Hull flare influence on ship motions in waves

(1)

HELLENIC INSTITUTE OF MARINE TECHNOLOGY

TECHNISCHE

_UNIVERSITEff

Laboratorium voor

ScheepehYdrornechanlca

.Archlef

Mekelweg 2,2628

_{CD Oeft}

TeL: O15786873

_{Fax 015. 781838}

IFTH INTERNATIONAL CONGRESS

ON MM'1NE TECHNOLOGY

ATHENS '90

L

MAY 1990

(2)

q

HULL FLARE

INFLUENCE ON SHIP MOTIONS

IN WAVES

-R. Klshev, D. Radev

jgarial' Ship

HydrOflarnics Cerflre, Varna, BULGARIA

Y. Netzvetaev. Y. Kaitanou

lov &'ip Research Institute, Leningrad, USSR

In this

perce an atterpt ras been made to in-CII liane InÇ1uerCI.tritO practical skeepthQ withOut breattfl tee tradItiOnal motion

,yaluatiofl schemes. Renaming wLthiO the frame, o4 tee etrip theOry arid maU amplitude excitation,

the ccr,Site'S the waterline instanta

nØOUS ctaflfl' in the evaluatIon 04 the hydrostatic. inertia and O&mpifl forces. The added mass and

dar

ping terms, ottgiriClIY tiredeendant,

are consice-railY simplifie0 by the ç.as-statiC (Io'. frequency) nçueptlO, whiCh converts tee dependence Ofl tine into dependence on instantaneCScraft, The approach

as brefl ver(:cO by lcrCeC oscillation tests of

floating cylindra «:th sh:rliie crosssections. as .11 as by sea) eerie; tests of ship models in steep nvas, the retu:td of which correlpte well with the calCulJtiDnG ettaifled by tnt ne'. technique.

NOr.EULATIJCO

-

instantaneous .e:titr.al creo

a.. - sectional acre: mas,

- sectional Ca:ng :re4a:ieht d - instantaneo_5 graft

Diet - substantial 0CC

ivtve 000ratcr

F.

-

hydrcdyfla'nic fortes acttng en the Mull h - ocre hct;ht

k - wave number

1<. - coefficients of mOOed mass expansion on

instantaneous Craft - generali:ed mass values

- coefficients of damping expansion on Snstantaneous draft

- p?ocess el trie r.lative vertical motions

ge added resitnc..

-r

- perioc cf metbon

-- speed of advance

- process of ship notion at l-tC sode - sect:cnal otOth

- instantaneous wave elevation

- effective wave elevation accounting for

Smith effect

-- ave length

- nondimensienal ¿COtO resistance coeffiCient

Subscni ptai

O - fer equilib'ium position a - for amplituce

D - lar damping farces for inertia farce. R - for restoring fcrce5

I. INTRODUCTORY NOTES

- The

engineering

methods commonly used in ship

motion calculations, aro based an the assumptionS cf

smelt amplitudes and wallsided Niait fores. The mo-dern trends of development of iMp design.

lead to

unconventional

hull fare g tien with so-phisticated boo and stern geometry and well CevelO pod flare al-ong larQe portions of th. ship length. Another important issue Steins to be the raising of

the operational demands, which farces the ship into more severe environment. The combination of these two factors mates the pplicatiOni cf standard linear motion theories doubtful and consequently imposes the involvement of

nonlinear

effects.

On the other hanf, for pactical design

purpo-ses, simplified approaches are often preferable in vie.. of providing reasonable computing timeat nul-tirariarit calculations.

Thus, the ajo of the reportee investigation was the - development of a motion calculation procedure, idrich could account for the presenc. of flared hull sections remaining in the frames of the linear strip theory and it. subsequent realization as an option

to the mtandard seakeeping computer program.

2. SASIC FOPJtULATIONS

The motion of a slender ship with flared bow and stern sections,

advancing

in head regular steep waves, is considered.

Folle.iing the assiin'ptien for aCditiVefless el

the forces acting on the ship hull, trim longitudinal motion equations are composed, as follows:

M.d. (t) - F.(tl F (tI F..(t) ill

i 3,2

It Is assumed further that the ship reactIons

remain linear and th. strip tr.eory is still aopli-Cable (2, thus the total forces on the hull can be

Obtained by integration cf corresponding sectional forces along the ship length. He , the fare. cur-vature. and the large amplitude relativo vertical motions at the ends require

consideration

of the

in-stantaneous

waterline position in the farces evalua-tion. RccO.ding to 123, (43 and 123 tee force

con-pa-nent.

in eq. Cl) ere expressed, as follows: F..it) - pg

- -fD

[aesa,t

Drx(x,t) dt dt

- Sasmie.tid6t5mit)_2m1t)'

(2) -

_{(e,t)3s"'°de}

-dt

-F.oCtI da e -i 3,2

.here, tP,e relative motion i. substitutCd by trie folioi.ing expression:

TECHNISCHE UNIVERSITEIT

Laboratorium ',00r

ScheepshydromecMa,ij

239 rchIef

Mekelweg 2, 28 cD Deift

TL O15-78N73.F

015.78183S

(3)

xtf

eleCt)

ç(e,t)

(3)

sectional

added esses

and

danping

are

jg-nalIy considered to be time-dependent.

_pUAS1STAT!C AFPROXIMATION ADDED MASSES AND

ØADlP1

At lo

frequency assumption the .ectional added

and damping dependence ori

time

cari be

re-ced to S0fli

quasi5t.tic function of instntafleous

sraft

afl(x,t)

-- bawls.d, U)

(4)

-

a.0 *

mu

of this function was

investigated

in

(4 by

too

series

of

4erce

oscillation

tests,

naul y!

small

anpltude

osciIlations

at

different

drafts C - (0.5

l.Z)d.;

large

anpltude oscillations with respect to

a0

processed

by

nonhineal

identificatIon

technique.

-

-The

tests

were carried out on a nurber

edcy-lindrical bodies with flared cross sections

resenD-ling th bow bnd stern seattons of a 20 000 Ct fast

caritaiflerChip

sh..n

in Fig.!. The results Obtaiflel

in Fiç..2 and 3 she.. good

coincidence

between

the

-

e0perimental and tire theoretical quasistatic

estima-tians end the nonlinear identification., which allow

the

adaption

f an apprcaimate relationship of the

following type:

-K...Ca,u)

co.

- I(o(s,)[

The

form

of

ti-e

eoperirentally

obtained

'coefficient,

in

the

above qucraic erpansion Is

dunrcn,trate

in Figs. 4 and Z.

Qn tire basis of physical consideraticn,

_{it i.}

a5!um,d

_{further on that the prjncial hydroc.?nanic}

forces cOuld be eopressed. afollcws:

co,

- bo.,Cv,t)X..t)

-

_f

_a(e,tld

(7)

- !.

_J

_b(u,tgt

Sobstituti

_{of eq. CD) finally leads tos}

- siOs)

IC(.,u)

(5)

- ho(is)

PJo(e,u)

where, a. and b's are hydrodynamic added mass and

damping coefficients for the equilibrium draft.

Th, verification of the

aqove

espression.

is

demonstrated

in

Fiq.6,

where

the

hatched

area

cover, the lOX fluctuations of the eeperimefltal data

around ihm

mean

squared

value,

the

dotted

line

represent. a, and b5 calculations by the estended

Lewis form technique C13

and

the

d

circle,

give

the

correction,

to te calculated

value.

according to eq.(B). It

is clear that th, suggested

corretlon brings

the

calculations

in conformity

with

the averaged esiperimental values. Meanwhile, a

comparative analysis in Cf) proved

the

coincIdence

of the hydrodynamic coefficients prediction effected

by

the

different

techniques

(close

fit

and

conformal mapping).

The

restoring

forces

could

be

corrected

analogously,

considerIng

then

poportional

to

a

certain sectional

idth y, which corresponds to the

ge increment of the cress section arpa for

one

period

of

motion

due

to the curvilinear section

shape.

4, PRACTICAL APPLICATION

The

main consequence of the above

ratiocinati-ons is that the standard linear ship notion theories

could be used for seaireepinq calculations in case of

complicate hull section forms atso, simply

by

sub-stituting

the

a,a, b.. equilibrium values by

rele-vant corrected ones.

Practically, the procedure has been imple...ented

as an

option irtorporated in the standard seakee;ing

prediction program based on the l;near strIp

tnen-y

nethod

C3. The calculation :r:ces. is crçani:ed by

successive apprcnimations.

Initially, the

hydrodynan:c

coefficient,

and

motion

amplitudes

are

attained

by a

standard

procedure

without

taking

consideration

of

the

eventual

section flare. Then, the amplitudes of the

relative vertical motion

are

evaluated

for

every

section

and for those with well developed flare the

espansion coefficients K, and N.

are

estimated

by

linear reçression of the corresponding values in the

region (do t r,_).

The

corrected

added mass and

damping

coefficients

and

the

relevant

effettive

section

widths are suppli.d bacb in the calculation

scheme. The newly

obtained

notion

characteristic.

are

compared to the previous onus and if necessary,

the

procedure

is

rerun

until

sane

prestribed

accuracy is reached.

(n C43

the announced engineering .pproa:h has

been

applied

¿or

evaluation

of

the

seakeedlng

qualIties of a 20000 Cot fast containership .ho.v. in

Fig.!.

To- validate the procedure, ectended Ccberi

cents ..ere rarrted out in regular ..aves at different

wave steepness. The principal results have been

com-pared in t..o aspects

as linear frequency

response

(unction. (in Fig..B + lI) and as a direct

response-eocitetion

relationship

¡t

constant

f reouer.cy

- (Fig.. 12 + ID).

In principle the

eepericental

result,

fellow

the

common

tendency

al

response

decreasing

at

resonant area

arid

- of

slight

increasing

at

high

frequencies.

The

systematic

calculation.

clearly

-ha.. that

the

flare

accounting

leads

te better

fitting

of

tire

theoretical

and

the espertmental

predictions, though fo. tire

ship

investigated

the

- NwCo,u)

C (e, t) (Z)

du

P4.(C,u)t

72

(4)

.arsl0ß fra.

standard

nall-sid.d' pr.diCtlo.as

- are relat1&Y

5,.all.

me mcst

significant deviation 04 the

esperi-ntai pOittt5 from thu Un.ar response

secitation

is

observed

¿t Nigh 4reencies (short

o.t the absolute amplitude values

are

small

and

their

influent,

in forming the g.neral

thet'

ship b.h.Vi0" is minor. For

.

t L. the linearity

e4

,cton is retained for all reanenable values e:f nave

steepActS afld

the

same

can be stated for aver.;.

adr4 renistante dependence on squared wve

h.i;.'tt.

0, the5

grounds the application. of the tinear nt-ip

mith t,.aSlstLtital COrr,CtiO,ra 4cr predicting

5teePi1

qualities

of

flared

ship

hulls

is

juntifim

..u.

,.,u.

U.

-Fag. 2 S.ctima.l added ..ss and CalnQ dependenc, ma instantaneous draft

(quasiatatital ape:achl

f 1Hz

SPip theery

X 0X7 s i

X00.io. JCXP(OIaiUII

Fag. 1 Pody-plan of to. 20000t. Centatnerahip

I. LSd. tfld.

tSj.

t.

/

Strip (hr,,y

'

tall,

tra.. S.C.. REFERENCES

Fig. 3 Sectional added aus. and diede; dependence en instantSdteoul

draft

(dyfrealcil approach

finit. aeglittadel

t. 1.111. 1.211. tjW.

241 Athanassaulis G., Loukakis X., An

Estended Lutais

Fore Family of Snip Sections and Applications

_to

Seakeeping Calculations - NTIJA, Athens, 0993.

9

R., Elisgard F., Time History Simulation

of Vertical Motion and Loads on Ship

in

Regular

Head Waves of Lar;, Amplitude, NFR. No.2, 19go.

Boroday.!., Netzvetaev Y., Ship MotiOns In Waves,

Sudostroenie PubI. House, 1969.

Kishev R., Ra.v D., Hull Flare Influence on

Len-gitudinal

Motions in Engineering Seakeeping

Cal-culations, Final Project Report, BSHC, 1999.

S. Vuoramoto Yet al.,

Nonlinear

Ef4.ct

for

Ship

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