ARCHIEF
y. Scheepsboj
Teclrnische
HogschooI
DeîffPAPERS
OFSHIP RESEARCH INSTITUTE
An Experimental Investigation into the Unsteady cavitation of Marine Propellers
by Tatsuo ITO
March 1966
Ship Research Institute
Tokyo, Japan
Cavitation of Marine Propellers
by
Tatsuo ITO
Synopsis
The propeller of a single-screw ship works in the ship wake with
an unfavourable velocity distribution. If the cavitation occurs on the propeller, it is unsteady because the angle of attack of the flow into the
blade element of the propeller varies owing to the circumferential wake distribution. From the tests on the unsteady cavitation of the oscillating,
blade in uniform flow, it has been found that the reduced frequency of the blade element is one of the most important factor for the unsteady cavitation and that the critical reduced frequency, at which the
cavita-tion becomes most violent, is around O. 3O. 4.
The reduced frequency of the blade elements has different values at each point of a propeller disc. Generally speaking, the reduced
fre-quency for the back cavitation becomes critical near the tip of the
pro-peller blade in high wake zones and for the fáce cavitation at O. 7-0. 8R (R : radius of the propeller) in low wake zones for a single-screw ship.
To avoid this critical reduced frequency, the wake distribution (i.e. the
ship hull form) as well as the propeller should be improved. As it is rather difficult to remove this critical reduced frequency for the face
cavitation at O. 7-0. 8R, the face cavitation should be avoided complete-ly in designing propeller.
Introduction
The risk of the damage of marine propeller blades caused by the
cavitation erosion has been increased by the increased loading of
propel-lers of modern merchant ships with the greater speed and size of ships
and the greater output of marine engines. The propeller of a
single-screw ship works in the ship wake with non-uniform velocity
distribu-tion. Since the first construction of the cavitation tunnel with the flow
regulator in the Netherlands, the cavitation tests on the propellers have
been carried out in non-uniform flow as well as in uniform flow23.
When the author carried out some propeller cavitation tests in
non-uniform flow at the Netherlands Ship Model Basin during his stay in the Netherlands in 1960, he was greatly impressed by the great differ-ence between the cavitation patterns in uniform flow and those in
non-uniform flowthe cavitation in non-non-uniform flow is very unsteady mainly because of the variation of the angle of attack of the flow into
the blades of the propeller due to the
circumferential non-uniform velocity, while the cavitation in uniform flow is steady. Then at thepropeller cavitation tunnel of the Transportation Technical Research
Institute (now the Ship Research Institute), he made some fundamental
tests on the unsteady cavitation which was produced by the lateral
oscillation of a blade in a uniform flow, after his coming home.
In this report the results of the propeller cavitation tests in non-uniform flow will be given to show the unsteady cavitation patterns,
and the results of the tests of the oscillating blades and some discussion on the analyses of the wake patterns of single-screw ships will be shown.
1. The Propeller Cavitation in Non-Uniform Flow
The wake distribution to be reproduced in the cavitation tunnel is
obtained in ship model basin by Pitot tubes. Fig. i shows the axial
wake distribution over the circumference for each radius of the screw
disc for a single-screw tanker model ship, where w" is the wake tion* at each point on the propeller disc and iv' is the mean wake
frac-Numbers designate bibliography at the end of the paper.
* Wake fraction w = (VsVA)IVs, where Vs is the speed of a ship and VA is the
I.0 0.5 o MIN. 2 iLn r INDUCED VELOCITY
Fig. 1. The Circumferential Wake Distributions of a Tanker Model (Full Loaded Condition)
Fig. 2. The Velocity Diagram of a Propeller Blade Element
tion at a given radius which is equal to the mean height of the curve
of w"-distribution from O to 360-deg. at the radius of interest. The
0-deg. position corresponds to upward vertical position or top position of the blade. The circumferential wake variation at a given radius is
denoted by 4w" for top or bottom position. From the velocity diagram in Fig. 2, it appears that the profile angle of attack varies according
to the wake it is positive in high wake zone and small positive or
negative in low wake zone. By Lindgren's calculation3, this variation
of the profile angle of attack at 0. 75 R for a certain propeller is about + 3. 4.' 1. 0-deg. owing to the axial wake variation and about + 4. 0---2. 0-deg. owing to the tangential and, axial wake variations.
TANKER
0B=°774
--U/F.T/1'
95R ? 30 60 90 120 150 180 360 e dog.) 270 TOP BOTTOMThe cavitation tests on three five-bladed model propellers in the
wake patterns, as shown in Fig. 1, have been carried out at the small
cavitation tunnel at Wageningen4. The particulars of thepropellers are
shown in Table i and they are made of aluminum alloy having the
diameters of 250mm and the pitch ratios of 1. 00.
Table 1.
Fig. 3 presents the cavitation patterns of M. P. No. 1184, where
the face (pressure side) cavitations are denoted by f so as todistinguish it from the back (suction side) cavitations and
K ;
thrust coefficient, T/pn2D4,T; thrust of propeller, p; density of water, n; number of revolutions,
D; diameter of propeller,
Cp cavitation number of propeller, (p0e)/('/2pVA2)
Po ; static pressure, e; vapour pressure,
and V4 ; speed of advance of propeller.
For convenience sake the blade positions are numbered in the direction
of rotation, every 18-deg. from O at the top to 19.
The cavitation is unsteady and very unstable, the boundaries of the
sheet cavitation being shown by the full and dotted lines in the figures.
The most extensive back sheet cavitations do not occur at the wake
peak positions (Nos. O and 10 positions) but between No. O and No. i
and between No. 10 and No. li positionsthere is a
phase lag dueto the unsteady intake velocity to the propeller blades. The same can
Model Propeller Number Type of Section Boss Ratio Pitch Ratio Expanded Area Ratio Blade Thickness Ratio Max. Blade Width Ratio 1131 AU' 0.180 1.00 0.500 0.050 0.226 1136 AU 0.180 1.00 0.650 0.050 0.294 1184 Wageningen4Modified-B o 185 1. 00 0. 550 0. 055 0.245
M. P.NO.I 184
¡<T; 0.222
6V_P; I O
LOOKING AFT
IO
Fig. 3. M. P. No. 1184, the Back and Face Cavitation Patterns in Non-Uniform Flow of Fig. i
be said for the face cavitations. It is worthy of our notice. that the
cloud cavitation occurs .when the sheet cavitation is diminishing.
Al-though the face sheet cavitation at around 0. 8 R is very small, it is
accompanied by the cloud cavitation which is the type of cavitation that
is most dangerous in causing erosion4. No cavitation erosion is
SHEET BUBBLE CAVITATION EROS I ON DAMAGE 6_Pa IO 0.222
Fig. 4 M. P. Nos. 1131 and 1136, Back Cavitation Patterns
at 18-Deg. Position in Non-Uniform Flow of Fig. i
IO
KT 0.234
M.PNO.II3 M.PNO.1136
8 KT 0.222
Fig. 5. M. P. No. 1131, the Cavitation Erosion Damage at 0.9 R
cavitation, however, corresponds fairly well to the general region of
erosion36.
Fig. 4 presents the cavitation patterns of M. P. Nos.. 1131 and 1136 at No. 1 position. They do not show any face cavitations in the tests while they show the back cavitations, and M. P. No. 1131 suffers
cavita-tion erosion damage on the back sides near the trailing edges at 0. 9 R after the severest test condition (K = 0. 234 and a.= 8) in the range of
8 0.234
IO
KT- 0.232
Fig. 6. The Quasi-Statical Angle of Attack of the Oscillating Blade
the tests. The region of damage corresponds fairly well to the
down-stream part of the region of heavy cavitation where the unstable cloud
cavitation occurs. The erosion damage of the blade is shown to the left
of Fig. 4 and in Fig. 5 where the trailing edge at 0. 9 R is bent to the
face side and partly shed, and many tiny pit holes are recongnized
around the shed part.
In the case of the cavitation tests on the above mentioned three
propellers in the uniform flow which were performed beforehand with
the severer test conditions, the stable sheet cavitations and tip vortices
were observed and no erosion was recognized.
2. Unsteady Cavitation of the Oscillating Blade
To investigate the effect of the variation of the angle of attack of
the flow on the unsteady cavitation, some fundamental tests on the blade performing small lateral oscillations in a uniform flow have been carried
out.
As shown in Fig. 6, if the lateral oscillation is given by
YYo cos wt
(1)the quasi-statical angle of attack is shown by
?P
sin wti sin
ç (2)\
t,
Fig. 7. The Apparatus for Oscillation tests
Fig. 8. Blade A o II, 9.10 u) o o 3 -u) t 5.25 3.88 ou,
12
7.5 BLADE A TUNNEL WALL Fig. 9. Blade B TO OSCILLATOR PIVOTING POINT loo BLA9E B
Fig. 10. The Arrangement of the Blades
u, N
6.25
where w ; circular frequency,
V; speed of the uniform flow,
'p; phase.
The test apparatus is shown in Fig. 7 and the blade models, Blades
A and B, which are made of aluminium alloy are shown in Figs. 8 and 9. As shown in Fig. 10, the blade is fixed to a steel bar at the top of
it. The steel bar is supported by a universal ball bearing and the top
of the bar is connected to the oscillator by which the blade is swung,
the amplitude of the blade section being naturally linear to the distance
from the pivoting point (the ball bearing). The steel bar is guided by a guide so as to swing laterally. The oscillator is controlled by a
auto-stabilizer. Although Blade B has a flat face, the face of Blade A is not
flat but is twisted at the lower end as shown in Table 2.
Table 2.
Fig. 11 shows the cavitation patterns of the back side of Blade A
at every phase of oscillation, where
a; cavitation number, (Po - e) / (p V2),
w. (chord)
k; reduced frequency of oscillation, 2V
a0; initial angle of attack.
and fr is the simple amplitude of I1 at the distance of 50mm from the
tip. It is worthy of our notice that the sheet cavitation is largest at
the phase of about (3/4) ir which is about (1/4) ir behind the phase of
(2/4) ir
(=max.) and that the sheet cavitation is smallest at the
phase of about (7/4) ir which is (1/4) ir behind the phase of (6/4) ir (?F= min.) as shown in Fig. 11. According to the theory of oscillating
wing there is phase lag between the phase of the maximum or
mini-mum lifting force and that of the maximini-mum or minimum quasi-statical
angle of attack. The case of the cavitation is similar to that. When
the sheet cavitation is diminishing at p of about (5/4) ir, unstable and
Distance from Tip (mm) 0 25 50 75 100
so=
6'= 1.5
cÇ 4
Fig. 11 Blade A, the Cavitation Patterns at Every Phases
cavitation which is very changeable.
In Fig. 12 the effect of the reduced frequency on the unsteady cavitation of Blade A is shown for the phase of (3/4) r (the largest
sheet cavitation) and (5/4) r (the most extensive cloud cavitation). It
seems that the reduced frequency of O. 3O. 4 is critical the
° 0.211
0.395
0.632
p=iit
Fig. 12. Blade A, the Cavitation Patterns at Every Reduced Frequency
L.L
Fig. 13. Blade B, the Cavitation Patterns at Every Reduced Frequency
Some preliminary tests were carried out beforehand with the follow-ing conditions:
V=5 mis, a=l. 5, a0=2. O deg., Yo=l. 4mm,
w=2l. 1-47. 4/sec., k=0. 211-0. 474, =0. 67-1. 5 deg.,
where : and are corresponding to the blade section at the distance
of 50 mm from the tip of the blade. From the preliminary tests it has been found that the cavitation for k=0. 474 is less violent than that for k = 0. 3-0. 4 although i of the former is larger than that of the latter. It may, therfore, be said that the effect of k is greater than that of
on the unsteady cavitation. In Fig. 13 the result of the tests on Blade
B is shown where ' corresponds to the blade element at the distance
of 100 mm from the tip. The critical reduced frequency for Blade B seems to be 0. 3--0. 4, the same as for Blade A. The cloud cavitations
and the tip vortices are, however, thinner than those of Blade
A-Blade B has uniform section. The circulation distribution over the span
or over the radius of propeller may, therefore, be also very important for the occurrence of the cloud cavitation, and the gradient of circula-tion, ar/ar, should therefore be made as small as possible where T' is the circulation of the propeller blade section at r, the radius of interest.
According to van Manen's comparative tests2 on propellers with various
circulation distributions, the propeller whose circulation distribution is determined by the condition for minimum loss of energy, showed the
best results from cavitation erosion point of view. It has the smallest gradient of circulation at radius of interest, 0. 9 R.
3. The Wake Distribution and the Reduced Frequency
In the preceding section it has been found that the unsteady
cavita-ion becomes critical at the reduced frequency of 0. 3-0. 4. In this
section the actual reduced frequency will then be shown for the propel-ler working in the wake of the single-screw ships. As shown in section
1 the back and face cavitation of the propeller should be noticed at the
ranges following the peaks of the high and low wake zones respectively.
Therefore the reduced frequency should be estimated in those ranges. As the angle of attack varies according to the wake, the frequency of
frequen-kf 2 o kb 0.4 0.6 0.8 1.0
nR
Fig. 14 The Reduced Frequency of M. P.
No. 1131 in the Wakes
cy of the variation of wake at the range of interest at radius r. Vi, the real flow velocity (include induced velocity) can be well approximated by V, the flow velocity (exclude induced velocity). If w, V and c, the propeller blade width at r are given, the reduced frequency, k can be estimated by the following formula:
k = wc/ (2V)
Fig. 14 shows kb, the reduced frequency for the back cavitation and
k, that for the face cavitation which are estimated for M. P. No. 1131 in the wakes of the single-screw ships, the tanker model (Fig. 1) and
Series 60 parent ship model of CB=0. 78)
It can be said that kb
be-comes critical at 0. 9.-1. O R, especially at the top, and kf at 0. 7-0. 8 R. It is unfortunate that the critical reduced frequency occurs on the above mentioned radial positions because the back and face cavitationsgeneral-ly occur on such the radial positions. M. P. No. 1131 suffers erosion damage at 0. 9 R on the back side whose reduced frequency, kb is
criti-cal at the top as shown in Fig. 14.
Fig. 14 suggests that there is a possibility to avoid the critical
reduced frequency for the back by improving the wake distribution (i.
the tip out of the propeller disc, because the kb-curves are different for
the ship forms. But for the face cavitation it is rather difficult to avoid that because ks-curves have the same tendency and they cross the
criti-cal value at O. 7-0. 8 R which is far from the edge of the propeller
disc. The great care must, therefore, be taken for the design of the
blade sections at O. 7--0. 8 R so as to avoid completely the inception of
0.5
Fig. 15. The Circumferential Wake Variations
(270°) STARB. (90°) ,, MIN. BOTTOM I I I 0.4 0.6 0.8 1.0
r/R
TOP (0°) WAKE MAX. MAX. BOTTOM (180e) LOOKING AFTFig. 16. The Dangerous Cavitation Zones for a Propeller of a Single-Screw Ship
DIRECTION O
\ROTATI ON
the face cavitation which will easily turn into the dangerous cloud
cavitation.
Fig. 15 presents the circumferential wake variation,
Jw"/(lw')
for both ship forms. Although the effect of the amplitude of the varia-tion of wake is less than that of the frequency, the large variation isstill to be avoided. The adoption of the ciger type stern is very
hope-ful9.
In Fig. 16 the dangerous cavitation zones on the propeller disc are summarized by the hatched areas for the propeller of the single-screw
ship.
Conclusion
The problem of the unsteady cavitation of the propeller working in non-uniform flow is very complicated. Some interesting conclusions
can, however, be drawn from the investigation reported in the paper
and summarized below:
From the tests on the oscillating blade in uniform flow, which are useful to study the unsteady cavitation, it has been found that the
reduced frequency of oscillation has the most important effect on the
character of the unsteady cavitation, and that the critical reduced f
re-quency, at which the cavitation becomes most violent and is
accom-panied by the extensive cloud of vapour, is O. 3O. 4.
For the propeller working in the wake of thesingle-screw ship,
the reduced frequency for the back cavitation becomes usually critical near the tip of blade, while that for the face cavitation becomes always
critical at O. 7O. 8 R. There is a possibillity to avOid the critical
re-duced frequency for back cavitation by some modification of ship hull
from, but it is not easy to avoid the critical reduced frequency for face
cavitatioH by small modification of ship hull form. The great care must
be taken for the design of the blade section at O. 7O.8 R so as to avoid
completely the inception of the face cavitation.
The gradient of circulation of the blade over the radius of
pro-peller is also important factor for the occurrence of cloud cavitation,
Acknowledgements
The author would like to express his gratitude to Mr. K. Tsuchida,
Head of the Ship Powering Division, Ship Research Institute, for his encouragement and advice, and to many members of S. R. I. staff for
their assistances. The author also would like to express his gratiude to Prof. W. P. A. van Lammeren, Director of the Netherlands Ship Model
Basin, Dr. J. D. van Manen, Assistant Director of N. S. M. B. and
meny members of N. S. M. B. staff for arranging the opportunity to work with them and for their technical guidances.
Bibliography
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J. D. y. Manen and J. D. Crowley, Some Aspect of Circulation Theory Design of Screw Propellers, Internat. Shipbldg. Progress, Vol. 7 (1959), No. 62.
H. Lindgren, Cavitation Tunnel Tests with Merchant Ship Propellers, Trans.
Instn. Engrs. Shipbld. in Scotland, Vol. 104 (1961), Pt. 7, pp. 283-340.
J. D. y. Manen, Fundamentals of Ship Resistance and Propulsion, Part B, N. S.
M. B. Course: Publication No. 132a.
K. Tsuchida and others, Open Water Test Series with Modern Five-Bladed Pro-peller Models, Journal of Zosen Kiokai, No. 102, 1958, pp. 109-114.
H. Takahashi, A Prevention from Face Cavitation by varying the Form of Blade
Sections of a Screw Propeller, Rep. Transport. Tech. Res. Inst., Report No. 38,
1959.
R. L. Bisplinghoff and others, Aeroelasticity, Addison-Wesley Pub. Co., Cambridge. Mass., 1955.
G. R. Stuutz and others, Series 60-The Effect of Variations in Afterbody Shape Upon Resistance, Power, Wake Distribution, and Propeller Excited Vihratory
Forces, Trans. Soc. Naval Archit. Marine Engrs., Vol. 68 (1960), pp. 292-363. J. D. y. Manen ànd J.. Kamps, The Effect of Shape of Afterbody on Propulsion.. Trans. Soc. Naval Archit. Marine Engrs., Vol. 67 (1959), pp. 253-289.
