Effect of forward speed on roll damping of a destroyer model

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I +National

Council CanadaResearch institute for Marine Dynamics

Canad

Conseil national de recherches Canada Institut de dynamique marine SYMPOSIUM ON SELECTED TOPICS OF MARINE HYDRODYNAMICS St. John's, Newfoundland August 7, 1991

EFFECT OF FORWARD SPEED ON ROLL DAMPING OF A DESTROY MODEL

M. R. Had4tra and D. Cu.Lng

Facu1y of En&Lna.ring _{d Appli.d Scienc., Meaorial. Un.Lv.rsLcy of .vfound1and} Sc. John's N.wfoud1 CANADA A1.8 3X3

Natioia1 Research CouocLl, Institut. for Marine Dyrtaaics

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I o

Nalionál Research Council _{Conseil ñationaj de} recherches

CnadaCanada

Institut de Øynamiqu manne lflstitût6 fôr Marne Dynarhics

SYMPOSIUM ON

SELECTED

_{TOPICS OF}

MARINE

_{IiThRODyNtJIj}

St. John's, Newfoundland

August 7, 1991

r4

Ç-.

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A3CT

An extensive experiment.,l program has been

carried out to study the eff.c

_{of forward}

speed on the roll damping of

_{a self-propelled,}

9 meters long destroyer _{model. The experimental}

set.up was deèmed te be as clos,

_{to reality as}

practical in a towing tank

_{sstng. The roll}

decay _{records vere analyzed usf.ng} _{the Energy}

approach, and a mcv _{flOndi.monsional.ization scheme}

vas used. This scheme allowed

_{to identify}

certain trends for the data,

meid

to relate

daping of

the. model moving _th _non-zero

forward speed te that for _{à non a&vancthg model.}

Thà damping vas found

_{to vary n0linearly with}

forward speed.

I. rgraopUcyxov

One of che primary

_{sources of error in}

existing ship motion prédiction Algorithms is

caused by inadequate methods

_{of estimating roll}

damp ing. This

is

especially true when

considering large angles of roll.

Roll damping

h.ù recently received much attenion from the

research counity

as

scientis

_strive

_to

forujate improved

_{criteria to}

_{increase the}

margin of safety against capsizing. Estimation

of roll damping

_is

_{still larly based}

_on

empirical formulatio _{derived fròm physical}

mádel experiments. _{The purpose mf the} _present

investigation La to provide

_{a daca base of roll}

da2ptng infornaej _{for a warship hull form} _and

to study the

_{characteristics 0f the damping}

moment

at

_large

_roll

_amplitude _to

better

w1derstd the physics

_{of roll damping.}

The damping

_{coefficient ealmates in this}

paper were obtaine _{using the} _{rgy approach}

described in (lj

_{- The primary admncage of this}

method is the áiltty

_{to analyze 'enry short roll}

decay recorda. _{The accuracy of che}

method was

tested by

_{recenstrcting the roll decay}

curves

using the estimated damping coeicienta

for a

larg. number of _{ca-ges (2-4 j.}

_It

_{.0 been shOwn}

that the damping

_{coefficients obnsd from}

the

analysis of a single

_{roll decay cycle} _produced

mere accurate raU. _{decay Curves than}

those obtained using _the

_classj

averaging tâchnique

-The preàemt paper _{describes the results of}

an experimental program _{carried mut using}

an

EFFECT OF FORWARD SPEED ON ROLL _DAMPINC

OF A DESThOY _MODEL

N. R. Haddara and D. Cumiiuing

Faculty of Engineering _{d AppU.d Science Mémorial University of Xevfoundland}

S t. John' s, _{Nevfowd1a, CANADA All}

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National Research CouncU, _{Institute fOr Marine Dynamics}

St. John's, _{Nevfoundlanci} _{CANADA, All 3T5}

unconstraixed selfpropeLL.d warship_{model in} the Clear Vater Towing _{Tank of the Institute}

for Marin. Dynamics () in St

John's,

Newfoundland. Roll decay di _{vere obtained for}

a range of forward speeds

_{static stability}

conditions for the

_{odeL fitted wich and}

without bilge keels. This _{rk compliments a}

previous test carried out using

_{a laterally}

constrained model described in (2J.

An urow,antior

_{isen-sionlji0}

scheme is introduced. This _{scheme helps in} shoving the consistency of trénda in the data

and helps in de undersri.rw1fng of the behaviour

of damping as a function_{of other variables.}

IX. _{ERThENTAL PROCZg}

Th. roll decay empeniments_{vere carried}

out on a 9 meter long. 1:1.3.5 scale warship modal in the IND 200 m x 12 e towing tank. A

body plan of the model La_{provided in Figure 1.} The _{twin-screw model wns appended with}

propeller shafts

_{/brackets, five blade}

propellers _{a large emororline rudder.}

Bilge

keel particulars _{are presented in TAble 1.} Table 1. luge Keel Details

The bilge keel length is_{3.093 n and its span}

is 0.045 e.

The odel wag self-propelled_{under the} towing tank carriage using_{two 3 Kv electric} propulsion motors. A singl,_{steel wire fitted} from the bow of the _{model to a fixed point} under the carriage_{was used to tow the model.}

during acceleration. Thea

_{a steady state}

forward speed Vas attained_{and the model was} being propelled under its _{awn power, the tow} cable vas permitted to go slack. Model rolling was then inkiced by the release _{of a moment}

St&tioQ _Distance.fo _Disiance

ßaseljne (n) Centerline's) 12 11 10 9 8 7 6 0.465 0.483 0.495 0.500 0.497 0.482 0.45$ 0.138 0.120 0.115 0.117 0.121 0.124 0.132

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Applied to a 2.5 m mast located at the model cântr. of floatation. s the modal -vas

uncon.serained during the collection of

roll

decay data. The model vu restrained during deceleration by applying. tension to a single steel vire fitted from the stern of the modal, to

a fixed point under the carriage.

For zero

forward spa ed runs, the bow and stern toe vires wir, disconnected fról the model and tb. modal

arranged across the tànk to avoid tank vail

reflec tien. The experimental set-up was deemed

te be as close -to the te.ality as prActical in a

tow tank setting. S difficulty vas

experienced contrólling mich

a large

model

within the restricted tas; area under th. tow

carriage afld

for several runs, only a few

quality decay cycles vere attained.

Roll amplitude vas measured using a 2-aXis

electro-mechanical gyro fitted on -the model

centerline. The analog signal from the gyro vas igitized at 20 Hz and recorded on the carriage licroVax It computer.

Data vere collected for five metacentric

height..., five forward speed.. (F5 - 0.0 to 0.25)

and initial heel angles from 5 to 27 degrees.

The five motaceneric heights are given in Table 2

where B i..

the model breadth and Ql is the

metacencric, height. Ballast weights were moved

laterally to preserve a constant roll moment of inertia. All five conditions-were tested for the

nodal fitted with bilge keels, however., lack of time permitted only four cinditions (Ql 61 of

basa vas omitted) to be tosted for the model without bilge keels fitted. A total of 259 runs

vere executed for the model fitted with and

without bilge keels.

III. DATA ANALYSIS

The free roll decay curves were analyZed using the Energy method. The method has been

discussed _{in several previous publications, see}

for example (l.4J; and it vas shown te produce

fairly accurate predictions for the linear and

nonlinear damping coefficieflts.

It was also

shown, that _{the method is especially suited to}

short roil decay recorde, for which none of the methode available in the iLterature are suited.

We vili give a ver)! brief description of

the method here, for the sake of completeness.

Ve asume that the fr.. _{response of a ship}

rolling in cala sea

_{can b. described by the}

following differential equation:

28

e D(+) - 0 (1)

where is the roi-1 angle, if and D are the

damping and restoring moments per unit virtual

mass moment of inertia of the ship. Dots over

the variable indicate djff.rentiaeion with

respect to tise.

Equation (I) can be revriete.n in the

following form

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where E(t) is the total energy of cha ship p.r

unit virtual moment of inertia. E(t) can be

expressed in th. following form

E(e) -0.5

+ G()

where

G(+) -fac+de

Equation (2) is am expression of th. equality of the rate of total ship energy loss and the

rate of energy dissipation by the damping

moment.

Integrating equation (2), we get

E(e2) - 2(Ç)

_-f

N(,)sdt (3)

Ct

Equation (3)

can then b. used to

identify the parters of the

dLng

moment. However, a form for the moment has to b. chosen

first. The Energy method can deal with any of the well known forms. As a matter of fact, it

can deal with a general polynomial form where the damping moment is expressed as a function of. the velocity as well as the dLsplacemcnt To

perform a parametric study of the damping of the destroyer hull, one can use the simplest

form for the daing moment. That is the

equivalent linear damping. It bas becO found that this form is very useful in studying the

effect of varying- d different parters e.g.

velocity, fxequey .

.etc on th. damping.

However, it w.st be bastzed that a monlinear

model should, always be used for response prediction especially when large motions are

considered.

-Considering a d.ing moment given by

N(+.) -N04

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Table 2. List of Metacentric Heights Tested.

Condition

Very High (VH) 0.12

High (H) 0.10 Medium (M) 0.08 Low (L) 0.06

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i - Zero Forward Soee4

In this cale eh. _nondjmenajo1 equivalent linear damping coefficient is given

by

t,4 - 8,4/p T' e

Th. mond1esional damping _{coefficient has}

been plotted, for th.

_{case of zero forward}

speed, as a function of F1.

_{It should, b.}

mentioned her, that for thi,

_{case F1} Ls

proportional to the mean amplitude .#. These plots are shown in Figures _{2 and 3 for the} cases of the model fitted vieh sOd withOut bilg, keels. For both cases, on. can identify the following trends:

For snail values of the _{parameter F1, the} mondinaionai damping coefficient - is

inversely proportional to F1. Thismeans that

the dimensional damping

_{coefficient 54,}

a constant independent of the amplitude

of oscillation.

For large values of F1, the_{curves of 3} _for eh. different values of CX_{converge to almost}

the san.

_{conleant. In other words,} _the

nondtns tonal damp ing coefflc Lent _becomes independent of F1. This indicatos _{that the}

dimensional equivalent linear damping

ce.ffjcijat becomes a linear function_{of the}

1inud

_{of the roll motion.}

_{Thus, the}

r.lationship between B _{and #. is e straight}

line. The value of P at which this region starts decreasing as the _{metacentric height}

decreases. This _indicates _that _sa _the

metacentric hait decreases, the

_{diflg tends}

to be more viscous at smaller angles

_{of roll.}

This can b. easily explained, since a decrease

in the metacentric height, in

_{this case, is}

caused by a rise in the vertical level of the

centr, of gravity which vili result in an

increase in the magnitude of _{the damping fórce}

arm.

2 - _{Forvardsoeed Greater than -Zero}

From the nondimensjonalization_scheme

aggzsted above, one can relate the _dlmensianaj.

equivalent linear damping coefficient for the

model moving with forwaxd speed V, _{to that for}

the model roiling at _{zero forward speed as}

follow.:

$44v - B _{G (F,. ø,) Ii.} _(V/ca,0r)2J

The function 01 Ls a function of the

foriord velocity _{the natural frequency. The}

analysis of the, damping data has shown_{that the}

function c1 can be written as

- G2(P,)x o4

E(e) Sty.. above,

fr.. roll decay curve, using the(3) Ls evaluated from an experimentally obtained_{expression for} and substiD:1.ng in eh. L.LS. of equation _(3),

least square algorithm. The &.H.S. in _squacion

the .agnteud. of N can b. obtained using a

/

Tb. equ.ival.nt linear damping

_cosfficj.n,

$. can be obtath.d from N0 by multiplying _the

latter by eh. virtual moment of in.rtja

_{of the}

ship. It is assuned that 3oo La

_{function of}

eh. moan roll amplitud. #..

_{It vili b. shown}

lacer thac this assumpUon is based on

.xp.rimectal evidence.

Iv. _{NOIOmALYZATION SCHENE}

The follOwing nondiensional _quantities

ar. used:

- B

_{rj, s/p u2 T}

/(G2, $)

where

02 - Va

_T+)2

and p L the water density and

_{T is the ship}

draft.

A pseudo Frouda number F1 _{is defined as}

and the following expression _{is used for Fronde}

F, - VI v'T

The velocity U, used in the aforementioned

non - dimensjona.ljzatjon scheu.,

_{is the resultant}

of two velocities:

_{the forward speed of the}

model, V. _{a velocity representative of the}

transverse velocity caused by the rolling

motion, T

_..

_{The ratio of the lattet to the}

foraer can b.

_{cortsjdered as a measure of the}

angl. of attack of

_{the hull when treated}

_{as a}

wing section for

_{the purpose of finding the}

mognitud. of the lift

_{damping, The rational.}

behi.d ch. chOic, _of _these _{nondjmensional}

parameters lie., in the fact that lift damping

beco..s signLfIc _{vieh forward speed.}

V. RESUL _{AND DISCUSSION}

The fre, roll decay _{curves obtained}

experimentafly vere _{analyzed using the Energy}

method and

_th.

_equivalent _linear

damping

coefficient of the model _{vas evaluated for the}

dLffere _{cases outlined above. The results}

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C2 is plotted in Figur. 4 for the modal fitted with and without bilge keels. It is shown that

C2 is independent of the natural frequency.

The .quival.nt linear 4aaping coefficjei

for the modal moving with forward speed can tham be obtained, from the damping coefficient of model rolling at zero speed by multiplying

-latter by the function G3 given b

G3 - G1[l.(V/o03]

obere G3 can be obtained from Figur. 4.

The n.c effect of forward speed am the

damping coefficient, 1 C the function C3) ha..

been plotted in Figure 5 for the eases with and

without bilge keels. It is clear that in both

cases,

the effect is noñlinear.

owev.r, the

nonlinearity becomes more pronoied as the cacencric height decreases. This behaviour is

justified by the fact that G3

La a nonlinear

function of the natural frequency.

For the -same step in forward speed, the chaitge in C3 for the case with _{mo bilge keels} appears much larger than for the model with

bilge keels. This óccurs, even though _{the change} in the damping coefficient should _{b. smaller f.m}

the absence

of bilge

keels. This apparent

contradictión is caused by the fact that

_the

zaro speed damping coefficient far the _del without bilge keels is only

_{a fraction of the}

coefficient for the nodal with bilge keels.

Thus, if the-coefficients increase by thØ same

amount, the increase in the case of the model

without bilge keàls would be much

_{larger than}

that in the case of the model fitted _{with bilge}

kaels_

fl.

CONCLUSIONs

In this work, we have pré.sented the results of an experimental study _{of the damping} moment of a self-propelled 4estroyer _{model. The}

model vas allowed to have six degrees of freedom. The main objective

_{was to study the}

effect of forward speed on the damping at large rolling angles. The Energy method proved to be

a very valusbie tool for the analysis of the

free roll decay curve!, since most of the roll

decay curves obtained had only _{on. or two cycles} that can be analyzed.

_{The accuracy of the}

standard methods of _{analysis would be greatly}

Çuestionable in this case.

The nondimeflsionslization _{schame used her.} proved useful in shoving _{the consistent trends}

in the results. It

_{showed that for large vilues}

of rolling amplitude _{the nondinensi1 damping}

b.comes independent _{of both the roll amplitude}

and the natural frequency. _{It also allowed us to}

derive an _expression _relating _damping

coefficient for the model _{moving with forward}

speed from the Coefficient _{for the model rolling} at zero speed.

30

One of the main conclusions of this work

is the -confirmation of the fact that the

additional ding caused by forward speed is a nonlinear function of the speed. A method of lift damping prediction which is based on a

nonlinear theory ii still lMking. At present, a study is being conducted to develop such £

method.

AGOVLEDGq5

The authors would like to express their

gratitude to the Defence Research E.tabl.Lsheent

Atlantic and ch. National Science and

Engineering Research Coil for supporting this research financially.

-REPE&CES

i.

Bass, D.V., Haddara, M.R.'Nonljnear Model, of Ship Roll Damping', Internacion4

Thiobuilding Progxess, Vol. 35 No. 401 (1988). pp. .5--24.

Cising, D., Haddara, M.L, Crah, Ross 'Experimental Investigation of Roll Damping Characteristics of a Destroyer Módel',

Proceedings

of the

Fourth International Conference oñ Stability of Ships and Ocean Vehicles (StAB '90), Naples, ItalySeptémber 24-28, 1990, also 11W report No. LI-1990-3.

Raddara, M.R., Bennett, P. 'A Study of

the Angle Dependence of Roll Daping Monent',

Ocean EneineeriUg, Vol. 16. No. 4. w. 411.

-427, 1989.

4.. _{Maddara, M.ft, Bass, D.V. 'On the Form of}

Roll Damping Moment for _{Small Fishing}

Vessels', PceanEi,eineerfn,g, Vol. 17. No. 6, pp.525-539, 1990.

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.7igur. I. Mod.l body plan

and

rdinats axes.

03DI)(s1óaIL ¡04-04 y £ MODEL 391 BODY PLAN 0.00

P!ZUVO 7I! WUMO!! PÌ

Fig. 2 Zero

Forward Speed, Model with B.R.

01 5 ₀₄

rozuo i» _ri

Fig. 3 Zero _FOrwax.d

Speed, Model without _s.jc. MCOWDITXO DCOJiDmoj - Ya ÇOWDITTO1I 0.06 4 31 0.01 maa pvtqcrioi - - VLcQKØmow.w,c Mcomoa.vpz V!coxomops.Tpg N COD1TIO. X5C

-.-.- Va

corDrnoN. M)E 71000! NV1E2 rs'

Fig. 4 Forward _{Speed Effect,}

Speed Function G2.

VI.corDmoy.Ya(

Va COWDI?IOj( 1F5

N IrDLTIO5,. ßE

Va Coi(DrnoN. M)!

78001E MUI!?p

Fig. 5 Forward Speed _Effect,

Speed Function G3.