Pressure fluctuation on the ship hull oscillating in beam seas

(1)

Beam Sea Condition (C

(C K

Pressure Fluctuation on the Ship Hull

Oscillating in Beam Seas

By Fukuzö TASAI

35 B Bi

J F1 43 2

B

eprinted prom

JOUINAL OP SEIBU ZÖSEN KAI

(THE SOCIETY OF NAVAL ARCHITECTS OF WEST JAPAN)

N0. 35 February 968

-

AUG. 1976

Lab.

heuwkunde

(2)

* JLI1Jf)?

(4210

'C)

103

Beam Sea Condition

(J±)

iE.

r

IB

:t

Pressure Fluctuation on the Ship Hull

Oscillating in Beam Seas

By Fukuzi3 TASAI

Abstract

The calculation method of the pressure fluctuation on the ship hull oscillating in the beam sea condition was given in this paper. And also, a numerical example for the ship

model. Todd 60 series C=0. 70, was shown.

We have taken into consideration the hydrostatic pressure. hydrodynamic pressure caused by heaving, swaying and rolling motion in still water, pressure in the incident

wave and hydrodynamic one due to the reflection of waves from the restrained hull.

The symmetric distribution of the pressure is mainly due to the heaving motion and

the large asymmetric distribution is caused by the rolling hydrostatic pressure.

Lastly we discussed on the wave measurements by means of the "Shipborne Wave

Recorder ".

(tf):ii,

L:EEJj

j.i:,

.l](Ñl:1L-t

l:tb:l±,

EL.<

estimate -:

t0

E0

C1J,

t:t)l

T2

midship < -llIIlL4

jlE:-

l±. strip method

Lheave

pitcb.0

midship

_J1[IÍ

<iJ)p, heaving motion

tUt:C2J0

_l.

heaving motion

6O°*Ll

P/pgh(P=

)jj, h=iJ) l, il0.5,

II

1.3j) order

o,i

iii ii)

j-t.iz

li-t: :i-Jl,

(.

Ji

t:bl:l.heave ttc <

sway, yaw roll

t

. *El:/

jijt, (

Ij

L, 2

5{*

l,

(3J, C4J.

C6J0

(3)

(0 L

(y5 z)

O - Y

±l:,-(17

Lewis form cylinder 4 =0coswt

heaving motion

IEGt.,',( (ye, Z5) i:j, <

hydrodynamic

pressure

3)

Uf

3

Q)t

PH=pgO(P"Hcosc.)t+P"dfIsinwt)

...(2.1)

r

(P5B0+PA0\

f P5A5P,B0

A+B

I.

P dH=fB\

_A+B

(2.2)

(2)

heaving motion

ij([fo){

pg0cosot '

heaving motion -l-Jfjj P11'

1H'=pg0 (1 +P"511) cosot +P"dJr,sinrot

U

P'H =P,j'/pg,,

=(1 +F"ßH) coswt +P 'd ¡1sinot

(2.4)

Lewis Form secflon

H=! 0,

(1=09404

i H0=B/2d=1.0. (I i{)=0. 9404 cl) Lewis form NJ

jsa

0=0°, 10°,

. Lewis form section contour

Fig. iQ section cylinder 7 heaving I}QP"011, F"a11 Fig. 2

Fig. 3 i:. 1+P"ff

Fig4 l:cj0 i: P"011 1i, inertia effect l 2.0 e 60° 9 70°

Fig. 5 i: I'HI

= ¶/(1+P"aH)2+PdH2 jc-4

104 k 35

¡I. *

)ÁiCÇ" 2

{$jy heaving. swaying rolling motion hydrodynamic pressure

(4)

(2.5)

p _r

as

B( p24Q2

t0

e71,

C6J

'1 + Pm f2,, (m. 6.

m1

,=.,+Q255 .f2,,5(m

, Ea)

( cQosPo

s-P'=P,/pgs5

p"2 + p,L'2 cos(o-1,)

Fig. 1 Q):1Q) Pas", Pd,"

Fig. 6,

7 i:,

I =v1

2+P»7

Fig. 8 I P,'

9=00

9 Q)-]l,

_),

_{O =90°J[H', Load water line}

Heaving motion I: ,,t 7,

'JjE)Jli,

Q)-C jj

swaying motion

f7a

i: O Q) ç = ç0cos$ rolling motion ftij ') hydrodynamic pressure

P11=pgBcoo/2 (PaR" COs4)+P,R" sinot)

¿'sii.

P,,". P," t

C6D Etji7.

Ea i

ePo+aQo\

r, ,,

Eaf &Q0',P0

al?

_P2+Q

_). dR ₂ _p2+Q,,2

(2.9) 2C-,

PR'=PR/pgBcp,/2= pa. + 'dR C0S(Wi-8R)

Fig. i

Q) cylinder P",,11.

P"dp '3i)

I Pi?'

Fig. 9, 10.

11i

ji.

rolling

ßl:<

_{ij()TÀ'íLl.}

jE-B

pg ₂ç,,ycosasl

(9. L. =y.,/B/2

G0 Q)11)Q) rolling motion Q)i'tli.

ti,iß

-C sway

0.Q)JQ) roll

Lt-l-'

ÖG,,/B/2=a0

L, a,=0.1. 0. 0.1 (Ø.i G,,

0Q)El

i) Q)FI,

PR' I

Fig. 12

Fig. 1Q)ifi-, 9>40°Q)-. G0

Q)I5 PR'

O>40°Q)(jl, a,,> O

swaying - O )Q) rolling motion Q)EE a,,<0 Q)

rolling Q)l swaying motion Q)'

Il:.

Beam Sea Conditioni: K 105

Q)Jo

1.0 11',

_ß3-'l±'J'

<

),

Ij)fy 1.0 z 9 } K

Z. Fig. i

Q), 9=60° Q)ßCl,

s(1.0 1

[PH'I--l.O ¿2)

hyciroclynamic pressure Q)

'j'

cos4 swaying motion lFIQ) hydrodynamic pressure '

P, = pgs,',, (P0,costa + P,sinot)

}

(5)

106

II.

Beam Sea Condition lT'lj

o

irij-,

o-ft10

7) =J-KC1 cos(Ki, ot) (3.1)

fflLh=4), Krr2ir/,

o

2,r/T, T

)U)l

o -

íio

-Beam Sea Condition

)jjj:

drift heaving, swaying StU rolling motion t.

f5

4)jQ)fl., heaving 'f

, swaying i, rolling IU drifting velocity v

Jy

C-10 L/.»U,

(3.1) Q)iQ)l.

, , q

t

U-c, kaìU-c,

-

heZcos (Ky

t)

0. U

Beam Sea

aj

WeW

(3.2) IZ5I'<

(3.3)

:4f)

orbital velocity t U acceleration ' tò 'tl , k Q) downward = hwe 'sin (Ky

-,w= _ho7eKZcos(Ky_wt)

i1

w= _ho.ezcos(Ky_4)

(35)

- hoeRZsin(Ky_ Ú)j) , rQ) heave, sway roll

heave, sway, roll

heave : sway

=cos(wi)

roll : 1. heave j roll < a ) heaving

P=rpg0cos(wt-_)

b ) rolling : P1

-pgç5cOst_,t1,)

2.

Ñij heave, sway roll

'bOEii

11 î)- Ut: 2

P2H = pgoCPH"cos(t

c) +PdH"sin (et - ) J

P2s pg,oCP,,"cos(et - E)+Pd.S"sin(et

-= pg oCPaR"CO5(Ct - E) + P"sin(wt - J f

3. FroucleKrilov

[fJ)

(6)

Beam Sea Condition ( f)}j 107

lEI.. < , , tU- v

ijl:ttfl(,

-i:'j

q)-clIt?çt..

4.

t I riy44j4

t:< J3jj

Q)31.

i:

ci orbitalvelocity

)4

/

2 ( sway force, roll

moment

C7J

LU, Tj

(/1.t: )t'Q)

.5

(3. 4), (3.5) Q) orbital velocity, acceleration

li.

(ye, z)

f

j0

i:.

d =

=d,r

= hwesinúi

,,= hw2e'coswt

-e,,, «) heaving motion

¿l

9, K l (2.2)

((dK:

3 Got,

d/2 y = O

ñ,o= hwe'"2 cosút

= he'2 sin,at

f($j:-, -

Q) swaying motion I UQ)JfJJl

:Q)íill:-)

,

(2.1) (2.6)

1fl

P4= pghe

(Pali" coswt+P,/' sinot)

±pgheKd12 (Pa3" S1flWtPd3" cosa)

UEQ)J-EtLC,

f)jPi

P_Plg+PIR+P211+P2s+P214+P3+P4

heave, sway, roll l:7fE» P. P7. P3

Q) P.

P=P+P,+P+P,,

(3.15) P; = ,gh [A;coswt + Bsinot$

A;= (1+Pat,")cose;P3jj"sin;.

B;(1+P,,j")sin+PJf"cosE;,

0=,/h

(3. 16) P = pghA,cosot +BsinwtJ (Pa3"COS&Pd8"Sjfl) = (P8"sin+ PdS"cos&,), o = = pgh,,A,cosot + Brsincotj

A=

(9+PQ,")cos8oPdR"sinw

(7)

108

B= (+P,,j,,")sin.+PdR"cosE,,

,,=B/2h=eßÇO/®W,

0a

Q)til, B2,2/P)

= pghAco&et +B,,,sina'tJ

A = - (eKZScosKy,, + e-KdP"0ff + eKd/2P"d,,)

B = -

e""2P"as)

: A

Am,,, Awa - (e_KZscosKy.,+edP0g") A,,0= _e_Kd/2P,,,"

iJi: B, :-t--t ,

B,,,= _eKP"ajz, B,,,,=eKd/2P,,,,"_e-KZ0sinKy

...(3. 18)

, P/pgh =p' (3.19)

u,

P',,,, ,

Pao ¿4o

(3. 16) - (3.18)

P',,o. bao. P'

i

P'.,,, = A8coswt + B,,sinwt = C.,,cos(wt

-(FIL A,,='AçC,,+Aw,,

B,,=By C,,+B,,

P'ao=Aacoscot+ B0sint = Cacos(wl

-(Efl.

A0=A,,+Aç0+A,,0

B0=B,2 ,,+Bo+Bwa

.

=Ccos(wto)

y,,>0l:U(i±,

C =v

A-iB,,+B;5

,

Y,,KO i:Lj,

C =VA_A)2+(B,,J,,)2, =-' (:I:)

IV.

úø'J

Todd 60 series C=0. 70 Beam Sea Condition

heave, sway, roll /

¿

Q±lii1U,

* '*Ijf

(-UCWlI

(8J,

l5yl:. If,,=1.0,

-0.9

:Tt, Fig. 1Q) If,,=1.0, o=0.9404 «)

Fig. 2-42

Ei±ii,,

i?5Qth

LppxBxDxd=3.00mxO.428mx0.261mx0. 171m, L/B=7.0, C1=O. 70 C=0. 71. Ca=0. 985, C,,=0. 785, W=153. 7kg

(pitch)=0.24L,,,. Bilge Keel L0

G,,M=2. 78cm, KG,,= 14. 66cm, OG,,=2. 44cm

a,,=O,,/d=0. 142

Rolling

l.6l4. heaving 1.03j?

pitching ,

(3. 16)

(8)

Beam Sea Condition i:)j, <

Hjj

109 T

£j1Q) +*J, heave

roll o k)

4)l

T0. 1. 03 1. 61 0. 649 0. 266 0/h 1.21 1.07 heave ₇₄₀ 6.5° 0. 58 0. 82 Sway I 264° 269°

ce/)

0. 35 7.5 roll 176°

Sway

/0co]Q roll

a0=0.142 :)ct-

G0 )))o roll

« (+P"oa) $3zJ

P" ° Fig. 13, 14 3l

roll i:

hydrodynamic pressure

T=1. 03ì

rolling motion I'j'4

U, heave, sway

bI:1

Ejt*10

Fig. 15 lQ)**it0

f111

e heaving %c.

9

o4==74°

Fig. 16 :)-

C0

0=0° -*'0.6.

e =90°-*&)1.5

(3Jm,

Steepness 2h1X=30

h/d=ro/ed,

-

Te,,

=1. 03w,

=0. 649 -,

0=1/207)Q)

h/d=0. 242,

:

0/d=0. 290

t 7

IfYÌJ

0. 13d, ij 0. 24d, 0. 4M f .7

QEEJJQ) ) 4

(C3 J *Ji)

0ji''i

i: roll [J1 (T=1.61) t1)-j roll, sway,

j301Jc heave Q)3-tLt:0

Fig. 17:Q

JjQ).j-jij

_{C8 l'J4 <}

, C

heave 2U sway Q)iJl'J'4 <,

JQ),

7i(OEQ)ft0

=1/50 q

o,t=176°

Î0 Fig. 18 LtO 3ZJl

\. Shipborne Wave Recorder l( \C

M. J. Tucker 0

Shipborne Wave Recorder C 9 J li, íJ < 1EJ P7

Q)ETU

rtll'1L. 42JLheaving

PT 4

fl4

u,

1HQ)

T0 1O JI

Q)r]

heave downL°f

14TkL, kQ)FQ)tlì1i)3EJ

Pr-10

P=pgT/ieTcos(Ky8_o1)} +Pj

(5.1) (5. 1) P :- < hycirodynamic pressure

T=T0+

(5.1) IA-Ll

Pr pg{T0+.0cos(otS) _heKT0(1_K)cos(Ky3_ot)} +P

1 l:Jt--( K

l

_-JEI:'i'4

Q),

i:

(9)

lo

¿i'<

*E)PtUf P=PrpgT,,

P=pg0c.os(o,t_,t)_pgheKT0cos(Ky3_ot)+P . (5.3)

.:T PD=OHtf

P/pg-0cos(stt) = _he1CTocos(Ky_wt)

. (5.4) Tucker

C 9) t,

(5.4) Ky8, KT0

'js't.

0 .5

1ilALíEiE U<

t:

(5.4)

htj%tf

P/1gh = P' = C0cos(øt ) eKTocos(Ky8 col) (5. 5)

t&ot:

tt:,

EEfl 2

EE±'1

l:-UL Kys

'j'Ftti,

(5.5) Ii (3.20)

iQ)

5 t:ì.

C8cos(col s) = C0cos(cot ) eKrocoscoi

(5.6) M-4- .5

£titLl P0= O

.5

:t0 (5.6)

j,

oCP"ajiCO5(t

c) + P"5sin(wt 8)J = e-K8 (P"dffsin + P"ajjcoscot) ...(5. 7)

),

(5.7) .5

ef:: *Y

LO 3[lt: PD= O

EEfiG') ().

li

KT,8. Ky8 'J' }ji

zt'tl

., Shipborne Wave Recorder 1±,

Q) heaving

K,

'Mljti PD

j'J' <--< i

K 9'l-t:

\I. re

Beam Sea Condition heaving, swaying .t rolling motion 7II 3jJ]E)j '

t:

-c'y4jiJ

_IJ-

kQ)kM1-Ut:0 k*lt:

heaving fj IJHEJJI±. heaving motion t:

_E)Ja1.t:,

swaying motion t:

E)jkftt, Load Water line Et:e,

1.5(,Qk

rolling I,

K , EEJYI

-kv'.

t,

,'j'

V'a hydrodynamic effect t'J' '

Shiphorne Wave Recorder t: .5 heaving

tt'J'

K

LC, heaving t:

< hydrodynamic pressure P1, tFÇl7z' tt-t'j'

it:ih7

t:<

PD= O .,t .5 heaving

t,

tt:F3 U t: Irt]Il

t:,,4-4

tg)0

(45. 10. 10)

cl)

s

fti i

*

(

2j:t:--

l21,

042G(

2)

[

'

"An Approximater Calculation of Hydrodynamic Pressure on the Midship

(10)

rl-0 -o -02 .0 3 .0 4 -o5 .0 6 Heave

500'

8 0' Fig 3

-Beam Sea Condition _{l:Wj ,< 2ÍhEEJJ} 111

3C

Vol. XIV, No.48, 1966.

C 3 J F. Ursell "On the Heving Motion of a Circular Cylinder on the Surface of a Fluid"

Q.

j. M. and A. M., Vol.

II. 1949.

C 4 J 1H 4 "On the Damping Force and Added Mass of Ships Heaving and Pitching"

JL)c1J )ji

Vol. VII, No. 26,

1959.

C 5 J

W. R. Porter

: "Pressure distribution, added mass and clamping coefficient for cylinder

oscillating in a free surface" 1960.

Cfi) W

j

"Hydrodynamic force and moment produced by swaying and rolling oscillation

of cylinders on the free surface"

Vol. IX. No.35. 1961.

C 7) W

t ) - : "The Calculation of Hydrodynamic forces and moments acting on the

Two-dimensional Body"

Ii

- No. 26, 1963.

C8J W

"Beam Sea

flJ"

No.30. 1965.

C 9) M. J. Tucker

: "A Shipborne Wave Recorder" T. I. N. A. _1956.

Heave

(11)

112 02 -04 -06 -08 -I 0

-2

Sway Sway

Fg 7

Fig S 045 09 30

(12)

Beam Sea Condition < Fig 9 s way O i5 010 0 05 O-4 06 Fig. IO 113 B Roil Ro/l

(13)

-114 020 Roll

(o=ö/8i2=0)

03 I-o 02 Roll 005 Q-004 0-03 002 001 (5o/a/2)

r

61 60 90 Fig 2 02 4 0-6 08

-

Fig. 14 Ro li

/H.IC. a.o.i I

Oo. 0142 1 00 70 - 63 0 0-2 04 06 0-8 Fig. 13 0 20 30 40 20 60 70 40. 3 Q 20 o.

(14)

-90

-00 20

70

O

Beam Sea Condition < flEJi

90

P-

-c Co("'f-)fl 90 60 -30

y, <o

Yo_ -y. = o Tw 03 sec 30 60 90

-- .-O

Fig. 15 T 03 ec -t 74 O (d.qree) Fig. /6 -60 30 0 30 60 90 O(degrce) _{Fig. 17} 60 ¡20 60 115 20 I-0-0

---y.>O

y < o P.O P Po P Po 30 601 1 90 o -90 30 O 20 I0

(15)

116 -

35--2h/À