A power prediction method for high block coefficient ship with transom stern

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4 IJEC. 1919

ARCHEF

A Power Prediction Method

for High Block Coefficient Ships with Transom Stern

Lab.

y. Scheepsbouwkunde

Technische Hogeschool

Deift

November 1976

MITSUBISHI HEAVY INDUSTRiES, LTD.

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A Power Prediction Method for High Block Coefficient Ships

with Transom Stern

Kinya Tamura*

A dead water zone is clearly observed behind a transom of high block coefficient ship model of oil tankers and bulk carriers. Such a phenomenon is considered to occur even on a ship since it is mainly governed by the size and shape of transom. This is the

feature of transom stern of full ship forms which is different from those of high speed boats and destroyers running in high speed,

where water separates from the bottom of after end.

A method of predicting the resistance of high block coefficient ships with transom stern is proposed on the basis of the base drag concept. The model tests to evaluate their base drag were carried out in Nagasaki Experimental Tank. lt was shown that the base

drag of tanker models could be treated in a manner similar to that of three-dimensional bodies such as missiles and projectiles.

The results of power prediction which takes the base drag of transom stern into account show some amount of speed reduction from those obtained by the ordinary method. The speed reduction will become significant when the area ratio of transom to midship

section becomes larger.

IntrOduction

Recently, high block coefficient ships such as oil tankets and bulk carriers with transom stern have increased in num-ber. This comes not only from the advantage of its simple construction and ample deck area at the stern part but also from the possibility of improving its propulsive perform-ance by simplifying the flow pattern around stern.

The flow state behind the transom of a high block co-efficient ship model is completely different from that of a

high speed boat or a destroyer running in high speed.

Namely, a dead water zone is clearly observed instead of

flow separation from the bottom of after end. Such a

phenomenon is considered to occur even on a ship since the extent of dead water zone is mainly governed by size and shape of a transom. Therefore, it is necessary to exam-ine how to separate the resistance component due to the

presence of dead water behind a transom from other

components and how to convert it into full scale, in order to predict the resistance of a ship with transom stern from its model test results by use of the model-ship correlation data for ships with ordinary stern.

In making such an investigation it seems to be conve-nient to apply the base drag concept which is used in the calculation of resistance of a missile and a projectile in aerodynamics. For this purpose, it is necessary to confirm

the applicability of this concept to the case of a ship

which has free surface and to find out a method to evaluate

its base drag.

In the present paper, the author describes the results of measurements of base drag due to transom of a tanker model and the proposed method to predict the resistance of a ship with transom stern in full scale.

Base Drag

At the base of a missile or a projectile exists a pressure

drag which is termed base drag. The base drag depends largely upon the boundary layer arriving at the edge of the base, and the thicker the boundary layer is, the smaller the base drag becomes. This thickness is proportional to the frictional resistance originated along the surface of a body.

Now let us define the frictional drag coefficient CfB of the body by

Rf

_S CfB= 1 ₂

=Cf

. (1)

--pv

AB

where, V = advance speed of body

p = density of water

4B = area of the base

S = wetted surface area of body (forward of the

base)

Rfand Cf = frictional resistance of body and its

non-dimensional expression (Cf=

_Rf/+pv2S)

S. F. Hoerner gives following expressions for the base drag coefficient CDB as

a function of Cfß. These were

derived from the analysis of test results on bodies of

aeroplane, on missiles and projectiles, and on

two-dimen-sional bodies such as wing sections.

Base drag of three-dimensional body

DB 0.029 CDB= _i ₌

--pr2AB

,/CfB

Base drag of two-dimensional body Base drag due to blunt trailing edges

CDB = 0.135

Base drag at sheet metal joints 0.10

CDB

= /CfB

(4)

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MTB 115 November 1976

Fig. i shows base drags of these equations. Each CDB seems

to reach a constant value as CfB increases.

According to Hoerner, rounding or tapering the blunt end of a fuselage body effects the base drag only as far as a round edge is able to "pull" the flow somewhat into the space behind the base. However, in bodies with CJ'B in the order of 0.5 and higher, the effect of rounding the cut off end is expected to be hardly noticeable. For larger taper angles, or in cases where drag and boundary layer thickness

of the fore body are much larger, rather the maximum

cross sectional area of the body must be considered as "base". The base drag is then determined for the corres-ponding CfB values. These statements of Hoerner may give useful information in the application of transom stern for high block coefficient ships.

Now let us evaluate the base drag of transom stern of a 200,000 tonner for both model and ship by use of above equations or Fig. 1. In this calculation it is simply assumed

that only a half of the wetted surface area of the hull

affects the base drag of the transom, as it is situated in the upper part of the hull and only a part of flow which passes along the surface of hull contributes to its base drag. In CfB

not only the frictional resistance of equivalent flat plate

but also the form resistance is included. Table i shows thus obtained C.,-B values for both model and ship and the three

kinds of base drag derived from Eqs. (2), (3) and (4)

respectively for eachCfB.

It is evident that CfB given in Table i are considerably larger and thus CDB gives almost the same value for both model and ship.

Namely, it may be said;

in the case of three-dimensional body,

CDBS, CDBM 0.03

in the case of two-dimensional body

CDES, CDBM 0.1

0-e

Bose drag of three-dunrens,ono body

0.02e

Cou__

06

Base drag due to blunt trailing edges

0135

Cs-Bose drag at sheet metal joints

0.4 ₀₁₀ 0.2 (2) _ii__ (3) °° C?BRt/íLp2

Fig. i Base drag of bodies

Table I Investigation on the scale effect of base drag for a tanker with transom stern

200,000DWTtanker,Full load, 16 knots Sh p log ItLJVL/vl = 9.340 (15Cl Cfs = 0.001 235 (Hughesl K = 0.415

CfB =fsl1+K)Cf,B

= 1.33 CDB= 0.025 (2) 0.123 (3) 0.091 (4) Mode) log10 (VL;VL/v) = 6.889 (15°C) 'fm = 0.002795 (Hughes) K = 0.415 CfB

Cf1)1+K)

, = 2.57 CDB = 0.018 (2) 0.099 (31 0.073 (4)

where suffix S shows a value for ship and suffix j'Í for

model.

3. Measurement of Base Drag of Transom Stern on Models The base drag is defined in aerodynamics as the resist-ance increment due to the presence of dead water zone caused by cutting off the body from the resistance of the body streamlined to its after end. The base drag of transom stern of a ship model can be obtained in the same manner.

Thus, the resistance tests of two kinds of 200,000 DWT tanker models with different block coefficient were con-ducted in Nagasaki Experimental Tank for both cases with

and without the smoothly extended stern, in order to

obtain the base drag of transom stern. Table 2 shows the principal particulars of M.2022 and M.2039 and Figs. 2 and

3 show the stern profiles and the water lines of both

models. Symbol A means a hull form with smoothly ex-tended water line at the stern and symbol B means a hull form with transom stern which is derived by cutting off A at the stern. The tests were made on two different drafts to examine the effect of depth of transom stern. Table 3 shows test conditions of both models. Fig. 4 shows a photo-graph of the stern of M.2022-A which has a smoothly ex-tended water line. The total resistance measured is given in

Mode) M.2022-A M.2022-B M.2039-A M.2039B Stern form Extended Transom Extended Transom

Lpp 7.000m 67125m B 1120.00mm 1101.04mm d 426.55 mm 424.86 mm 2 8049kg 2 8035kg 2 7730kg 2 1322kg Cb 0.8529 0.8525 0.8678 0.8676 Cm 0.9946 0.9973 I.pp/B 6.358 5.993 Bld 2.581 2.636

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Deep Load Water L.ne

-V-n BLI.CL AO _¼

Fig. 3 Stern profile and water line form of M.2039

Fig. 5 in the following non-dimensional form

CDM=

Rt/--PV2AM

(5)

where, AM sectional area at midship

R

= total

resistance of model corrected to the

water temperature of 15°C

The resistance increase due to transom stern is clearly observed in Fig. 5. Figs. 6 through 9 show photographs observing the free surface flow around stern of models with and without the smoothly extended water line. The base drags of both models are calculated and shown in Fig. 10. The values of thus obtained base drag seem to be in-dependent of speed and may reduce to the following values

irrespective of depth of transom, although considerably large dispersion exists.

for M.2022

_{COB °°°}

for M.2039 COB 0.04

These values of CDB correspond to the base drag in

Table 3 Test conditions of models

Fig. 4 Stern part of M.2022-A (Extended stern)

three-dimensional body as explained in the previous sec-tion. lt may be practical to consider COB 0.03 for base drag of transom stern of high block coefficient ships, since M.2039 is a little bit fuller than hull forms in common use. 4. Power Prediction Method for Ships with Transom Stern From the studies n sections 2 and 3 it may safely be said that the resistance due to the presence of dead water behind a transom stern can be regarded as base drag which is used in the calculation of the resistance of a missile and a projectile in aerodynamics, the coefficient of which is

Full Lood Water Lins De!p Load WaterLlnItI

A

Model M.2022-A M.2022-B

Condition Deep load Full load Deep load Full load LWL Im) 7.597 7.438 7.140 7.128 d (mm) 497.34 426.55 497.34 426.55 (kg) 3 315.6 2804.9 3309.2 2 803.5 Bld breadth of transom 2.214 2.581 2.214 2.581 B area of transom

-

0.364 0.251

-

_-

0.073 0.030 AM Model M2039-A M.2039-B

Condition Deep load Full load Deep load Full load

LWL linl 7.199 7.048 6.862 6.843 cJ (mm) 504.06 424.86 504.06 424.86 (kg) 3 337.1 2773.0 3332.4 2772.2 Bld breadth of transom 2.222

-2.636

-2.222 0.330 0.063 2.636 0.220 0.022 area of transom AM - - /2 .1/4 s.l. l.CL A

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MTB 115 November 1976 0.14 alo 0.12 Q 0.11 010 O. I 4 013 a 012 (J OElI 0.1 0 c R/LFtJ.A A Extended Stern B Transom stern Ac'Sectional oreo at mldshp

Deep Load

010 0.12 0.14 016 0.18 020

Fig. 5 Total resistance coefficient, CDMof M.2022 &

M .2039

M.2022-A (Extended stern)

M.2022-B (Transom stern)

Fig. 6 Free surface flow around stern (Deep load, 16 knots)

independent of speed and is

applicable to ship without

correction for its scale effect.

According to this concept the total resistance of a model with transom stern is separated into wave and viscous

resistance components in the usual manner after the base drag is subtracted. Namely; ABm Sm Ctm - CDB = Cw + Cf m (1 +K) Vm 2/ (6)

M.20 22-B (Transom stern)

Fig. 7 Free surface flow around stern (Full load, 16 knots)

Fig. 8 Free surface flow around stern (Deep load, 16 knots)

The total resistance of a ship is composed by the resistance components in the similar way.

AB2

CtS=CDB'

o/

+Cw+Cfs(1+K)+Cf

(6)

base drag concept and K1 denotes that with base drag

con-cept.

There is another problem for ships with transom stern what model-ship correlation factors are to be chosen for its power prediction. The analysis of some speed trial data of ships with transom stern will be necessary for this pur-pose. However, it is natural to consider that the correlation factors may scarcely be affected by the adoption of tran-som stern, since there are only a few changes in hull form

and n the arrangement of propeller between ships with and without transom stern. The dispersion of correlation factors may also make it hard to distinguish the difference between them, if there are any. Thus the same correlation

o Deep Load factors as for a ship with ordinary stern should be used. Foil Load _{Figs. 11 and 12 show SHP curves of M.2022 and M.2039} M.2039 _csa D

/-?)

e

respectively ¡n which predicted results with and without

° _{the base drag concept are compared. According to these} -csBoo4 _{figures the attainable service speed of ships decreases by}

S

0.10-0.15 knot in deep load condition and 0.05-0.07

Fig. 9 Free surface flow around stern (Full load, 16 knots)

knot in full load condition. lt

is clear that the larger the

.

area of transom is, the larger the speed reduction becomes.

.

5. Concluding Remarks

The author proposed a prediction method of resistance

018 020

for a high block coefficient ship with transom stern, which is based on the base drag concept. The measurements of Fig. 10 Base drag coefficient, CDB of M.2022 & M.2039

where, C = total resistance coefficient (=Rt/__pv2VY3)

wave resistance coefficient

(=Rw/.pv2V2/3)

K = form factor

V = displacement volume

LC1 = model-ship correlation factor for resistance (or roughness allowance)

The same values of C, K and 6'DB are used for both model

and ship.

Although it is desirable to obtain CDB for each ship by model tests in the same manner as stated in the previous section, CDB° 0.03 may be used as a practical approxima-tion. The form factor K decreases by taking the base drag into consideration, Table 4 shows the comparison of form factors, where K0 denotes the form factor obtained without

Note: K0 : Base drag is disregarded. K1 : Base drag is considered.

40.000

30.000

2 0.000

10.000

io

Bose drag (COB' 0.03) IS consIdered

Base drag s disregarded.

4

Vs f4 n)

Table 4 Comparison of form factors

16

Fig. 11 Power prediction of M.20 22-B

M.No. Condition A B K5 K1 K0 KI/KII Deep load 0.420 0.419 0.449 0.933 M.2022 Ful) load 0.413 0.402 0.414 0.971 Deep load 0.501 0.498 0.533 0.935 M.2039 Full load 0.478 0.462 0.474 0.975 M. 2022 008

.

o COB 003

.

004 o

.

s e o o o 010 012 0.14 0,16 008 o 004 o

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MTB 115 November 1976 6 40.000 30,000

o-I

(J, 20.000 0.000

- Bose drag lCoe'004)is corrsidered

Bose drag is disregarded.

Fig. 1 2 Power prediction of M.2039-B

base drag of transom stern were conducted on two kinds

References

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Hoerner S. F., Fluid Dynamic Drag (19581. som Stern (in Japanese), Technical Review of Mitsubishi Heavy (2) Tamura K., A Power Prediction Method for Ships with Tran- Industries, Ltd., Vol.12, No.5 (1935).

of 200,000 DWT tanker models.

lt was shown that the

base drag coefficient of tanker models was nearly the same as that of three-dimensional body like a missile or a pro-jectile.

The results of power prediction by the proposed method

for these models show about 0.1 knot speed reduction

from that by the ordinary method, although the models in the present report have rather smaller transoms. The area of the transoms is within several percents of the midship section area even in deep load condition. Therefore, one should not overlook the effect of base drag on speed reduc-tion, as it will become significant in such a case that the transom has larger area ratio to midship section area than,

say, 10 percents.

The method proposed here is also applicable to the prediction of resistance of container ships, ferry boats and cargo ships with transom stern, provided the flow state

behind transom is similar to the present case.

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