Cavitation

Cavitation

Prof.dr.ir. G. Kuiper

Report 1257-P June 2000

Published in: Proceedings of the 34th WEGEMT School, :Developments in the Design of Propulsors And Propulsion Systems, 19 - 23 June 2000, Deift

University of Technology, ISBN 90 3 70-0486-6

TU Deift

Faculty of Mechanical Engineering and Marine Technology Delfi University of Technology Ship Hydronsechanics Laboratory

Developments in the Design of

Propulsors and Propulsion Systems

Edited by P.W. de Heer

DELFT LNIVERSITY OF

_TECHNOLOGY

Department of Marine Technology

19 -

23 Juni 2000

TU Deift

Printed by: DocVision BV Leeghwaterstraat 42 2628 CA Delft The Netherlands Phone: +31 15 2784642 Fax: +31 152781749

CIP-DATA KONINKLUKE BIBLIOTHEEK. DEN HAAG Heer, P.W. de, Edited by

Proceedings of the 34th Wegemt School "Developments in the Design of Propulsors and propulsion Systems, edited by P.W. de Heer, Facuity of Mechanical Engineering and Marine Technology, Ship Hydromechanics Laboratory, Delft University of Technology.

ISBN 90 370-0486-6

Session 1

Hull Form Design

09.30 -10.00

10.00- 10.45

10.45- 11.00

11 .00 - 11 .30 Coffee break

11.30- 12.15

"Lecture on Hull Design"

M. Hoekstra, MARIN, The Netherlands

12.15- 12.30

Discussion

12.30- 13.30

Lunch

Session 2

Noise and Vibration

13.30- 14.15

"Noise Production of Ships Propellers and

Waterjet Installations at Non-Cavitating

Conditions"

R. Parchen, TNO-TPD, The Netherlands

14.15 - 14.30

Dkr!!on

14.30- 15.00

Coffee break

15.00- 15.45

"The propeller as a source of noise and

vibration"

H. J. C. y Wijngaarden, MARIN, The Netherlands

15.45 - 16.00

Discussion

17.30 - 19.00

Drink Restzwrant "Vlaanderen", Beestenmarkt

16 in Delft

"Fundamentals of Propeller Design" G.Kuiper, MARIN, The Netherlands

"Practical Aspects of Hull Form Design"

A. Aa/bers, Deift University of Technology,

The Netherlands Discussion

Tuesday June 20

Session 3

Propulsor Production

09.00 - 09.45

"An integrated design and production concept for ship propellers"

T. van Beek, LIPS Thrusters BV, The

Nether/an ds

09.45 - 10.00

Discussion

10.00 - 10.30

Coffee break

10.30 - 11.15

"Propulsors Problem and Solutions - In

Service"

P. Fitzsimmons, Lloys Register London, United Kingdom

11.15 - 12.00

Discussion

12.00- 13.00

Lunch

Session 4

Propulsor Design

13.00- 13.45

"Marine Propulsor Design Methodology" G. Po/itis, National Technical University of Athens, Greece

13.45 - 14.00

Discussion

14.00 - 14.30

Coffee break

14.30- 15.15

"Propulsor Design"

J. Holtrop, MARIN, The Netherlands

15.15-

15.30

Discussion

Wednesday June 21

08.15

We

leave off from the Auditorium of the TU

Deift to LIPS

09.45 -

1 2.00 LIPS - Drunen

12.30

Lunch

14.00- 16.00

MARIN - Wageningen

this School will be continued in the future. We hope t1at the written version of the lectures as presented now, will be a reference for the participants and other readers in their daily work.

What remains to us is to thank the EEC and WEGEMT for their financial support and Lips and Marin for their hospitality during the excursions. We express our special thanks to Dineke Heersma and Piet de Heer for their hard work and enthousiasm when organising this School.

On behalf of the organising committee, prof. ir A. Aalbers

WEGEMT COURSE 2000

CAVITATION

Prof. Dr. Ir. G.Kuiper, Marin/TJniversity of Technology Deift.

June 15, 2000

i

CAVITATION

Cavitation is the phenomenon that water changes its phase into vapor in flow regions

with very low pressures. These low pressures are caused by local high velocities.

Cavita-tion is different from boiling because the process of vaporizaCavita-tion in cavitaCavita-tion is nearly isothermal, while in boiling the vaporization is fed by heat transfer. The formation of

vapor requires some heat, but in cavitating flow this amount is so small that only a very

thin region around the cavity has a lower temperature than the mean temperature. The process of beginning of cavitation is called cavitation inception . Pure water can

withstand very low pressures without cavitation inception. A prerequisite for inception is the occurrence of weak spots in the flow, which break the bond between the water

molecules. These weak spots are generally tiny gas bubbles called nticlei . The presence

of nuclei in water depends on the circumstances. In sea water ample nuclei of all sizes

are present, and the inception pressure will be equal to the vapor pressure. At model

scale a lack of nuclei is common and the inception pressure will be lower than thevapor pressure. This is a major cause of scale effects at model scale, which means that the model conditions differ from those at full scale. There are many causes of scale effects, which make it difficult to simulate cavitation properly at model scale. In this chapter these scale effects will not be treated. The picture given below of cavitation and its

effects is therefore very schematic. As always reality is infinitely more complex and this

is very strong in case of cavitation.

mi

g-i T

me Lavitatlon INumoer.

The situation at full scale is that cavitation inception occurs when the local pressure

is equal to the vapor pressure. The local pressure is expressed in non-dimensional terms as the pressure coefficient 6. Similarly the cavitation number is expressed

non-dimensionally as

Po - Pv

- O.5pV

i

cavitation index determines the pressure in the test section of a cavitation tunnel

3

Types of Cavitation.

The main parameter controlling this appearance is the pressure gradient. However, cavitation has many different appearances and the judgment of the effects is complicated. Some types of cavitation will be mentioned first in a schematic way. After that the effects of the various types of cavitation are discussed. Again it should be emphasized that the following classification of cavitation is very schematic.

3.1

Bubble Cavitation.

When the fluid elements in the flow experience a gradual decrease in pressure, cavitation

will occur in the fluid. The nuclei will be the cause of isolated cavities. These cavities

move with the flow. This type of cavitation is called bubble cavitation . It occurs when

the minimum pressure on a blade section is in the midchord region and when this mini-mum pressure is lower than the vapor pressure. An example is given in Fig. 1. This type

of cavitation occurs when the blade sections are relatively thick and operate at a small angle of attack. Near the root of controllable pitch propellers, where the chord length is

restricted because the blades have to pass each other while the strength requires thick

blade sections bubble cavitation is sometimes difficult to avoid.

3.2

Sheet Cavitation.

When the pressure distribution has a strong adverse pressure gradient the flow will sep-arate from the body and a region of cavitation occurs. This happens typically whena leading edge suction peak is present on a profile while the minimum pressure is lower

¿1., .1..

...

#:.. _.., C' .. ...

iii.

L)i jJi

tL(. .Li.i LL(.i (L

I1(

Lt. ULL W. .. L.(. J.iL)fl

attached to the foil and the flow moves around the sheet. The pressure in the cavity is approximately equal to the vapor pressure. An example of such a sheet cavity is given

in Fig. 2.

On commercial propellers the sheet cavity gradually merges with the tip vortex. The rear of the cavity is smooth in such cases, as in Fig. 3.

The extent of sheet cavitation can vary with the blade position when the propeller operates in a wake, as illustrated in //Fig. 4.

Figure 1: Bubble cavitation on a model propeller blade

3.3

Root Cavitation.

At the blade root a type of cavitation can be present with a typical shape, as is illustrated

in Fig. 5. The root cavity has the shape of a wedge. The top of the wedge can be at the leading edge, but it can also start on the blade itself. Root cavitation is related with the horse shoe vortex which is present at the blade root.

3.4

Tip Vortex Cavitation.

At the tip and hub of a propeller blade strong vortices leave the blade or the hub. The pressure in the core of these vortices is low and when this pressure is lower than the vapor pressure vortex cavitation occurs. An example is given in Fig. 6. The vortex is generally very stable, so that the end is far downstream in the flow. When the vortex passes a strong wake peak it may break up and cause a complicated type of cloud cavi-tation.

In general the tip vortex is connected with a sheet cavity at the leading edge, as

shown in Fig. 3.

3.5

Propeller Hull Vortex Cavitation.

A special form of vortex cavitation occurs when a strong wake peak interacts with the propeller in such a way that the tip vortex connects with the hull. In that case a pro-peller frail vortex occurs (PHV-cavitation), as shown in Fig. 7. This type of cavitation causes damage to the plating and an extremely high noise level.

Figure 2: Sheet cavitation on a propeller blade

3.6

Unsteady Sheet Cavitation.

A propeller blade operates in a wake. The angles of attack of the blade sections will therefore vary during one revolution and consequently the cavitation extent will vary with the blade position. In most cases there are blade positions outside the wake peak

where no cavitation will occur, or where even pressure side cavitation will occur at the

pressure side of the blades. In the wake peak cavitation will occur at the suction side. The growth and collapse of cavitation causes a break-up of the sheet cavitation into a cloud of vortices and bubbles. Such a type of cavitation is called clond cavitation. An

example is given in Fig 8.

The development of cloud cavitation occurs when during the development of the uee cavuy

pir

unc cavlzy paraLc5 iiom cile main c;iL na conapse

pi

while moving with the fluid.

3.7

The Mechanism of the Development of Cloud Cavitation

As mentioned above cloud cavitation occurs at the rear edge of a steady sheet or as a result of unsteady behavior of the sheet. The mechanism which controls the develop-ment of cloud cavitation is not clear, but some aspects are important.

Figure 3: Sheet cavitation connected to a tip vortex

-Figure 4: Variable sheet cavitation in behind condition.

The first aspect is the occurrence of a re-entrant jet at the rear end of the cavity. In Fig. 9a a typical cross-section of a sheet cavity is shown. The contour of a cavity has

very little friction, so the flow can be considered as inviscid. The pressure in the cavity is

Figure 5: Root cavitation

Figure 6: Tip vortex cavitation

equal to the vapor pressure P. The streamline just outside the cavity will approach the

profile surface at a large angle and the pressure at the surface will be much higher than

Pv In case of a cavity closure perpendicular to the profile contour the pressure in the

fluid at the rear of the cavity will even be equal to the stagnation pressure Po ± 0.5 pV2. This condition cannot exist in static equilibrium. At the rear of the cavity a jet develops

into the cavity, as shown in Fig. 9b. At some moment the re-entrant jet hits the cavity surface and a complex situation occurs, where a part of the cavity becomes separated

Figure 7: Propeller hull vortex cavitation

Figure 8: Cloudy cavitation at full scale

from the sheet (Fig. 9c). It will move with the flow and collapse when arriving in a region with higher pressures. The collapse is very complicated, because the shape of the separated vapor region is far from spherical or two-dimensional. Instead the vapor separates into parts and vortical structures are often observed. This complex system of

vapor and fluid is called cloud cavitation.

b

Figure 9: Development of cloud cavitation through a re-entrant jet

Figure 10: Cloud cavitation on a profile

In two dimensional flow the process of separation can become very violent, when the

re-entrant jet hits the front of the cavity and a large part of the sheet separates. This is illustrated in Fig. 10. The view is on the suction side of a profile in a narrow tunnel.

Cavitation can have four possible detrimental effects: erosion, radiated noise,

4

Noise and Erosion.

All types of cavitation generate noise. Bubble cavitation is generally considered to be

erosive. Cloud cavitation is considered very erosive. From experience pressure side

cav-itation is also erosive. In propeller design it is therefore tried to avoid these types of cavitation.

First the mechanism of erosion and noise generation will be discussed. Generation of vapor from the fluid is a very rapid process. This means that a vapor bubble, which moves into a lower pressure, will expand rapidly while the pressure inside remains very

close to the vapor pressure. When such a cavity arrives in a region with a pressure

higher than the vapor pressure the same occurs: the bubble decreases in size without the pressure inside becoming higher. When the bubble becomes very small the surface tension also becomes large and this accelerates the collapse. The cavity therefore

col-lapses violently. This is the source of noise. \'Vhen this occurs close to or on the surface,

the surface may be damaged. This damage is called erosion. (Erosion is mechanical damage while corrosion is chemical damage to the material)

4.1

The Implosion of a Single Bubble Cavity.

There are two mechanism of surface erosion. Consider a small bubble which collapses

close to the wall. In the final stage the bubble does not remain symmetrical but deforms,

as sketched in Fig. 11. In the center of the bubble a jet is formed in the direction of the wall. The velocity in this microjet is very high and the pressure when hitting the wall can be several thousands of bars. This equals a hit with a very small hammer on the wall. The result of cavitation erosion is a pitted surface.

Shock-waves

/7/

Micro-jet

/J

Figure 11: Collapse of a cavity near a wall

9

During the collapse of the cavity the velocity of the cavity wall becomes extremely high, far higher than the velocity of sound in the fluid. Although the fluid is generally

(nucleus) is already required. During the expansion of this nucleus gas is collected in the

cavity by diffusion (Cavitation is an effective means of de-aerating the water). At the end of the collapse a small amount of gas at very high pressure remains (The pressure is so high that the gas can radiate light). This gas expands again and the bubble cavity rebounds as numerous small bubbles. These bubbles act again as cavities and collapse

again. In this way the collapse of a single bubble cavity can produce a multitude of pits and a very complex noise spectrum.

When a cloud of bubbles collapse simultaneously, the collapse can be more violent than the collapse of single bubbles in the cloud. This is because the pressure distribution in the cloud during collapse produces a higher mean pressure in the center of the cloud, thus illtensifying the collapse of bubbles in that region. This explains why the collective collapse of bubbles, as occurs in cloud cavitation, is so erosive.

Noise Radiation and Vibrations will be treated seperately in this course.

4.2

Thrust Breakdown.

Partial cavitation on a profile will not affect its lift. On the contrary, a small amount of

cavitation may even increase the camber of the profile and thus increase the lift. The

effect of cavitation on the pressure distribution at the suction side of a profile is shown in Fig. 12. At a cavitation index above 1.25 there is no cavitation and there is a leading

edge low pressure peak with a minimum pressure coefficient of -1.18. At a cavitation index of 1.0 cavitation occurs (a < C(min)). Due to cavitation the minimum pressure

coefficient becomes equal to the cavitation index, which means that the pressure at the cavity is equal to the vapor pressure. The pressure in the leading edge pressure peak is

thus increased. The cavitation extent, however, is larger than the length of the mini-mum pressure peak, so the pressure behind this peak is reduced. As a result the effect

of cavitation on the lift is minimal. This goes on until the cavity length is a considerable fraction of the chord length (o- = 0.5). 1vVhen the mean pressure is further reduced the

.avitaLiuu

ii

u. ductioi f tli lift. TI1 ductiüu i

d, LuL fu.iil,

On propellers different blade sections will suffer from a decrease of lift at different conditions, so the effect of cavitation on the thrust will be more gradual than on a single profile. When the cavitation becomes very extensive at all radii the propeller thrust will

disappear and the propeller suffers from thrust breakdown indexthrust breakdown. On

commercial propellers this will rarely happen, because the propeller loading and the ro-tation rate will be low enough. On highly loaded propellers and especially on propellers

Figure 13: Open water diagram with cavitation

Figure 12: Pressure distribution on a profile at various cavitation numbers

The B-series propellers have been investigated at different cavitation numbers, so

that from the corrected open water diagrams the effect of cavitation on thrust and

torque can be found. An example is given in Fig. 13.

11 Prollel 2

-5

ÁO.o294 r0,,07500

- _-TT_

-: 1,25 o

/7

0.5 p

1t

- ,. --2'

/

---_

75 t. :05 i I e'-is %.0

f:

'7 :

_E

'41kt,._

_j:::

s' s -U 's 1 s, u i

O

1

-SHEET CAVITATION

PRESSURE SIDE

Figure 14: Cavitation bucket of a foil

A measurable effect of cavitation on thrust is often encountered at Navy-ships at full

power or at tugs in towing condition, but also the performance of fast ferries and fast

containerships can be affected by cavitation.

5

The Cavitation Bucket.

On profiles the minimum pressure coefficient determines the inception of cavitation. The

minimum pressure coefficient C(min) is generally plotted as a function of the angle of attack as in Fig. 14

At small angles of attack the minimum pressure varies only slightly with the angle of

attack. The cornerpoints of the bucket indicate the angles of attack where the leading

edge suction peak begins.

The cavitation bucket 'is important to judge the risk of cavitation on the profile. The criterion for occurrence of cavitation is the minimum pressure being equal to the vapor

pressure, or when the cavitation index is equal to the minimum (negative) pressure coefficient. When the cavitation index and the angle of attack is known the risk of cavitation can be read from the bucket. The value cr is plotted on the C axis of the cavitation bucket. The range of angles of attack at that Cr-value within the bucket is

the range where the minimum pressure is higher than the vapor pressure. No cavitation will occur there. Outside the bucket cavitation will occur. The position outside the cavitation bucket gives an indication of the type of cavitation. When the cavitation

Cp (miri) 2

11n the past tile plot was rotated over 90 degrees, so that the curve had the shape of a bucket. This

a degrees. o

Naca 0.8 cainber!ine

Naca 66 thickness distribution: tic=0.06

-4

Figure 15: Cavitation buckets for varying camber

index is in the range of the horizontal branches of the bucket sheet cavitation will occur, caused by the leading edge suction peak. When the cavitation index is lower than the bottom of the bucket bubble cavitation will occur.

The cavitation bucket belongs to the profile geometry. An increase in maximum

camber ( using the same camber distribution) results in a mainly vertical shift (upwards) of the bucket. An increase in maximum thickness (using the same thickness distribution)

results in a wider bucket ( both cornerpoints move in opposite directions). Because the minimum pressure also decreases when the profile becomes thicker the bottom of the bucket moves to the right at the same time.

A variation of the maximum camber is shown in Fig. 15. A variation of the

maxi-mum thickness is shown in Fig. 16.

It should be mentioned that instead of the angle of attack a cavitation bucket can

also plotted against the lift coefficient. Because of the nearly linear relation between the

two this does not change the shape of the bucket.

The cavitation behavior of a propeller is represented in the inception diagram as given in Fig. 17. The design condition of the propeller is indicated with a cross. The inception lines of the various types of cavitation are given on the basis of the propeller thrust coefficient. The sets of curves for sheet and tip vortex cavitation form again a

kind of bucket. When the operational condition is in the bucket there is no cavitation of that type. A typical curve of the propeller at various ship speeds is also given in Fig. 17. As shown the thrust coefficient changes only slightly with increasing ship speed, which

indicated that both the thrust and the resistance increase with -n2.

I

Q

-3 -4 -s

Figure 16: Cavitation buckets for varying thickness

6-U 4 Cp(min)

IIit1ßIiUiililliHu1!

_e

-.aama I

à

a

-0 01 02 0_4 K1

Figure 17: Inception diagram of a propeller

6

Cavitation Testing.

Cavitation is generally investigated at model scale using a cavitation tunnel. This is a

closed ioop iii which the water is circulating. A cross section of a large cavitation tunnel

BACK SKEET

nhiIIlli::LJ!I

_III

_fIIII1IU

-

'tUI! 'IIIi!I!

u

_uIlIII1.IiU.T

Rsoftr

Figure 18: Cross section of a cavitation tunnel (GTH)

(the Grand Tunnel Hydrodynamique in Val de Reuil, France) is given in Fig. 18.

The velocity in most of the circuit is very low and the pressure is high, so that

turbulence can disappear and gas bubbles from the cavitation in the test section can

rise to the surface or dissolve. Upstream of the test section a contraction accelerates the

fluid, so that in the test section the velocity is high and the pressure low. A propeller in the test section can be driven by a shaft, mostly from downstream. A square angle drive from the top of the tunnel is also applied.

An alternative for a tunnel is the Depressurized Towing Tank of Marin (Fig. 19), in

which large scale models can be investigated in cavitating conditions.

In cavitation testing scaling problems are dominant. There are basically two

cat-egories of scaling problems: wake scaling and scale effects on cavitation, especially on cavitation inception. In discussing these scale effects the possibilities and restrictions of both types of facilities will become clear.

6.1

Wake Simulation

In general a cavitation tunnel has no free surface. Consequently the Froude number disappears as a scaling law and propellers can be tested at higher rotation rates than according to the Froude scaling law. This is important, because at low Reynolds num-bers the hoindarv laver at the trnpeller blades remains laminar ovrr large areas, whi'h

results in scale effects on cavitation inception and on performance. As will be mentioned

later these laminar flow effects are eliminated at Marin by application of roughness at the leading edge of the propeller blades. This has to be done with care, to avoid that cavitation is controlled by the amount of roughness.

The absence of a free surface does not completely remove effects of gravity. There

is still a variation in pressure over the height of the test section. This results in a

distribution of the cavitation index over the height of the test section, and thus over the

15

Figure 19: Depressurized Towing Tank

propeller disk. This distribution is only similar to full scale when the Froude number is maintained. vVhen e.g. the rotation rate of the model propeller in the test section is taken twice the rotation rate according to Froude, the cavitation index varies lessover the height of the propeller. This is illustrated in Fig. 20.

Although this effect is generally neglected, it can cause deviations in the cavitation behavior on a blade in various positions. Deviations from the Froude scaling is typically a problem of cavitation tunnels, in which no free surface is present. In the Depressurized Towing Tank the Froude number is maintained and no scale effect occurs.

An important aspect of cavitation testing is the scaling of the wake. Most tunnels are too small to accommodate the complete model, and even when that is possible the

wall effects will be large. Instead of using a complete model, a scaled dummy model is

often 'rd

front of the propeller. This dummy 13 of

ut

gornct:1xJ!y 5calcd

part of the hull. The breadth and the height may have different scale factors. The

use of wires and sandroughness on the dummy makes it possible to control the wake distribution to some extent. When such a dummy is used the wake which is generated

in the propeller plane has to be measured and if necessary adjusted to make it the

same as the target wake distribution. The target wake distribution is the nominal wake distribution from the towing tank, corrected for scale effects. Such a correction is also

used for the extrapolation of the wake fraction of a propulsion test.

O (ml 3 5 g S SR FA C C 301 1.0

7

Cavitation Inception

A major scale effect on cavitation is found in cavitation inception, that is the condition

in which cavitation begins. Cavitation is the occurrence of vapor in the fluid and the rule

of thumb is that this phenomenon begins when the local pressure is equal to thevapor

pressure. The conditions at which cavitation begins are called the inception conditions.

1vVhen cavitation has just started the cavitation is therefore called incipient cavitation and the process of the beginning of cavitation is called cavitation inception.

The assumption that cavitation inception takes place at the vapor pressure is a simplification. Pure water will not cavitate at pressures far below the vapor presure.

A simple test was carried out by Zwick, who used a Z-shaped tube, rotating about its

center of gravity. Due to the centrifugal force the pressure in the center of the tube could

be lowered until -50 bar until cavitation occurred and the fluid was thrown out of the

tube. For all practical purposes it can be stated that pure water will not cavitate

For cavitation inception to occur a mechanism to break the bond between the water molecules is necessary. The most frequent mechanism is the occurrence of small gas

X MODEL LENGTH SOULS FACTOR

r, PROPELLE.R RATE OF ROTATION Po STATIC PRESSURE

Pv VAPOUR PRESSURE

MASS DENSITY 0F WATER

O PROPELLER DIAMETER

A G FULL SCALE OR MODEL SCALE WITH 0Wodr,I "ship iT FROUDE I A 02 MODEL SCALE WITH "rr,odeI 2 rr5r,jp

Figure 20: Variation of the cavitation index in height at two rotation rates. propeller. The interaction between propeller and hull is different however, from the interaction between propeller and screen, so this technique requires much experience. Also the tangential velocities in the wake are not properly simulated withscreens.

Po - 2v 2. /2 p o 2 2.0 2.5 3.0 Rn 17

2.4 2.0 12 o OE8 04 -0 08 15 A a 1Oin 20

Figure 21: Bubble radius as a function of the outside pressure

The curve shows a minimum, and when the radius is at that minimun the radius increases with increasing pressure. This is an imaginary situation, which cannot be

r =68F

= 0005 Ib

NT i.33.10'°

LI Nr

IL-Locus of critical radius

the bubble is equal to the outside pressure p plus the surface tension 2s/R. Here s is the surface tension in N/rn. The pressure inside the bubble is the sum of the vapor pressure

Pv and the partial gas pressure Pg So 2s

Pv+Pg (2)

In isothermal conditions the gas pressure is inversely proportional to the volume, so the

gas pressure can be written as -, where K is a measure for the amount of gas in the

nucleus. The relation between the bubble radius R and the pressure p is given in Fig. 21 for two values of the amount of gas K.

Rcrit 3K

2s

19

reached. 'vVhen the pressure reaches the minimum value equilibrium is _{no longer} pos-sible and the bubble will grow so rapidly that inertia terms have to be included in the equilibrium equation. This will be done in a separate chapter. The minimum radius at which a stable condition is possible is called the critical radius.

The critical radius can be found from differentiation of the pressure:

3(Po Pv)

-DR

from which condition it follows that

(3)

The pressure at which this critical radius is reached is taken as the inception pressure

p. This pressure can be found by substitution of the critical radius in eq. 2 and is:

Pi = Pv 4s (4)

The difference between the vapor pressure and the inception pressure, as expressed in eq. 4, decreases with increasing critical radius and thus with increasing nuclei size in the undisturbed flow.

This leads to the important conclusion that

The inception pressure depends on the size of the largest nuclei in the fluid

7.2

Scaling Laws

This conclusion can be expressed in a non-dimensional way. The pressure is expressed

as the cavitation index

PO - Pv 1/2pV2

where Po is the pressure in the undisturbed flow at the same location. The surface

tension s is expressed as the Weber number T'Ve

We=

pV2 r0 (5)

s

where r0 is the radius of the nuclei in the undisturbed flow. Eq. 2 is valid in the

-Elimination of Rcrit ,p and expressing the equations in cavitation index and Weber

number results in

2--Pcrbt - Pv cîWe

POPv

3(1+)

The difference between inception pressure and the vapor pressure, as expressed in the left hand of this equation, can also be written in non-dimensional terms as

Lcr

o-where

Pcrit - Pv l/2pV2

This gives the final non-dimensional form to the inception pressure:

LcT

2---

_ciWe

a

3/(1)

(6)

Eq. 6 gives the difference between the vapor pressure and the inception pressure in

non-dimensional terms. This has severe implications for scaling of cavitation inception. It

c+14.

. _--b.-1...

IIiCt... ..A1(Lt . i... .fl.L, .. - ... CU.,.'J b'.

u;'..k

b £ii. b.L) u

the same at model and full scale. So the Weber number is an additional scaling law, introduced by the surface tension as a new parameter. The Weber number can also be

derived as a scaling law using the fl-theorem in dimension analysis.

7.3

Scaling of the Nuclei Size

Assuming the same fluid density p and surface tension s at model and full scale, a proper scaling of cavitation inception of the Weber number means that

Or

=

V2R03

For a proper scaling of the inception index the nuclei

size at model scade should be larger than at full scale by

a factor a/k2

21

The scaling law can be relaxed, however. Because inception of cavitation is deter-mined by the largest nuclei available, this scaling rule is required for the largest nuclei only.

7.4

Effects of Nuclei on Inception

A systematic investigation was carried out by the cavitation committee of the ITTC in

the Large Cavitation Tunnel (GTH) to assess the effects of nuclei on cavitation inception.

Fig. ?? gives the results.

The effect on inception of tip vortex and bubble cavitation is extremely large. In the case of tip vortex inception a low number of nuclei also increases the difference between

inception(begin) and desinence (disappearance) of the cavitation. This difference is called hysteresis of inception.

R03 ₍₇₎

When the Foude number is maintained this means that

=

_{In that case the}

nuclei at model scade have to be larger than the nuclei at full scale by a factor equal to

the scade ratio. Most cavitation inception tests are carried out in a cavitation tunnel without free surface, and the velocity is higher than required by the Froude law. When

this increase is expressed by a factor k, the relation between model and full scale velocity

is

V k

-

',/a1pha

where k is not more than about 3. With the relation for nuclei scaling (eq. 7) this leads to one of the important problems in cavitation testing:

Figure 22: Inception data with varying nuclei content

8

Scaling of the Nuclei Density

For a proper representation of cavitation at model scale the number of cavities at model

scale should be equal to the number at full scale. This leads to the simple requirement

that the number of nuclei at model scale should be larger than at full scale with a factor

a3.

This requirement, together with the fact that the size of the nuclei should be

in-creased with a factor a makes that the free gas content of the water at model scale

should be higher than at fall scale with a factor at'. This leads to serious problems, because such water will have the appearance of 'soda pop". Visualisation will not be possible and the compressibility of the water can no longer be neglected. The latter

affects not only the pressure distribution on bodies in the flow, but also the noise

radia-f-infl. inr f hr' vr'lnr'itv nf cnund br' rrastira11 lnwrreri. T!i r'nditinn i

to obtain in practice.

The requirement of a similar number of cavities is not always necessary. In fact it is a requirement which stems from the scaling of noise radiated by bubble cavities. Every cavity acts as a noise source and therefore the number of nuclei should be scaled. This is of course only sensible when the noise production of a single cavity is also properly

scaled and that is a problem in itself. So the requirement of scaling of the number

density can in practice be relaxed considerably.

inception desinence % diff.

case i (maximum tension) 0.24 0.24 0

case 2 (medium tension, low nuclei number) 0.86 0.93 8

case 3 (medium tension,. high nuclei number) 0.95 1.01 6

case 4 (minimum tension) 1.00 1.03 3

Tension Type Surface Cavitation (S)

inception desinence % diff.

case 1 (maximum tension) 0.97 1.03 6

case 2 (medium tension, low nuclei number) 0.99 1.05 6

case 3 (medium tension,. high nuclei number) - -

I

23

SMOOTH SMOOTH SMOOTH ROUGHENED

1=0

I = 1.2A I = 2.4 A _{I = 2.4A}

Figure 23: Bubble cavitation with increasing nuclei content

For a proper scaling of cavitation inception it is sufficient to define a minimum

encounter frequency of the largest nuclei. This means that a blade section, moving through the wake peak in behind condition, encounters at least a minimum number of nuclei during the entry of the wake peak. When the largest nuclei are large enough to cause inception close to the vapor pressure, the scale effect will be the time delay between the moment the vapor pressure is reached and the moment a large nucleus is encountered. Both conditions are required for cavitation inception.

8.1

Effects of Nuclei on the Appearance of Bubble Cavitation

The appearance of bubble cavitation witl1 a low nuclei density will be different from the appearance with a high nuclei density. The number of nuclei will determine the number

of bubble cavities on the blade surface as well as the maximum size of these bubbles. This is illustrated in Fig. 23, where the nuclei content is increased using electrolysis in front of the pronelier. These picturr are taken in the Depressirized Towing Tank, which has a low nuclei content due to the standing water.

In Fig. 40 a typical pattern of bubble cavitation at a low rotation rate (Reynolds

number) is shown. At a low rotation rate the tunnel pressure has to be very low to arrive

at the required cavitation index. Although it seems that there are plenty of nuclei in the

flow, only a few explode into cavities on the blade. This is because the amount of nuclei

passing through the low pressure region on the blades is still very limited. A further

Figure 24: Bubble cavitation at low Reynolds number

Figure 25: Bubble cavitation at high rotation rate (1450 rpm)

When the same propeller is run at a high rotation rate (the maximum is determined

by the tunnel velocity and the power of the driving system) at the same cavitation index

Figure 26: Bubble cavitation on a roughened blade

tests section and their radius will be smaller. At the same time the Weber number

(eq. 5) will be much higher. The scale effect, determined by eq. 6 will consequently be

much smaller and nuclei will grow to cavitating bubbles at a lower cavitation index. These two tendencies are opposite. The result in Fig. 25 shows that in this case (the large cavitation tunnel of MARIN) the decrease of the nuclei size due to the higher

pressure in the test section dominates over the earlier inception due to the smaller scale effect. The bubble cavitation has decreased significantly. Except for some streaks it has

almost disappeared, although the pressure on the blades is certainly below the vapor

pressure. An increase in Reynolds number, which for other reasons is often assumed to reduce the scale effects, increases the scale effects in this case and increases the need of

additional nuclei. The maximum size of the additional nuclei in Fig. 25 can be smaller than in the condition with low nuclei content.

The streaky appearance of the bubble cavitation in Fig. 25 has a viscous origin. This

will be discussed separately.

An effective method to bring ample nuclei in the region of cavitation inception is

application of leading edge roughness. When the leading edge of the propeller of Fig. 25

is roughened, the result is as in Fig. 26.

The leading edge roughness apparently generates very tiny nuclei, which cavitate in the low pressure region. The scale effects on inception decrease drastically and inception

takes place when the local presure approaches the vapor pressure.

Due to the large amount of cavitation bubbles the maximum bubble size decreases. So does the radiated noise. Although bubble cavitation has a reputation of being very

25

LO.. PETERSON eIcE - IHOECGAPIÇYI oO.49 -. zMoevIII 1F H WAIF.H I Gl1LOV(r23I (»1N S'1UM 5 I4JRSF

Q III 4ENT Si JOY IIIOH AIRCoNTE)Ir

-I4Cpm.o'0.7G

ILC'.V AUI CONTENT

-7pçi,, oO 44 ÍELDBEI1GB.SCIII. EI.FIF'4SON(I7) ARNDT 8 KELLER 132) lAR CCNTENT-1C5pç.'t KELLER 8 WEITENXRFI3I) - (GRSSEDWATER) e 1 IO-' 10 NUCLEI RADIUS (ml) o lo-,

Figure 27: Nuclei density in various conditions (Gates)

These measurements have been made with various measuring techniques. These

techniques wil be discussed in a separate chapter. The nuclei density in this Figure is

expressed as

N

(R1 - R2)

where N is the number of nuclei with a radius between R1 and R9. The unit is therefore

m4.

The slope of the distribution was found to be similar in many cases, although the log-log scale hides makes the curves very insensitive to variations. When this slope is assumed to be a universal property of water it is sufficient to measure only a limited

27

When such a size distribution at model and full scale is assumed it is possible to

calculate the density of nuclei which become unstable both at model and full scale. This

can be used to calculate the encounter frequency both at model and full scale. This makes it possible to describe scale effects in terms of the probability of a cavitation

event . A cavitation event is the unstable growth of nucleus into a cavity. Since this

cavity implodes when it arrives in a region of higher pressure, cavitation events can be

counted by the noise peaks of their implosion.

9

The Presence of Nuclei in Water

The question arises what the origin of the gas nuclei in the fluid is. A small gas nucleus will have a high gas pressure due to the high surface tension and consequently diffusion

of the gas into the fluid will occur. For a 10 micron diameter gas nucleus it is a matter of seconds to go into solution and disappear! Larger gas nuclei, on the other hand, will rise to the surface and disappear there. 2 In standing water there will be no nuclei left

after a short time.

In moving water this may take more time and nuclei may be kept in the fluid. But the due to the surface tension the pressure in the gas bubble is higher than in the surround-ing fluid and diffusion of gas from the bubble into the fluid will occur. So after some time the nucleus will go into solution unless the water is supersaturated with air.

Many mechanisms have been proposed to explain the persistent presence of nuclei in water, although the nuclei size distribution can vary widely. A reduction or stop of diffusion has been found when surface affectants form a kind of impermeable skin on the nuclei. Random generation of nuclei by atmospheric radiation has been proposed. Biological life has unpredictable effects on the creation of gas nuclei. None of these

hypotheses has given a convincing explanation of the fact that it is difficult to get

completely rid of nuclei in water. The most practical model is that of Harvey, who

assumed that gas was "hidden" in cracks of solid material. The gas remains inside such

cracks when the material is hydrophobic, which means that the solid material is wetted by the fluid, as shown in Fig. 28.

The pressure in the gas pocket is now lower than the pressure in the fluid since the surface tension is directed outward. Diffusion will occur into the gas pocket and a cer-tain equilibrium with the finid can be reached. When the solid is a small solid particle the combination of ga.s and solid can he neutrally buoyant and the particle can remain

indefinitely in standing fluid.

This model is only a model. Whatever the mechanism, it is very difficult to remove nuclei completely from natural water such as sea water. On the other hand it is very difficult to control the nuclei size distribution and thus the inception pressure.

2For the rise velocity of small nuclei the Stokes law can be used. This law yields Vr = 1/18e,

Figure 28: Gas nucleus trapped in a crack in solid material

The actual nuclei distribution in sea water is not very important though. Nuclei of 10 microns are abundant in sea water. Using a representative entrance velocity of blade

sections of 30 rn/sec and a minimum pressure coefficient of 1.0 the value of o- can be

calculated from eq. 5 to be

1000 x 302 x

We= =120

0.075

From eq. 6 the value of ¿o can be calculated, when for o the value of the minimum

pressure coefficient 1 is used:

- 0.031

This is a very small deviation of the 'normal cavitation index of 1, so

At full scale the deviation of the inception pressure from the vapor pressure is expected to be negligible.

This leaves the problem at model scale. At a model scale of sav 25 and Fronde

scaling the required radius of the nuclei will be approx. 250 microns. This is not evident at all and generally requires additional measures.

9.1

Nuclei Seeding

Additional nuclei are sometimes supplied to ensure that the inception pressure remains close to the vapor pressure. Three types of precautions are mentioned Fiere.

29

The first technique to generate nuclei is to increase the total air content of the _tank

or tunnel water. _{However, the inception pressure is not depending on the total air}

content, but only on the free air content, which is the fraction of air which is not in solution. This is generally only a small fraction of the total air content. In cavitation tunnels, however, there are many locations where dissolved gas can come out of solution

and form nuclei. Such locations are locations where flow separation _{occurs, such as in} corners, on honeycombs etc. As a result the total gas content has a relation with the free gas content and with the nuclei distribution. It is important to keep in mind that

this relation is facility dependent.

Better facilities with very few separation locations have a too low nuclei content. This is especially true for tunnels with an absorber, which is a leg in the tunnel with a high static pressure, which also has a large volume so that the residence time of the

tunnel water is long. As a result the nuclei will go into solution. A way to supply nuclei

is by jets of supersaturated water which blow into the upper leg of the tunnel. It is very

difficult, however, to control the maximum size and the size distribution. An additional

problem is the screening of the nuclei, which takes place in the test section, where the larger nuclei tend to move to the top of the test section.

The third way to ensure sufficient nuclei is electrolysis. A set of two wires or strips is

put under tension and as a result of the conductivity of the water the water is dissolved

into oxigen and hydrogen. These gases are cut away from the electrodes and form a mist

of nuclei in the fluid. There has to be sufficient mixing downstream of the electrodes to generate a unifoiin distribution. This technique is useful at lower velocities. At high velocities the nuclei remain very small and the current has to be very high. In a closed

system the gas mixture should be carefully controlled because it is highly explosive. An example of the application of electrolysis is the Depressurised Towing Tank, where the standing water contains very few nuclei and where seeding of nuclei is required.

10

Viscous Effects on Cavitation Inception

Sheet cavitation is relatively insensitive to the nuclei density and size. Only in extremely

low nuclei densities it has been found that sheet cavitation does not occur when the pressure is below the vapor presslre OLC of the reasors is that sheet cavitation does not need nuclei to support its existence, as is the case with bubble cavitation. In a

stationary situation a single nucleus is sufficient to generate a sheet forever.

However, sheet cavitation has its scale effects too. These are mainly related with laminar flow regions on the propeller blade. It has been found that when there is a

laminar boundary layer in the region of low pressure, no cavitation will occur. On simplified forms such as headforms this resulted in the inception pressure being equal to

the pressure coefficient at the location of transition or, in case of a laminar separation bubble, to the pressure coefficient at reattachment.

Figure 29: Paint test in uniform inflow

On model propellers laminar regions occur frequently. This can be observed with a simple paint test, as shown in Fig. 29.

At the leading edge (left) the paint has been removed due to the higher velocities and

the resulting higher friction. At inner radii the paint streaks point outwards, indicating

a laminar flow. In the middle of the blade the laminar flow becomes turbulent, which is

shown by the more tangential direction of the streaks. Also the thickness of the paint decreases suddenly.

At outer regions the paint streaks are tangential from the leading edge on. This is the region where a leading edge separation bubble exists. The separation bubble is so short that is is not visible in the paint streaks.

Inside of the radius where leading edge separation begins, no sheet cavitation will

occur, even at very low cavitation numbers. In the outer region with a short separation bubble sheet cavitation will occur at the vapor pressure.

The effect of a laminar boundary layer on sheet cavitation is shown in Fig. 30 \'- -,+',! r! i'c 9-

cl-c rt'c.m

- LS _ l_1 L J. - LLSI.L - L_ I_LA L SL _{L.LLLJ. J} _L

___;-for a few roughness elements which cause streaks of turbulence. It is only at these

streaks that cavitation occurs in the form of spot cavitation.

At inner radii laminar separation is present and a smooth sheet occurs, as in the tip

region (this is a propeller with an unloaded tip).

So the rule is that only in regions with a laminar separation bubble sheet cavitation occurs at the vapor pressure. In regions of laminar flow sheet cavitation occurs as spots on surface imperfections.

Figure 30: Effect of laminar boundary layer on sheet cavitation

from the leading edge on. This does not occur at model scale. It requires high Reynolds

numbers close to the full scale to obtain that. In that case it is expected that no scale effects will occur either, so that inception takes place at the vapor pressure.

An example of a paint test a t high Reynolds number is given in Fig. 31. This

Figure shows that at high Reynolds numbers the boundary layer becomes thinner and the roughness of the surface is sufficient to cause turbulent spots. These spots will cavitate in low pressure.

The effect of high Reynolds numbers is therefore that the natural roughness of the

blades is used to trip the boundary layer. This can also be done artificially by the application of roughness at the leading edge. This has been standard practice at Marin for the last decade. An example of the effect of leading edge roughness is shown in

Figs. 32 and 33.

In regions of laminar flow a sheet occurs due to the roughness. In regions with spot cavitation a closed sheet is also formed. Bubble cavitation becomes also more dense, as has been discussed before.

The difference between cavitation tunnels and the Depressurized Towing Tank is that ìn Tunnels, with a higher Reynolds number, less roughness is required to trip the boundary layer. In large cavitation tunnels the natural roughness of the surface will suffice. In the depressurized Towing Tank the roughness has to be applied. Standard practice is 60 microns of carborundum. The leading edge contour has to be maintained with care. This is controlled with the leading edge microscope, of which the results are

shown in Fig. _3Zf

Figure 31: Paint test at high Reynolds number

Figure 32: Cavitation on a smooth blade

11

Cavitation Calculations

Calculations on the size and dynamic behaviour of bubble cavitation do not exist. The

Figure 33: Cavitation on a roughened blade

In principle potential calculations of cavitation can be done using the boundary condition of vapor pressure on the cavity area and tangential flow on the wetted area.

The first problem is that these areas are unknown and the solution has to be found

iteratively.

This has been done two-dimensionally, which revealed the next problem: the closure

condition. At the end of the cavity both the pressure and the velocityare prescribed

and these two conditions are contradictory. It is only possible when the cavity ends

tangentially to the foil surface and reality is that it is closer to perpendicular to the

surface. This leads to a discrepancy and many simplifications have been used to solve this. The problem is that at the closure of the cavity both viscosity and two-phase flow

phenomena play a role and the flow is no longer a potential flow field. The main problem

is that the choice of the closure condition has a strong influence on the size and length

of the cavity.

The cavitation problem has therefore not been solved two-dimensionally. In three dimensions the problem remains the same, but possibly the sensitivity of the solution to the closure condition is less. Investigations in that direction are scarce.

The simplest calculation of the cavity length and shape is the fully linearized one, as developed by Geurst. He uses conformal mapping, so a two-dimensional approach,

and neglects blade thickness. Assuming parabolic camber a diagram of the length of the

sheet cavity based on angle of attack and cavitation number can be calculated. These

calculations are used in the determination of the induced pressures, which will be treated separately.

Figure 34: Leading edge contour with and without roughness

12

Interpretation of Cavitation

Interpretation of cavitation is necessary because nobody is interested in cavitation as

such. It is because of the detrimental effects that cavitation observations are made. The effect which has to be judged from observations is erosion. Because only observations are used, this has to be done qualitatively.

Another detrimental effect of cavitation is vibrations. The dynamic behaviour of a

sheet cavity can be observed, although still photographs are not well suited to estimate

the rate of change of the volume. Therefore cavitation induced pressures have to be measured.

When extensive cavitation is present thrust and torque become affected. This is relevant when the rotation rate of the propeller in those conditions is important. This

effect can be measured. The most reliable measurement is in the Depressurized Towing

Tank, where the effects of cavitation are taken into account in the propulsion test, so

with propeller hull interaction.

For Navy applications inception conditions are important. Cavitation inception causes a jump in the radiated noise of the propeller and the speed at which this oc-curs has to be as high as possible. In such cases an inception diagram is made, which reveals the type of cavitation and the speed at inception.

Figure 35: Sheet Cavitation

12.1

Conditions

Cavitation tests have to be done at full scale propeller loading. So the resistance and rotation rate have to be extrapolated first from a propulsion test. Corrections on the

rotation rate have to be applied based on the torque and thrust measurements in cavi-tating conditions.

In the model tests with cavitation the wake should also be scaled. This can be done in a cavitation tunnel, although with very high inaccuracy. In the depressurized Towing

Tank it is not possible to change the wake behind the model and the wake distribution of the model wake is applied, with the mean wake (propeller loading) of the ship. In practice this is also done in many cavitation tunnels.

In propulsion tests the model propellers are not roughened. Although this would be consistent, the statistics and available corrections are based on smooth propellers, as is the ITTC scaling procedure for thrust and torque. In cavitation tests the propellersare roughened, certainly when they are used in the Depressurized Towing Tank, where the

Reynolds

iì1r is lower.

12.2

Interpretation of Erosivity

This is the main subject of the interpretation of cavitation patterns. It is also a target to design propellers with non-erosive cavitation. It is therefore useful to determine which

mechanism makes the cavity erosive.

A sheet cavity with a smooth edge is not erosive. This is e.g. the case at the inner radii of the propeller in Fig. 35. This Figure also reveals the mechanism which causes

Figure 36: Cavitation with sheet connected to tip vortex

the break-up of the sheet at outer radii. The triangle at inner radii reflects the re-entrant

jet, which is water blowing into the cavity. In this case the re-entrant jet is directed outwards. Art the outer radii the re-entrant jet is directed opposite to the flow and this water merges with the re-entrant jet of the inner radii. The result is a cloudy type of cavitation, caused by shedding of the trailing edge. It is the same phenomenon which

caused the massive shedding of cavitation on the foil in Fig. 36.

To avoid such a cloudy region it is advisable to connect the smooth region with the tip vortex. This makes the whole sheet very smooth and not erosive. An extreme

example is given in Fig. 36.

This type of sheet cavitation is required in all the blade positions in which cavitation

occurs. It often requires a relatively heavy tip loading and this in turn causes a strong

tip vortex in the wake peak.

The tip vortex is considered not erosive, at least when it collapses in the flow. A strong tip vortex can cause considerable noise when it collapses downstream of the

nrnneller. _{This hs caused noise} nrnhlpnic in crìise vel .A!n fjn vnrtev hit the rudder. This can lead to erosion on the rudder and a high inboard noise level.

The gradient of the sheet cavity is also sensitive to the manufacturing accuracy.

When flat spots are present on the leading edge length variations can occur, which lead to a cloudy entrainment, as shown in Fig. 37

Dynamic behaviour of a sheet which is smooth in steady conditions is also a common observation. An extreme case is shown in Fig. 38

where the remnants of a sheet at the outer radii are stili visible. This sheet has just collapsed in the niiddle of the blade. In such cases the sheet detaches from the leading

Figure 37: Cloud cavitation at full sca'e behind a sheet with varying extent

Figure 3: Implosion of a sheet in a sharp wake peak

edge and collapses on the blade or on the trailing edge. That is often the cause of a bend

trailing edge. It is the purpose of cavitation observations tosee if such things happen. A dynamic collapse can also occur three-dimensionally.In that case a cavity develops

a thick bulge and this collapses on the blade, as shown in Fig.38

It is a matter of judgement if such an occurrence will lead to erosion. Such a judge-ment can only be given in terms of risk and requires experience, often depending also on 37

Figure 39: Traces of bubble cavitation at inner radii

the facility. Qualitative measurements of erosiveness have been tried using black stencil

ink on the surface of the model propeller. Although this method gives an indication where risk of erosion exists, it is very difficult to calibrate and no quantitative results

are found from such a method.

Observations at model scale can reveal the existence of scale effects. When relatively

long spots occur in a certain region this indicates the presence of a laminar region. In

that region sheet cavitation has to be predicted. In critical cases the difference between bubble and sheet cavitation may be small. Application of roughness will shift the balance to sheet cavitation, a low Reynolds number will tend to bubble cavitation.

12.3

Interpretation of Bubble Cavitation

The difference between bubble and sheet cavitation is only relevant when the effects are different. The rule of thumb is that bubble cavitation is erosive and should be omitted.

T4rccr inditr'n' 2r

1,b

f f11 _qç'1 ' ,c.

reputation says it is.

Full scale bubble cavitation occurs very infrequently because it is generally omitted. An example of traces of bubble cavitation is given in Fig. ??.

No problems with erosion in those regions were experienced, however. Indications

are that bubble cavitation occurs more frequently at full scale than predicted at model scale. This is in line with the experimental data with leading edge roughness. The

application of roughness stimulates the occurrence of bubble cavitation and it makes its structure much smaller (see Fig. 40. )

39

Figure 40: Bubble cavitation at model scale with leading edge roughness At full scale it occurs even earlier and it structure is a fine mist of bubbles.

12.4

Scaling of Tip Vortex Inception

Tip vortex cavitation is a special type of cavitation because viscous effects play a major

role in its inception. This means that at model scale cavitation inception occurs much

later than at full scale. No proper model of the tip vortex has yet been developed.

An empirical rule is that derived by McCormick in the sixties, which says that the

inception index scales with the 0.35 power of the Reynolds number. This rule is widely

applied. Application of such a (large) correction i necessary to avoid large errors. The

determination of inception at full scale is difficult enough to lead to large scatter of the