Comparison of the Strip Theory and the Panel method in computing ship motion with forward speed

Conseil national de recherches Canada Institut de dynamique marine SYMPOSIUM ON SELECTED TOPICS OF

MARINE HYDRODYNAMICS

St. JohnTs, Newfoundland August 7, 1991

COMPARISON OF THE STRIP THEORY AND THE PANEL

METHOD IN COMPUTING SHIP MOTION WITH FORWARD SPEED

C.C. Ksiing arid Z. Hua.ng _/

Depa.rtmeri ci Mechariical Eneering

Technical tierzity of Nova. Scotia.

-1;-!'i:. Nova. Scotia.

V S

8I&L'9IO

IjJOQ _{Go asa ' ßOM1OIØ}

OWOJPMJSdOOII,S JOOA

ii3llSll3AJpjfl 303VNH331

1+

National ResearchCouncil Canada institute for Marine Dynamics

-J.

1+1

Reseasc

Institute For Marne

Dynamics

Conseil nationai de recherches

Canada Institut de dynamique manne

SYMPOSIUM ON

SELEC1iI)

_{TOPICS OF}

MARINE HYDRODYNAMICS

St. John's, Newíoundlajyj

August 7, 1991

b

COMPARISON OF THE STRIP THEORY AND THE PANEL

METHOD IN COMPUTING S}

_{MOTION WITH FORWARD SPEED}

C.C. thung and Z. Huang _/

Department of Mechanical Engineerin Technical t'nivexsity of Növa Scotia

Ñova Scotia

ABSTRACT

The motions of two ships, one is a full form

-.g vessel and the other is a container ship, are

-pnzed and' presented in this paper. The coxriputa&i

based on the two-dimensional strip theory and the t-e-dJmensjonal panel method. The panel method

mputing ship motion with forward speed is deiSed

by making use of the 3-D Creen function of zero-speed. The numerical results from both methods are compared

a: different ninthng conditions.

L Introduction

The. strip theory has been widely used for

seakeep-ing analysis. _{However, the strip theory is based} three assumptions: (a) the hull fórin is slender and the

longitudinal geometrical, variation is small, (b) low -azd speed, and (c) high frequency of encounter.

aumptions limit the applications of the strip they

The complete and linearized boundary value pro

ir ship thotion in waves has been given by Newman II in 1978. Until now, _{none of the solutions has b}

und such that the' linearized body boundaryconcfitic a.d free surface condition_{are completely satisfied. The}

p.a.nel method using the, 3-D Creen function offorwa.-d speed has been developed to compute the ship mo as given in [2] and [3]. However, the numerical results have never been satisfactory because theCreen funcric

ociy satisfies the simplified linear free.surface _conditioc.. a.d because the steady flow in the boundary c'onditi a:d in the hythodynamic:pressure _{is based on the}

-&rm flow..

'The valldatjòn of the numerical methods is an

-portant work in order. to determine which nuniesical

stherne is 'an effective_{one to obtain reliable results. h} ¿epends on the comparison between the numerical and experimental data for various ships tinder different _oea'

dltions (4] [5J. Based

_{on the results of the valirk}

sudies,

the _{appropriate paneL number in the 3-D} method or the_{proper station number in the 2-D m-)iricl} ca. _{also be determined for asjiecifiedship.}

In this paper, based on the theory derived by

Salvesen, et al. _{[6], a thrèe-dirni'cionaI panel rnet}

w _{devised by using the three-dimensional Green}

f-tioni of zero-speed to compute ship motion with forward

advancing speed. According to the coc.ational

re-sults in Refs. [7] and [8], the panel me using the

3-D zero-speed Green function would give becter results than that using the 3-D nonzero-speed C function. The computed results of ship motionusing - strip

the-ory and the pane! method are presented. 'The

copar-isons are made for a full form fishing ves _{a.d a sleiider}

container ship at different running cond-i

IL Formulatioú of the Panel Method

In the. panel method, the idea in R 6 is adopted

to formulate the.unsteady potential with -'-.rd speed. Instead of the two-dimensional Green ft.con as given in [6], the three-dimensional zero-speed G _function. which has 'no restriction on the slende

of theship

hull, is used.

11-1. Potential Functions

When a ship moving in regular waves. e unsteady

potential function can be decomposed

h' = (i +o +

(1)

j=i

where is the incident wave potential.o i the

diffrac-tion potentia1,, is the radiadiffrac-tion poten

_unit

mo-tion and

_{is the amplitude of the j me öf motion}

of the ship. The defibition of the ship and the

coordinate system are shown in Fig. 1.

The incident wave potential used in _{work is in}

the following formi

= "

- (2)

where ( and w are the amplitude and freiii.cucy of the incident waves, respectively

_{p is the &ea.ion of the}

wave propagation relative to the positrvex-s and the

wavenwnberkw2/g.;'

,

"

'

The diffraction potential satisfies tbe owing

con-ditions: -

-V24D=O, for

z<O.

₍₃₎

and

the radiation conditián,

where m, = 0, for

j =

1,2,3,4; and rn5

=

n3, m4 =

-From Ref. [61, the ôo and can be

prsed. io

ternis of the zero-speed pocential and as:

(9) and for

¡=1,2,3,4,

(10) o

-

5

+

3, (11) 5w A AO AO W6 - -1w

Neglecting the ind, the diffraction potential and

the radiation potential of zero-speed can be obtained

from:

ÔD

ô1

Onen'

the r iaxioncondition,

where

U

is the steady forward speed of the ship and S is the mean wetted ship hull surface. The radiation

potential satisfies the following conditions:

on S,

=

JjQ(G(î1w)dS

where i

= (x,y,z)

is the field point,

(=

(,q,C) is

the source point, Q() is the strength of

source, and

G(OE,1) ¡s the 3-D zero-speed Green functioa.

=

+

!..

..CL

'

e((z

_C)coae4.(p_).sd9dk

(14)

here k,

w/g, and c

is the frequency of encountér. In equation (13), the potential fùnctiôahas no

Wa-erline integral and also lacks theeffect

? steady waves. 'he evaluation of_{zero-speed Green's function is much} impler than that of_{nonzerosee(J Green's function}

[91

101.

II-2. Added-Mass and Damping

Coefficients The hydrodynaniic

pressure due to the radiated

wave is (5)

The hydrodynarnic forces due to the radiated waves on the ship hull can be writtenas:

F1

= -

JjPrn

1dS =

PJjnidS(_ics

_{+ U)E}

_77kk

=

(16) for Tj

=

PJjni(iwe

₊

UL)hdS

=iAJk(i.)

icEìBJk(w), (17)

where Ajk(Wg) and Bjk(w) are added-mass and damp-ing coefficients,respectively. Applydamp-ing Stokes' theorem to (17) and aurcing n1 being a small quantity, we have

=

-PiJtJjnikdS+PUJjmi%kdS.

(18)

II-3. Wave Exciting FOrces and Moments

The hydrodynainic pressure due to the incident and "

diffracted wav is

=

_{-p(--iw,, + U-)(o, +}

to). (19) The wave exciting forces or momenrs acting on the ship

can be written as (13)

F1

-pzw,

Jj(h

o0)n1dS + OD)72JdS

=F(r)F5,

forj=1,2,...6,

(20) where =

-pi

¡j

jn1dS pujj

-hn1dS =

_{_PwJjjôinidS,}

for

j = 1,2,...6, (2]:)

are. the so called Froude-Krylov forces, and

=

_icPjj0DflJdS

+PUjjnidS

fori = 1,2...6,

(22)

are the forces due to diffracted waves. Again, using the

and

Pr = -p(-i,

+ U-)

qkk. (15)

V1=O,

foc

z<0,

(6)

[(-iw(

_U)2gJj =0,

onz=O,

(7)

Stokes .heorem, we obtain the following exprezsi:

=

_üepJjoajdS+PUfjmJOS

forj=1,2,...6.

(23)

U-4. Ship Motion in Regular Waves

Suppose the unsteady motion of the ship in regular waves in the j mode to be

forj=1,2...6,

(24) the equations of motion in regular waves can be written in the following form:

e

+

Ajk) iBJk

+ CJk]qk = F_.1, for

j=1,2...6,

(25) where Mj& are the components of the generalized mass matrix of the ship,

_Ak

and are. the components of

the added ¡nasa and damping coefficient matric,

re-spectii-ely, C,, are the ponents of the hydrostatic

restoring coefficient matrix, and F,,j are the components

of the complex amplitude vector of the exciting brees

and moments.

UI. Comparisons and Discussiöns

Two ships, a fishing ressel and a container ship, are used in the present computation, L,,/B = 2.46 and

V 187.4 in3 for the fi!Ihing vessel [11], and Lu/B

=

8.385 and V =' 56,097 m3 for the container ship [121, respectively. In order to reduce errors due to the logitu-dinal division of the ship hull in applying strip theory, 22 stations are used for the fishing vessel and 23 stations

for the container ship accding to the recommpnatioa

of the Sealceeping Commic:ec of the 19th ITTC [51- The

panel number is 174 for the fishing vessel and 190 for the container ship, respectively.

Fig. 2 and Fig. 3 are the heave and pitch motions

for the fishing vessel. The experimental data _{are taken} from Ref. [11]. The same hull offsets _{are used in the}

panel method and the strip theory. For the heave

mo-tion. both methods have no significant difference in the long wave range. The results of the panel method .açee

With the experimental results better

_{than that ci the.}

strip theory. Rowever, the panel method _{oves-predicts}

the peak value, at the Fronde number

_{0.19. The strip}

theory gives lower values in the. pitch

_{motion. Fig. 4}

and Fig. 5 show the motions at high Froude number,

Fn = 0.38. It can bese _{that satisfactory results have}

been obtained from the panel method.

_{But the strip}

theory may give better results of pitch motion foc long

waves. In view of the whole range of wave frequescy,_the panel method should be applied for high 'Froude nmother

conditions. The ship motions in oblique heads _are

given in Fig. 6 and Fig. 7. ¡t. can be seen that the panel method is supes-lot to the strip method in this case.

Fig. _{8 and Fig. 9 show the motions of the}

con-tainer ship. The experimental dataare taken from ReL

[12]. Both methods overpredict the heave motion, but the panel method gives good results ed pitch motion.

Therefore, the panel method would be preferred also for slender ships.

In order to investigate the, panel resolution effect, computations west carried out for the .ing vessel with 174 panels and 230 panels, respectively. The' numerical

results are shown in Fig. 10 to Fig. 13. Fig. 10 and. Fig. 11 are the heave and pitch motions at F,, = 0.19

in the head seas. Fig.

12 and Fig. 13 are the heave

and pitch mdtioas ¡t F,, = 0.38 in the head seas. The

results show that the difference due to these two panel resolutions can be ignored. From to our experence, the

hull surface ax one. side of the ship with 21 stations is

suggested to bue discretized into a mirr-nim of 5 panels between every two stations. Further in-easing the panel resolution would not improve the ntimescal results for a mono-hull ship.

IV. Conclusions

The following conclusions are draw-n basedon the

above computations and comparisons.. 1. For ships cl full form in head sea.v

At low Freude numbers, the paoel method may

overpredict the peak value of heave

_{moon but it may}

give fairly good results of heave motion in the whole range of frequency and it gives muth better results of pitch motion than that from the strip theory.

At high Froude numbrs, the' panel method

is better than the strip theory.

_{The sip theory will}

underpredict the ship ¡notion. The panel method is rec-ommerided för this case.

2. For ships of full form in oblique head seas, the panel method is sùpesior to the strip theory. The strip theory, in general, undes-predicts the pitch motions.

3. For slender ships, the strip theory wonid overpredict the ship motions, especially in the _{ghborhood. of the} resonant frequency.

4. _{For an overafl evaluation, the panel method is} su-perior to the strip theory, especially fora full ship and

for high Froude numbers. However, the panel method

requires much more computer time, and the panel

re-sulotion also affects the compúted results. _Normally,

With 200 paklels on a ship hull surface, the converged numerical results can be obtained.

Reference

Newman, J. N.,.'The Theory of Ship Motion", Ad-vances in Applied Mechanics, VoL 18, 178.

\ijisawa, Y. et aL,"Study_{on the Ch racteristics of} Hydrodynaxnic Forces and Motions on Large Offshore Structures with Forward Speed in Waves", Proceedings

of the Nineth Interooa1 Conferenceon Offshore

Me-chanics and Arcc Êngineerrng, VoL 1, Houston, 1990. Eua.ng, Z.and Hsiun,g, C. C., "Computing Ship

Mo-tion with Forward Speed in Wives by The Three Di-mensiocal Sour Dtribution Method", Technical

Re-port NA-89-1, The Citre for Marine Vessel Design and Research, Technical University of Nova Scotia, March

1989. _J

Standing, R. Gi'he Verification and Validation

of Numerical. Mod, with !inples Taken from Wave

Diffraction Therzy, Wave Loading and Response", Pro-ceedings of RJTAM Syniposium, Dynamics of Marine

Vehicles and Strnes in Waves, London, 1990. Report of tbe Seakeeping Committee, 19th ITTC,

Madrid, Spain, Seprexaber 1990.

Salvesen, N., Tuzk, E.O. and F8ltinsen,O.,"Sbip

Mo-tions and Sea L." Thansactioas of SNAME,

_Vol.78,

1970.

Hsiu.ng, C. C. and Huang, Z.,"A New _{Approdi to} Computational Seakeeping Prediction", Technical Re-port NA-90-8. The Centre for Marine Vessel Design and

Research. Tech.aca1 University of Nova Scotia, _October

1990.

Beck, R. F. and Loken1 A. E.,"Three-Djrnensjonaj

Ef-fects in Ship ReLative Motion Problens", J.S.R, VoL33, No.4, Dec. 1989.

Ye, H. and Esiig, C. C.,'Motions

_{and Sea Loads}

of a floating Body with Zero Forward Speed", Techni-cal report NA-86-1. Dept. of MechaniTechni-cal _Engineering, Technical University of Nova Scotia. Feb. 1986.

Ye, H. and Hsinng, C. C.,"Computing

Hydrody-narnic Coefficienns and Wave Exciting Forces_{on a}

Float-ing Body with Sv Forward

_{Speed by 3-D Flow The-}

-ory", Technical R.e.,ort NA-86.2,

_{Department of Me-}

-chanical Engineerixg. Technical University _{of Nova} ScÖ-tia. Apr11 1986.

Narppinen, T.On the Effect of WideBeam on

Ses-keeping Cia _{..srics óf Small Fishing Vessels", Rept.} LTR.SH-361, Dec 1983.

Flokstar C.Ciparison of Ship

Motion Theories

with Experimeunç foe _{a Container Ship", LS.P., VoL21,}

1974.

Inglis, R.. B. and Price, R. C.,"Compa.rison of

Cal-:ulated. Responsees foc _{Arbitrai,j Shaped Bodies Using}

rwo and TI _{e-Di.Th,IOflal Theories', I. S. P., voL 27,} o. 307, 1080. 1.3 0.6 o ¡.6 I.' 1.2 0.3 0.6 0.4 0.2 o ,3HEAVE PtT4

p.ea'v

q4-AOI.t _YAW

Fig. i Ship Motion and Coordinate System

STAVI AXPtZTV'DE/TAVE AMPIITUDS

4 z Ql grip theoty P! method (174 pa.) O expeent psd method (174 peoda) o O pen ¡.5 2 2.5 $ 3.5 4 4.3

WAVE LENGTH/SHIP LENGTH

r. 3 Pua

Moo@ (or the Thing Ve1_{(F = O.l9.p = 180')}

RLVE a.trruDE,'vAve AiUD2

1.5 2 2.3 3 3.3 4 4.3 WAVE LENGTH/SHIP LENGTH

4 ! Motk to, the Thbig VI (F. 0. 180')

LS 2 2.3 3 3.3 4 4.3

WAVE LENGTH/SHIP LENGTH

?. 2 !

Mota tjc

the r8 VeI (F.

a = L80°)

PIT i_1/!4!E SWPE

1.4 12 0.3 0.6 0.4 0.2

ptTC AMPUTUD/WAYE SWPE.

HEAVE AMPUTUDE/WAVE JUTUDE

*

-atziptheoc1

'r

0.8 E- 0.6'-04

2

o 02 o strip theory _{o -.}

...-..--

ethc _{(174 r--)} 1.5 2 2.6 S 3.5 4 45

WAVE LENGTH/SHIP LENGTH Fig. 6 He*ve Uoio _{(or the Tibiag Vmi (F = O.iIp =}

?TTB &MPUTUDE,'wAyE SWP!L

paieI met (174 pe*s)

I 1.5 2 2.5 3 3.5 4 43

WAVE LENGTH/SHIp LENGTH

Fig. T Pitch Modeo for the _{Fiebi*g Ve1 (F. = O.iS,p = U)}

12 HEAVE AMPI. UDE/WAVE AMPUTUDE

0.6 1 _1.4

WAVE LENGTH/SHIP LENGTH

Fig. 6 Heate Modos_{foe the Coct.jc,er Sbip (F.}

= oj 1.5 0.3 ¡.2 0.8 0.6 0.4 0.2 1.4 1.2 0.8 0.6 0.4 0.2 o !r!ÇH A.MPUTUoE/.*vtSwpe .t1p theory 1.5 2 2.5 3 2.5 4

WAVE LENGTH/SmP LENGTH

Fig. 10 HeseModo. (or the ghi. Y (F = 0.19.p = 180°) - etbod (190 peocia)

G p.riaeoi

ftre - - e

p...I.

-oz 0.6 1 1.4. 1.

WAVE LENGTH/SH]P LENGTH

Fig. 9Pitch Mcsce (or theCøcia (F,, = 0.245, = 180°)

HEAVE Agpt rTJD!/vAvE AJaUTDE

¿ '.5 _{2 2.5 3}

3_3 4 4.5 WAVE LENGTH/SHIP LENGTH

Pig. 11 Pitch Modo. forib.Fishing V tF. = L19,s = 180°)

HEAVE AMPUTUDE/VAVE A3CPLZTU

¡.3 2 2.5 S 3.3 4 4.5

WAVE LENGTH/SHIP LENGTH

Fig. 12 E. Modo. fo. the .bin V (F. = 0.3$,t = 180°) 4

¿.5 2 2.5 3 3.5 WAVE LENGTH/SNIP LENGTH

Fig. 5 Piicb Moio for ib. r.hzg Vs1 (F. O.*i 180)

PIT AMPUTUDE/AYE .0Pg 1.4 o

-

ctbod(174 peo) r

--! e

0.6-strip theory 0.41 0.2 e 1.2 0.8 0.6 0.4 0.2 o

0.5

o

PITCH £UTUD/W! .O?E

2

¡.5

¡5 z z.z 3 s.s

WAVE LENGTH/SHIP LENGTH

r. 13 Pitch Mos k ths rbg VI (P O.SS,p 180')