Development of HighPerformance Stator Fin byUsing Advanced Panel Method
TETSUJI HOSHINO* 1

AKIRA OSHIMA* 1

KAZUNOBU FUJITA* 1
FUMIO HAYASHI* 2

TAKAO KUROIWA* 1
ETSUO YAMAZAKI* 3

Stator fin, an energy-saving device applicable to a high-speed slender ship, is installed to the rudder behind of thepropeller for recovering the rotational energy loss of the propeller. The stator fin was designed for a car carrier andevaluation was carried out using theoretical calculations and model tests. Further, in addition to the full-scale speedtrial, the stress measurement, vibration measurement and observations of the stator fin were carried out in order toconfirm the reliability and performance and to acquire the basic data regarding the stator fin. The results showedthat the stator fin had no problem whatsoever regarding energy-saving effect, strength and vibration. The stator fin
is on the verge of being regarded as a standard device to be installed in car carriers built by MHI. Its application to
the ships equipped with higher-power main engines, such as container ships, etc. is under study.
with the axial velocity component Vx and circumferential
velocity component Vt accelerated by the propeller. Bymaking an appropriate angle of attack against W, a thrust
Ts is generated as the axial resultant component of lift L
and drag D generated by W. This Ts can reduce the propeller thrust, i.e., the power of the main engine.
In order to recover the propeller rotational energy loss,
MHI has developed and commercialized the energy-saving
devices such as the reaction fin installed at the front of thepropeller and contra-rotating propeller (CRP). The CRP
capable of recovering the rotational flow most effectively
is not in common use because of its complicated mechanism and high cost. Reaction fin and stator fin, on the otherhand, are the devices with front or rear propellers of theCRP fixed, and are therefore more convenient and less expensive than the CRP.
Since the reaction fin itself becomes a resistance, it has
so far been applied to low-speed, full ships with low velocities at stern and small resistance as compared with theenergy- saving effect. The reaction fin has not applied tohigh-speed, slender ships because high velocities cause
large resistance. In the case of stator fin, the fin itself generates thrust and hence can be expected as anenergy-saving device for high-speed, slender ships.

1. Introduction
Energy saving in ships has become all the more an important factor from the standpoint of reduction of operating
cost and CO2 emissions for preservation of global environment. So it becomes more necessary to optimize hull formand develop various energy-saving devices.
Among such energy-saving devices, Mitsubishi HeavyIndustries, Ltd. (MHI) has developed reaction fins to install at the front of the propeller for recovering therotational energy loss of the propeller, and has installed
them in low-speed, full ships such as tankers, etc., withexcellent results. MHI has further developed a stator fin
as an energy-saving device to be installed to the rudder
behind of the propeller that can be applied also to highspeed, slender ships. This paper describes the principle anddesign of stator fin as well as the full-scale validation.

2. Principle of stator fin
Among the various energy-saving devices, the energysaving hull appendage is defined as "a device installed at
the periphery of the propeller for reducing ship resistanceand improving propulsion efficiency."(1) The energy-saving
devices that recover the energy normally wasted when theship is operated can be divided into following types depending on the energy to be recovered.
(a) Device for improving the efficiency by recovering theenergy loss in the slipstream of the propeller(b) Device for improving the efficiency by reducing the propeller load(c) Device for improving the efficiency by diffusing hub vortex of the propellerThe stator fin belongs to the category of (a).
The principle of stator fin is shown in Fig. 1
1. The stator
fin operates in the resultant velocity W that is combined*1 Nagasaki Research & Development Center, Technical Headquarters*2 Shimonoseki Shipyard & Machinery Works*3 Nagasaki Shipyard & Machinery Works

Axial velocity
component Vx
Circumferential
velocity
component Vt

Propeller blade
Axial
direction

Stator fin
Lift L

Rotational
direction

Drug D
Fin
Circumferential thrust Ts
direction
Fig. 1 Principle of stator fin

Mitsubishi Heavy Industries, Ltd.
Technical Review Vol. 41 No. 6 (Dec. 2004)

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Table 1 Principal particulars ofTRANS FUTURE 3
Length(m)162.7

Width(m)25.0Depth(m)12.4

Draft(m)7.5

Dead weight(t)7 893
8 UEC 50 LSII

Main engine

Fig. 2 General arrangement of TRANS FUTURE 3

15 700 PS X 127 rpm (MR)14 130 PS X 123 rpm (NR)

Service speed (kt)

Input:
Particulars of propeller and stator fin
geometry, calculation condition

21.1

Panel division:
Propeller, propeller trailing vortex,
stator fin, fin trailing vortex

Calculation of propeller inflow velocity

Calculation of velocity potential of propeller
Fig. 3 Calculation model for propeller and stator fin
Calculation of induced velocity at stator fin

3. Design and evaluation of stator fin
A stator fin was designed for the car carrier "TRANS
FUTURE 3". Its propulsion performance and structure(strength and vibration) were studied. The particularsof TRANS FUTURE 3 are given in Table 1 and the general arrangement is shown in Fig. 22.
3.1 Design
In order to ensure a high energy-saving effect, thestator fin must have a particular that generates effective thrust. From Fig. 1. The thrust Ts generated by theentire stator fin can be expressed by:Ts ∝ ZsL = 1/2 ρ ZsW 2CLS/(1 + 1/AR)
where;
Zs: Number of stator fin blades
CL: Lift coefficient
S: Blade area (= Lc x Ls)
Lc: Average chord length
Ls: Blade width
AR: Aspect ratio ( ≒ Ls/Lc)
The lift coefficient is a function of attack angle α andhas upper limit. Further, since Ls is smaller than propeller radius, it is effective to increase either the chord
length Lc or the number of blades Zs. In practice, however, Lc and Zs are determined taking into consideration
the stern arrangement around the propeller and the easefor manufacture. Further, the velocities into the fin fluctuate periodically due to the propeller; so, it is necessarythat Zs does not coincide with the number of front propeller blades so as to reduce the vibromotive force. Since
the propeller of TRANS FUTURE 3 has 6 blades, thestator fin with 9 blades was adopted.

Calculation of inflow velocity to the stator fin

Calculation of velocity potential of stator fin

Calculation of velocity potential differenceof stator fin trailing vortex

No

Calculation of induced
velocity at propeller position

Yes
Calculation of flow velocity and pressure distribution
on the surface of propeller and stator fin

Calculation of hydrodynamic force and moment
Fig. 4 Flow chart for calculation of propeller and stator fin

Further, high-accuracy estimation of velocity W into
the fin is indispensable to the design of the fin. Hence, acalculation model was constructed to analyze propeller
with stator fin by using the advanced panel method (2).
In the model, the propeller , propeller trailing vortex,
the stator fin and fin trailing vortex are divided into
small panels as shown in Fig. 3
3, with the velocity potential on each panel regarded as an unknown quantity andsolved as the interference between propeller and stator
as shown in Fig. 4
4. This calculation method was used todetermine the final particular of the fin.
Mitsubishi Heavy Industries, Ltd.
Technical Review Vol. 41 No. 6 (Dec. 2004)

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Fig. 6 Cavitation test

Fig. 5 Stator fin arrangement for model test

3.2 Propulsion performance and cavitationperformance
The model of designed stator fin was manufactured andtank tests were carried out to confirm the performance.
First, resistance and self-propulsion tests were carriedout with and without stator fin to evaluate the propulsion performance. The test arrangement for the case withstator fin is shown in Fig. 5
5. The result showed the power
reduction effect of the stator fin to be approximately 4%.
Next, the cavitation test was conducted for the casewith stator fin in the cavitation tunnel. Fig. 6 shows thecavitation test carried out under the conditions corresponding to the maximum output of the main engine at
sea trial with minimum draft depth. No cavitation wasobserved on the stator fin, with the tip vortex cavitationof propeller confirmed to pass through the outer side of
the stator fin without touching the fin. Hence, it was
judged that there was no danger of damage caused by cavitation such as erosion, etc.
3.3 Strength
In order to study the stator fin strength, the stressacting on the root of the stator fin blade was measured at
the tank tests, and the acquired data was used to obtain
the hydrodynamic force acting on each fin and on the entire fin. Further, these measurement was carried out not
only at straight running condition in calm sea, but also atoblique running condition to simulate maneuvering condition and at the running condition in rough sea
The allowable stress σ all against the maximum operating stress was determined on the basis of the base metal
yield stress σ y, taking into consideration the safety factor. The stress σ i acting on the blade root in full-scale
was estimated on the basis of the blade stress measured
in the model test. The stress σ i is maximum at operation in rough sea, but since the stationary component σi/σall = 0.10 at operation in calm sea and the amplitude offluctuation σ i/ σ all = 0.54 in rough sea, the σ i/ σ allcomes to be max. 0.64, ensuring an allowance of approx.
1.5 times. Study was further made on the fatigue strengthof the blade root against the fluctuation stress and thestrength of the welding connection between stator fin andrudder to provide substantially high safety factor at thetime of design.

f=42.2 HzFig. 7 Analysis of stator finvibration

3.4 Vibration
In order to study the vibration-proof design of the stator fin the vibration characteristics of the stator fin werecalculated. First, the initial study was made by using
simplified taper beam model. Then, the confirmation wasmade by FEM calculation using the combined model stator fin, rudder and rudderFig. 7 shows the result of FEM calculation. The natural frequency of stator fin in water comes to be 42.2 Hz,
conforming to the standard of vibration-proof design ofreaction fin(3) (with natural frequency exceeding 3.3 NpZ;
Np: propeller rotational frequency, Z: number of propeller blades).

4. Full-scale Test
4.1 Test arrangement
The stator fin applied for the first time to an actual
ship was subjected to the measurement of items given
below by using the test arrangement shown in Fig. 8 inorder to confirm the reliability and performance and toacquire the basic stator fin data, besides being put tonormal speed trial.
State of occurrence of cavitation on the stator fin
Blade root stress of the stator fin
Natural frequency of the stator fin..
.

Strain gauge signal line

Stator fin observation windowPipeStrain gauge for fin
stress measurement
Fig. 8 Full-scale test arrangement of stator fin

Mitsubishi Heavy Industries, Ltd.
Technical Review Vol. 41 No. 6 (Dec. 2004)

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Tip vortex cavitationof propeller

0.006
KTS

Tip vortex
cavitationof stator fin(Slight and intermittent occurrence): Full-scale: ModelFinblade
No. 9Finblade
No. 80.004
0.002
00.2

0.4

0.6

0.8

1

1.2

BHP/BHPmax
Fig. 9 Thrust generated by stator fin

Fig. 10 Result of observation of full-scale cavitation

4.2 Propulsion performance
Assuming the load Fi acting on each blade of the stator
fin at 60% position of the stator fin radius, the Fi was obtained from the blade root stress σi. The load Fi on eachblade was used to calculate the stator fin thrust Ts, which
was plotted as the non-dimensional thrust coefficient KTS(= Ts/ ρ Np2Dp4, ρ : seawater density, Dp: propeller diameter) against the main engine output BHP as shown in
Fig. 9
9. The model and the full-scale data show good agreement, and the power reducing effect in full scale can be
estimated to be the same as in the model test.
4.3 Observation of cavitation
Fig. 10 shows the state of the full-scale stator fin cavitation occurrence, with the intermittent tip vortex
cavitation observed only on the blade No. 9 located closest
to the water surface, while no cavitation was observed on
the other blades. Further, the propeller tip vortex cavitation is seen to pass through the outer side of the stator fin
without touching on the fin blade tip. Taking account of
the fact that the draft in actual operation is deeper than insea trial, it can be deduced that no erosion caused by cavitation occurs on the stator fin of the ship.
4.4 Strength
Since the stationary component of the stress acting on
the blade root, measured during test running, is maximum
σi/ σall = 0.11, closer to the predicted value σi/ σall = 0.10
through model test. The result obtained through the model
test can be evaluated to have substantial accuracy.
4.5 Vibration
1 shows the results of hammering test in air andFig. 1
11in water, with the natural frequency of stator fin blade being
45.8 Hz, thus satisfying the condition of 3.3 NPZ or over.
Further, since the natural frequency when measured during sea trial was found to be 46 Hz and the blade root stress
was found to be small causing no excessive vibration, theavoidance of resonance was achieved.

Tetsuji Hoshino

Akira Oshima

Frequency (Hz)70

: In air: In water

60
50
40

3 BF

30

2 BF

20

1 BF

100
1st

2nd

3rdFig. 11 Natural frequency of stator fin

5. Conclusion
Theoretical calculations and model tests were carriedout in order to study on the stator fin, an energy-saving
device installed to the rear of the propeller, from the standpoint of structure (strength and vibration) as well as
propulsion performance. Full-scale measurements werecarried out for verification at the sea trial of the car carrier equipped for the first time with the stator fin. The
results indicated that the stator fin showed off the energysaving effect as had been expected, with no problems
whatsoever found in the strength and vibration. The stator fin is going to become a standard device to be installedin car carriers manufactured by MHI. In the future, theapplication of stator fin to the ships equipped with higherpower main engines, such as container ship, etc. will be
studied.
References(1) Terminology Explanation 5, Energy Saving Hull Appendages,
Bulletin of the Kansai Society of Nava Architects Japan, RAN
No.48 (2000)(2) Kawakita, C., Hoshino, T., Hydrodynamic Analysis of Ducted
Propeller with Stator In Steady Flow Using a Surface Panel
Method, Transactions of the West-Japan Society of Naval Architects, No.96 (1998)(3) Sakai, D., Nemoto, T., Watanabe, E., Zensho, Y., Study on
Reliability of Mitsubishi Reaction Fin, Transactions of theWest-Japan Society of Naval Architects, No.76 (1988)

Kazunobu Fujita

Takao Kuroiwa

Fumio Hayashi

Etsuo Yamazaki

Mitsubishi Heavy Industries, Ltd.
Technical Review Vol. 41 No. 6 (Dec. 2004)

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