Wake
Dstributon of Fu Form Ship
1. introduction
Knowledge of the flow field around the stern of a vessel is :eat importance in assessing scale effects on propulsion pe:fonnance, accomplishing optimum propeller design and in evaluating propeller excitation force. However, in or-daxy full-form ships, the heavy cross flow around the pr:ei1er makes estimation of the wake distribution dif. On the other hand, the wake fractions which are c:aned from propeller characteristic curves with reference te
erque and thrust forces of a propeller during self.
ç:::ilsion model tests or sea trial runs are largely affected b:. scale effects: namely, a large difference in wake
d:ribution exists between models and actual ships. In
fa:t. even in the case of actual ships, the existence of cross fw as yet remains uncertain. Only recently have a number of ersons begun to report the results of investigations on tuie existence of cross flow astern with respect to- model )(. In these developments, efforts have also been
rae to concentrate on actual ships.
Despite such eL±elvors. no substantial results have as yet been acquired cri quantitative analysis. This lag in technology, however, is :esing a problem to naval architects vhp wish to design a uU with the most optimal wake distribution of increase the fullness of vessels for transport economy.Fully realizing the significance of the problem, the a..o:s studied the flow field in and around the boundary laver in the vicinity of tite surface of the hull, over the e-re range of the stern half of a 7 m model using a towing tari in the Il-li Ship Model Basin, Research Institute. The
By:
Masaaki Narnimatsu and Kenji Muraoka
1shikavajima-Harirna Heavy 'Industries Co., Ltd.
-
Summary
In order to investigate the wake distribution of full ships, the measurement of the flow around the sternof a 20 000 DWT tanker together with its Iwo model ships, 7m and 30 in models respectively, t'as carried out using 5-hole spherical Pitot tubes. For both the ship and its 30m model, the measured section was forward of the propeller at a distance of 907 of the propeller diameter, while the 7 in model was measured at several additional points, besides the foregoing allocation. In addition to these experiments, a detailed study of stern flow through bounda,y laver measurements of the 7 in model was conducted with a 3-hole arrow type Pitot tube. Thepressures through the 5-hole and 3-/tole Pito t tubes were nzeasured using autobalancing pressure transducers anda digital record system.
The boundarj.' laver measurement revealed the flow in the vicinity of the hull surface. tite mechanism and grolt'ing process of tite bilge vortex. Front the wake measurement it was proven that the complicated flow, other-wise known as bilge vortex, exists in a ship's wake as well as in its model wake, and a met/tod for estimating the wake distribution of ships from tit eir model which had been proposed by Dr. Sasa/imais also applicable
to full
form ships. Moreover, when this method is applied to the estima tion of the flow direction of a s/tip 's wake, the estimated direction will prove itself to be in fairly close agreenient with the experimental values.
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authors also measured the wake pattern one section ahead of the propeller of a new 200,000 DWT tanker (300 m-L.P.P.) by utilizing the five-hole pitot tubesO3). Another study group conducted a number of tests at sea on a 30 m large-size model ship (analogous to the one used for the wake pattern measurement) as one part of a full-form ship research and development, project. In addition to the above tests the authors also completed a wake survey of this
model.
The authors thoroughly examinated the data, and the results are as follows.
2. Measurement of flow alongside the hull walls
2.1 Ship and model used for testsThe 200.000 DWT tanker "Ryuko-Maru." a 30 in large-size model, scaled to
i/lo
of the original, and a 7m
standard analogous model available at the IHI Ship Model Basin, all used for test purposes, are detailed in Table 1. The hull type examined is a full-form with a single screw
propeller and a bulbous bow. The length-breadth ratio
(LIB)is 60. and block coefficient (C1) is 0.83.
The 30 m large-size model is made of steel, finished to a high accuracy of ±10 mm. and is coated with oil paint. while the 7 m model is made of urethane foam finished willi lacquer paint. The actual ship is equipped with a
propeller measuring 9.2 m in diameter. The large-size analogous model is provided a propeller reduced to scale. The 7 ni model is equipped with a 210 mm stock propeller.
2.2 Tests 2.2.1 7m model
The wake distribution between the propeller position
and station 3/4 and the boundary layer near the hull
surface between station 4 and station 1/2 were measured utilizing the fìvehole pitot tube and three-hole pitot tube, respectively. For the measurements, the five-hole pitot tube (having a spherical head of 10 rn/rn in dia, and angle of 20° deg. between the center hole and side hole) was shifted
port and starboard and up and down by means of a pulse motor.
The pitot tube pressure was transmitted by a pressure transducer (self-balancing type, capacity: 0.05 kg/cm2; accuracy: Class 0.2%) and an AD converter (VF type, reset time: 2 sec.), from which the output signals were then fed to a minicomputer aboard the towing carriage. The outputs
of the
minicomputer were then processed for more sophisticated analyses, such as plotting of the wake pattern, by a UNIVAC-1 108 computer. (The above is one of the standard methods practiced in the IHI Ship Model Basin.) The average time was set at 8 to 10 seconds where pressure fluctuations were conspicuous and at 4 to 6 seconds where fluctuations were less.The measuring points for the 7 in model are shown in Fig. 1, in which plane corresponds to the points where wake patterns of the actual ship and tIse 30m large-size model ship were measured, and plane © the point selected nearest to the propeller without hindering the use of the five-hole pitot tube during propeller operation.
The wake distribution of the 7 m model under full.load conditions are shown in Fig. 2. As is clear from Fig.2, a cross flow originating from station 3/4 (usually called the bilge vortex) grew larger on the rear parts. Under ballast condition (see Fig. 3), the bilge vortices were more
notice-able than under a full.load condition (see Fig. 2). Fig. 4 shows the results of measurements taken while towing the full-loaded model astern; boundary layerwas hardly
observ-ed at measuring points, from which the observobserv-ed flow is
considered to be like that resulting from a fluid without viscosity or potential flow.
Since neither the contour diagram nor the vector
diagrams show the existence of cross flow, it is thought that the aforementioned bilge vortex are attributable to a change in boundary layer due tó viscosity. Changes in cross flow are shown in Fig. 5. Streams extending downward
(Note) Test condition
Table i Particulars and test conditions
(Note) The value marked with (*) denotes the speed at which the boundary layer was measured.
Ship Item
Actual ship
(200,000 DWT tanker) 30 m large-shemodel m model
Name Ryuko-Maru
Margaret M.S. No. 300
Load condition Full load Ballast Full load Full load
Ballast
Length between perpendiculars (L) (m) 300 30 7
Breadth (B) (m) .. 50 5 1167
Mean draught (dM) (m) 18.86 l067 1.912 0A43 0.249
Fore draught (dF) (m) ii 8.63 " 0.201 Aft draught (d4) (m) . 12.72 " 0.297 Displacement (r) (t) 241,200 133,100 244.6 3.004 L355 Block coefficient (CB) 0.83 0.80 0.83 0.83 080
Measuring speed (Vs) (m/sec) 8.33 (16.2 kt) 9.26 (18.0 kt) 2.63 1.27 (1.30*) 1.41
Water temperature (t) (°C) 21.0 14.7 13.0 13.4
VoL 8 No. 4 1974
25 T; Towing S: Self-propulsion A: Towing asternPlane Corresponding to the plane measurement of actual ship
Fig. i Measured section of 7 m model
Plan
Load condition
Full load Ballast
T
T. S. A T. S
© T
T. S. A T. S
rum
26
(J IO
(Note) : lowing
Measured by five-hole pilot lube---: Self-propulsion
Towing Measured by JIS type pitot tube
Fig. 3 Flow pattern of 7 m model at ballast condition
Fig. 4 Flow pattern of 7 m model at astern test of full load condition
(Note)
mm
50
Towing } Measured by five-hole pitot tube
Self-propulsion
- - - : Towing Measured by JIS type pitot tube
Fig. 2 Flow pattern of 7 m model at full load condition
Plane © J I [S.L , (11L 1W
t
null C. Efrom the datum level are hatched. Near the hull surface, the downward velocity component is larger as it returns. Both the vertical and horizontal velocity components are small around the center of the vortex.
With reference to Figs. i to 5 , it vas found that the bilge vortex generated near the 3/4 station grew large at the propeller. However, this is not enough to clarify the mechanism of vortex development.
Accordingly, the authors measured, in the way explained below, the boundary layers near the hull surface especially in the range where there was something closely related to the occurrence and growth process of bilge vortex. The 7 m model was towed, and the arrov.tpe three-hole pitot tube (see Fig. 6 ) employed to measure vectorial veloities. The pitot tube was drivn normal to the hull surface by
means of a pulse motor. Its positioning accuracy was
2/100 mm. The pressures detected by the pitot tube were
processed in the same manner dS ill the case of the five-hole pitot tube.
Japan Shipbuilding & Marine Engineering
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Fig. 5 Sketch of flow pattern of 7 m model at full load condition
Fig. 6 Arrangement of 3-hole pitot tube
The measurements were conducted at 49 points on the starboard side aft. For example, Fig. 7 , shows the vectorial velocity components at station
1. The arm of the pitot
tithe was set parallel to the tangential plane of the hullsurface, and the measured flow directions designated
"positive" for downward with respect to the arm of the pitot tube and "negative" for upward. The distribution of velocities and flow angles in the boundary layer differed greatly depending on the points measured, but no such flow accompanying the two-dimensional separation was observed. Characteristically it was found that the thickness
of the boundary layer around the bilge was thin, and that the direction of flow changed sharply near the hull surface.
Vol. 8 No. 4 1974
Topressure transducer -a, 3-hole1=
0.5 Screw rod-.
Universal 1OInt ?'\-.)
o iceDistance from hull surface 1mm)
o
(a) s'_i C + r Downwardf10 - r UpwardflowFig. 7 Example of boundary layer
measurem-27 10 o -10 -20 (b)
Distance fromhulls'jrface
13
.0
22.2 30 m largesize model
The rotating arm with a gang of six five-hole pitot
r. (see Fig. 8) was thrned by winding and unwinding tTe wire rope connected to the arm with the other end cected to the windlass on the deck. The rotating angle then measured with the potentiometer on the shaft
(see Fig. 9).
The five-hole pitot tube used was 20 mm in diameter
a: 0
in hole angle. In addition, a JIS type pitot tubeprinter
circuit j
j
(5-hr-i)
Pen recorder (5-channel) e transducer x 5
ear solenoid valves
Fig. 10 Flowchart
8 Testing arrangement of 30 m large model ship
To winch To winch
;. 9 Arrangement of swing arm of 30 m model
Control panel
Pitt tube Smp. 5-hole pitot tube x 3Opcs 30m model: 5-hole pitot tube x 7pcs
was attached near the shaft of the rotating arm.
As in the case of the 7 Ui model, a digital recording was taken using pressure transducers and AD converters. A pen recorder was also used as a monitor (see Fig. JO). The pressure transducers used were rated at 0.1 kg/cm2, and a printer with an averaging circuit was employed instead of the minicomputer used in the tank test. The pressure differences between the center and side holes were
meas-ured in each of the five-hole pitot tube. Since the recording system was for five-hole pitot tube coverage, solenoid valves
were used to measure the 7 pitot tubes one at a time by changeover. In the piping arrangement scheme, 1 mAq of negative pressure was developed to generate bubbles which protracted measuring time and degraded measuring accu-racy. To cope with this problem, deaerated water was used in the piping with results far better than expected.
The test area was off Isogo, Yokohama, in Dec., 1972. The speed trials were conducted utilizing mile posts
special-Fig. 12 Testing arrangement of ship
't
Fig. 11 Flow pattern of 30 m model
at full load condtion
I
Japan ShipbuiMing & Alarme Engineering
s c
(LS
t'
(cl Joint Shell 100 2 To pitot tubeFig. 13 Truss, pitot tube and joints (ship)
(a) full-loud condition
\
iii disC Section "B" s» (b) Ballast condition'V'
'_\
¿ A "t,",- :
ist Run :2nd RunFig. 14 Flow pattern of ship at MCR
Vol.8 No.4
1974 29ly located at the Yokohama Shipyard. The wake measure-ments were performed
for both full-load and ballast
conditions; the measurements for the ballast condition left much to be desired because the weather was bad. The wake distribution obtained under the full-load condition is shown in Fig. 11,
2.2.3 Actualship
Measurements were performed to clarify the wake distri-bution ahead of the propeller of the 200,000 D\VT tanker "Ryuko-Maru" which was to go to Aloi Shipyard for final outfitting after being built' at the Yokohama Shipyard
(see Fig.12 ). Full-load measurements were performed between Omaezaki (Shizuoka Pref.) and Daiozaki (Mie Pref.), while the ballast measurements, together with speed trails, were conducted on a radio log course off Hinomisaki (Wakayama Pref.). In both cases sea conditions were so
favorable that the results of the measurements might dispense with corrections with respect to waves and wind. The measuring point corresponded to planej shown in Fig. 1, that is, 13,4 m forward of A.P. or some 8.5 m ahead of the propeller.
Various methods were studied and compared for safe, accurate measurements at points as near to the hull and propeller as possible. Tile method selected utilized a truss overhanging the hull in order to attach a five-hole pitot tube (see Fig. 13 ). To be more precise, a truss composed of 114.3 to 139.8 mmÇ pipe was attached to the hull, and 30 five-hole pitot tubes and 2 JIS type static pressule tubes were mounted on it at an angle tilted 20° against the hull center line in order to be almost parallel to the
hull surface. The five-hole pitot tube was 80 mm in
diameter with a 30° hole angle, exactly, the same as that used in SRIO7 ,except for the stem length of the five-hole pitot bubes and the shape of the pipe outlet. The pitot tube pressure was obtained by connecting a copper pipe laid along the truss to the vinyl pipe in the hull through the joint in the hull provided in the middle of the truss.
I u E c 0) 'o u 0) '0 50 E E o C") E E
Te joint was made of a welded steel plate with 152 rie:.es of copper pipe running through it. (see Fig. 13 (c)).
Far the sake of safety, all vinyl tubes were run through a -t-v valve in order to separate the hull interior and
exior in the event of an emergenc'.
T tubes leading into the hull were connected to an of small magnetic valves which were designed to r:zch measuring points from one to another and lead the :essures of the selected points to the pressure
trans-d.i (self-balancing type, capacity: 1.0 kg/cm2). The preaures of all
holes in one pitot tube could thus be
nea:ed by switching only once.
:.e measuring system was designed, as with the 30 m lage-scale model ship. to have the pressure difference
bereen the center hole on one hand and the holes in
the :.. bottom and sides on the other detected.
This ara-zement minimized the influence of such unfavorable fa:::s as draft change, pitch, roll and waves.same instruments used in the 30 m large-size model were also used for recording. The averaging time was set at te 30 seconds for each pitot tube.
method described above was found to be very
sa--.j:-::tOrv in view of measurement accuracy, prepara-tio: workability, safety during experiments, labor-savings an. si.plicity in processing data. The wake distributions un:e: full-load and ballast conditions are given in Fig. 14.
i Fig.14, the root of the arrow shows the location of pitot tube, with the contour line expressed by the fo:c.ing equation.
W= 1 - Vx/Vs
St 3
03 11
where, Vx: Velocity component parallel to the ship's center line; Vs: Ship's velocity obtained by correcting the bottom log measurements (electromagnetic) with the results of the speed trial runs.
In Fig. 14(b), a comparison is made between the results of wake distribution measurements, one outgoing and the other incoming, with the ship's velocity measured during speed trial runs. Accuracy and repeatability of the measure-ments may then be clearly understood.
The figure above also refers to MCR operation. Te.sts were conducted at various speeds including MCR, but the results revealed that the speed difference created was not large enough to necessitate discussion of the effects of the Reynolds number. Details on this point are therefore omitted here.
From the same figure
itis apparent that the flow
around an actual ship is accompanied by bilge vortex, which will be discussed later in comparison with that of the model.
3.
Occurrence and development of bilge
vortex
With regards to the bilge vortex of the single-screw propeller full-form ship, various experimental efforts have been made to observe the flow patterns utilizing circulating water channels or wind tunnels or to quantitatively analyze
them by means of the pitot tube
or hot-wireanemom-eter (2)(4)(6) While the three-dimensional boundary layer
around the ship is now beginning to be dealt with by
theoretical computation, complicated flows such as the
Fig. 15
1 -
VX/VS at bilge (boundary rayer measurement)¿LX)
E 'w
(Note) V1: Towing speed y: Velocity of secondary flow Fig. 16 Secondary flow
Japan Shipbuilding & Marine Engineering
bilge flow inherent in full-form ships has not as yet been reproduced. To challenge simulation of flow by computa-tion with practical accuracy, the authors measured boundary
layers by penetrating into the mechanism of the flow
field observed with a 7 m model which has thus far been used- for the collection, of various data such as from self-propulsion tests, etc.
The measurement results were reduced to wake fractions (lVxIVs), which are drawn in contour lines in Fig. 15. The velocities, Vx, measured on the lines normal to the hull surface at the stations, do not always represent the
velocities on the planes of the respective stations, but
may he considered to he almost the same as those by
the five-hole pitot tube. Distribution of the secondary flow velocities measured by the three-hole pitot tube is shown in Fig. 16, in which the velocity and direction of each stream are shown vectorially with the towing speed of the model as reference. For increased legibility, the patterns are modified by enlarging the measuring lines
-
Calculated Measured O 10 Angle of secondary flow (degree) (a) St.2Fig. 17 Comparison of limiting and outer flow
L.W.L
Cl..
vr/v
CL.
0 '.1 -02 O 10 - 0.1 02-0.3
Pressure Angle of secondary Pressure
Coeff cient(Cp) flow (degree) Coefficient)Cp(
Fig. 18 Example of calculated potential flow
with reference to the transverse section of the hull. and are not equal to those given in Fig. 15.
In Fig. 15, the low velocity layer around station 3,
near the bottom of the
hull, is forced outwards, thusappearing as drift. This isolated layer is then forced upwards by the rapid upward flow passing around the bilge near station 2 1/2, inflating the contour lines again from a little above the bilge near station 1 to form bilge vortex. This
cross flow then runs into the propeller.
In the range from station 2 to station 1 1/2, on the other hand, the flow around the bilge accelerates in velocity,
intensifies near the hull, arìd makes the boundary layer very thin. At station 1 1/2, the ascending flow passing
around the bilge will eventually wade as it means along the hull surface, running apart from the hull. Then, another flow above it will assume control, running on the inside track to form bilge vortices. That part of the bilge which
lies aft of station
1. is turned sharply, and establishesstrong vortices which seem to combine with a counterfiow to form a large, violent cross flow.
Fig. 17 shows the external flow and the flow in the vicinity of the surface (i.e., limiting flow). lt is immediately perceived from Fig. 1 7 that the bilge cross flow is formed.
lt
is considered natural that the external flow is
a potential flow. The development of vortex is dependent solely on how the boundary layer changes with reference to the flow as a whole. Therefore, it is of great interestto compare the potential flow with the actual viscous
flow. In pursuit of this interesting subject, the authors calculated the potential flow around the ship by means of the Hess & Smith method, and the results compared with the measured values in Fig. 18 by way of an example.
Correction of the displacement thickness of the bound-ary layer and the effects of viscosity with respect to the shape of the hull for which calculation was made, were all disregarded. The measurements did not cover these
parts that were far enough away from the hull to represent potential flow.
Both results however, are qualitatively in fairly close agreement, thus suggesting that simulation of bilge vortex by theoretical computation is feasible.
4.
Correlation between actual ship and
model
A comparison between the aforementioned two model ships and the actual ship with respect to wake distribution at statioñ® discloses that the smaller mode] has a wider boundary layer thickness which grows narrower as the ship's size becomes larger, with the result that the actual
ship has the narrowest thickness of the three.
For simplicity's sake, the flow patterns for only the actual ship and 7 m model are shown superposedly on
Fig. 23 - Looking at the arrows, it is found that even
with the actual ship the cross flow is at almost the same level as with the model; under ballast conditions, for both the actual ship and model. equi-wake lines grow into a large peninsula, evincing that both flow fields are the same in nature. lt should be noted however. that the velocity
and direction of flow at a corresponding point differs
greatly between the actual ship and model.
In order to deal with the matter quantitatively, three
r
-J -J-Ji! r
O12345678
2 3 4 5 6 30m model scale in m Ship scale in m ShipscaleinmDistance from hull centerline (Y) Distance from hull centerline (Y)
Fig. 19 Comparison of Vx/Vs at typical water lines
7;
100 W.L.
100 200 300 400
(a) Full-load condition
+Calculated potential wake Astern test of 7m model
}
7m model Towing Self-propulsion Self-propulsion l 30m model -300m Ship 1.0-JrTon9
7m model / , Self-propulsion j } 30m model300m Ship Calculated potential flow
+ + + 1SOW.L.
o--10-I
-20/
1/ i i 200 3(1) 400 0.2 i u4 06 08 io 7m model scale in mm I2 3 4
5 6 7 30m model scale in mShipscale in m Distance from hull centerline
+-¿ 0-o 0, 0.5 . -20 a 20- IO-o
:
o-o 140 W.L. 100W.L. 100 200 300 400 )b) Ballast condition Towing } 7m model Self-propulsion 300mShip 180 W. L. Towing 300m ShipSelf-orooulsio /*ii 7m model scale in mm 7m modelFig. 20 Comparison of /3v artd,i at typical water lines
140 W.L.
Japan Shipbui1dng & Marine Engineering
0.2 0.4 0.6 0.8 1.0 7m model scale in mm 10- ISO W. L. 20 IO o -10
(a) Full-load condition (b) Ballast condition
20-10 ßJ, + + 7m model scale in mm
Distance fromhull centerline
100 200 300 400 Ship scale in m
-+---100W.L. + -10- Astern test of 7m Iirepresentative waterlines, IOU W.L., 140 W.L. and 180 \V.L.
at station were selected and compared with respect to direction and velocity of flow as shown in Figs. 1 9
and 20, with figures 100, 140 and 180, denoting the
heights above the base line of the water levels referring to the 7 m model. The hetght of 140 W.L. is approximately on a level with the propeller shaft.
ß11 and ß. denote the horizontal and vertical angles of flow direction, respectively. In the figure for full-load
0.5
O
(a) Full-load condition (b) Ballast condition
L0
1.0-0,5 180 W. L
1.0- Ship experiment
140 W. L.
SS' (a) Full-load condition
>'
....: S» L-.' \S 1.0 1 W.L. Os 0.5 o \Estimated from 7m model tcst 0.5 Estimated from 30m model test O 25678 910
2345678 91011
Ship scale in m Ship scale in m
Distance from hull centerline (Y)
(b) Ballast condition
\..
"S -180 W.L 10W. 100 W. L.conditions, tite potential flow calculated by the Hess & Smith method and the equivalent potential flow obtained by towing the model astern are shown, both meeting at the external flow far from the hull. By way of comparison, the signs of the measured resubs for astern towing are reversed accordingly.
The wake distribution of the models and actual ship agree to some extent, with the pattern of the potential flow on the external part of the boundary layer.
C) C) o
-
10 o o O o u C) -to o 20(a) Full-load condition
20 j Ship experiment HOWL ii \Estimated from 7m model lest Estimated from 30m PH
(a) Full-load condition
's 107W. L. modeI test O 10 io 10 1 (b) Ballast condition 180 W. I.. 140W.).. 10) W. L. (b) Ballast condition
Fig. 21 Estimated Vx/Vs at typical water lines Fig. 22 Estimated ¡av and sa at typical water lines
Actual ship (300m) Ship experiment
Model 17m) Estimation from model test
Fig. 23 Comparison of flow pattern between
ship and 7m model Fig. 24 Estimated flow pattern of ship
VoL 8 No. 4 1974 33
IO 11
o
2345678910
2456
Ship scale in m Ship scale in m
Distance from hull center line (Y)
O 0.5 1.0 O 1.0 O 180 W. 1.. I4OW.L 110W. L.
In the Y direction (abscissa), the patterns are arranged in the order of the ship's size or Reynolds number. AS regards the 7 in model, the noticeable difference existing between self-propelling and towing manifests the attractive effect developed by the propeller. The propeller load under the self-propelled state corresponds to that of the actual ship under MCR propeller operation.
For convenience in instrumentation, the measurement of wake distribution was performed on the port side for the 7 m model and on the starboard side for the actual ship and 30 m large-size model. The effects of the propeller rotational direction and stock propeller are ignored for the ensuing comparative study because the existence or nonexistence of the propeller has little bearing on the difference in wake distributions.
Dr. SasajiniaC» has proposed a method for deducing the wake distribution of an actual ship from that of its
model.
According to his method, the wake distribution of a model is divided into potential wake and frictional wake
flows, and the latter corrected
in proportion to
the frictional resistance coefficient (CF). Fig. 21 shows a comparison of the actually measured values (Vx/Vs) for the actual ship and the values (Vx/Vs) estimated for the actual ship by transforming the values (VxIVs) obtained in Fig. 19 for the self-propelling 7 m model and 30 m large-size model in proportion to the ratio of (Cf(+4CF,)/(C, + JC1).
Although the bilge vortices greatly complicated the flow field, accuracy of the estimation was very high, thus proving the effectiveness of Dr. Sasajima's method.
It is quite interesting to note in the directional flow pattern shown in Fig. 20 that the difference in /9,, or Pv
between the actual ship and model is analogous to the difference in Vx/Vs. To be more precise, PH or ß in
Fig. 20 is almost identical to the quantity in Y-direction of VxIVs shown in Fig. 19.
As in the case of Vx/Vs,/9,, and /9v measured for the model and transformed in proportion to the ratio of C1 are compared in Fig. 22 with those measured for the actual ship. The results conform satisfactorily. Since it
is claimed that the velocity and direction of flow are
related to the ratio of C,., it is then possible for the vector diagram of a body plan, obtained from a model test, to be thifted along the waterline by the ratio of CF.
An estimated wake pattern of the actual ship according to the method explained above is compared with the actual measurement in Fig. 24. The followiri method was applied in drawing the estimated flow diagram. Firstly, according to Dr. Sasajima's method, wake fraction W of the actual ship was estimated, and the values recorded in the form
of contour lines on the wake distribution diagram for
the model. Secondly, estimated wake fraction W was read out at the locations of the pitot tubes used in measuring
the actual ship
(actual ship measuring points selected through comparison). The corresponding points were then plotted on the wake distribution contour diagram for the model in order to estimate the vectors of the model, at those points, from the nearby arrows by interpolation.Thirdly, the interpolated arrows are
translated to the
locations of the pitot tubes on the actual ship. The vector diagram for the actual ship can be drawn in this way.
With reference to Fig. 24 , estimation of the velocity
at the lower parts is not as good as at the upper parts,
and may attributed to the fact that the rapidly ascending
flow passing around the bilge is discarded by simply making the model and actual ship correspond along the waterlines. lt seems therefore that a comparatively high coincidence between the actual and estimated values could be achieved by shifting the main stream along, say, in the direction of the potential flow.
In the same figure, the potential flow is without required correction with respect to the effects of displacement.by the boundary layer, and will not be of any major conse-quence. In the event greater accuracy is required of the estimation, microanalysis, previously described for ad-vanced theoretical treatment of the bilge vortices, must be employed.
In the foregoing. comparisons and considerations have been concentrated oi those parts which lie ahead of the propeller, but in actuality, behavior data on the propeller plane is often required for practical design and engineering. The discussions have corroborated the correlation of the same vortices as on the propeller plane, and may be workable in the handling of vortices around the propeller.
5.
Conclusion
The flow fields ahead of the propellers of the 200,000 DWT tanker "Ryuko-Maru" and 30 m large-size model ship were measured utilizing five-hole
pitot tubes, and the
results compared with the findings obtained from the 7 m model which was subjected to tank test.
As regards the 7 m model, the boundary layer which probably effects the occurrence and development of bilge vortices and wake distribution around the propeller plane, the common measuring stations on the aforementioned ship and model were measured.
The results of the tests are summarized below.
The so-called bilge vortices seen around the propeller plane of an ordinary full-form ships with a single-screw propeller show rapid progress aft of station 2, and are
not created by an isolated layer with a low velocity drift around the bilge, at the rearmost end of the parallel part of the ship.
The bilge vortices are a three-dimension separation phenomenon in which a rapid flow passing around the bilge aft of station 2 is forced to separate from the hull by another current running in from the top thus causing the resultant cavity. The main cause serving
the growth of tile vortices is acceleration of the flow near the hull surface since tile boundary layer around the bilge becomes thinner at the rear part.
An actual ship develops bilge vortices similar to those of the model, but their distributionrange is narrower.
The bilge vortices of an actual ship are considered to be almost on the sanie level or a little above that of the model.
Dr. Sasajima's method, claiming that the wake
distri-bution line of an actual ship is nearly equal to that
obtained by reducing the wake distribution of its model by the ratio of the frictional resistance coefficient (C'1), has been corroborated experimentally.
The directional distribution of the wake pattern of an actual ship is nearly equal to the corresponding
directional flow pattern of tile model which is reduced by the amount specified under item (5) above. Namely,
the actual ship and model hold the same velocity coef-ficients and flow directions at nearly identical positions. 7. When measuring the flow fields around the actual
ship with the five-hole pitot tubes, it is recommended, from the viewpoint of measurement accuracy and labor-savings, to provide a. through hole in the hull body for piping to the -self-balancing type pressure transducer to permit digital measurement using an integrating AD
converter.
In the above summary, sorne points follow or serve as corroboration of the achievements publicized thus far. In order to elucidate the complicated bilge vortices more accurately, prudent experiments and the accumulation of more data are almost indispensable. The authors hope that the findings discussed here will stimulate theoretical re-search and contribute to the development of ideal ship forms by estimating the performance of an actual ship simply within a short time.
References
Sasajima, et al: Wake Distribution of a Full-form Ship, the Journal of the Society of Naval Architects of Japan, No. 120, Dec. 1966, pp. 1-9.
Tagori: A Pair of Vortices Generated at the Stern Bilge, Bulletin of the Society of Naval Architects of Japan, No. 450, Jan. 1967. pp. 14-15.
Tagori, et al: An Experimental Study on the Stern Bilge Vortices of a Full-hull Form Ship, the Journal
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Sasajima: Bilge Vortex of a Full-form Ship, the
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W.C. Webster & T.T. Huang: Study of the Boundary Layer on Ship Forms, Journal of Ship Research, Sept. 1970.
Hatano, et al: Computation of Friction Resistance Based on the Three-dimensional Boundary Layer Theorem, the Journal of the Society of Naval Archi-tects of Japan. No. 130, Dec. 1971, pp. 1-10. G.E. Gadd: The Approximate Calculation of Turbu-lent Boundary Layer Development on Ship Hulls. R.I.N.A., Jan. 1971.
Himeno & Tanaka: Computation of Three-Dimensio-nal Turbulent Boundary Layer Around The Hull, Journal of the Kansai Society of Naval Architects, No. 147, Mar. 1973, pp. 61-74.
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Acknowledgments
The authors would like to express their deep apprecia-tion to the personnel of Sanko Kisen K.K. who were so generous in making their newly-built 200,000 DWT tanker, "Ryuko-Maru." available for the present study. Thanks are also due to many experts and researchers, who advised and guided us and without whose assistance the present paper could hardly have been prepared, to the Shipbuilding Engineering, Technological Department of Osaka University,
Ship Research Institute of Ministry of Transport, Sasebo Heavy Industries, Ltd., SR 107 Committee, (The Shipbuild-ing Research Association of Japan) and No. i Working
Group of the Japan Towing Tank Conference, and to
Prof. Hikoji Yamada, Chubu Industrial College. and also to many individuals of the Naval Hydrodynamics Research meeting (a private meeting of the Research Institute for Applied Mechanics, Kyushu University).
