Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 3.1.4 - Water Quality Effects on Sheet Cavitation Inception on a Ship Propeller Model
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 Material Information
Title: 3.1.4 - Water Quality Effects on Sheet Cavitation Inception on a Ship Propeller Model Cavitation
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: van Rijsbergen, M.X.
van Terwisga, T.J.C.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: cavitation inception
free-stream nuclei
dissolved gas content
 Notes
Abstract: Cavitation research for the maritime industry is mainly carried out in model scale facilities such as a cavitation tunnel or a depressurized towing tank. A first requirement for correctly scaled results is that cavitation inception occurs at the vapour pressure. Each facility has developed its own methods to ensure this, such as controlling the dissolved gas content, application of leading edge roughness or the free-stream nuclei content or a combination of these. A fundamental understanding of the inception mechanism, especially for sheet cavitation on roughened propeller blades, is still missing. Therefore, experiments have been conducted in MARIN‟s Depressurized Towing Tank at various dissolved gas and free-stream nuclei contents with a propeller model which was tested extensively before. A conceptual model for sheet cavitation inception is presented which explains the experimental results. It is concluded that both leading edge roughness and sufficiently small free-stream nuclei are essential for sheet cavitation inception on propeller models.
General Note: The International Conference on Multiphase Flow (ICMF) first was held in Tsukuba, Japan in 1991 and the second ICMF took place in Kyoto, Japan in 1995. During this conference, it was decided to establish an International Governing Board which oversees the major aspects of the conference and makes decisions about future conference locations. Due to the great importance of the field, it was furthermore decided to hold the conference every three years successively in Asia including Australia, Europe including Africa, Russia and the Near East and America. Hence, ICMF 1998 was held in Lyon, France, ICMF 2001 in New Orleans, USA, ICMF 2004 in Yokohama, Japan, and ICMF 2007 in Leipzig, Germany. ICMF-2010 is devoted to all aspects of Multiphase Flow. Researchers from all over the world gathered in order to introduce their recent advances in the field and thereby promote the exchange of new ideas, results and techniques. The conference is a key event in Multiphase Flow and supports the advancement of science in this very important field. The major research topics relevant for the conference are as follows: Bio-Fluid Dynamics; Boiling; Bubbly Flows; Cavitation; Colloidal and Suspension Dynamics; Collision, Agglomeration and Breakup; Computational Techniques for Multiphase Flows; Droplet Flows; Environmental and Geophysical Flows; Experimental Methods for Multiphase Flows; Fluidized and Circulating Fluidized Beds; Fluid Structure Interactions; Granular Media; Industrial Applications; Instabilities; Interfacial Flows; Micro and Nano-Scale Multiphase Flows; Microgravity in Two-Phase Flow; Multiphase Flows with Heat and Mass Transfer; Non-Newtonian Multiphase Flows; Particle-Laden Flows; Particle, Bubble and Drop Dynamics; Reactive Multiphase Flows
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Bibliographic ID: UF00102023
Volume ID: VID00074
Source Institution: University of Florida
Holding Location: University of Florida
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Resource Identifier: 314-Rijsbergen-ICMF2010.pdf

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7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010



Water Quality Effects on Sheet Cavitation Inception on a Ship Propeller Model


Martijn X. van Rijsbergen* and Tom J.C. van Terwisga*T

Maritime Research Institute Netherlands (MARIN), Wageningen, The Netherlands
f Delft University of Technology, Delft, The Netherlands
m.v.rijsbergen@marin.nl and t.v.terwisga@marin.nl


Keywords: cavitation inception, free-stream nuclei, dissolved gas content



Abstract

Cavitation research for the maritime industry is mainly carried out in model scale facilities such as a cavitation tunnel or a
depressurized towing tank. A first requirement for correctly scaled results is that cavitation inception occurs at the vapour
pressure. Each facility has developed its own methods to ensure this, such as controlling the dissolved gas content,
application of leading edge roughness or the free-stream nuclei content or a combination of these. A fundamental
understanding of the inception mechanism, especially for sheet cavitation on roughened propeller blades, is still missing.
Therefore, experiments have been conducted in MARIN's Depressurized Towing Tank at various dissolved gas and
free-stream nuclei contents with a propeller model which was tested extensively before. A conceptual model for sheet
cavitation inception is presented which explains the experimental results. It is concluded that both leading edge roughness
and sufficiently small free-stream nuclei are essential for sheet cavitation inception on propeller models.


Introduction

Cavitation inception in the flow over foils and propellers
does not necessarily occur when the local pressure falls
below the vapour pressure. To a large extent, the moment
of inception is dependent on the water quality of the flow
(see e.g. Keller, 1974). For cavitation research, water
quality comprises gas nuclei, dissolved gas and
micro-particles. In a Cavitation Tunnel (CT) gas nuclei are
normally generated by the pump impeller, sharp covers,
etc. at a sufficiently high dissolved gas content. In a
Depressurized Towing Tank (DTT), however, these
mechanisms are not present and gas nuclei that exist will
either rise to the surface or dissolve. As a result, no
cavitation at all or cavitation on parts of the propeller
blades is observed, in conditions where cavitation in a CT
or at full scale is present.
Noordzij (1976) found that additional nuclei provided by
electrolysis at wire pairs upstream of the propeller model
could improve sheet cavitation inception on smooth
propeller blades in MARIN's DTT. In most cases, however,
the sheet was not fully developed but remained limited to
spots or patches. Kuiper (1981) confirmed this, but also
reported a fully developed sheet cavity on a propeller
model in the DTT by the application of leading edge
roughness. Nuclei seeding by electrolysis could not further
improve the extent of the cavity. It was hypothesized that
the roughness elements, which are located in the minimum
pressure region, create microscopic, turbulent low-pressure
regions which cause dissolved gas in the water to come out
of solution. Key elements in this nucleation process are the


very thin boundary layer and the locally supersaturated
water. In a later publication (Kuiper, 1985) it is argued that
micro-cavitation at these roughness elements is required to
generate nuclei from the dissolved gas which in their turn
enable macro-cavitation. Van der Kooij (1986) suggested
that micro-scale free- stream nuclei are forced to grow by
diffusion and instability due to the high pressure
fluctuations and strong vortices at the roughness elements.
Van Rees et al. (2008) confirmed the essential role of
free-stream nuclei for sheet cavitation inception on
roughened propeller blades by showing good agreement
between the pressure side sheet cavity of a propeller in the
DTT with nuclei seeding and the CT at a standard air
content. However, this seemed in contradiction with the
findings of Kuiper.
Inspired by this ambiguity, a test programme was made
with the objective to determine the primary inception
mechanism for sheet cavitation on propeller models with
roughened blades. Cavitation observations were conducted
on the propeller used by Kuiper in MARIN's DTT The
effect of the water quality on sheet cavitation was studied
for a range of propeller loadings and Reynolds numbers.
This work is expected to contribute to a better
understanding of the physics of cavitation inception by
systematically studying the effect of the free-stream nuclei
content and dissolved gas content. As a result, it helps to
define the limiting conditions for inception. This is
relevant for experiments aimed at finding the risk of
cavitation erosion, as well as for experiments measuring
the hull pressure fluctuations and radiated noise from a
cavitating propeller.






7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


Nomenclature


Cpmm

CPmm r
D


P -P
minimum pressure coefficient P -P1 0
Spn2D2
min. pressure coefficient on roughness eleme

propeller diameter

acceleration of gravity


propeller shaft submersion


I electrolysis current


J propeller advance ratio
nD
k average roughness height
T
KT propeller thrust coefficient p
pn2D4
n propeller rotation rate

Po pressure at shaft submersion PT + pgh

Pc critical pressure

PG total dissolved gas pressure

Pmim minimum pressure on blade section


Pmn r

Pref


minimum pressure on roughness element

reference pressure


PT tank pressure

Pv vapour pressure of water

r local radius on propeller

R propeller radius

Ro free-stream bubble radius

Rc critical bubble radius

Rn propeller Reynolds number


roughness Reynolds number

surface tension


nD2
v
Uk
v


N/m


propeller thrust


Test set-up

The weak connection between the dissolved gas content
and the natural free-stream nuclei content of a DTT may
ent seem a disadvantage, but it is an excellent basis for an

m independent variation of these water quality variables.
Most of the research as mentioned in the introduction was
m/s2 carried out in MARIN's DTT and therefore it is used for
the current experiments also. The towing tank which
m measures 240 x 18 x 8 m in length, breadth and depth
respectively is designed for cavitation experiments on ship
models up to 12 m in length. The pressure above the water
S surface can be lowered to satisfy both cavitation number
(on) and Froude number identity.
m For the present experiments a propeller open water test
set-up was used. Interaction with the water surface can be
neglected at a propeller shaft submersion (h) larger than
Hz 1.5 propeller diameter (D). This enables a variation of the
Reynolds number (Rn) at a constant thrust coefficient (KT).
Pa The used propeller was originally designed to study
Pa isolated sheet cavitation (Kuiper, 1981) which is
designated as the S-propeller. Its geometry and some main
Pa particulars are shown in Figure 1. Carborundum roughness
with an average grain size of 60 pm has been applied on
Pa the leading edges of all four propeller blades, conform

Pa standard practise.
The propeller is mounted in the open water test set-up
Pa which provides measurement of propeller rotation rate (n),
thrust (T) and torque. An electrolysis grid was positioned
Pa 1.6 m upstream of the propeller. It consists of nine pairs of
flat steel rods with a span of 0.515 m each. Further details
are provided in Figure 2.


4 BLADES
S = 0.340 m
AE/A0 0.60
cQ71D 0.34
t c07 = 0.033


Figure 1: Geometry of S-propeller.


U local velocity


reference velocity


V towing tank carriage velocity
pn2D2R,
Wn Weber number pn2D2R
S
v kinematic viscosity of water

p mass density of water

on propeller cavitation number

T tensile strength of water


P,-PP
20 pn
pn2D2


m/s

m/s

m/s



m2/s

kg/m3



Pa


---------- ----- ---

ioo

-394 38


1600

Figure 2: Setup of propeller with electrolysis grid, and a
detail of the steel rods in the grid (dimensions in mm), side
view.









The nuclei content of the propeller inflow can be
influenced by varying the current (I) on the electrolysis
grid, since the total gas volume produced through
electrolysis is proportional to the current. The current was
varied in steps of 1.2 A between 0 and 3.6 A,
corresponding to a range of 0 to 0.78 A/m for each pair of
rods. The current was set to 0 A between runs.
The dissolved air content of the water in the DTT can be
controlled by supplying pressurized air to a perforated tube
located on the bottom of the towing tank. Depending on
the tank pressure (PT) and the total dissolved gas pressure
of the water (PG), the rising air bubbles will aerate or
deaerate the water by diffusion. PG was determined using
an In-Situ T300E tensionometer which measures the gas
pressure in a gas permeable membrane tube. The readings
are taken at a depth of 0.5 m. After aeration or deaeration,
the maximum spatial variation (x, y position in the tank) of
the converged readings was about 0.5 kPa.
The test programme consisted of two series of tests. In the
first series, the nuclei spectrum was varied by a systematic
variation of the electrolysis current for a range of propeller
loadings and Reynolds numbers. After some initial tests in
the second series, the paint and leading edge roughness
was re-applied. With the re-applied roughness, the
dissolved gas content was varied with and without the
unpowered electrolysis grid upstream of the propeller. The
roughness before and after re-application is designated as
roughness 1 and 2 respectively.


Results

Delayed cavitation inception behaviour results in typical
gaps in the sheet cavity along the span of the propeller
blades, see left and middle picture in Figure 3. To quantify
the results, the radial cavitation extent is defined as the
range of r/R values covered by sheet cavitation.


Figure 3: Typical observed sheet cavities at on = 1.7, KT =
0.15 and Rn = 1.2-106 with grid. Left: I = 0.0 A, middle:
I = 0.0 A (30 s later in the same run), right: I = 3.6 A.

Free-stream nuclei
The influence of electrolysis current on the radial
cavitation extent of the S-propeller for a range of thrust
coefficients is shown in Figure 4. Symbols indicate the
average values. Error bars indicate the maximum and
minimum values found on the four propeller blades. The
tests are carried out in the order given by the legend.
Without electrolysis, the radial cavitation extent is nearly


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

zero at the lowest two thrust coefficients. With an
electrolysis current of 1.2 A, the radial cavitation extent
increases significantly at the smallest thrust coefficients. At
the higher thrust coefficients, the gaps in the sheet cavity
are closed. A further increase of the current decreases the
difference in cavitation extent between the blades and
slightly increases the average radial cavitation extent,
except for the highest thrust coefficient where it remains
approximately constant. After the test runs with the highest
electrolysis current, two repeat runs were made at I = 0.0 A.
Slightly larger radial cavitation extents are observed
compared to the initial runs.

0.7
SI= 0 0 A
*I=12A
0.6 Al=23A
Sl=36A
= 0 0 A repeat
0.5


0.4


L 0.3
.2
0.3
m
0.2


0.1


0.0


0.08 0.10 0.12 0.14 0.16
Thrust coefficient KT


0.18 0.20


Figure 4: Influence of electrolysis current on radial
cavitation extent for a range of propeller loadings.
Roughness 1, C, = 1.71, Rn = 1.2-106.


0.7


0.6


S0.5
c-

0
0.4


> 0.3


" 0.2


0.1


0.0


0.6 0.7 0.8 0.9 1.0
Reynolds number


1.1 1.2 1.3
x106


Figure 5: Influence of electrolysis current on radial
cavitation extent for a range of Reynolds numbers.
Roughness 1, on = 2.2, KT = 0.19.


A l=24AI


' ' '









Reynolds number
The effect of Reynolds number on the radial cavitation
extent is investigated with and without electrolysis at Cn =
2.2 and KT = 0.19. The radial cavitation extents for 6.5-105
< Rn < 1.2-106 are shown in Figure 5. At the lowest Rn
value, without electrolysis, two blades show no cavitation
at all. At the second lowest Reynolds number only one
blade shows no cavitation. For Rn = 9.5.105 (n = 10 Hz)
and higher, all blades show cavitation and the average
radial cavitation extent does not further increase with Rn.
With an electrolysis current of 2.4 A only some gaps in the
radial extent of the sheet cavity can be found at the lowest
Reynolds number. For Rn = 7.9-105 (n = 8.3 Hz) and
higher, the sheet cavity is fully closed and marginal
variations in the radial cavitation extent only occur at the
outer ends. So, in general, inception improves with
increasing Reynolds number.

Reproducibility
Repeat measurements with and without grid showed
deviations in the average radial cavitation extent of about
0.1 r/R. This value was found both for differences between
runs (repeatability) and differences between the first and
second series reproducibilityy). Although the number of
observations is limited, the value of 0.1 r/R is taken as a
measure of the reproducibility of the average radial
cavitation extent.

Dissolved gas content
The influence of the presence of the unpowered
electrolysis grid on the radial cavitation extent has been
investigated at high and low dissolved gas contents at an =
1.71. The results are shown in Figure 6 for Rn = 1.2-106
(n = 11.7 Hz) and in Figure 7 for Rn = 9.7-105 (n= 9.2 Hz).
The dissolved gas content is expressed in a supersaturation
ratio, defined as the total dissolved gas pressure (PG)
divided by the pressure at the propeller shaft (Po). The
variation in PG/Po between the Reynolds numbers results
from an adaptation of the tank pressure to obtain the same
cavitation number at another rotation rate. The average
radial cavitation extents are shown on the basis of the
measured thrust coefficient, because the grid decreases the
propeller inflow velocity. Solid and dotted lines indicate
the trends for the observations with and without grid
respectively. Error bars indicate the maximum and
minimum values found on the four propeller blades. For
each condition, the dissolved air content is expressed as the
supersaturation ratio PG/Po.
Both figures show that there is no consistent effect of the
presence of the grid on the radial cavitation extent at low
PG/PO values (2.5 -3.8). The variation between the blades in
radial cavitation extent is not affected by the presence of
the grid. At moderate PG/PO values (5.0), the grid gives a
minor improvement of the radial cavitation extent of about
0.1 r/R. This is comparable to the reproducibility of the
observations. Because it does so for the whole range of
propeller loadings, it is considered to be significant. At the
high propeller loadings, the presence of the grid decreases
the variation between the blades.


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

At the highest supersaturation ratio (7.5), the presence of
the grid causes the largest increase of the radial cavitation
extents. Again, the variation between the blades decreases
with increasing propeller loading once the grid is present.
No consistent effect of a higher rotation rate on the radial
cavitation extent can be seen at the lowest supersaturation
ratios (PG/P = 2.5/3.8). The radial cavitation extents found
at Rn = 1.2-106, P/PO = 5.0 are slightly larger than at
Rn = 9.7-105, P/PO = 7.5. The differences are small but
they are found over a range of KT values, both with and
without grid.


0.7


0.6


0.5


S0.4
.0
S0.3


5 0.2


0.1


0.0 --
0.08


0.10 0.12 0.14 0.16
Thrust coefficient KT


0.18 0.20


Figure 6: Influence of presence of grid and supersaturation
ratio on radial cavitation extent for a range of propeller
loadings. Roughness 2, on = 1.71, Rn = 1.2-106.


0.7


0.6


- 0.5


S0.4
.2
S0.3
C5

* 0.2


0.1


0.0 -
0.08


0.10 0.12 0.14 0.16
Thrust coefficient KT


0.18 0.20


Figure 7: Influence of presence of grid and supersaturation.
ratio on radial cavitation extent for a range of propeller
loadings. Roughness 2, on = 1.71, Rn = 9.7-105.









Finally, a comparison can be made between the current
observations and those made by Kuiper (1979) at similar J,
on and Rn values, see Figure 8. The observations made by
Kuiper show a perfect sheet cavity without electrolysis.
The current observations at a slightly higher cavitation
number show however only some streaks of cavitation
without electrolysis, while with electrolysis the sheet
cavity is similar to that observed by Kuiper.


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

point (Johnson and Hsieh, 1966). Smaller nuclei may get at
the minimum pressure area (Pmn), but they have large
critical pressures. Leading edge roughness may overcome
this problem.


Pmmr << mm

Pmm


*--.U


Figure 8: Comparison of sheet cavities at J = 0.6, Rn =
1.1.106, I = 0.0 A. Left: from Kuiper (1979) at cn = 1.6;
middle and right: from present study at on = 1.7, I = 0.0 A
and I = 3.6 A respectively.


Discussion

Conceptual model of sheet cavitation inception
Rood (1991) defines cavitation inception as the initial
rapid growth of vapour- and gas-filled bubbles as a
consequence of hydrodynamic forces. Using a bubble
approach to model cavitation inception (Kuiper, 1981), the
critical pressure (Pc) below which a gas nucleus or bubble
will grow exponentially is given by:

4S
P=-PV-C A T= (1)
3Rc

where Pv is the vapour pressure, x is the tensile strength of
water, S is the surface tension and Rc is the critical bubble
radius. Table 1 shows that with a vapour pressure of about
1.7 kPa, these tensile strengths for typical bubble radii have
a significant influence on the inception pressure.

Table 1: representative values of tensile strength (r) as a
function of the critical radius Rc (using S = 0.0735 N/m).


Figure 9: Local pressures at the leading edge of a propeller
blade with a single roughness element.

The minimum pressure coefficient of a roughness element
located in the minimum pressure area on the leading edge
of a propeller blade can be written as:

P r Pef
CPn r m ref (2)
2 Urf
where Pmn r is the minimum pressure on the roughness
element. The reference pressure and velocity, denoted as
Pref and Uref respectively, are ambient values for the
roughness element, but local values on the scale of the
blade. Pref is assumed to be equal to Pmm.
A first approximation of the undisturbed velocity at the
leading edge (U) is:

U = nDJ2 +( )2 (3)

Pmmn results from Uref being higher than U. On the other
hand, the boundary layer decreases Uref. For simplicity, it is
assumed that Uref = U.
If cavitation inception occurs at the point of minimum
pressure on the roughness element, then Pmm r = Pc. Using
equations (1), (2) and (3), the propeller cavitation number at
which inception occurs on the roughness element (ci) canbe
written as:


8S
=1 = -_Cp- m (j2 + (r )2)CP
3pn2D2Rc


Rc T
[lm] [kPa]
1 98.0
5 19.6
10 9.8
50 2.0
100 1.0
500 0.2


A blade section at an angle of attack has its minimum
pressure area very close to the leading edge as sketched in
Figure 9. Large free stream nuclei with small critical
pressures may be screened from this area by the stagnation


The first term on the right hand side is the minimum
pressure coefficient of the blade section. The second term is
the nondimensional tensile strength. It decreases oc; this
effect is stronger for smaller nuclei and lower rotation rates.
The third term is the effect of the leading edge roughness
and it increases a,. The value of Cpmm r is dependent on the
roughness Reynolds number (Rk) which is defined as:
Uk
Rk = (5)
V

where k is the roughness height. When Rk is small, Cpmm r
will also be small.









With the introduction of the Weber number as:

Wn =pn2D2Rc (6)
S

equation (4) can be written in a simplified form as:

C1 = -Cpn f (Wn) + f,(Rk) (7)

This shows that both the Weber and Reynolds number can
affect sheet cavitation inception.

Free-stream nuclei and propeller loading
The experimental results show that addition of nuclei by
electrolysis stimulates sheet cavitation inception at
locations where no cavitation was present without
electrolysis (see Figure 4). Apparently free-stream nuclei
arrive at the minimum pressure area on the propeller blade.
Observations on smooth blades of the same propeller by
Kuiper (1981) show that even with electrolysis, the sheet
cavity contains gaps in the radial direction. This suggests
that the roughness plays an essential role in the cavitation
inception process. On a smooth blade only relatively large
free stream nuclei can grow to a sheet cavity. But due to the
bubble screening effect, these events are very scarce. On a
roughened blade, however, also smaller nuclei can grow
due to the lower pressures at the roughness elements. From
this stage of micro cavitation, a sheet cavity on the blade
section can grow.
Figure 4 also shows that in case of insufficient free-stream
nuclei, sheet cavitation inception is suppressed at the more
lightly loaded conditions. Two aspects play a role here: the
leading edge roughness and the free-stream nuclei content
of the water. At small KT values, the minimum pressure at
the leading edge is closer to the vapour pressure and is
located further downstream. This corresponds with lower
local velocities and a relatively thicker boundary layer
which decreases Rk and thereby Cpmm r. According to
equation (4), a, decreases and cavitation inception at the
roughness elements is prohibited. Using equation (1), it can
be seen that in this condition, relatively large nuclei are
needed to enable cavitation inception. These larger bubbles
are, however, more scarce than smaller bubbles and if
present, they are more likely to be screened by the leading
edge.

Free-stream nuclei and Reynolds number
A decrease of the propeller Reynolds number at a constant
oC and KT suppressed cavitation inception on the
S-propeller without electrolysis (see Figure 5). In particular,
this occurred for propeller Reynolds numbers below 9.5-105
(n = 10 Hz). The observations show that in these conditions
either the whole blade is free of cavitation, the inner radii, or
the outer radii.
Again the contribution of leading edge roughness and the
free-stream nuclei content of the water may be used to
explain these results. At a low Rn, Rk is also lower. Due to a
smaller Cpmm r in equation (4), c, is smaller and cavitation
inception is suppressed. Incidentally, cavitation inception
occurs at some roughness elements due to a favourable


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

combination of a slightly lower than average pressure on a
roughness element and the presence of a nucleus with the
right size.
The contribution of the free-stream nuclei content to the
observed sensitivity to the Reynolds number is illustrated in
Figure 10. Equation (4) is used to show o, as a function of
rotation rate with the critical bubble radius as parameter.
The value of Cpmi. is set to -5 on the basis of inception
measurements (Kuiper, 1981). For Cpmm a value of -0.5 is
estimated on the basis of experiments at low Reynolds
numbers (see e.g. Keller, 1974). In this example it is
assumed to be independent of Rn. Withvalues ofJ = 0.4 and
r/R = 0.6, the third term in equation (4) is approximately 2.
Lines for o, with constant Rc values between 3.5 and 500
pm are plotted to fill the space between the condition of the
test (o, = 2.2) and the -Cpmn = 7 line.
The natural nuclei content of the DTT is assumed to have a
maximum bubble radius of 25 pm on the basis of nuclei
measurements and evaluation of its rise velocity which is
about 7 cm/min (Kuiper, 1981). Due to bubble screening
effects, it is assumed that only bubbles with radii smaller
than 15 im arrive at the roughness elements at a rotation
rate of 10 Hz. It is noted that this value is chosen only to
illustrate the conceptual model, but it is considered to be a
realistic order of magnitude. According to Van Rees et al.
(2008), the deflection of the bubble path normal to the flow
streamlines is proportional to Ro2U-, where Ro is the
free-stream bubble radius. For simplicity, in the following
calculations Rc is taken equal to Ro. At n = 6.9 Hz, this
results in a maximum critical bubble radius of 12.4 Vim.


5 6 7 8 9
n [Hz]
Figure 10: Effect of rotation rate
size on cavitation inception number.


10 11 12 13

and susceptible nuclei


The shaded area above the -Cpmm = 5 line indicates the
nuclei that can cause micro cavitation at the roughness
elements. The shaded area below this line indicates the
nuclei that can cause sheet cavitation on the blade section.
Both areas are further limited by the speed dependent
maximum bubble radius, imposed by the bubble screening









effect. Ultimately this effect will suppress cavitation
inception below a certain (rotational) speed and above a
certain cavitation number, independent of the free stream
nuclei content. Double ended arrows indicate the ranges of
nuclei that are susceptible to cavitation inception for
n = 6.9 (red) and 10 Hz (green).

1,000
670 n = 10 Hz
420 =6.9 Hz


E

0.


Weber bubble
number screening
E




10
0 5 10 15 20 25 30
R [pm]
Figure 11: Effect of Weber number and bubble screening
on susceptible number of nuclei at n = 10 Hz (green) and
n = 6.9 Hz (red)

Nuclei measurements in the DTT (Kuiper, 1981) show a
typical distribution of the form:

log(N) a-bRo (8)

This relation is used in Figure 11 together with the range of
nuclei as limited by the rotation rate and bubble screening.
A significantly smaller number of nuclei is available for
cavitation inception at 6.9 Hz, which explains the smaller
radial cavitation extent. Electrolysis increases the
free-stream nuclei content and due to a higher event rate,
cavitation is still established at this low rotation rate. The
lowest speeds occur at the inner radii, which results in U =
3.1 m/s and Rk= 151.
Finally, it should be noted that the conceptual model
presented above has some serious limitations. The viscous
effects are poorly quantified and the bubble screening
model is very simple. These aspects should be investigated
into more detail by Lagrangian bubble tracking in viscous
flow computations and micro-scale high speed observations
in order to obtain a more complete understanding of sheet
cavitation inception on a foil or propeller blade.


Dissolved gas content

The experimental results show that cavitation inception is
improved by a higher supersaturation ratio of the water, but
only to a limited extent (see Figures 6 and 7). The initial
hypothesis formulated by Kuiper states that the required


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

nuclei for sheet cavitation inception are generated at the
leading edge roughness elements. This was based on the
observation that bubble cavitation inception was strongly
enhanced by the application of leading edge roughness on
a propeller designed to study bubble cavitation. Because
diffusion plays a role, this process is enhanced by a higher
dissolved gas content. It was thought that if nuclei were
generated by the roughness elements, which could cause
cavitation inception at the midchord location, also sheet
cavitation at the leading edge could benefit from these
nuclei.
Apparently, there is a mechanism which prevents this,
since the effect on the average radial cavitation extent is
small. For example, nuclei which are attached at the
roughness elements or embedded between the roughness
elements have a lower critical pressure due to the contact
angle. Borkent et al. (2009) have shown that bubbles in
nanopits have a 2.4 times lower critical pressure than free
bubbles of the same initial size. Further, if nuclei detach
before reaching their critical radius, they move out of the
low pressure area very quickly.

Grid
The observations show that the unpowered electrolysis grid
upstream of the propeller improves cavitation inception,
but still large gaps remain present in the radial cavitation
extent. The grid affects the inflow to the propeller in
several ways. First, the grid reduces the average advance
speed of the propeller, second it produces turbulence and
third it produces nuclei.
The reduction of the average inflow speed to the propeller
increases the loading of the propeller. By comparing the
radial cavitation extent on the basis of the measured thrust
coefficient, such as in Figures 6 and 7, differences in KT do
not have a hidden influence on the interpretation of the
results.
According to a semi-empirical formula (Roach, 1987), the
electrolysis grid produces a turbulence intensity of 0.5 % at
the propeller position. Because there is no consistent effect
of the grid on the radial cavitation extent at low
supersaturation ratios of the water, it is concluded that this
turbulence level is not sufficient to enhance cavitation
inception. This is confirmed by findings of Van Rees et al.
(2008), who concluded that a turbulence intensity of 1.0 %
did not have an influence on sheet cavitation inception.

Nuclei
Observations of the water at a condition with the highest
supersaturation ratio with the grid upstream of the
propeller show a large number of bubbles with sizes up to
several millimetres. Observations without the grid at the
same dissolved gas content of the water do not show these
bubbles. At low dissolved gas contents with the grid
upstream of the propeller only occasionally some bubbles
are visible in the flow. The possibility of cavitation at the
horizontal grid rods can be evaluated by comparison of the
cavitation number (to) and the minimum pressure
coefficient (-Cpmn) at the rods. The oa values at the rods
vary between 3 and 10. The rods have slightly rounded









edges. The -Cpmm can be estimated to be not higher than 2
on the basis of various experiments with blunt profiles.
Further, the improvement of cavitation inception is
independent of the oa value. Therefore, it is not likely that
cavitation occurs at the rods of the electrolysis grid.
Combined with the significant effect at high
supersaturation ratios of the grid on the radial cavitation
extent it is concluded that the grid rods generate free gas
(not vapour) nuclei from the locally highly supersaturated
water.
The size of the generated bubbles may be relatively large
and can be screened from the leading edge of the propeller
blades. This would explain the remaining gaps in the sheet
cavities. In this respect it is interesting to review the
experiments carried out by Kuiper (1981) once more.
Maybe an explanation of the nearly perfect sheet cavity in
his observations without electrolysis can be found. All
these tests in the DTT were conducted with an electrolysis
grid upstream of the propeller at PG = 69.4 kPa. At C, = 1.7
and Rn = 1.1.106 this results in a supersaturation ratio of
4.5 which is moderate compared to the current experiments.
Kuiper's grid had cylindrical wires with a diameter of 0.3
mm. In comparison with the thickness of the rods that are
currently used, this is a factor 4 smaller. It is therefore
likely that smaller gas nuclei were generated, which also
have a smaller risk of being screened from the leading
edge of the propeller blades. A complete verification of the
relation between the wire thickness and the generated
nuclei in supersaturated water would require measurements
of the nuclei spectra between the grid and the propeller.
Since this is quite an elaborate task in the DTT, it is
proposed to verify this hypothesis by repeating the
experiments at a high and low dissolved gas contents with
a grid with 0.3 mm wires.

Reproducibility
Figures 6 and 7 show that the reproducibility of cavitation
inception improves with increasing KT at a constant on,
provided the presence of the grid in highly supersaturated
water. Apparently, free stream nuclei, which are generated
by the unpowered electrolysis grid are essential in this
process. At a larger angle of attack, the minimum pressure
on the blade is lower. This lower pressure causes smaller
free stream nuclei to expand, which are larger in number
(see e.g. Figure 11). Thus the probability of cavitation
inception is increased.
The experimental results show that re-application of
leading edge roughness only changes cavitation inception
locally. No significant change in the average radial
cavitation extent is found. This may be explained by the
random distribution of roughness elements. Effective
minimum pressure levels are dependent on the local
distribution of roughness elements. On average, these
random variations level out to an effective roughness
height distribution which does not change significantly
after re-application of the roughness. On the basis of these
considerations, the possible influence of a change in
roughness and its application on the leading edge between
the current experiments and those reported by Kuiper is


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

considered limited and cannot explain the differences
between the nearly perfect cavitation inception observed
by Kuiper and the sheet cavities with gaps observed in the
current study.
Eventually, free stream gas nuclei will all rise to the water
surface. With the above-mentioned rise speed, a bubble
with a radius of 25 pm at a depth of 70 cm will reach the
surface in 10 minutes. There are some indications, however,
that remnant bubble nuclei have influenced the
reproducibility of the current observations:
* The second observation run at I = 0 shows slightly
larger average radial cavitation extents (see Figure 4).
* There are three cases at high KT values where the
presence of the grid seems to work at low
supersaturation ratios (see Figures 6 and 7).

Velocity
The experimental results show that at a constant propeller
loading a high velocity is more effective for cavitation
inception than a high supersaturation ratio. This effect may
be explained by several mechanisms. A higher advance
velocity can change the nuclei distribution generated by
the grid. Further, a higher velocity at the leading edge of
the blade decreases the necessary size of the nuclei for
cavitation inception, see equation (4). Because smaller
nuclei are generally larger in number, there is a higher
probability of cavitation inception. The limited effect of a
high supersaturation ratio indicates that no higher ratios
need to be tested. This agrees with the moderate
supersaturation ratio used by Kuiper.


Conclusions and recommendations

The effect of the free-stream nuclei content and the
dissolved gas content on sheet cavitation inception has
been investigated on a research propeller in open water
condition in MARIN's Depressurized Towing Tank. The
following conclusions and recommendations can be made
with respect to sheet cavitation inception on roughened
propeller blades:

* In general, application of leading edge roughness only
is insufficient for sheet cavitation inception.

* Without additional nuclei seeding, a higher angle of
attack and a higher rotation rate enhance cavitation
inception.

* In all cases, the combination of leading edge
roughness and nuclei seeding through electrolysis led
to cavitation. The same cavitation extents were found
by Kuiper (1981).

* The deteriorating effect of a lower rotation rate on
sheet cavitation inception is thought to be a
combination of a nuclei size effect governed by the
Weber number, bubble screening and a Reynolds
effect on the minimum pressure at the roughness
elements.










* Gas supersaturated water is not required for sheet
cavitation inception. An unpowered electrolysis grid
can, however, generate free stream nuclei at high
supersaturation ratios.

* It is hypothesized that the good cavitation inception on
the same propeller without electrolysis found by Kuiper
(1981) was caused by the generation of micro-scale
nuclei on the unpowered wires of the electrolysis grid
at a moderate supersaturation ratio of the water.
Kuiper's grid had thinner wires than the present grid.
To verify this, it is recommended to conduct additional
observations with the propeller with an electrolysis grid
with the same wires as used by Kuiper. Repeat
observations with the present grid can be used for
reference. Preferably the nuclei spectrum should be
measured to confirm the role of free stream nuclei in
the inception process and to quantify the critical size
and density of free stream nuclei.

* It is recommended to investigate the bubble screening
effect further by Lagrangian bubble tracking in viscous
flow computations for a typical propeller blade section.

* Additionally, high speed micro-scale observations on a
2D foil in a cavitation tunnel are recommended to
answer the following remaining questions.
o What is the maximum bubble diameter that can
arrive at the minimum pressure area, given the
bubble screening effect? What is the effect of the
velocity?
o What is the minimum bubble diameter that can
cause cavitation inception as a function of the
velocity?
o How does the local geometry in the roughness
distribution influence the cavitation inception
process?


References

Borkent, B.M., Gekle, S., Prosperetti, A., Lohse, D.,
"Nucleation threshold and deactivation mechanisms of
nanoscopic cavitation nuclei", Physics of Fluids, arXiv:
0906.0556v1 (2009)

Johnson, VE., Hsieh, T., The influence of trajectories of
gas nuclei on cavitation inception, 6th Symposium on
Naval Hydrodynamics (1966).

Keller, A.P, Investigations concerning scale effects of the
inception of cavitation, Proceedings Conference on
Cavitation, Institute of Mechanical Engineers, Edinburgh,
Scotland, pp. 109-119 (1974)

Kuiper, G., "Some Experiments with Distinguished Types
of Cavitation on Ship Propellers", ASME International
Symposium on Cavitation Inception, New York (1979)


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


Kuiper, G., Cavitation inception on ship propeller models,
Ph. D. Thesis, Netherlands Ship Model Basin, Wageningen
(1981)

Kuiper, G., Reflections on Cavitation Inception, ASME
Cavitation and Multiphase Flow Forum, Albuquerque
(1985)

Noordzij, L., Some experiments on cavitation inception
with propellers in the NSMB-depressurized towing tank,
NSMB Publication No. 526, ISP Vol. 23 No. 265 (1976)

Roach, P., The generation of nearly isotropic turbulence by
means of grids, Heat and Fluid Flow, 8(2), June, pp. 82-92
(1987)

Rood, E.P, 'Review-Mechanisms of Cavitation Inception',
Journal of Fluids Engineering Vol. 113 (1991)

Van der Kooij, J., Sound Generation by Bubble Cavitation
on Ship Model Propellers; the Effect of Leading Edge
Roughness, Int. Symp. on Cavitation and Multiphase Flow
Noise (1986)

Van Rees, W.M., Van Rijsbergen, M.X., Kuiper, G., Van
Terwisga, T.J.C., An Exploratory Investigation of
Cavitation Inception on the Pressure Side of Propellers,
ASME FEDSM Jacksonville, Florida (2008)




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