3 Scy.
1984ARCHIEF
SYMPOSIUM ON
"HYDRODYNAMICS OF SHIP AND OFFSHORE PROPULSION SYSTEMS"
HOVIK OUTSIDE OSLO, MARCH 20. - 25., 1977
"AN EXPERIMENTAL STUDY OF THE PRESSURE FLUCTUA-TION ON A PROPELLER BLADE IN THE WAKE"
By Hiroharu Kato University of Tokyo, Japan
SPaNSOR: DEI NORSKE VERITAS
Ref.: PAPER 19/3 - SESSION 2
17)
lab. i. Sckeepsbouwkunde
Technische Hogeschool
Abstract
This paper treats the measurement of a non-cavitating
model propeller running in the behind condition. The pressure
fluctuation was successfully measured in the model wake
by mounting small high sensitive pressure pickups on the blade.
The pressure fluctuation is large near the blade's bottom
position which is contrary to the results of theoretical
analyses such as unsteady liftïng surface theory. In these
analyses only the axial velocity component are taken into
consideration, and the discrepancy appears to be caused by
the tangential wake component. The theory which includes the
tangential component agrees fairly well with the experiments.
Several theories, Hanaoka-Koyaina's lifting surface theory,
simple quasi-steady theory, and two-dimensional gust theory,
were also compared and it was found that the quasi-steady
l Introduction
The pressure distribution over a propeller blade is an
important and fundamental variable for understanding the
propeller performance deeply. By
integrating
this pressure, the thrust and torque of the propeller are obtained. Theabsolute pressure valué also gives an important indication of
the occurré'ne and degree of cavitation.
Several researchers have reported about the blade pressure
measurements. For example,
Mavludoffm
measured the pressuredistribution ofa three-bl4ded propeller modél.
HØiby2
rnóunted 27 pressure pickups on a b,lad.e and measured the pressure.
Recently Ito et
àl3 measured the
pressure distribútion at O 7R of a three-bladed propeller These measurements weremade in a uniform flow and the time-mean value,ie. steady
pressure component was only treated.
The propeller behind à ship works in the wake and the
pressure changes 'according to the anular position of the i.
blade This unsteady pressure fluctuation is important because
it causes the. propeller xciting. foráes. The unsteady pressure component is also an essential factor in the inception and
collapse of cavitation. The propeller cavitation of a merchant
ship is usuälly intense when the blade rotates to its top
position where the static pressure is low and .thewake influence
is large To get better understanding about this unsteady
cavitation problem, the knowledge of the unsteady propeller.
pressure fluctuation is indispensable. . .
ecently Tsakonas et
al41
Bauschke etal5,
andHänaoka-Koyarna61 have made. theoretical analyses about the
the actual measurement of the fluctuating blade pressure has
not been reported because of the measurement difficulties.
This requires that small high sensitive rapid response pressure
pickups are mounted on thin propeller blades, and the pressure
signals then are taken out from a rotating shaft.
Very few papers have treated this unsteady pressure
measurement, and the comparison between theory and experiment
has not been possible untill now.
This paper treats the measurement of the unsteady pressure
fluctuation of a non-cavitating propeller blade in a model
wake. The experimental results are compared with the theoretical
analyses, using Hanaoka-Koyama's unsteady lifting surface theory,
simple quasi.-steady theory, as well as two-dimensional gust
theory.
2. Experimental Apparatus
2.1 Model Propeller
A f ive-bladed Troost type model propeller with a 250mm
diameter and 125mm pitch was used. Its particulars are
summarized in Table 1. On the backside of a blade, two small,
high sensitive pressure pickups were mounted at positions
X and Y:
Position "X" R/R0 = 0.4 C/C0 = 0.2
Position "Y" R/R0 = 0.64 C/Co = 0.4,
where R/Ro and C/Co are the radius ratio and chord ratio,
respectively. The pressure pickup is a diaphragm type whose
strain is measured using semi-conductor type strain gauges.
Dimensions of the pickup are 2.8mm Ø x 8mm and its capacity
for unSteady pressure measurements, high sensitivity and good
frequency response, its size waS a problem because its length
is too long to fit flush along the blade surface.
If one wants to measure the steady pressure component,
the pressure pickup can be mounted. on the inside of. the bladé
and the pressure measured through a small hole. But using
such an apparatus the pressure response would be reduced which
is undesirable in the present .study After some cons_iderations
the final arrangement shown in Figs. i and 2, was selected.
Fig 1 shows the position of two pickups A perspex
cover was installed the blade face to..keep its water tightness
and to. prevent possible damage from the centrifugal forces and
water's dynamic pressure. ( Fig. 2 ) This cover is large
compared tò the blade size añd.p.robably affects the steady
component of the pressure distribution But it should have
little affect on the unsteady pressure fluctuation which develops
from the time-dependent components such as the wake distribution
etc. . . . ,
Fig.. 3 shows photographs of thé model propeller.
Because a semi-conductor type pressure pickup will asily
drift' in a témperature gradient,, the tethperature distribution'
of the towing tank where this experiment was made,. was measured
using a copper-constantan thermocouple along both its length'
and depth. A large tempeature. gradient is present near the.
water surface, but at the depth where the propeller rotates
( 20mm ±, l25m ), the gradient is small, 'only ± 0.12°C,
which corresponds to pressure change of ± 1.3mm Aq. Therefore
the drift caused by temperature 'change was neglected.
pickup and the attachment as shown in Fig. 2, otherwise the
pickup also "feels" the bending moment of blade which will also
cause "drift".
Fig. 4 shows thrust coefficient KT torque coefficient
and efficiency ri of the propeller. The circles are experimental
measurements and the full lines were calculated by
Hanaoka-Koyama's lifting surface propeller
theory7
The experimental KT and KQ decrease more steeply than theoretical predictions.Fig. 5 shows that the pressure change at positions X and
Y calculated by Hanaoka-Koyama's theory decreases according to
the advance boefficient J.
2.2 Model and Wake
The model is wall-sided type with parabolic waterlines.
C L X B .x d = 2.4m x 0.48m x 0.38m ) Its body plan is shown in Fig. 6. The propeller centerline is set 250mm under the
water surface. C Fig. 7 ) The wake distribution was measured
using a 5-hole Pitot tube. The axial wake component C Vx )
is shown in Fig. 8. The center of wake skews to the port and
the wake pattern is not symmetric along the center line. Near
the bottom position ( e = 1800 ) there are a pair of bilge
vortices whose position is lower than those developed from an
ordinary V-shape stern because of model is wall-sided, extreme
U-shape. Fig. 9 shows the wake patterns at rädii X ( R/R0 =
0.4 .) and Y ( R/R0 = o.64 ).
Vectors of the secondary flow are shown in Fig. 10, where
the skew of wake can also be observed. Fig. 11 shows the
tangential component of secondary flow, where clockwise revolution
changes rapidly at the bottom position because of the vortex
flow. This is shown cearly in Fig. 12.
2.3 E, erienta1, Apparatus
The setup of the expérimental apparatus is shown in Fig. 7.
The model propeller is driven by a 00W DC electric moter. The
shaft RPM is counted by a mechanical micro-switch which is set
at the propeller shaft. The signal from pressure pickups is
taken out through a hollow shaft and a slip ring, and then
recorded by a data recorder. I.t is then proces.sed by an A-D
convertor and digital computer. The signal wires in the hollOw
shaft were installed sponge rubber packing in the hole to
prevent noise component caused by the wire movement
3.. Experiment and Analysis
The experiments' were made at a towing tank ( 45m x 5,5m X
3 5m ) in University of Tokyo The model ship with running
model propeller. was towed by a carriage. 6 experimental
conditions were selected as shown in Fig 13
3.1 Calibration
In the: first plaôe the calibration Of pressure pickups was
made by rotating the propeller very slowly. ( about 0.4 rps )
while the model was stationary. At this condition the
hydrodynam.ic force is so little that the pickup output is only
the static pressure which changes sinusoidally according to the
angular position of the blade This amplitude should then be
equal tO the .static pres.sure difference, 100mm Aq peak.to peak
at thé pickup X and 160mm Aq at the pickup Y respectively.
Fig. 14 is an ecampIe .of such digitized data at a
run and the overall gain of the apparatus was easily checked.
.3.2 Noise Level
Before the towing tank experiments, the model prbpe1le was
rotated in the air and pickup noise level, was examined. Fig. 15
shows the comparison of Fourier analysis of the experiments in
the water and that in the air. This comparison indicates that
the nóise levél is so low that one can neglect the niose caused
by the slip rings etc.
Fig. 16 shows another analysis of the näise level. In this
figure the auto-correlation of the data is shown. It also appears
that the data obtained at the in-air rotation have no correlation
with eàch öther so the nojse,level is sufficiently low.
3.3 Experiment
The experiments were made as ol1ows First, the calibration
data was.obta'ined by rotating the propeller very slowly in still
water., and then the propeller RPM was increased to the,desired
value and the carriage ran at the desired speed. The data was
recorded on a magnetic tape and later sampled and digitized using
an A-D convertor The sampling interval was 2ms and usually 1000
samples were analysed as a data set using a computer.
3.4. Experimental Results
The préssure fluctuation during one revolution is shown Figs.
17-18 The abscissa is the angular position of the blade where
the top position of the pickups i s taken as zero degree. The'
broken line is the static pressure change caúsed by blade
revbluti.on, which changes sinusoidall.. :Thè thin solid line,
is the Föurier series* fitted to experimental data.
Thick solid lines show the calculated result using
Hanaoka-Koyama's lifting surface theory, which includes static pressure
change. It can therefore be directly compared with experimental
results which are denoted by dircies. In Koyarna's original
papert61 he treats the propeller blade as thin vortex sheet and
naglects its thickness effect. The pressure distribution thus
cannot be calculated directly. Okut81. modified this theory using the concépt of "equivalent two-dimensional wing section"
in which the original camber line is replaced by calculated
camber line deformed. by the induced velocity effects.
The thick solid lines shown in Figs. 17 - 18 are those
calculated by Oku using the above mentioned concept for the
author's study. This exact calculation was made for experimental
numbers 21,23 and 24.
4. Discussion
4.1 Phase Shift
There seems a certain phase shift, say 10 - 30 degrees,
between theory and experiment. ( Figs. 17-20 ) A possible reason is the time delay of the marking. The timing mark is
recorded when a rotating bar hits a mechanical micro-switch.
If there is a lOms time delay in this mechanism, it corresponds
to 23.00, 28.8°, and 38.4° at 6.4rps, 8rps and 1O.67rps
respectively. If we assume this correction fr
phase shift, then the agreement of phase will be improved. But
in this paperno correction was made.
4.2 Scatter of Data
Y ( R/R0 0.64 ). That means the Fourier. series does not
decay even at higher order term which is clearly seen in Fig. 14.
This appears connected to the large fluctuationof the wake! flow,
but deèper investigation was not made..
4.3 Unexpected Tendency. at Bottom Region
The agreement between the theory and experiment is poor in.
the bottom region ( O .= 180° ), even we consider above two
discussions. The experiment shows a much lower pressure than
the theory, when the blade is in this bottom region The
change in pressure s large and rapid in the bottom region
compared to the top region, which is contrary to ti.e theoretical
prediction that there is a large change in pressure at the top
region where the axial wake is large.
When one examines the pressure change of position X in
detail, it has. a peak just before the bottom position., then
falls rapidly just after passing through the bottom position
of blade. This tendency seems unexpected and cannot be
adequately explained by the above mentioned theories
The author examined the. effect of the following three items
to study the basis for this unexpected tendency
1 Static pressure change in wake
Suòtion of propeller. . . .
Tangential velocity component. . .
4.4 Static Pressure in Wake
The static pressure does not change linearly in the wake.
For example it must be low in the vortex core The static
the data of the 5-hole Ptiot tube. The deviation of the static
pressure from linearity was found to be not large. In the
present case the deviation was estimeted within about ± 7mm Aq.
This value is rather small and it does not explain the
unexpected tendency of the experimental deviation from theory
which reaches 40mm Aq at maximum.
4.5 Suction Effect of Propeller
It is well known that thé wake distribution is deformed
by the propeller suction. Then the wake pattern effective to
the propeller should be different from those obtained during
the wake survey. This deformed wake pattern should be considered
when the exäct theoretical analysis is discussed.
From à simple consideration, this effect also appears
unable to explain the present problem. The propeller suction
effect emphasizes orly the tendency obtained by the theoretical
analysis, namely that the pressure fluctuation becomes larger
not at the bottom .positioñ, but at the top position.
4.6 Tangential Velocity Component
The tangential velocity component V0 is not small in this
wake field as seen in Figs. 11 and 12. The author made a
quasi-steady analysis of the tangentialvelocity component. This
analysis is very simple. The pressure in a uniform flow is
expressed as
P = Cp .r
V2,
(1)where V is the tangential velocity of the blade at the certain
location. The pressure deviation caused by the tangential wake
P0 = Cp [( V - Ve
)2
- V2]
-CppVV0, (2)
where V0 is the tangential component of the wake. Combining
(1) and (2),
or
ACp02VO
P V Cp
V
The value of Cp at positions X and Y was already calculated as
shown in Fig. 5. Using the measured tangential wake ( Fig. 12 ),
the quasi-steady pressure caused by the tangential component,
then can be easily calculated.
Figs. 19-20 are a comparison between the experiment ( same
as Figs. 17-18 ) and the theory with the addition of this
tangential component.
The quasi-steady theory for the axial wake component V
was calculated as follows. First dCp/ dJ was calculated using
Hanaoka-KOyalfla'S steady lifting surface theory. The pressure
fluctuation Cp is calculated as
LìCp = = Js ( i - w ), (4)
where
J5 =V5 /
( ND ).The curve "Quasi-Steady + V0 in those figure is the vector
summation of LCp and The curve "Theory ( Koyama ) + Ve"
is obtained by a similar procedure. As seen in those figures the
agreement between theory and experiment is improved, except near
the top position. It is also concluded that the tangential
component can not be neglected in estimating the unsteady pressure
change on the propeller blade.
Usually the tangential component is neglected and the
calculation agrees with the experiment for propeller exciting
force etc. This is perhaps because of cancellation of
tangential component when integrating the pressure along the
radial direction of a blade.
4.7 Fourier Analysis
A Fourier analysis was made of all experimental data as
well as calculated pressure fluctuations. The resulting amplitudes
are shown in Figs. 21-26.
The first harmonic component of the experimental result
includes the static pressure change which was eliminated, by a
vector subtraction. But the experimental amplitude and the
static pressure change are of the saine order as seen in figures
and this subtraction reduces the accuracy.
In Fig. 21 C Exp. No. 21 ), the results of three
theoretical analyses are compared. Those are Hanaoka-Koyama's
unsteady lifting surface theory, simple quasi-steady theory
and two-dimensional gust theory. As seen in the figure, the
two-dimensional gust theory gives too large value of amplitude,
but the quasi-steady theory gives a fairly good approximation
to Hanaoka-Koyama's exact theory. This tendency has been
noted in many previous papers. It is surprising that the
contribution of the tangential wake component V0 is larger than
that of the axial wake component V. The result of calculation
with tangential component agrees fairly well'with the experiment
for most cases.
Figs. 22 and 23 are analyses for Exps. No. 23 and 24,
where the unsteady lifting surface theory and the simple
quasi-steady theory with and without the tangential wake
component are compared with the experiment. In these figures
agrees better with the experiment and that this quasi-steady
theory can be considered as an approximation of the exact
lifting surfáce theory for a practical purpose.
Figs. 24-26 are comparisons between the quasi-steady theory
with the tangential component and thé experimeñt of three
additional Exps. No. 22, 25 and 26.
4.8 Tangential Component at Stern
The tangential component of wake cán nOt be nglected in.
the predicting the pressure fluctuation In these experiments
the tangential component's contribution is even larger than
that of the axial. components. A Wcus. of wake components to the
angular position of blade was drawn to examine whether or not
this is true for usual ship hull forms such as tankers or
container ships.
Figs. 27 (a) and (b) are the wake locus drawings at radii
X and Y respectively Numbers in the figures are the angular
position in clockwise direction where top position is zero
Amplitudes of axial and tangential components are of clearly.
the same order of. 'magniiudes. . ..
Fig. 28 is similar locus of average tanker model wake
fields91
( average of 5 similar models ) where (a) and (b) areat R/R0 ' 0.1 and 0.9 respectively. Fig. 29 is. the wake field
of a. container ship with twin
screws9
As seen in Fig. 28 the locus Of tanker wake is rather, complex ands.yrnmetricto thevertical axis because the wake field is assumed symmetric along
the centér plane.. Contrary to this, the locus, of wake of a
twin-screw container ship is sinple but nonsylnmetric. 'In these
figures the tangential wake component is also the same order of
and container ships. That means the tangential wake component
must be taken into consideration for even a conventional hull
form when estimating the unsteady pressure fluctuation on a
propeller blade.
5. Conclusions
Measurements of the unsteady pressure fluctuation were
successfully performed by mounting small pressure pickups
on. the blade of a propeller model in the behind condition.
The pressure fluctuation is large in the bottom region
which is opposite to the theoretical prediction using
only the axial wake component which greatly change in the
top, region.,
The cause of this discrepancy was examined and'the tangential
wake component was determined to also effect the pressure
fluctuation.
A simple quasi-steady theory for the tangential wake component
is proposed.
Three different theories, Hanaoka-Koyama's unsteady lifting
surface theory, simple quasi-steady theory and two-dimensional
gust theory were compared with these experimental results
both directly as well as using Fourier analysis.
Two-dimensional gust theory predictions are too large
compared to the exact lifting surface theàry. On the
contrary the quasi-steady theory predicts a good approximation
Aáknowledgement
The author would like to express his ackriowledgements to
Mr. M. Oku at Kobe Steel Co. Ltd for his kind calculations of
thé lifting surface theory for the author's tèst pröpeller,
also to Prof. S Tamiya, 'Mr. A. Kirita and members at Laboratory
of High Speed Dynamics of Ships at University of Tokyo for
their valuable discussions and assistance during the preparation
of this papèr. Nöménclatures C Chord directidn. C0 Chord length Cp Pressure coefficient D Diameter of propeller J ' Advance coefficient
Advance coefficient based on ship speed,
Js = J5/( ND
Torque coefficient
Thrust coefficient
Harmonï order of Foúrier series
Re volu t io n Radial .diréction Radius of pròpeler Velocity Wake, fraction ' ' O Angular position Deñsity of water ' KQ KT.
$ubscripts
s Ship
x Axial direction
O Tangential direction
References
i. MOVLUDOFF, M.A. Measurement of Pressure on the Bläde
Surface of Non-Cavitating Propeller Model. Written
Contribution to the Propeller Session, 11th ITTC, Tokyo
(
1966 )pp 290-292.
HØIBY, O. Three-Dimensional Effects in Propeller Theory.
Norwegian Ship Nodel Experimental Tank Publication, No. 105
1970 ).
ITO, Y. and ARAKI, S. On Measurement of Surface Pressure
of an Acting Model Propeller ( ist Report ). SRC Technical
Note, No. 4 (
1967
)pp 25-34
( in Japanese ).TSAKONAS, S. et al An "Exact" Lifting-Surface Theory for
a Marine Propeller in a Ñon Uniform Flow Fluid. J. Ship
Res.
17 (.1973): 4 pp 196-207.
BAUSCHKE, W. and LEDERER, L. Zur NumerIsche Berechnung der
Druckverteilung und der Kräfte an Propeliern im Schiffsnachstrom.
Institute für Schiffbau, Der Universität Hamburg, Bericht s
Nr. 309 ( 1974 )
HANAOKA, T. Numrical. Lifting-Surface Theory for a .Screw
in Non-Uniform Flöw ( Part 1 Fundamental Theory ), Report
öf Ship Res. Inst. 6 (
1966 ): 5 pp 1-14
( in Japanese ). andKOYAMA, K. A Numerical Method for Propeller Lifting. Surface.
Arch. Japan, 137 ( 1975 ): pp 7887 ( i Japanese ).. KOThNA, K. A Numerical Ana1yis for the Lifting Surface
Theory of a. Marine Propeller. J. Soc. Naval Ardh. Japan,.
132 ( 1972 ) : pp 91-98 ( in Japanese ) .
Personal communication.
VAtI GEÑT, W. and VAN OOSSAÑEN, P. Influence of Wake .ön Propeller Loadinq.aid Cavitation. 2nd Lips Prop. Symp.
List of Tables. and Figures
Table 1. Particulars of Model Pröpèiler.
Fig. 1. Propeller Sections and Locations of Pressure
pickups.
2 Detail of Pickup..
Model Propeller.
Theoretical and Measured Propeller Characteristics
for Troos.t B-5-55.
5.. Theoretical Pressure Values on Blade.
Body Plan of. Wall Sided Model.
Experimental Apparatus.
8 Axial Wake Component in Propeller Disk
Axial Wake Components ät Radii X and Y.
Sedondary Flow Component.
Il. Tangential Wake Component ( V0 ).
12 . Tangential WaJç Components at Radii X and Y.
Conditions of Expêriment.
Calibration by Slow Rotation.
Fourier Analysis of Measured Pressure..
Auto-Correlation of Pressure.
Pressure Fluctuation during One Revolution at
Position X ( Ecp. Ño. 24 ).
Pressure. Fluctuation during One Revolution at
Position Y ( Exp. No. 24 ).
i9 Comparison between Experiment and Theories with Tangentiäl Component at Posjtion X ( Exp. No. 24 ).
2O Comparison between Experiment and Theories with Tangential Componént at Position Y ( Exp.,. No. 24 ).
Position X
Position Y
Fig. 22. Harmonic Components of Pressure Flúctuation
Exp. No.23 ).
Position. X
-positkon y
23.
Harmonic Cponentsof.Pressure Fluctuation
( Exp. No. 24 ).
Position X
Positiön Y
24. Harmonic Component of Pressure Fluctuation
.( Exp. No; 22 ).
25. Harmonic Component of PressUre Fluçtuation
(Exp. No. 5 ).
26. Harmonic Compdnent of Pressure Fluctuation Exp. No
6 ).
27. Locus of Wäke Components during One Revolution
behind the Wail Sided ModeL
28. Löcùs ö Wake Components during One ReVôlitipn
behind Tankr Models [91.
29 Locus of Wake Components during One Revolution behind a Container Ship Modèl [9).
Table 1. Particulars of Model Propeller
Type of section
Diameter
Pitch
Expanded area ratio
Boss ratio Rake angle Number of blades Turning direction Troost B 25 Omm 125mm ( Constant )
O.5
0.185 90 5 Right turningPOSITION
61.15
1e--POSITION X,
R/RçO.64
50R
R/R0a0.4
WING SECTION AND POSITIONS
OF PRESSURI
PICKUPS.
FIG.
i
TIP
PASTED
BLADE
PLASTICS
COVER
ATTAC.HMENT
PRESSURE PICKUP
SUCTION SIDE
ROOT
GLUED
0.03.0.3
0.02-0.?
0.0,-0.'
o
-4;
KT
KQ
'Z
k
/
/
/
.
THEORY (KOYAMA)
EXPERIMEN
,
.
o
o
o
b
N
0.7
0.6
f11.0.5
0.4
0.3
0.2
O.'
0-O
01
'0
O
O.I
0.2
0.3
0.4
0.5
0.6
0.7
J.,
Fig.
4Theoretical and Measured Propeller
Characteristics for Troost B-5-55
. .
-1.0
-0.8
Cp
-0.6
-0.4
-0.2
o
0
0.2
0.4
0.6
0.8
'J
5
4
3
2
9
8
Fig. 6
Body Plan of Wall Sided Model
7
6
JJJj
PEN
STRAIN
METER
ELECTRIC MOTOR.
/.
¡MARK.ER
.PICKUPS
PROPELLER
TO PENRECORDER
& DATA RECORDER
o'
oL
AD
CARD
COMPUTER
CONVERTER
PUNCHER
DATA
R E CO R.DER
SLIP RINGS
PRESSURE
Fig.
EXPERIMENTAL
APPARATUS
.2700
0.9
0.85
0.8
0.9
Fig.
I-w
o
8=0
orod
1800.
Axial Wake Component in Propeller Disc
PROP. DISC
0.85
90°
t t I t I t
'SO-I-w
0.8-POSITION
X
0.4-
R/RØ -0.4
C/C0
O.2
0.2
o
TOP
1.0-I-W
0.8
.60
POSITION
Y
R/R0
O. 64
C/C0 -0.4
I t I IFig.
9Axial Wake Componerts at radii X and Y
I I
120
180
BOTTOM
-180
I2O
-60
o
60
120
180
BOTTOM
TOP
BOTTOM
-180
-120
SCALE
Ve/Vs
o
8=0
1800
c_20(mm)
o
leo
Fig.
lo
Secondary Flow Component
?700
8=9°
V0/Vs>Q
0.I
o.
I1800
sFig. 11 Tangential Wake Component ( V0
PROP. DISC
-o'
BOTTOM
-120
-60
-0.2
-0.4
-0.2
POSITION
X
R/R0 O.4
-
C/C.0 20.2
TOP
o.4-
POSITION
Y
R/R0 -064
V9/V
C/C0 204
12Q
60
I2O
180
BOTTOIY
Fig. 12 Tangential Wake Components at Radii X and Y
180
BOTTOM
TOP
BOTTOM
0.4
Ve/Vs
0.2
-12
I Idb
4p.
PI.
I.10.71-
23
/
(r
¿
8.04 21
25
26.
,6.4I/*22
0.6
0.8
1.0
1.2
Vs (m/s)
Fig. 13
CONDITIONS OF EXPERIMENT
200
160
I2O0
0%,d0
0
w
80
o
Fig. 14
00
00
.0
o
,0
0;g0%
o
00
Oo
U0
o
o
. .o
o
o
E
E
o
o
.
.. w ..
e.
s_
so
MARK
I
2T(sec)3
4
CALIBRATION
BY SLOW ROTATION
0.00
O0
o
0.
0&
00
°cP
POO
00
0
o
o
80
60
p
(mmAq)
40
20
\..
N 8.0rps
TEST NO.21
Js=O. 4
o
t
X"
N .8.Orps
o
TEST NO.21
Js.=O. 4
o
IN AIR
IN AIR
O, .i."-.
.e.-4
0123456701234567
m
m
Fig. 15N
8.Orps
0.8:
o
.1 N WATER (EXP. NO. 21 x)
IN
AIR
0.6
o
j:
40.4.00
c Oo
LUo
o
%
o
-O00
00
(sec)
0.20
0
o
0.2-0000
%
o
o
10.4
Fig. 16
AUTOCORRELATION OF PRESSURE
I.Øo
POSITION
THEORY
(KOYAMA)
---STATIC
PRESS.
EXPERIMENT
120
leO
240
3OO
360
Fig. 17
Pressure
Fluctuationduring One Revolution
at
Position X
(
150
100
AP
(mrnAq)
50
-50
-loo
-150.
o
6O
o
r,o
rilo
01120
18000
IEXP. NO. 24Y
DATA NO.
89
R/R0 -O64
C/Ço =0.4
N
8.Orp.s
-0.30
J
=0.224
O.
00
\
Fig. 18Pressure Fluctuation during One Revolution at Position Y
(
Exp. No. 24
300
360
o
BOTTOM
THEORY (KOYAMA)
-STATIC
PRESS.
o
8
I -I IVI.
I I i. I I IBOTTOM
EXP. NO. 24X
DATA NO. 87
R/R0
-0.4
c/ce
0.2
N
-8.Orps
=0.30
J
=0.224
THEORY(KOYAMA)+ V9
QUASI-STEADY
Fig. 19Comparison between Experiment and Theories .wi-th Tangential Component at Position X
(
lOO
(mmkq)
50
o
20
180
u
!30O
360
o
EXP. NO. 24Y
DATA
ÑO:.
89
o
R/R0 O.64
C/C0 -O4
N
8.Orps
0.3O
J
NO.224
Fig. 20Comparison between Experiment and Theories with Tangential Component at Position Y
(
Exp. No.
24
o
THEORY (KOYAMA) + V9
QUASI STEADY+V9
0O
o
150
LX
[iO. 21X
EXPERIMENT 'lEASURED STATIC PRESSURE WITHOUT STATIC P. THEORY EXACT (KOYAMA) QUASI STEADY 2-DIM.Gusi
V9 COMPONENT EXACT + V9 QUASI STEADY + V9 EXPER ¡MENT THEORY EXACT (KOYAMA) QUASI STEADY 2-DIM. GUST V9 COMPONENT EXACT + V9 QUASI STEADY + V9 EXPER i MENT THEORY EXACT (KOYAMA) QUASI STEADY 2-DIM. GUST V COMPONENT EXACT + V9 QUASI STEADY + V9 0.02 0.011 0.06 0.12 0.114 I I I I I 1.,?
I Ii1 = 1
M = 2 [1 = 3LXP. RO. 21Y EXPERIMENT ÎÌ1EASURED STATIC PRESSURE WITHOUT STATIC P. THEORY EXACT (KOYAMA) QUASI STEADY 2-DIM, GUST V9 COMPONENT EXACT
+ Ve
QUASI STEADY+ Ve
EXPER I MENT THEORY EXACT (KOYAMA) QUASI STEADY 2-DIM, GUST V9 COMPONENT EXACT +V9
QUASI STEADY +V9
EXPER I MENT THEORY EXACT (KOYAMA) QUASI STEADYJ
2-DIM. GUST V9 COMPONENT:i
EXACT+VØ
11=3
QUASI STEADY + I I 1 11 = 1 M = 2 CP 0.06 0.08 0.10 0 0.02 0,014EXPI ROI 23X
Ex EftlllE NT ME ASURE D STATIC PRESSURE WITHOUT STATIC P. THEORY EXACT (KOYAMA) QUASI STEADY Ve COMPONENT EXACT + V6 QUASI STEADY + V6 EXPERIMENT THEORY EXACT (KOYAMA) QUASI STEADY V6 COMPONENT EXACT+ Ve
QUASI STEADY + V9 EXPERIMENT THEORY EXACT (KOYAMA) QUASI STEADY V9 COMPONENT EXACT + V6 0 0.02 0.04 0.06 0.08 0.10 i I IiM = i
M = 2
M = 3
I QUASI STEADY+ Ve
Fig. 22a Harmonic Components of Pressure Fluctuation
EXP. O. 23Y EXPER I PENT MEASURED STATIC PRESSURE WITHOUT STATIC P. THEORY EXACT (KOYAMA) QUASI STEADY V9 COMPONENT EXACT + V9 QuAsI STEADY + V9 EXPERIMENT THE ÖRY EXACT (KOYAMA) QUASI' STEADY V9 COMPONENT EXACT + V9 QUASI STEADY + V9 EXPER I MENT THEORY EXACT (KOYAMA) QUASI STEADY V9 COMPONENT EXACT + V0 QUASI STEADY + V0 0.02 0.04 CP 0.06 0,08 Q.10
Fiq. 22b' Harmonic Components of Pressure Fluctuation
EXP. NO. 2IX EXPERIMENT MEASURED STATIC PRESSURE WITHOUT STATIC P. THEORY EXACT (KOYAMA) QUASI STEADY V9 COMPONENT EXACT + V9 QUASI STEADY + V9 EXPER I MENT THEORY EXACT (KOYAMA) QUASI STEADY V9 COMPONENT EXACT + V9 QUASI STEADY + EXPERI MENT THEORY EXACT QUASI STEADY V9 COMPONENT EXACT +
V9
QUASI STEADY + V9 o CP 0.02 0.014 0.06 0.12 0.114 0.16 I I Iu
¿f I M = i M = 2Fig. 23a Harmonic Components of Pressure Fluctuation Exp. No. 24 ) - (a) Position X
EXP. NO. 2'4Y
EXPÉR IMENT MEASURED STATIC PRESSURE WITHOUT STATIC P1 THEO RÏ EXACT (KOYAMA) QUASI STEADY V6 COMPONENT ExACT. Ve QUASI STEADY + V0 EXPERIMENT THEORY EXACT (KOYAMA) QUASI STEADY V9 COMPONENT EXACT + V9 QUASI STEADY Ye I IM=
i
El = 2 EXPERIMENT THEORY EXACT (KOYAMA) QUASI STEADY V9 COMPONENTEXACT+Ve
N=3
QUASI STEADY + V9Fig. 23b Harmonic Components of Pressure Fluctuation
O 0.02 0.014 0.06 0.08 0.10
EXPERIMENT EXPERIMENT V9 EXPERIMENT
J
EXP. NO. 22 POSITION Y 0.02 0.014 0.06 0,08 I I I I IM=1
I 11 = 2 I EXPERIMENT QUASI STEADY + V9 EXPERIMENT QUASI STEADY + V9 EXPERIMENT QUASI STEADY+ Ve
I I Fig. 24Harmonic Component of Pressure Fluctuation
Exp. No. 22 I 0.02 0.014 0.06 0.08 I I I I M = i I
M=2
= 3EXP. NO. 25
EXPERIMENT EXPER I MENT
+ Ve
EXPER I MENT 0.02. .0.914 0.06 0.08 I I ii
¡1 =2
EXPERIMENT QUASI STEADY + V6 EXPERIMENT QUASI STEADY + V9 cP 0.02 0.014 0.06 0,08 i Vi
ri= 3
Fig. 25Harmonic Component of Pressure Fluctuation
Exp. No. 25 I Li = 2 EXPERIMENT
Ii = 3
QUASI STEADY+ Ve
IM= i
POSITION X POSITION YEXP. NO. 26
EXPERIMENT EXPER I MENT EXPERIMENT
i PoSITioN X 0.02 0.1OLt 0.06 0.08 i r i i i i ¡1.= 2
I
M = 3 EXPER I MENT QUASI STEADY + V9 EXPERIMENT QUASI STEADY + V0 EXPERIMENT QUASI STEADY .+ V9 O Fig. 26Harmonic Component of Pressure Fluctuation
Exp. No. 26 POSITION Y cP 0.02 0.0/4 0.06 0.08 i i T t N = i rl = 2
-0.3
-0.2 -0.1
0
0.1
0.2
0.3
(b.) POSITION
Y
V9
-0.2 -0.1
0
0.1
0.2
Ve
(a)
POSITION
X
Fig. 27-0.2 -0.1
6oVii!r 300
21'
150
TANKER
120
240
0.8
vx
0.7
L I1,
-0.3 -0.2 -0.1
0
0.1,, 0.2
0.3
vo
0
0.1
0.2
vo
(a) R/R0=O.7
Fig. 28Locus of Wake Components during One Revolution behin
Tanker Models
(b) R/R=O.9
CONTAINER SHIP
i. i
vx
240 300
¡501.0
330
120
0
90
(a)
R/Ro0.66
T
T
0.2 -0.1
0
0.1,, 0.2
.0.2-0.1
0
0.1
0.2
vo
.
vo
(b) R/R0=O.95
Fig. 29Locus of ¶Jake Components during One Revolution behind a Container Ship Model