Hydrodynamic models and their influence on added resistance predictions

Doift UniversilY of TechnOoy

Ship Hydromechanics

Laboratovy

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Deift

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PbonaSl 15 ?8&373-FaX 31 15781838

ØTDRODTIAMIC )CDß AID

mELI

UYLUU

01 ADV RESiSTANCE PRKDICTICMS

Grant E. Beam, HydrocèchafliCa Beseareb Group,

Koon Chung Tong Department of Naval Architecture and Shipbuilding,

Slew Mtng Lau Univéraity. of ewcastle upon Tyne. UK

£BSTEACT

This paper is principally concerned with the application of alternative

hydrodyTlaatc modela to determine the first and second order wave induced fluid

loadings on advancing oscillating structures. Both near field and far field

added resistance calculation procedures ame presented. For the first tine

full 3D hydrodynsaio interaction analysis are used in otudying the added

resistance of ship forms. Predictions of the bydrodynaniC coefficients, the

motion responses and the added resistance are coepared with experiment.al

easureflt5 and strip theory predictions. The limitations of the different

applied procedures is discussed.

ImoocTI01

A vessel advancing in waves experienCes a resistive force additional, to

that due to its advance in 5tiIl water. This additional force, termed the

added resistance in waves, can also be viewed as the steady second order

longitudinal force induced by the incident waves and the resulting motions of

an advancing vessèì.

The theoretical calculation of the added resistance of a vessel in regular

waves generally falls into two categories. In the near field approach the

8dded resistance is evaluated by direct integration of the dynamic pressure

acting oc the vessel's wetted surface. In the tar field approach the added

resistance is derived froc conservation of the total energy or the total

mocentum of the fluid.

Bere we. consider the influence of a generalised 2D and two 3D fluid

structure interaction analyses on the predictions of added resistance. The

generaliséd 2D based method is cccbined with the near field prediction

t.chfliqUC.

In the first 3D methOd (methodi) the near field approach i

combined with a low forward speed 3D hydrodynasic aingularity analy3is. In

the alternative 3D method (method2) the far field approach is ccmibined with a

3D bydrodynamic translating pulsating singularity distribution model. In

etbod 2 pitch fluid damping predictions are very important to the prediction

of added resistance. Therefore the added resistance predictions are repeated

jth 3ust the theoretical pitch fluid damping replaced by its experimentally

.ea3ured value. These calculations arè designated method

2E. The 3D

enhancements developed by the author3 thus permit, for the first tine,

comparIson of experimental measurement3 with 2D near field, 3D near field

arid 3D tar field predictions of added resistance.

2. PASIC FLUID

MDDIS.

To make the near field and far field exact theories applicable certain

choices regarding the exact manner of undertaking the solution of the forward

speed ship motion problem must be made. The full 3D interaction analySis can

be formulated as a perturbation of the steady advancing or wave caking

resistance problem'. However unlesS simplifications are introduced both the

rigid body motion and the fluid structure interactiOn problems would have to

be solved simultanèously in the time domain. The introduction of perturbation

expansions and consideration of fluid behaviour on the instantaneous free arid

wetted surfaces in terms of fluid behaviour on the surfaces associated with

the steady fOrward advancing problem leads to a first order perturbation

formulatIon of the unsteady potential. However the steady and unsteady

potentials also interact in this model through complex inhonogeneous boundary

conditions which häve to be satisfied on the moving surtaces(1). Further

simplifications are required to make the problem formulation tractable. The

fluid structure interaction model to be used thus requires neglecting the

interaction of the steady and unsteady potentials.

Bere ve proceed directly to the statement of two alternative simplified

linearised 3D formulations for an advancing vessel in waves. That

is, denoting

the time independent incident, diffracted and radiation potentials by $, D

and ,k we are required to satisfy:

V2($D,

k)

= O everywhere in the fluid,

32 k

[ g . U2 +

2 iw U w2 _J ( ) = O on z = O, e e. D 3x ax on S,, where mk = O k = 1,2,3,, n = n3, and n = on _SW. (A) 303

It is aleo necessary that

and k 0 as z

- and satisfy an appropriate

radiation condition at large distances fron the vssel.

Within the literature Fosulation (A) is usually sisplified using

slenderness assumptions to reduce the 3D interaction analyses for _{O to a}

equivalent set of 2D roraulations. Here we solve the equations as stated _and

also provide a second. 3D alternative analysis by assuming that the _forward

speed is auch that

u

L

«

ax

Consequently defining the set of potentials as satisfying the wetted

surface condition

= _{: k=1,2,..., 6}

it

follows

that

k:1,2,3,11, With $ = a _and = _y5

The alternative sinplified 3D analysis thus corresponds to satisfying

=

2 8

_-

W ₁

O everywhere in the flüid,

) O On z = O,

asD

a1

-.!iwn.

_ex

and

-an an

Also and O as z + - and the potentials satisfy the Somerfeld

radiation condition.

For the _head sea condition a special diffraction analysis

ut be

developed for the equivalent strip theory approach based on the assumptions

of formulatiofl (B). This is not repeated here since it has already been

published

in

sôe detail(2)

Fr here on there is no need _{to differentiate between the velocit.y}

potential predictions based on the foraulations (A) & (B).

FLUTh STRUCTURE iaiuWTION JMALYSIS

One partcular approach to solving the 3D interaction problems posed is

the source distrlbütion technique based on the identity

= f

O(

G(x;) d$()

+

_I

_0k)c(x;

_ndy,

S I

for Formulation (A). For Formulation (B) the second term, representing the

waterline integral, is inappropriate and unneccssary. _{The coaplexity of the}

on the mean wetted surface.

Oreen function G selected

in each case will autocaticillY

echo the

r.quireeants of the aelected formulation.

Thus in Formulatlofl (A) the source

strengths, , relate to translatifl

pulsating sources distrIbuted over the

wetted surface f the vessel.

Whereas in the sinpier Formulation (B) the

source strengths, 0k' relate to

aource3 pulsating at the wave encounter

frequencY. We assune tram this point onwards

that the indicated radiation and

diffraction potentialS are

available, together with the means of processing

th to provide hydrodYflamiC

reactiVe and active coefficients and the motion

nalySi5

of the vessel. With the potentials

and motion responses known the

¡econd order mean forces can be evaluated.

FI..D gLu1T1ON

OF SEcOND ORDER MEAN FORCES..

Faltinsen et.ai have derived an added resistance

formula applicable to

any wave direction based on

integration of the near field pressure using strip

theory. The analysis is

identical, except for the forward speed correction,

to second order drift force calculations

on stationarY vessel. Beam and

Tong2

bave generalized the near field

5econd order force expressions and

shown that the added resistaflóe can be expressed as

2 P ₁

Ira

g dl -

p f

I V41$ Ti dS Bet81

F'

) L SW

-

_f

Imt Vs1] FL dS - p U J Retß Vç ) Ti dS la la lx S pg AWXcf Ret1, 6) 1c ... (i)

where the first order force term is given by

-

p5 (

-

dS Pg(0,o,n3Aw

-fl5Axr) ... (2)

and we bave introduced thé term

2 2 1/2

N =

(i1

n2, n3) / (n1

n)

...

()

to account for the slope of the wetted

surface at the free surtace2).

Evaluation of Equation (1) is critCallY dependent upon the

solution of

the first order velocity potentials and the notion responses.

5.

Tar

Field EvaluatiOn of Second Order Mean Force.

Mruo'

derived a theoretical formula for the added resistance based Ofl

the far field approach. The formula is valid for any wave

length and head

but i difficult to apply directly.

However, by introducing slenderness

8sSuSPtiOflS, the formula can be reduced

to an integral involving the so called

Using the conServation of mcentum approach, some involved integral

transforms and other manipu1ations5, and Nèwn'a6 áymptotic limits _tor

the potentials

and D lt

can be shown that the added resistance is

expressible in the. form1

cl

with. =

- K2

source st.rength distributions

boundary value problems(1,2). the fluid flow and associated

can be evaluated. From the

coefficientS and First order

,a) ₌

°k exp(c) exp[-ic (

SW

I - 2i COSQ ±

I

i - III

cos.3

2 eos2 a

hence the mot-ion Iesponses predicted.

Since no assumption has been made regarding the dimensionality of the

solution domain in which °k or are to be determined we may now use, in

principal, either of the added resistance prediction techniques. _{Here the}

possible combination of hydrodynamic model and second order force predict-ion

technique is confined to the three approaches defined in the introduction 306

cosa + r ama)) dZ

o

-For convenience 07 is used to denote the source strength associated with the

diffraction potential.

The term can be identified as. the contribution from the interactions

of the incident wave potential and the body potential, whereas the term RBB is

due to the interâction of the body potential with itself. By body potential

we mean the sum of the radiatioñ änd diffraction potentials.

6.

oRcÀrrshTIc4

OF CILCUUTIO«S

For each identified fluid structure interaction mode]. the first order

can be determined by solving the appropriate

Subsequently thé velocity potential arid hence

longitudinal

rates of change of fluid velocity velocity potentials the hydrodynamic reactive wave excitation forces. can be determined and

R ; RIB _RBB

- pw

where RIB

st cw

Re (H(k,ß)) cosS

1/2

31/2 cosa ... (14) ... (5) RBB

L {[

J 8! _-1/2 +

f

+

J

)IH(m,a)l .-. a0 1/2

/1

-

¡It COS

,

:1_cL0 H(IC2,)I2 d } . - ...

(6)

v/i -

4t cosa

where = Uwe / g, k = w2 / g and a0 is vero for ( 1/14 and eqûals

arc cos(0.25/r) for i > 1/14. _{Here the generalised Kochin function B is. given}

by

b _nkHk

H,

... (7)

- i

omputeP based analysis techniques can be used

to provide two quite

diltiflOt sets of calculations.

The first set may consist of those results

jcb ca1 be directlY compared

with measurable physical quantities. Thus

(itbin imposed space iimitation5) ve can

compare the predicted hydrodynamic

r.actt coefficients,

the motion responses and the added resistance with

experimental measureeflt5.

The second set of calculations may be considered as those

intermediate

result5 or copofleflt5 of B measurable quantity

which may not itself be

directlY or indirectly measurable.

The expressions for the second order

forces can be split into a number of identifiable

components. Thus in the near

field formulation, Equation (1), six

components can be readily identified. It

would be very difficult to separate out

these components in an experimental

programme. the other hand within

theoretical predictions it is possible to

provide measures of each component whilst producing the required

total added

resistance. For example the relative contribution of these components for the

Viober's tanker model of CB = 0.85, has been previously

published(1), and it

is known that the first term, representing the contribution

of the changing

vetted aurface area due to the

relative free surface elevation, is the

dominating contribution. In the case of method

2, EquatiOn (il), we consider

the partitioning of the added resistance into (a) RIB and RBB

components and

(b) the subdivision of RIB into heave,

pitch and wave diffraction components.

It is often this second group of calculations

which provide insight regarding

inequalities observed when comparing predicted and experimentally

measured

values.

The particular applications considered in this paper are

limited to the

Series 60 parent form for block coefficient, %,

values of 0.6, 0.7 and 0.8

and a finer form container ship. For each increasing

CB value, for the

Series 60 forms, the Froude number (FN) in each analysis is

decreased from

0.266 to 0.2 to 0.165. For the finer container ship model SR-lOS with

CB = 0.559 the Froude number is 0.2.

8. D1SJSSIOI OF RJLTS.

The added resistance predictions for the 3

Series 60 forms and the SR 108

model are presented in Fijures 1- respectivelY.

In Figure 1, corresponding

to a C8 0.60, two setS of experimental results taken

from Strom_TeJSefl(6)

and SibUl(8) are coopared with the two 3D

interaction analyses of Newcastle

and th 2D predictions of Gerritsma(1) and Salvesen(h1).

In this particular

caSe the heuristic approach of GerritSma(1)

provides a significantly larger

peak added resistance prediction. In fact all

resistance values exceed thé experimentally measured peEk values used. The

lowest theoretical peak value of added resistance is predicted using method 1.

ID

Figur. 2, corresponding to a CB

0.70, we again use the experimental

aeasurenta of StromTejaen

and

erritsma0)

but now present the enhanced

2D method

pr.dictions(2),

the 3D method

i

predictions together with three

sets of predictions based on method 2.

This last group of predictions uses

two distinct discretisations and

for the more refined discretisations the

added resistance predictions have been repeated with the theoretical value of

pitch fluid damping replaced by the experimental value of Gerritana(10).. We

now note that the so called method i

and method 2 based on experimental pitch

damping provide, the lowest peak added resistance values. These two sets of

results also

agree quite

closely until

considering

the

higher encounter

frequency regime.

In this figure we note that the 3D rnethod

i compared with

the 2D implent.ation leads to a more significant improvement in the added

resistance predictions than the doubling (almost) of the number of facets in

method 2.

Algo,

replacement

of

the

theoretical

fluid

damping by

the

experimentally measured values has more influence on

method 2 than increasing

the

levêl

of

discretisation

in

the

numerical

model.

In

Figure

3,

corresponding to a CB = 0.80, we again compare

StrÖmTejsen(B) experimental

measurements with the prediction of Gerritsma(10) and the two 3D procedures

using oomparable levels of discretisation.

Again,

there is a significant

difference between the 2D and 3D predictions although the difference between

the

two 3D method

is

almost negligble over most of

the. frequency range

investigated.

In

Figure

, we compare

the

experimental measurement of

Fu3ii12

and Nakamura(13)

together with the 2D

theoretical predictions

of

Takagi(1)

_and

_{Gerritsma(1) with the two 3D based}

_methods.

_{In this case}

method 2 predicts

a peak value

twice

the

size

of the other theoretical

predictions and experimental measured values of added resistance. Thus froc

Figures

1

to 3 we might have been lead to consider that rnethod 2 became more

unsuitable s.s

it was applied to vessels of fuller

form. However, this thèsis

is quickly disposed of when considering the highly questionable values for the

fairly fine form of the containership rnodel SR-108 ie. a

C8 value of 0.559..

In an attempt to explain the differences between the predicted values of

added

resistance generated

from

the

two 3D based methods we consider In

Figures 5 &

6 and Figures 7 & 8 respectively the hydrodynamic coefficients

and the motion amplitude predictions for heave and pitch. In each of these

four sets of results we compare the experimental measurements of Gerritsma(10)

with the predictions of the 2D and 3D implemented versions of Formulation (B)

together

with

the

predictions

of

Formulation

(A)

for

two

distinct

discretiSations. From Figures 5

& 6

the greatest differences exist in the

fjnent of the discretisation in Formulation (A) does little to improve the

predictiVe capability. In Figur. 7 the heave amplitude response

is more

,enaitive to the hydrodyflamic analysis used tri the lower frequency regime.

When considering the pitch

motOfl

amplitude in Figure 8 some

improvement in

te

predictions of FormulatiOn (A) are brought about by

combining the finer

discretisattön with the experimental damping values,

although once again the

less sophisticated Formulation (B) provides

predicted values luch closer to

the experimental measurementS.

In Figures 9 & 10 we consider the relative magnitudes of the

two

components of added resistance identified in Equation (a.) together with the

proportional make-up of the RIB components attributed to heave, pitch and

wave diffraction. In Figure 9 the effect of refining

the diacretisatiOfl and

the replacement of the predicted radiation damping by the

experimentally

measured pitch damping upon the two compOnents of added resistance is

clearly

seen.

The effect or experimental pitch damping is relatively more significant on

the RBB than the RIB components of the added resistance. This

is to be

expected since the _BB term, Equation (6), i

quadratically dependent upon

the motion response whéreas the RIB term, Equation (5), is linearly dependent.

The dominant feature of the pitch motion contribution to the added resistance

is also evident in Figure 10. At the peak of the Ourve the pitch motion

contribution in the RIB component accounts for about 67$ of the total added

resistance in head waves. In bow oblique waves the pitch motion renains

dominant arid those contributions from the lateral motions (not

illustrated)

are very small.

9.

UaUSI0S .AD flIAL

cOP9TS.

Application of the arid 3D based hydrodyflamiC interaction analyses based

on Formulation

(B) and the 3D based FrmulatiOfl (A) indicate:

3D effects are particularly noticeable in the hydrodyflamic pitch

damping arid the heave and pitch otiori predctiOfl5,

use of a more exact mathematiCal fluid structure interaction model

does not necessarily lead to closer agreement between predicted

values arid experimental measurements, and

the influence of the discretiSatOfl levels is more apparent in

Formulation (A) ba5ed predietiöns than in

Formulation (B)

When the two 3D bydrodyflamio modele are

reapeotivelY linked with the near

f ild and far field added resistance formulatiOfla, as per methode

I and 2,

then

(iv) the 3D based near field applicatiODS provide

a significant

improve-ment over' the based predictions, Newcastle and others, and is

much

supörior to

th

3D based far field method implemented,

Cv) the need to obtain good pitch damping coefficiente

Is clearly evident

from the edded resistance results based on the use of experimentally

measured dampiflg,

(vi) the pitch cponent of the R

term je dominant, and

(vii) the assumption made in other

body-body interaction component

wave-body interactiOfl component

the ship forms examined.

analyses e.g. saivesen(11), that the

is lese significant than the incident

has been demonstrated to be true for

In view of the fact that the amplitudes of the added resistance

determined

from method I and 2 are not always compatible it would be

useftIl to partition

the added resistance determined by' thod i into

the same components

considered in method 2. This would not be the normal partitioning of

the near

field approach but provided due care was taken then it would be possible to

undertake these calculations by carefully suppressing each motion in

turn

within the added resistance post_processing program

and then deducing the R

and terms through a judicious application of

algebra.

lo. acx0LÉD?TS.

The authors wish to acIaowledge the Science and

Engineering Reseàrch

Council

fOr the financial support received to undertake part of'

the work

reported in this paper. Part of the support comes

through the SERC Marine

TechDolOgy Directorate industrially sponsored

"Compliant Systems" Cohesive

PÉ'ogramme which made development of' the near field analysis possible

and part

through an SERC Studentship awarded to the third author.

Finally, Kay Thomas

in

thaDked for her patient typing and editing of this paper.

1. Searri, G.E., Tong, K.C., and Lau, S.L

'Sensitivity of Wave Drift ramping

Coefficients to the Hydrodyflámic Modela Used

in the Added Resistance

Gradient Method". proceedings of the Offshote

Mechanics and Arctic

Engineering Conference. Houston, March 1987.

2. HearD, G.E. and Tong, K.C.

'EvaluatiOn

of Low

FrequencY Daaping',

proceedin&3 of the Offhore Technology Conference. Paper

5176,

Houston, May

1986.

. $arUO, L 'The Excess ResiStance

Dt

a Ship in Rough Seas'.

International

pujldinA Progre!!., Vol. No.

35, July 1957..

NarUo. L Resistaflce in Waves'. Japan Society of Naval Architects,,

60th AnniverBary Serica, Vol.

8, 1963,

Chapt. 5

)iecan, J.N. 'The Damping and Wave ResiStance of a Pitching

and Heaving

Ship'. Journal of Ship Research, June

1959.

Faltinsen, O.M., )4insaSS, g., Liapis, N. and Skjôrdal, S.0.

'Prediction of

Resistance and Propulsion of a Ship in a Seaway"..

!toCeedi50! the 13th

Symposium Naval Hydrodynamics, Tokyo,

1980.

e.

Str-Tejsefl, J., Teh, N.J. and Moran, D.D. "Added Resistance in Waves'

Transactions of the SocietY of Naval ArchiteCt5 and Marine Engineers.',

Vol.81,

pp109-lO, 1973.

SIbul, O.J., 'Measuraments and CalCUlatiOñ of Ship Resistance

in Waves',

College ot gjfleering.Ufl1Ver5itY of California. Berkeley..

Report No. Na-71-2,

1971.

Grritsma, J. and Beulcelman, W. 'AnálysiS of the Resistance Increase in

Waves of a Fast Cargo Ship', International $hjpbuildiflg Progress

Vol.19,

pp2B5-283, 1972.

Salvesen, N. 'Added Resistance of Ships in Waves', Journal of HydronautiCs

Vol.12, No.1, pp24-3,

1978.

FujIl,

H. and Takahashi, T. "Exporinental Study on the Resistance IncreaSe

of a Ship in Regular Oblique Waves', Proceedings of the 1th International

TOwing Tank Conference. (ITTC),

pp351-3&O,

Ottowa,

1975.

Nakaura, S. "Added Resistance and Propulsion Performance of Ship in Waves",

The InteÌnationai Séinár on Wave ResistanCe,

pp199-216,

Japan,

_1976.

lE Talcagi, M, Hosoda, R. arid Shimasaki, H. 'An Improvement for the Calculation

of Added Resistance in Waves', Journal of Kansai Society of Naval Architects.

of Japan, No.11,

pp33, 1971.

,

_I.

_o Il. o

ii

T W D

t)

z 123

Q IL h % IL. .

00

Figures 1 & 2 Comparison of Predicted and Measured Added Resistance.

25 _o ÀOOEO .PSLSTANCE 3EPIS 60 I&1 OP C 0.60 vAv ,*AOIIc. PN 0.266 (XPT. ISIJIjLI 20.0 0 -AODEo PESISTANCE

.3PIS60JI.LL

C. 0.?

NAY! IA0II 1W FN - 0.2 tXPt (PI MRPIV9IA) 70 TPV vCAST.

-20 tOQ GEQIT9l* 20 ?f(T, 5ALVESN 266 F*ÇT_ I 06 FACE?- 'DCO 2

I

I'

:

(.26 FACt? - &26 FAUT - ITPO E

-o, -(I 20

a ISjO

I % I i

z

w LI Lt w (J u) (J

z t-

u-I Lfl Ui: Cr D W LI O 6 ADDED RESISTANCE 2 o I, (T '5._0 12.5 o 10.0 p.-

z

Ui LI u- D L) _uJ LI

z

I 5.0

u, W D W Q (3 AODEO RESISTANCE 5P-108 crIP

SHIP V*vt tA0IN& 160 FN. 0.20 o EAPT (NAXA*6) XPt IFUJIII

- - 20 ll*l'

,*XAca - - 20 DXÓPY GPQLTSNA

- 30e. FACET - ItT II I

Ó.FACFV - I1 ''2 0.0 3 S 6 0 I 2 3

og

0g

P-'

Figures 3 & 4 Comparison

of Predicted and

Measured Added Resistance.

S(PIES 60 UJL 0F C 0.60 VAVt PÇAOING FN 0.165 12 U EXPl t3tP0PI..YEJ,WI -20 TIÇT, &QQITSMA 296 tACET -T

''

I p. ai I0

'I

-I a) p.p., ai

I

-

_..SIF*CET -J :1 I Cr Cr

Ii

I II.

4, o 'O :HYDROOYNAM ÍC COEFFIC.! ENTS 5&QIES 60 I.LL flf! c 0.:?0 EAV COEFcICIEJS FN.0.2 .1 2 wJL3/q 3, p S ií

r.

-2 3 4

wJL /g.

o EEPT -- -- .--.O AVCASIL( ._..-.126' FACET' - PTID i 216 FAUT -THQQ 7 e.76 FACET -TPjO 2 5 50

H o PÓbYNAMIC COEFF IC lENTS

3PIS 60 IU..1

.0 '0.70

PlTOq C009CIEIII

FN

0.2

Figures 5 & 6 Comparison of Predicted, and

Measured Hydrodynamic Coefficient..

s 0.10,. o. 00 '0.06 0.04 0.02 0.00 0.20 0.15 0.10 0.05 0.00 '0 o

o 'ta'

-. 2T6 FACET .s A26 FACET s'. s S _ss b -I - . .5 1 a a u e

/ /

o

--.6 -. s

505s..q..e

ìss

/

1

/

u.

S

'-.'

s.

I 2 .

3.

wJt/g

3 7

u.

a 2 if s s o

MOTION AMPL I lUDE

SERIES 60HUU. OF C 0.70 VAVEHEAOING lO FN - 0.2

o

FXPT - GFPRITSMA -NEWCASTLE 226 FACET -METHOD I ----316 FACET - 'METHOD 2, "26 FACET -METHOD 2

-/o

-.

----'

-4 2 3 4

5

6

wIL/g

MOTION AMPLITUDE

SERIES 60 NUll OF C 0.70 WAVE HEADING ted' FN -0.2

Figures 7

R Comparison of Predicted and

tÇeasured Motion Amplitudes.

o E1IPT - 'GERRIT9(A

--21) - HEVCASTLE 226 FACET - HETP0 t 316 FACET -TMOO 7 26 FACET -Z 26

FACET - ItIPW 2E'

2.5 2.0 I.5 p-, / /

w

I,. O O..5 0.0 I