ORIGINAL ARTICLE

Fundamental research on resistance reduction of surfacecombatants due to stern flaps

Atsuo Maki1 • Jun Arai1 • Tatsuhiro Tsutsumoto1 • Keisuke Suzuki1 •

Yoshiki Miyauchi1

Received: 20 April 2015 / Accepted: 20 November 2015 / Published online: 23 February 2016

� JASNAOE 2016

Abstract It is well known that a decrease in ship resis-

tance may be achieved due to the installation of a stern flap.

Therefore, so far, a considerable amount of research on

stern flaps has been conducted. Previous research has

demonstrated that the primary mechanism by which a stern

appendage reduces resistance is a change in the pressure

distribution over the aft body of the hull, and secondly

through effects on the running attitude, near and far field

wave generation, and local transom flow among other

phenomena. However, the change in pressure distribution

is influenced by the other components. Hence, there is still

room for argument about the relative contribution of each

component to the pressure distribution. Therefore, as the

first step of the research, by conducting the model exper-

iment in towing tank and CFD (Computational Fluid

Dynamics) analysis, we examined the effect of running

attitudes and wave making at the after portion of the hull

on resistance reduction. As a result, it is concluded that a

flap affects a change in the wave generated at the transom

part and it could lead to a decrease in wave-making

resistance.

Keywords Stern flaps � Resistance reduction � Destroyer �CFD

List of symbols

Fn Froude number (¼ u=ffiffiffiffiffiffiffiffiffiffiffi

gLWLp

)

g Gravitational acceleration [=9.8 (m/s2)]

LWL Waterline length (m)

Cr Residual resistance coefficient

Cw Wave-making resistance coefficient

Rr Residual resistance coefficient (N)

U Forward speed (m/s)

r Volume (m3)q Water density (kg/m3)

1 Introduction

Stern flaps have been utilized for many recent naval surface

combatants to provide increased maximum speed and to

improve the fuel efficiency [e.g., 1]. Stern flaps are rela-

tively small appendages attached to the ship’s transom.

They have now been installed on new construction vessels

or as a retrofit on over 170 US Navy and US Coast Guard

ships [e.g., 2]. In particular, the US Navy has retrofitted all

28 ships of the USS Arleigh Burke (DDG 51) Flight I/II

class guided missile destroyer hulls with a stern flap [3]. In

the JMSDF (Japan Maritime Self Defense Force), JDS

Akizuki (DD 115) class destroyers are also equipped with a

stern flap. Cave et al. [4] showed that based on powering

model tests of the guided missile frigate USS Oliver

Hazard Perry (FFG 7), a stern flap decreased the delivered

power by 8.4 % at 26 knots, meaning that a decrease in

annual fuel consumption of 3.8 percent can be achieved.

Moreover, they emphasize that the flap will produce a

larger decrease in delivered power at full scale than shown

by the model experiments. Cusanelli et al. [5] estimated,

using the pre- and post–pre trials delivered power data, that

the annual time-averaged delivered power reduction for the

stern flap of 11.7 % can be achieved for the USS Spruance

& Atsuo Makiatsuo_maki@yahoo.co.jp

1 Naval Systems Research Center, Acquisition, Technology

and Logistics Agency, Ministry of Defence, 2-2-1

Nakameguro, Meguro, Tokyo 153-8630, Japan

123

J Mar Sci Technol (2016) 21:344–358

DOI 10.1007/s00773-015-0356-8

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(DD 963) class destroyers. The US navy has been making a

great effort to investigate the scaling effects between the

stern flap performance at real size and at model scale [6].

Moreover, it is noteworthy that stern flaps show beneficial

effects at Froude numbers of 0.8 or more for a patrol boat

with twin shaft and fixed-pitch propellers [7, 8]. Although

the present installed stern flaps are fixed, Cusanelli has

demonstrated test results for active stern flaps which aim to

improve not only the powering performance but also sea-

keeping performance [9]. Moreover, there exists an opti-

mization tool for stern flap design [10].

Cusanelli et al. [e.g., 1] explained that the primary

mechanism by which a stern appendage works is the

change in pressure distribution over the after body of the

hull, and secondly by affecting the running attitudes, near

and far field wave change, local transom flow and so on. As

experimentally shown in this paper, we also considered that

a flap improves the hull pressure distribution over the after

part, and that it is considered to be a primary mechanism of

resistance reduction. On the other hand, this change in

pressure distribution has an influence on the other sec-

ondary components. Hence there is still room for argument

about the contribution ratio of each component to change in

pressure distribution.

This study aims to clarify the point stated above through

fundamental tank testing. Although the change in running

attitude due to stern flaps can be easily observed in tank

tests, sufficient experimental data describing its effect have

not been reported. Therefore, first of all, we examine this

effect in detail through the tank tests. On the other hand,

visible large changes in the stern wave profile can be also

observed in the tank test. To investigate the effect of the

changes in the wave pattern, wave measurement tests and

pressure measurement tests are conducted for not only

several stern shapes but also stern geometries. Moreover, to

clarify the more detailed mechanism of the resistance

reduction, CFD (Computational Fluid Dynamics) is

applied.

2 Change in running attitudes

As stated in the Sect. 1, so far, it has been considered that a

primary mechanism of resistance reduction is an improve-

ment on the pressure distribution over the after part of the

hull [e.g., 1, 5]. On the other hand, it could be expected to

accumulate the knowledge for stern flap design by reviewing

the resistance reduction from several aspects other than an

improvement on the hull pressure distribution. Therefore, we

started the investigation into the resistance reduction

mechanism through fundamental model testing.

As shown in the following results, changes in trim angle

are clearly observed in resistance testing. Generally

speaking, changes in trim due to transom flaps for high-

speed planing craft affect the powering performance.

Hence, for such a ship and a craft, stern appendages are

effectively used for the purpose of changing the running

attitude [e.g., 11]. On the other hand, maximum Froude

numbers of destroyer-size ships are usually 0.45 or so, at

most. In this speed region, a ship experiences small chan-

ges in running attitude, and it appears that such a trim

change does not strongly affect the resistance reduction. So

far, this point has been examined in some research with the

conclusion that the resistance reduction is caused by a

mechanism other than trim angle [e.g., 12, 13]. However, it

is considered that sufficient data sets to explain this point

have not been shown. Therefore, as a first step of this

research, we tried to examine the trim effect on the

decrease in resistance through tank testing.

In this research, all the tests were conducted in the

Meguro basin of TRDI (Technical Research and Devel-

opment Institute). This tank has a length of 248 m, breadth

of 12.5 m and depth of 7 m. In this paper, according to the

purpose and contents of the test, three models having the

same DTMB 5415 hull form geometry are utilized. The

principal particulars and the body plan are shown in Fig. 1

and Table 1, respectively. The values shown in Table 1 are

those for the equivalent full-scale DTMB 5415. This hull

form is considered to be a good example of a benchmark

hull form for a naval surface combatant. This model has fin

stabilizers and bilge keels as appendages. For the tests

Fig. 1 Body plan of the used model (2.75 m model)

Table 1 Principal particulars ofDTMB 5415 (full scale)

Items Value

Length: Lpp 142.0

Breadth: B 19.06

Draught: d (m) 6.15

Volume: V (m3) 8424.4

Block coefficient: Cb 0.507

J Mar Sci Technol (2016) 21:344–358 345

123

discussed in this chapter, the model ship having the hull

form of DTMB5415 with a length of 5.779 m is utilized.

Figure 2 indicates the drawing and the picture, respec-

tively, of the model fitted with the selected stern flap, at a

10� angle relative to the centerline buttock at the stern, andwith a chord length of 1.0 % Lwl. This is a basic flap

geometry in this research, hence the authors call it flap 0.

In all the tests, test set-up is same described as follows.

The resistance is measured by load cells, and sinkage and

trim are measured using potentiometers. Two heave mea-

surement points are set at the forward and after end, and

these two values are converted to sinkage and trim. In the

wave measurement tests, a servo mechanism wave probe

was utilized.

At first, to confirm the performance of flap 0 designed

by the authors, model tests were conducted for model

conditions with and without flap 0. The obtained results are

shown in Fig. 3. In this paper, the definitions of the resis-

tance coefficients are defined by Eqs. 1 and 2:

Ct ¼ Rt=0:5qU2r2=3 ð1ÞCt ¼ Cr þ Cf ð2Þ

Cf is estimated by Schoenherr’s formula. The wave-

making resistance Cw, based on wave analysis, appearing

in this paper, is also non-dimensionalized by 0:5qU2r2=3.Sinkage is positive downward and trim is positive bow-up.

In this test, the range of Froude numbers from

Fn = 0.3–0.45 corresponds to Reynolds Numbers about

1.0 9 107–1.5 9 107. In Fig. 3, a ratio is also presented

which is calculated as the resistance reduction value divi-

ded by the resistance value for the baseline hull. In the

legend of each graph, w/o flap indicates the model condi-

tion without a stern flap, whereas w f indicates that with the

21 20 21 20

170

57.8

10

Fig. 2 The drawing and picture of the model fitted with flap 0. In this picture, white part is flap 0. Here, the vertical struts are the support guideof the flap for model testing

Fn

w/o flap

w/o flap

w f0

w f0

Fn

w/o flap

w f0

Cr

EHP

0

0.01

0.02

0.03

0.04

0.05

0.1 0.2 0.3 0.4 0.5

Cr

-0.5

0

0.5

1

1.5

2

0.1 0.2 0.3 0.4 0.5

Trim

( deg

.)

Fn

0

0.001

0.002

0.003

0.004

0.005

0.1 0.2 0.3 0.4 0.5

Sink

age /

L

-4

0

4

8

12

0.25 0.3 0.35 0.4 0.45 0.5Fn

Cha

nge i

n C

r and

EH

P (%

)

Fig. 3 Comparisons of the obtained residual resistance coefficient, the running attitude between with and without flap 0, and effect of stern flapon effective force power and residual resistance coefficient

346 J Mar Sci Technol (2016) 21:344–358

123

flap. The number behind w f is the utilized flap number.

This figure shows that flap 0 decreases the residual resis-

tance Cr and the effective horse power EHP at speeds more

than Froude number of about 0.3. The hump of the

decrease in Cr is located at a Froude number of about 0.35,

where EHP was reduced by about 6 % due to the flap in-

stallation. From these figures, it is confirmed that the

design direction of the base form flap, that is flap 0, is

appropriate. Moreover, in this figure, the running trim

shows visible change, whereas not so large change in

sinkage is observed. To analyze the trim effects on the

resistance reduction in depth, resistance tests for the w/o

condition model with the running attitudes of the w f0

condition, that is the trim and sinkage for the w f0 condi-

tion, were conducted. The test speeds are Froude numbers

of 0.35 and 0.45.

The obtained results are shown in Fig. 4 and Table 2.

Here, w/o R.A. indicates the condition that the running

attitudes are almost adjusted to w f0. As can be seen in

these figure and table, the running attitudes of w f0 and w/

o R.A. are well coincided, but the total resistance is only

slightly changed. The effect of running attitude on

resistance reduction is 19.94 % in Fn of 0.35 and

8.941 % in Fn of 0.45. From this fact, we can notice that

the change in running attitude improves the resistance

performance, but only accounts for at most 20 % of the

total reduction due to a flap in this test condition. This

result supports the opinion that the resistance reduction is

caused by a mechanism other than trim angle [e.g., 12,

13] with rigorous experimental data.

Secondly, the authors conducted a wave analysis.

Cusanelli also conducted a wave analysis using longitudi-

nal cuts to discuss changes in wave-making resistance [e.g.,

1]. Here, we utilized transverse cuts with a longitudinal

position of about 0.75 LWL (4.334 m) aft from the model’s

aft end. The measurements were conducted for Froude

numbers of 0.3, 0.35, 0.4 and 0.45. Figure 5 shows the

comparison of wave profiles between the w/o, w f0 and w/o

R.A. conditions. In this figure, the abscissa, Y, indicates the

transverse position from the centerline of the ship, whereas

the ordinate represents the wave height (mm). From this

figure, a noticeable change in the wave profile can be

observed over a portion relatively close to the ship cen-

terline, and the change in running attitude is observed to

not strongly affect the wave profile. It is also noticed that

the discrepancy between w/o flap and w f condition

becomes smaller with more distance from the center. This

tendency can be also found in the test data conducted for

other Froude numbers.

To investigate the contribution of the change in wave-

making resistance to resistance reduction, wave analysis

based on Thin-ship theory [e.g., 14] was conducted as

shown in Fig. 6. This figure shows a comparison of the

change in the residual and the wave-making resistance

coefficients for each condition. As can be seen, the ten-

dency of the theoretically calculated wave-making resis-

tance agrees well with that of the residual resistance

coefficient obtained from resistance tests. This fact implies

that the change in the wave-making resistance strongly

influences the total resistance reduction.

0.01

0.02

0.03

0.04

0.3 0.35 0.4 0.45 0.5

Cr

Fn

w/o flap

w f0

w/o R.A.

Fig. 4 Comparison of residual resistance coefficient between w/o, wf0 and w/o R.A. conditions, as a function of Froude number Fn

Table 2 Comparison of the test results

w/o w f0 w/o R.A.

Fn = 0.35

R (N) 87.28 83.54 86.57

h (�) -0.07067 20.1568 20.1570fG (mm) 17.00 16.40 16.41

Fn = 0.45

R (N) 220.0 213.5 219.4

h (�) 0.8836 0.6941 0.6925fG (mm) 28.25 27.68 27.59

Bolditalic values are nearly values each other

-30

-20

-10

0

10

20

30

40

50

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Hw

(mm

)

Y (m)

w/o flapw f0w/o R.A.

Fig. 5 Comparison of wave profiles between w/o, w f0 and w/o R.A.conditions with Froude number of 0.35

J Mar Sci Technol (2016) 21:344–358 347

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3 Experimental efforts from the viewpointof change in wave pattern

In the preceding chapter, it was confirmed that the wave

pattern after the hull is influenced by a stern flap. Subse-

quent to the above-mentioned work, the authors continued

the investigation from the same viewpoint as this chapter.

In the first section of this chapter, the effect of flap shape

variation on the wave-making resistance is investigated.

Therefore, stern flaps having different configurations are

tested. In the second section, the effect of stern configu-

ration on the wave-making resistance is examined. Here,

the similarity of stern flap effects to stern extensions is

examined through resistance tests and pressure measure-

ment tests using a model with a cruiser stern.

3.1 Effect of flap shape variation

At first, six stern flaps having different geometries were

examined in a resistance test. The hull form of the used

model is the same as that in chapter 2, but the model has a

length of 2.75 m. This model has fin stabilizers and bilge

keels as well as two shafts and their brackets as appen-

dages. In designing these stern flaps, the authors focused on

the flow around the transom end. For ships with a transom

stern and stern flap operating at high speed, the flow

smoothly detaches at the transom and an end hollow is

formed right behind the transom. A picture describing this

transom flow is shown in Fig. 7. Sakao et al. [15] described

this local flow as a hollow bounded by the flow detached

along the ship side part and along the ship bottom, with

water rising to a point where the two flows meet behind the

transom. During tank tests, the change in the flow behind

the transom due to stern flaps was clearly observed. This

flow change could influence the resistance reduction or

improvements in the afterbody pressure distribution.

Therefore, the authors sought to investigate the relationship

between resistance reduction and the change in generated

waves behind the transom by testing stern flaps with dif-

ferent shapes. The drawing of flaps 1–5 is shown in Fig. 8,

and their particulars are summarized in Table 3. In this

table, percentage means the length of the chord against the

ship length LWL. Further, the bottom area angle means the

value relative to the buttock at the stern, and the angle

concerning wall side area represents the value relative to

the ship side at the stern. In this test, the range of Froude

numbers from Fn = 0.3–0.45 corresponds to about Rey-

nolds numbers from 3.0 9 106–5.0 9 106.

Flap 1 and flap 2 are the flaps which extended to the side

upper part, and particularly flap 1 has an angle of attack

relative to the ship side. Flap 3 has only a side part, and is

intended to change the flow detached along the side. Flap 4

has only a center part. Flap 5 has the extended side part

similar to flap 2, but the chord length of the side part is

different. In these flaps, flap 1, flap 2, flap 3 and flap 5 aim

to deform the flap detached along the ship side.

Figure 9 shows a comparison of change in resistance

coefficients between flaps 1–5 at a Froude number of 0.45.

In this figure, concerning with resistance coefficients,

wave-making resistance obtained from wave analysis [e.g.,

14] is also plotted. Here, we utilized transverse cuts at a

longitudinal position of about 1.5 LWL (4.133 m) aft from

the ship aft end.

Here, as can be seen in Fig. 9, the correlation between

Cr and Cw in this chapter is relatively worse than the results

shown in the last chapter. In the last chapter, we utilized a

larger size model having a length of 5.779 m, whereas the

model size in this chapter is 2.75 m. The model scale could

affect the measurement accuracy of Cr and Cw. From the

wave analysis results, however, a tendency can be observed

that the flaps for which a large decrease in resistance

coefficient Cr is achieved also show a large reduction in

-0.0005

0.0000

0.0005

0.0010

0.0015

0.0020

0.0025

w f0(Fn=0.35)

w/o R.A.(Fn=0.35)

w f0(Fn=0.45)

w/o R.A.(Fn=0.45)

Cha

nge

in C

r and

Cw

Change in CrChange in Cw

Fig. 6 Comparison of change in the residual and the wave-makingresistance coefficients between w/o, w f0 and w/o R.A. conditions, as a

function of Froude number FnFig. 7 The picture describing change in the transom flow due to sternflap. Left picture indicates the transom flow for the model without

flaps whereas right picture does that for the model with flap 0

348 J Mar Sci Technol (2016) 21:344–358

123

wave-making resistance Cw. This implies a significant

correlation between the change in Cr and Cw due to the

stern flaps.

From Fig. 9, all flaps except flap 3 largely decrease

residual resistance Cr. Here, the flaps are categorized into

three groups by their tendency to produce a resistance

reduction. The first group consists of flap 0, flap 1 and flap

2. The second group consists of flap 4 and flap 5. The third

group includes only flap 3. Concerning the first group,

there is not a large difference between flap 1 and flap 2 in

residual resistance. From this fact, it can be inferred that

attack angle relative to the ship side does not strongly

affect the flow behind the stern, and that the resistance

reduction is not sufficiently achieved in this test condition.

However, wetness of the side part is not as large for this

case. Therefore, it could be concerning with small change.

Furthermore, the amount of reduction seems to be almost

the same as that for flap 0, so the decrease in the wave-

making resistance is established by changing the flow

detached along the ship bottom. Each flap in the second

group has a large bottom area compared with the other

Fig. 8 The drawing of the stern flaps 1–5

Table 3 Particulars of the flaps 1–5

Bottom area Wall side area

Center Side

Flap 0 1 % (10�) 1 % (10�) –Flap 1 1 % (10�) 1 % (10�) 1 % (10�)Flap 2 1 % (10�) 1 % (10�) 1 % (0�)Flap 3 – 1 % (10�) 2 % (10�)Flap 4 2 % (10�) – –Flap 5 1 % (10�) 2 % (10�) 2 % (0�)

Here, percentage means the length of the chord against the ship length

LWL. Further, the angle concerning bottom area means the value

relative to the buttock at the stern, and the angle concerning wall side

area represents the value relative to the ship side at the stern

0.000

0.001

0.002

0.003

0.004

0.005

0.006

w f0 w f1 w f2 w f3 w f4 w f5

Cha

nge

in C

r and

Cw

Change in Cr

Change in Cw

Fig. 9 Comparison of change in the residual and the wave-makingresistance coefficients between w f0, w f1 and w f2 conditions with

Froude number of 0.45

J Mar Sci Technol (2016) 21:344–358 349

123

groups, and it is considered that the resistance reduction for

this group could be achieved by the large bottom area.

Finally, the resistance reduction of the third group, that is

flap 3, is relatively limited in the high-speed region. It is

summarized from the above arguments that the decrease in

wave-making resistance Cw due to flaps could be achieved

by changing the flow detached along the ship bottom in this

condition.

Based on the above facts, the further tank tests were

conducted. The newly designed stern flaps here from the

viewpoint of changing the flow detached along the ship

bottom are shown in Fig. 10 and Table 4. Flap 6 and flap 7

have 10� angles relative to the centerline buttock at thestern, and a chord length of 1.0 % Lwl. Flap 6 and flap 7

have a span of seventy five percent and fifty percent of flap

0, respectively. Flap 8 has the same span as flap 0, but this

flap is at an 8� angle relative to the centerline buttock at thestern and at 12� relative to both side ends. The anglecontinuously changes in the span direction. Flap 9 has a 0�angle relative to the buttock at the stern, and this flap was a

chord length of 1.0 % Lwl, so it can be regarded as an

extension of the stern.

The hull form geometry is the same as that in the above-

mentioned tests, but the model has a length of 3.5 m. In this

test, the range of the Froude numbers from Fn = 0.3–0.45

corresponds to about Reynolds numbers between

5.0 9 106–7.0 9 106. Figure 11 denotes the comparison of

the resistance coefficients between flaps 6–9 at a Froude

number of 0.45. In this figure, wave-making resistance

obtained from wave analysis [e.g., 14] is also plotted. For

calculation of wave-making resistance, transverse cuts at a

longitudinal position of about 1.5 LWL (5.250 m) aft from

the ship aft end were used.

From this figure, in the same way as the above results, a

significant correlation between the change in Cr and Cw due

to flaps is observed. Comparing the results of flap 0, 6

Fig. 10 The drawing of the stern flaps 6–9

Table 4 Particulars of the flaps 6–9

Angle Span (%)

Center Side

Flap 0 10� 10� 100Flap 6 10� 10� 75Flap 7 10� 10� 50Flap 8 8� 12� 100Flap 9 0� 0� 100

350 J Mar Sci Technol (2016) 21:344–358

123

(75 % span of flap 0) and 7 (50 % span of flap 0), it is

noticed that the flap span strongly affects the resistance

reduction in these test conditions, so it is considered that

the wider span flap is more effective. Concerning with flap

8, which has the continuously changing angle relative to

the buttock, a larger decrease in resistance than the original

flap is achieved. This implies that a small adjustment of the

flap angle to span direction could lead to better perfor-

mance, and that such a design challenge should be explored

in future work. Concerning flap 9, it can be seen that the

flap at 0� shows a decrease in resistance. In the literature [5,10], the effect for flaps at 0� is mentioned, and the resultsobtained in this study correspond with the results shown in

this literature. As described above, the flap at 0� is regardedas a kind of transom extension, so this result implies that

there exists a relationship between the flap installation and

transom extension from the viewpoint of wave making at

the transom.

3.2 Research from the viewpoint of the transom

geometry

Next, the authors tried to investigate the decrease in

resistance from the viewpoint of stern geometry. Although

recent combatants usually have a transom stern which is

characterized by a near vertical ending, lower speed com-

mercial vessels and past combatants sometimes have a

cruiser stern. As shown in the literature [e.g., 16], a cruiser

stern shows better performance in the lower speed region.

On the other hand, it is usually considered that in the higher

speed region, transom sterns tend to generate less resis-

tance. In Sect. 3.1, the authors showed that the flap at a 0�angle, which can be regarded as a transom extension, is

examined, and has the potential to decrease the resistance.

It is considered that an extension of 1 % Lwl could

improve the wave behind the stern. In this section, based on

the results shown in Sect. 3.1, the authors attempt to study

the relationship between the transom extension and

installation of flaps.

The hull form of the used model is the same as that in the

above-mentioned tests, and the model has a length of 3.5 m.

A drawing is shown in Fig. 12. Here, c1, c2 and c3 have a

transom extension length of 5 % LWL, 7.5 % LWL and 10 %

LWL, respectively. In this test, not only resistance measure-

ments but also pressure measurements are carried out. Fur-

ther, Fn is calculated for the original LWL although the ship

length changes due to the transom extension. Here, pressure

taps P1 and P2 are set to 0.62 % LWL and 2.8 % LWL from the

aft end at the centerline, respectively. The tests were con-

ducted for the conditions in which the running attitudes are

free and fixed. This is because by comparing the data for

different transom shapes with the same running attitude,

dependence of the resistance and pressure on transom

geometry can be observed. In a fixed condition, the running

attitudes of each condition are set to be those of the w/o f

condition. In the following descriptions, fix means the con-

dition in which the running attitude is fixed, whereas free

means the condition in which the running attitude is free.

At first, the resistance test data for the free condition are

shown in Fig. 13. In the following, the change in the

resistance is the value based on the resistance for w/o flap

(free). As can be seen in this figure, c1 (free) shows a larger

decrease in resistance than flap 0 until about a Froude

number of 0.45.

-0.0005

0.0000

0.0005

0.0010

0.0015

0.0020

0.0025

0.0030

w f0 w f6 w f7 w f8 w f9

Cha

nge

in C

r and

Cw

Change in Cr

Change in Cw

Fig. 11 Comparison of change in the residual and the wave-makingresistance coefficients between w f0, w f6, wf7, w f8 and w f9

conditions with Froude number of 0.45

Fig. 12 The drawing of transom extension, that is c1, c2 and c3, andflap 0

J Mar Sci Technol (2016) 21:344–358 351

123

Figure 14 shows the change in the residual resistance

and wave-making resistance at a Froude number of 0.45.

As can be seen in this figure, the change in the resistance of

w/o (fix) is very small, so it is understood that the fixed

condition tests are successfully conducted. It can be also

noticed that the change in the resistance of w f0 (fix) is

small. This implies that the running attitude could not

strongly affect the decrease in this test condition. This fact

coincides with the results obtained in chapter 2. The

residual resistance and wave-making resistance for c1, c2

and c3 conditions exhibit a larger decrease. Here, we uti-

lized transverse cuts at a longitudinal position of about

1.5 LWL (5.250 m) aft from the ship original aft end. From

the wave profiles about c1 shown in Fig. 15, wave heights

become relatively smaller due to the transom extension, so

it contributes to the decrease in wave-making resistance.

Further, it is observed that the wave profile for w f0 (fix)

and w c1 (fix) conditions show a similar tendency in this

test condition. It could be our future task to explore the

mechanism of this point.

Figure 16 shows the pressure measurement results.

Here, the pressure is non-dimentionalized by 0:5qU2. It isunderstood from this figure that the flap installation and

transom extension lead to the increase of the pressure at the

after portion of the hull. Increase in pressure implies a

decrease in flow velocity.

Figure 17 shows the variation in pressure due to flap

installation at the P1 and P2 positions, respectively. Here,

the running attitude is free for both conditions. From these

figures, pressure of the ship after part decreases along with

an increase of ship forward speed, but the pressure is

recovered due to the installation of the flap. This recovery

at the after portion of the hull results in the decrease of

resistance. About the pressure improvement, the more

detailed explanation is shown in the next chapter.

4 CFD analysis

Through the extensive model tests in this study, the effect

of wave making on decrease in resistance is clarified.

Finally, in this chapter, in order to investigate this subject

more, CFD analysis was done using STAR-

CCM ? v8.06.007. The mesh geometry applied for CFD

-9.54E-18

0.001

0.002

0.003

0.004

0.005

0.25 0.3 0.35 0.4 0.45 0.5

Cha

nge

in C

r

Fn

w f0 (free)

w c1 (free)

Fig. 13 Comparison of change in the residual resistance between wf0 and w c1 conditions, as a function of Froude number Fn

-0.001

0.000

0.001

0.002

0.003

0.004

0.005

0.006

w/o f (fix) w f0 (free) w f0 (fix) w c1 (fix) w c2 (fix) w c3 (fix)

Cha

nge

in C

r and

Cw

Change in CrChange in Cw

Fig. 14 Comparison of change in the residual and the wave-makingresistance with Froude number of 0.45

-20

-10

0

10

20

30

40

50

60

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

Hw

(mm

)

Y (m)

w/o f (fix)w f0 (fix)w c1 (fix)

Fig. 15 Comparison of wave profiles between w/o, w f0 and w c1conditions with Froude number of 0.45

-0.05

0.00

0.05

0.10

0.15

w/o(free)

w/o(fix)

w f0(free)

w f0(fix)

w c1(fix)

w c2(fix)

w c3(fix)

P'

P1

P2

Fig. 16 Comparison of the pressure with Froude number of 0.35

352 J Mar Sci Technol (2016) 21:344–358

123

analysis is shown in Fig. 18. Here, by introducing the

symmetry boundary, computation is done only for half

width. The mesh was refined around the hull and free

surface to capture the Kelvin wave as shown in Fig. 18. We

also refined the mesh around the bow and transom to track

high waves occurring in these regions. The size of the mesh

refinement region was determined for each speed so that

the maximum wave height could be captured in about 20

grid points. The hull form of the used model is the same as

that in the above-mentioned tests, and the model has a

length of 5.779 m. To reduce computational costs, a bare

hull model is used here. The computational domain is

determined based on the guideline shown by ITTC [17]:

the length from fore perpendicular to inlet boundary is set

to 1.5 LWL, that from aft perpendicular to pressure

boundary is set to 3.5 LWL, and that from ship bottom and

side of the domain is set to 1.5 LWL. To prevent the wave

reflection on the boundary, VOF wave damping model is

applied in the region within 2 meter of each boundary.

The utilized setting data are shown in Tables 5 and 6. A

linear ramping of under-relaxation factors is used for tur-

bulence model and VOF model to mitigate the instability

caused by giving a uniform flow as the initial condition.

The thickness and the number of prism layers are the same

in all cases. We confirmed that the maximum y? of the

closest grid points to the ship surface was about 70 and the

wall model is valid in this range. The simulations were run

up to 45 s. However, calculated total resistance fluctuated

after 45 s calculation due to the unsteadiness. For this

reason, we took the mean value of Ct in the last fluctuation

cycle. The amplitudes of Ct in the last cycle were less than

0.5 % in most cases, except for three cases (Fn = 0.20

with flap and 0.25 with and without flap) having about 1.5

to 2 % fluctuation.

0

0.05

0.1

0.15

0.1 0.2 0.3 0.4 0.5

Cha

nge

in P

'

Fn

P1P2

Fig. 17 Change in pressure at P1 and P2, as a function of Froudenumber Fn

Fig. 18 Mesh geometry aroundthe hull (upper X–Y view, lower

X–Z view)

J Mar Sci Technol (2016) 21:344–358 353

123

At first, the authors validate the CFD analysis with the

tank test results. Figure 19 shows the obtained total resis-

tance coefficient by EFD and CFD. Here, CFD calculations

were done in 25 �C. Therefore, resistance coefficientsobtained by CFD were corrected to 10 �C in the samemanner as Longo and Stern [18]. Calculated resistance

coefficients are still about 2.5 to 6.1 percent lower than the

EFD results. These differences are considered to be caused

by the presence or absence of appendages. A bare hull

model was used in CFD, while a hull with fin-stabilizer and

bilge keel was used in EFD. Figure 20 shows the com-

parison of change in resistance coefficient by EFD and

CFD, and the results of CFD agree well with that of EFD. It

is noteworthy that the forward speed at which the flap starts

to work is well predicted.

Figure 21 (left) shows the longitudinal distribution of

mean pressure on the hull surface. The hull was split into

strips whose width was LWL/40. Then, pressure was inte-

grated on each strip and the integrated pressure was divided

Table 5 Dominant calculation models and common parameters

Item Model or parameter Item Model or

parameter

Time marching Implicit unsteady Under-relaxation factor (VOF) 0.8

Fluid flow solver Segregated flow Under-relaxation ramping (k, e,VOF)

Initial value 0.1

Linear up to 10

iterations.

Sub iterations 5

Surface capturing VOF model Surface mesh size on ship 50 mm

Turbulent model Realizable k-e Cell size in stern region 10 mm

Wall model Hybrid model of wall function and low Re RANS. (called as

All y? wall treatment)

Total thickness of prism layer 20 mm

Under-relaxation factor

(Pressure)

0.4 Number of prism layers, and

stretching ratio

15 and 1.1

Table 6 Calculation condition and dominant parameters

Fn Dt (s) Anisotropic refinement around free surface (over all) Anisotropic refinement around free surface (bow region)

Dz (mm) Vertical range (mm) Dz (mm) Vertical range (mm)

0.20 0.025 5 -60 to 60 9 -50 to 90

0.25 0.025 7.5 -75 to 75 10 -50 to 110

0.30 0.020 9 -90 to 90 10 -50 to 130

0.35 0.020 10 -100 to 100 10 -50 to 150

0.40 0.015 10 -130 to 130 10 -50 to 200

0.02

0.03

0.04

0.05

0.06

0.2 0.25 0.3 0.35 0.4

Ct

Fn

w f0 (CFD)

w f0 (EFD)w/o f (EFD)

w/o f (CFD)

Fig. 19 Comparison of the total resistance obtained by EFD andCFD for w/o and w f0 conditions as a function of Froude number Fn

-0.001

0.000

0.001

0.002

0.2 0.25 0.3 0.35 0.4

Cha

nge

in C

t

Fn

EFD

CFD

Fig. 20 Comparison of change in the total resistance obtained byEFD and CFD for w/o and w f0 conditions as a function of Froude

number Fn

354 J Mar Sci Technol (2016) 21:344–358

123

by the surface area of each strip to obtain mean pressure.

Here, the value is gauge pressure and non-dimensionalized

by the stagnation pressure. Figure 21 (right) shows the

difference in mean pressure corresponding to Fig. 21 (left).

As can be seen in these figures, the pressure on the ship

fore part is not disturbed by the stern flap, and it is only

affected on the hull before the flap. This pressure recovery

observed in the after body can be considered as direct

mechanism of decrease in resistance.

At first, to confirm the effect of the running attitudes on

the decrease, the calculations for reverse running attitude

condition (R.R.A) are carried out. R.R.A. means w/o f

condition with the running attitude of w f0 test data or w f0

condition with the running attitude of w/o f test data. Fig-

ure 22 shows the comparison of change in total resistance

due to stern flap between normal running attitude and

reverse running attitude (R.R.A). As shown in Fig. 22, an

almost equivalent order of decrease is observed even for

the R.R.A. condition, so it is concluded again that the

running attitude is not the dominant mechanism for the

resistance reduction due to installation of the flap.

Next, the authors conduct the investigation for the stern

flow using CFD analysis. As shown above, the stern wave

is affected by a flap and it could lead to the pressure

recovery in after body. Figure 23 shows the wave height

distribution with a Froude number of 0.35. In the region

soon behind the transom, contour lines for w/o f are

denser than those for w f0, and this means that the wave

steepness is larger. Generally speaking, steeper waves

may lead to the wave breaking, so stern flaps could

contribute to decrease the wave breaking soon behind the

ship. To look in more detail, Fig. 24 shows the longitu-

dinal wave cut on the center line in the vicinity of the

transom. Wave height increases just after the stern with-

out a stern flap. This makes the wave profile steeper. On

the other hand, that increases moderately with the stern

flap. However, higher maximum height appears in the

case with the stern flap. It seems that a steeper wave

profile rather than the wave height itself makes resistance

larger. From this point of view, it is a future work to

survey the relationship between these local changes of

wave profile and wave-making resistance. As Raven et al.

[19] pointed out, change in wave pattern of the stern

wave played a big role in the scale effect. Therefore, it is

desirable to consider the change of wave profile men-

tioned above from this point of view.

Finally, the comparison of stream lines is shown in

Fig. 25. As shown in this figure, the stern flap deflects and

slightly thins stream lines in the vicinity of the stern. These

deflections and thinning seem to cause pressure recovery as

shown in Fig. 21. Furthermore, the stern flap thickens

stream lines behind and makes a contracted flow. This

contracted flow seems to make a moderate wave profile as

shown in Fig. 24. It is also a future work to survey the

relationship between these local changes of flow pattern

and wave-making resistance as mentioned before.

5 Concluding remarks

The obtained primary outcomes from this research are

summarized as follows:

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

-0.2 0 0.2 0.4 0.6 0.8 1 1.2M

ean

pres

sure

of e

ach

stip

P'

x/L

w/o f(CFD)

w f0(CFD)

-1.0

0.0

1.0

2.0

3.0

4.0

5.0

-0.2 0 0.2 0.4 0.6 0.8 1 1.2

Diff

eren

ce in

P' [

%]

x/L

Fig. 21 Left mean pressure ofeach strip with Froude number

of 0.35. Here, concerning

x direction, 0.0 denotes fore

perpendicular, whereas 1.0

denotes aft perpendicular.

Pressure was non-

dimensionalized by the

stagnation pressure. Right

difference in mean pressure of

each strip with Froude number

of 0.35

-0.001

0.000

0.001

0.002

0.20 0.25 0.30 0.35 0.40

Cha

nge

in C

t

Fn

w f0

w f0 R.R.A.

Fig. 22 Comparison of change in total resistance due to stern flapbetween normal running attitude condition and reverse running

attitude (R.R.A)

J Mar Sci Technol (2016) 21:344–358 355

123

1. The decrease in resistance due to the installation of the

flap is successfully observed.

2. The effect of the running attitudes on the decrease is

examined by tank tests and CFD analysis, and then it is

concluded that the change in running attitudes is not

the primary mechanism of the resistance reduction in

the destroyer’s speed region.

3. The wave analysis results show that there is a

significant correlation between decrease in total resis-

tance and wave-making resistance. This suggests that a

flap affects a change in the wave generated at the

transom part. Further, it is confirmed that the primary

decrease in wave-making resistance could be derived

w/o f

w f0

(1) Overall

w/o f

w f0

(2) Stern region

Wave height [m]

Fig. 23 Waveheight distribution (Fn = 0.35)

-40

-20

0

20

40

60

80

100

0 0.1 0.2 0.3 0.4 0.5

Wav

e he

ight

[mm

]

Distance from stern / ship length

w f0 (CFD)

w/o f (CFD)

Fig. 24 Longitudinal wave cut on the center line in the vicinity ofstern (Fn = 0.35)

356 J Mar Sci Technol (2016) 21:344–358

123

by a change in flow detaching from the ship bottom

due to a flap in this test condition.

4. From the viewpoint of the stern geometry, the tank

tests are examined. Then, for a particular case, similar

tendencies of the wave profile between the stern

extension and the installation of the flap are observed.

The further exploration of this point could be our

future task.

5. The pressure recovery is observed in tank tests and

CFD analysis due to a flap. It is reconfirmed by CFD

analysis that the region in which this pressure recovery

only appears to the part of the hull just before a flap.

In this research, the authors attempt to clarify the

decrease in resistance due to the installation of a flap by

conducting several tank test measurements and CFD

analysis. As introduced in the first chapter, Cusanelli et al.

[e.g., 1] explained that the primary mechanism by which a

stern appendage works is the change in pressure distribu-

tion of the after body of the hull. Through this research, it

becomes clearer that there exists a correlation between the

hull pressure improvement and change in wave making at

the transom. Therefore, our conclusions are considered to

be one of the interpretations of the improvement on pres-

sure distribution from the aspect of wave making.

Acknowledgments First and foremost, I would like to thank Dr.Kazuyuki Yamakita (Director of Naval Systems Research center,

Ministry of defense) for his support and encouragement. The authors

are also grateful to Dr. Masahiro Tamashima from Fluid Techno Co.,

Ltd. for his technical advice for pursuing the research. Sincere

appreciation due to Mr. Hisatada Itoh, Mr. Minoru Atsumi, Mr.

Noriyuki Yokoyama, Mr. Mashiko Hidetake and Naofumi Yamato at

Meguro basin, for their assistance in model testing.

References

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w f0 (CFD)

w/o f (CFD)

Fig. 25 Stream line around the ship transom (Fn = 0.35)

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Fundamental research on resistance reduction of surface combatants due to stern flapsAbstractIntroductionChange in running attitudesExperimental efforts from the viewpoint of change in wave patternEffect of flap shape variationResearch from the viewpoint of the transom geometry

CFD analysisConcluding remarksAcknowledgmentsReferences