A study on the two-dimensional diffraction problem for Lewis-form sections

toPil

Lab. y. &heepsbouwkund

A Study on the Two-dtiene1onul I)iffracticr

Ie bsche Hogeschoc!

for Lewio-form Sections#

Deift

by Naoji Toki * To obtain the wave

induced

pressure distribution and wave-exciting forea and moment upon two-dimereional bodies in the beam sea condition, it is necessary to solve the two-dimensional diffraction problem.

Tara

calculated the wave-exciting force and rnonent for two-dimenioxia]. bodies of Lewis-form section, directly froc the diffraction potential, using the theory of Grim. However, the full solution of the two-dimensional diffraction problem was not treated so far. Bessho2) treated

theoreticadly the two-dimensional boundary value problem with the freu surface,

and

proved the full solution of the diffraction problem Le derived from that

of radiation problem. Tasa1 proposed the approximìte method by which the

diffraction

pressure is calculated as the linear combination of the radiation

pressure. His method is conEJdered to be the first orde: approximation by the perturbation theory.

In this paper, the author directly deals with the diffraction problem for Lewis-form section to obtain the full solution of it: The method of

numerical calculation is based on those of Ursell s.zd Tasai, The amplitudes and phase differences of the pressure field, rolling momnt, sway and heave forces are calculated making use of this method for two Lewis-forms, excited by a given set of incider1t waves. Those values are aleo calculated according

to the

other

two-methods

: beseho's

and Thsai's lEethod.

It is a

matter of

corse that as shown

in Pable 1 the values calculated by Beseho's and

present methods agree with each other quite well.

The model experiments are also carried out at the New Seakeeping Basin of the University of Tokyo, fr the measurement of the wave-exciting forces and moment, and. the pressure fluctuation on the surface of the nodel.

Some examples of the comparisons between the experimental data and the calculated results are shown in Fig.

i

- 7.

The aíriplitudes of wave-exciting

*

NagasaJi Technical Institute, J1it;ubishi Heavy Industry, Ltd.

# Summarized from the paper (in Japanese) published in Journal

of the Society of Naval Architects of Japan, vol. 133, 1973.

forc.e and. moment aro prtusented in

_{Fig. 1}

_{- 3, and those of proure fluctuation}

in Fig. 4

_{- 7.}

_{From these figures, it}

_{can be said that the experimental data}

and the calculated results agree with each other fairly well..

Reference a

i) K. Tamura

_{The Calculation of HydrodynLimic Forces and Momenta acting}

on

the Two-dimensional Body

_{- According to the Grim's Theory}

-Transactions of the West-Japan Society of Naval Architects

No.26, 1963

2) M. Beasho

¡

On the Theory of Rolling Motion of

Ships among Waves (in Japanese)

Scientific arid iineer Report of

_{the Defence Acadery}

Vol.3, No.1, 1965

5) F. Tasai

z

Pressure fluctuation on the Ship Hull

Oscillating in Beam

Seas (in Japanese)

Transactions of the West-Japan Society of Naval Architecte

No.35, 1967

4) F. Tasai

z

_{Rydrodynamic Force and Moment produced}

y Swaying and Rolling

Oscillation of Cylinders on the Free

Surface

Reports of Research Institute for

_{ppted Mechanics}

tomenclature for the table and figures

HO i

Half

breadth-draft ratio of Lewis-form SIGMA Sectional area coefficient

Sectonal area SIGMA

8xT

B * Breadth

T Draft

¡ Coordinate parameter of the Leio-form contour

= 00 _{Keel center line} 9O ¡ Weather side L.W.L.

-90° z Lee side L.W.L.

C

Swaying

force coefficient

C Heaving force coefficient Cr ¡ Rolling moment coefficient

Swaying force

amplItude

Heaving force

amplitude

Ch

y x g x X

Rllin moment amtilitude

W Displacement of the two-dimensional body

¡ Water plane area of the two-dimensional body

Incident wave amplitude

0

z Maximum wave slope of incident wave

K ¡ Wdve number, K

z Circular frequency of incident wave s Specific density of water

¡ Acceleration of

gravity

Reflection coefficient ; ratio of reflected and incident

wave he'ht

CT S Transmission coefficient

; ratio of transmitted and

z Complex coefficient of pressure fluctuation amplitude

on the contour of Lewis-form

Pressure

fluctuation

Re ( pg71C exp(4aat) )

¡

Absolute value

of C

labte 2. Marks for figures

Experimental data

Caku1atd results

Besshos ad

pre5ent method

Tasais

method

X

T&Ue 1. HO

1.2

SIGRA =

0.9

HO

0.6

SIGYA 0.5

KL/2

0.2

1'B/2

0.6

0.2 }:'B/2 0.6 c R 0,3(O601 ( o. £c'6i1 )

0.93c62

( 0.53167 )

Q.55753

( O.445793 ) 0.945O72 ( 0.9h3 107 ) C.922i77

0.452

0.F97cE2

0.1516

T ( O.9247 )

( o..5c26 )

( O.too6

)

( o.i3 )

cl

part

1!'.

Frt

Eral part

I.

rt ECFJ rrt

h.

part

Feal 11. rt L.Y.L. 0.91585 0.702?7

LOSSO8

1.563D3 0.93159 0.7(150

L07320

1.46002 (Vc. ie) ( 0.91E67 ) ( 0.7C2°3 )

( i.05 )

( 15E1 )

( 0.9L2 )

( 0.76226 )

( i.ci6 )

( 1.Gi4)

O.772O

C.E/()0

0.566

0.7228

0.7/172 0.51376

0.5402

O.7i90

( O.7477 ) ( ) ( ) ( 0.7298 ) (

O.7428 )

( ) ( 0.55451 ) ( 0.7P95 ) O.:'123 0.2121

0.((4

0.1151 0,2b345 0.27('83 C p

V--"J

( ) ( O.2C43 )

( 0.251 )

( 0.1i7 )

( 067(9

0.)97(9 ) ( 0.23í8 (o.27aoG ) -1

o.(98

-0.C36

0.2Lc56

-0.C.46 0.C4735 -0.07746 O.17E28 -0.01961 ( 0.69710 )

(-.o.oeo )

( 024077 )

(-C.L47 )

( 0.64292 ) (-0.07753 )( 0.)7E4 ) (-0.019E2 ) 1.W.L.

0.E384

2.lC255

0.323

-O.2&7O 0.7(550

-0.2EO

0.21350

-0.23061 (1*e s5de) (

(:835q )

(-o.lc.270 )

( 0.32362 )

(-O.2'9o5 ) ( 0,7(619 ) (-0.22660 ) (

0.21369 ) (o.23oE.2 )

*

The values calculated by present

4.0

o

X X

HO

5GMA

0.5

I I t

0.2

0.3

0.4

_0.5

O.G

0.7

Fig. i

2

*

X X X

3.0

X 's. 's X X X X X X X X

2.0

1.0

(DLfl

00

ir ti

-c

xx

//

O

cx,

0

/

/

/

/

/

X X )C X )( ).X )( X

xx»c

/

/

/

/

/

(o

o

/

/

/

/

/

/

Q

Q

CT

0.5

0.4

0.3

0.2

0.1

X X X

(HO

0.6

SIGMA

0.5

X X X X

\

\

X

x\

Fig.3

N N

N

X X X

0.2

0.3

0.4

0.5

0.6

0.7

_K8

2 X X X _X

I

ri.

A

0.5b

t-1.

-60°

-O°

_30°

_60°

90°

Fig.4

HO

_O.6

SiGMA

0.5

0.15

(j X

Fig.5

X

-00°

-6O

_-30°

_{0° 30° 60°}

_90°

HO

1.2

SiGMA

0.9

KB

_0.6

2

cp

1.0-(Ho

1.2

\ SIGMA

0.9

t,.

U'

2

0.6

/

t

\

\

_\

o.[

\

/

I

/

\%

/

J

/

\

_/

/

-X

H

I

-9

-O°

_{3O° 0 3C° 30°}

900 &

CPI

1.o

(Ho

O.6

SIGMA

0.5

KB.

= 0.6

2

H

I

N

0.5

J-/1

/

X

\\

/

/

N

/

X y X O I

-DC°

-GO° _33O DG SO

9Q° &

Fig.7