=OS, n=16Hz

Fig. 21. Ventilation inception by vortex formation based on experiments presented in Table 1.

Weber number a 180 10

| F S Ventilation I, Vortex Venlilj tion { No Ventilation

• K O Z 0 9 . W . P1374 • Koz09.FSV.Pi374 • Ko209^fV.P1374 KozlO.W. P1440 KOZ10.FSV. P1440 KOZ10.NV. PI440 • KoulO.W. P1440 • KoulO.FSV, PI440 • KoulO.NV. P1440 • KozlO.W. P1374 • Kozl6,FSV.PI374 • K o z i e . l W 3 3 7 4 - ' ^ voflax-9ghtiialion__ - ' - j c c ^ n r a n o i l t s i • • 1 • 1 • I < • 1 • • 1 . . 1

. 1

. :

j

i

Fig. 22. Comparison between altemative method of calculating if vortex ventilation will happened according to Eq. (7), and the boundary between vortex forming and non-vortex forming flow regimes, presented in Fig. 7.

b e t w e e n the c a v i t a t i n g / v e n t i l a t i n g v o r t e x and the pressure i n the core o f a g i v e n v o r t e x was investigated i n order to define the v o r -tex v e n t i l a t i o n i n c e p t i o n . As the result w e o b t a i n a f o r m u l a f o r the radius o f c a v i t a t i n g / v e n t i l a t i n g v o r t e x w h i c h depends o n the p r o -peller c i r c u l a t i o n and t h e c a v i t a t i o n / v e n t i l a t i o n n u m b e r . Therefore, the r e l a t i o n b e t w e e n t h e v e n t i l a t i n g m i n i m u m v o r t e x core radius and t h e m a x i m u m advance ratio f o r v e n t i l a t i o n to occur can be used to define v e n t i l a t i o n i n c e p t i o n .

Aclaiowledgements

This w o r k has been carried out at the U n i v e r s i t y Technology Centre o f Rolls Royce at NTNU ( T r o n d h e i m ) sponsored b y Rolls Royce M a r i n e . W e w o u l d like t o t h a n k the technicians and s t a f f at MARINTEK f o r t h e i r h e l p and expertise i n p e r f o r m i n g the exper-iments.

b e t w e e n the propeller and h u l l (or plate) (PHVC) and b e t w e e n p r o -peller and free surface (PFSW), w h i c h is f u r t h e r developed i n t o a v o r t e x . The occurrence o f the PHVC and PFSW depends o n the p r o -peller load coefficient Cj, t i p clearance r a t i o c/D and f l o w cavitation or v e n t i l a t i o n number.

I t has been described by M a r t i o et al. [12] t h a t the oscillation a m p l i t u d e due to PHVC reduced s i g n i f i c a n t l y b e t w e e n advance n u m b e r s 0.249 and 0.326 even i f s t i l l b o t h situations produce the double v o r t e x f l o w conditions. The n u m e r i c a l investigation shows t h a t f o r these cases the generated vortices f o r h i g h advance ratios

{]=0.325 and J = 0.433) do n o t i n t e r a c t w i t h p r o p e l l e r blades at any

blade positions. W e observe the s i m i l a r c o r r e l a t i o n f o r v e n t i l a t i o n v o r t e x phenomena. Above the so-called critical advance coefficient, w e observe that t h r u s t loss due to v e n t i l a t i o n is m u c h smaller t h a n f o r advance ratios b e l o w critical advance coefficient. This can p r o b -ably be explained b y t h e observation t h a t f o r higher advance ratios the generated vortices do not i n t e r a c t w i t h the p r o p e l l e r thus the v e n t i l a t i o n does n o t appear o n the p r o p e l l e r blades. The r e l a t i o n

References

[2] A. Califano, Dynamics Loads on Marine Propellers Due to Intermittent Ventilation, PhD Thesis, Norwegian University of Science and Technology, Trondheim, 2011.

[4] F. Gutsche, Der Einfluss der Kavitation auf die Profileigenschaften von Propellerblattschnitten, Schiffbauforschung, Heft 1 (1962) 196. |5] Huse, Propeller- Hull Vortex Cavitation, Norwegian Ship Model Exp. Tank

PubL, 1971, May.

[7] M. Jermy, W. Ho, Location of the vortex formation threshold at suction inlets near ground planes by computational fluid dynamic simulation, Proc. Inst. Mech. Eng. Part G: J. Aerosp. Eng. (2008).

|8 j K. Koushan, Silas Spence, Luca Savio, Ventilated propeller blade loadings and spindle moment of a thruster in calm water and waves, in: Proceedings of Second International Symposium on Marine Propulsors, Smpl 1, Hamburg, Germany. 2011.

[91 A.M. Kozlowska, S. Steen, K. Koushan, Classification of Different Type of Propeller Ventilation and Ventilation IncepHon Mechanisms, SMP 09, Trondheim, Norway, 2009.

[10] A. Kozlowska, S. Steen, Ducted and open propeller subjected to intermittent ventilation, in: Eighteen International Conference on Hydrodynamics in Ship Design, Safety and Operation, Gdansk, Poland, 2010.

212 A.M. Kozlowska, S. Steen/Applied Ocean Research 67(2017)201-212

[ 11 ] A. Kozlowska, K. Wockner, T, Rung, S. Steen, Numerical and experimental [15] N, Olofsson, Forces and Flow Characteristics of Partially Submerged Propeller, study of propeller ventilation, in; Proceedings of Second International PhD Thesis, Chalmers Tckniska Hogskola, 1996,

Symposium on Marine Propulsors, Hamburg, Germany, 2011. [17 ] Sato, et al„ Observation of flow on a horizontal Ilat plate above a working [12] J. Martio. T. Sipila, A. Sanchez-Caja. I. Saitso, T. Siikonen. Evaluation of propeller and physisc of propeller- hull vortex cavitation, in: Proceed.

propeller hull vortex cavitation using a RANS solver, in: Proceedings of Second Intemat.Symposium on Propeller and Cavitation, Wuxi, China, 1986. International Symposium on Marine Propulsors, Hamburg, Germany, 2011. [18] H. Shiba, Air-drawing of Marine Propellers. Technical Report 9. Transportation [13] A. Nakayama, ]JL Jones, Vortex formation in inlet flow near the wall, in: 34th Technical Research Institute, 1953.

Aerospace Science Meeting and Exibit, AIAA, 1996, pp. 96-0803. [14] S. Nishiyama, Experimental research on propeller-hull vortex cavitation.