A Seakeeping Computation Method ConsideringA Seakeeping Computation Method Considering

Fully Nonlinear Steady Wave FieldFully Nonlinear Steady Wave Field

by Mirel Nechitaby Mirel Nechita

Doctor of Engineering Course in Hiroshima UniversityDoctor of Engineering Course in Hiroshima University• Faculty of Engineering - NAOE DepartmentFaculty of Engineering - NAOE Department

• Ocean Space Engineering LaboratoryOcean Space Engineering Laboratory

Supervisor Professor Hidetsugu IwashitaSupervisor Professor Hidetsugu Iwashita

Developed Codes:Developed Codes:- Steady Flow - Steady Flow

Linear (UF, DBF)Linear (UF, DBF)

Nonlinear (FNL)Nonlinear (FNL)

-Unsteady Flow-Unsteady Flow

(UF, DBF, FNL)(UF, DBF, FNL)

- H- Hybrid ybrid MMethodethod

(DBF, FNL)(DBF, FNL)

MATHEMATICAL FORMULATIONSMATHEMATICAL FORMULATIONS

]),,([),,();,,(),,();,,( tits

eezyxzyxUtzyxzyxtzyx

Wave characteristics:

Wave amplitude

Circular frequency

Encounter circular frequency

Wave number

Total potentialTotal potential

Exact free surface boundary conditionExact free surface boundary condition

(1)(1)

(2)(2)

z

y

xn

n

O

SH

SF

-U

);,(02

12 2 tyxzon

zg

tt

A

0

eK

STEADY FLOWSTEADY FLOW

zKKK

zK

zK

z

zKKK

on02

11)(

2

1)(

21

)(2

1)(

1)(

1

00

2

00

02

2

00

2

0

HSn

on0

Boundary conditions for iterative scheme:Boundary conditions for iterative scheme:

2

0

)(1)2/1(

1

Ks

Steady wave elevation and steady pressureSteady wave elevation and steady pressure

(4)(4)

(5)(5)

(3)(3)

20 /where UgK

22

)(12

U

ps

UNSTEADY FLOWUNSTEADY FLOW

sj

jjjjjje

zK

i

zK

zK

z

zKKiK

on01

)(21

)(2

1)(

1)(

00

02

2

00

VV

VV

VVVVV

);6~1(for

jmi

Un

n je

jj

HSnn

on07

Boundary conditionsBoundary conditions

(6)(6)

(7)(7)

gK ee /2;/ gU e

Vr

Vrnnr

Vnn

),,(

((),,(),,(

(),,(),,(

654654

321321

zyx

))mmmnnn

)mmmnnn

WhereWhere

(8)(8)

gUjdSniK

igA

Ej

S

j

H

/where)6~1()()1

1( 0700

V

)6~1())(()(2

1)

11(

200

jdSnK

dSniK

Bi

Ai

S

jij

Se

ijij

HH

VVV β

s

jej

j

zji

K

iKzKA

on6~1for/

11

11

1

70

0

7

VV

Hydrodynamic forcesHydrodynamic forces

Unsteady wavesUnsteady waves

(9)(9)

(10)(10)

(12)(12)

)6~1(])([6

1

2

iECBiAM ijijijeijijj

e

Ship motionsShip motions

(11)(11)

Desingularized Rankine Panel MethodDesingularized Rankine Panel Method ((Jensen, Jensen, 1986 & 1986 & Bertram, Bertram, 1990)1990)

Constant source distributions on body surface and Constant source distributions on body surface and free surfacefree surface

Radiation condition Shifting techniqueRadiation condition Shifting technique

NUMERICALNUMERICAL METHODMETHOD

dSQPGQ

Q

P

P

FH SS j

S

j

),()(

)(

)(

)(

Ship hull form of Series-60 (Cb=0.8) Ship hull form of Series-60 (Cb=0.8) NNHH=1320=1320

Computational grids of Series-60, Cb=0.8Computational grids of Series-60, Cb=0.8(N(NHH=1320, N=1320, NFF=1717)=1717)

Steady wave distribution for Series-60 (Cb=0.8) Steady wave distribution for Series-60 (Cb=0.8) along several longitudinal axes at Fn=0.2along several longitudinal axes at Fn=0.2

Contour plots of the steady wave Contour plots of the steady wave for Series-60 (Cb=0.8)for Series-60 (Cb=0.8)

Hull discretization for Series-60, Cb=0.8Hull discretization for Series-60, Cb=0.8- unsteady problem- unsteady problem

Added mass and damping coefficients for heave and Added mass and damping coefficients for heave and pitch for Series-60 (Cb=0.8) at Fn=0.2pitch for Series-60 (Cb=0.8) at Fn=0.2

Wave exciting forces and moment for Series-60 Wave exciting forces and moment for Series-60 (Cb=0.8) at Fn=0.2, (Cb=0.8) at Fn=0.2, =180 degs.=180 degs.

Ship motions for Series-60 (Cb=0.8) Ship motions for Series-60 (Cb=0.8) at Fn=0.2, at Fn=0.2, =180 degs.=180 degs.

Contour plots of heave radiation wave for Series-60 (Cb=0.8)Contour plots of heave radiation wave for Series-60 (Cb=0.8)at Fn=0.2, KL=24.0 and t=0at Fn=0.2, KL=24.0 and t=0

Contour plots of diffraction wave for Series-60 (Cb=0.8)Contour plots of diffraction wave for Series-60 (Cb=0.8)at Fn=0.2, at Fn=0.2, /L=0.5, /L=0.5, =180 degs. and t=0=180 degs. and t=0

Ship hull form of Series-60 (Cb=0.6)Ship hull form of Series-60 (Cb=0.6)NNHH=1320=1320

Steady wave cuts for Series-60 at Fn=0.2Steady wave cuts for Series-60 at Fn=0.2(Cb=0.6 left, Cb=0.8 right)(Cb=0.6 left, Cb=0.8 right)

Steady wave contour plots for Series-60, Steady wave contour plots for Series-60, slender model (Cb=0.6) at Fn=0.2slender model (Cb=0.6) at Fn=0.2

Wave exciting forces and moment Wave exciting forces and moment for Series-60 at Fn=0.2, for Series-60 at Fn=0.2, =180 degs.=180 degs.

• The present Rankine panel method based on the desingularized method was confirmed The present Rankine panel method based on the desingularized method was confirmed to be effective to predict fully nonlinear steady wave field accurately. The solution to be effective to predict fully nonlinear steady wave field accurately. The solution obtained by this method is utilized to evaluate the influence terms of the steady wave obtained by this method is utilized to evaluate the influence terms of the steady wave field in the unsteady problem.field in the unsteady problem.

• The desingularized Rankine panel method is also effective for the unsteady problem The desingularized Rankine panel method is also effective for the unsteady problem but the shifting technique for satisfying the radiation condition numerically is applicable but the shifting technique for satisfying the radiation condition numerically is applicable only for only for >0.5, from the practical point of view. The method was examined for different >0.5, from the practical point of view. The method was examined for different hull forms and it was confirmed that the consideration of the fully nonlinear steady wave hull forms and it was confirmed that the consideration of the fully nonlinear steady wave field improves the estimation accuracy of the unsteady wave field.field improves the estimation accuracy of the unsteady wave field.

• For the high frequency range, the desingularized Rankine panel method was validated For the high frequency range, the desingularized Rankine panel method was validated by comprehensive comparisons of unsteady wave patterns with experimetal data. In this by comprehensive comparisons of unsteady wave patterns with experimetal data. In this range the bluntness effect of the hull form on hydrodynamic forces appears remarkably range the bluntness effect of the hull form on hydrodynamic forces appears remarkably in the pitch exciting moment. This suggests the significant effect of the hull form on the in the pitch exciting moment. This suggests the significant effect of the hull form on the pressure distribution at the bow and the stern part. The heave radiation wave, computed pressure distribution at the bow and the stern part. The heave radiation wave, computed by the present method, showed good agreement with experiments. A negligible by the present method, showed good agreement with experiments. A negligible discrepancy between computed results and measurements were observed for the discrepancy between computed results and measurements were observed for the diffraction wave, especially near the blunt bow. An insufficient grid resolution may be diffraction wave, especially near the blunt bow. An insufficient grid resolution may be one of the cause of this discrepancy. It was also made clear the necessity of extending one of the cause of this discrepancy. It was also made clear the necessity of extending the method to the the method to the low frequency regionlow frequency region..

Conclusions Conclusions RPMRPM

HYBRIDHYBRID METHODMETHOD

NEAR FIELD - Desingularized Rankine Panel MethodNEAR FIELD - Desingularized Rankine Panel Method

FAR FIELD - Green Function MethodFAR FIELD - Green Function Method

'),()(2'

)('

)(1

),()()(

*0

**

0

**

*

dyQPGQKix

Qx

Q

K

dSQPGn

Qn

Q

W

L

jjj

W

S

jj

j

C

C

Unsteady potentials for the far fieldUnsteady potentials for the far field

Free surface boundary condition for the far fieldFree surface boundary condition for the far field

nnjj

jj

*

* ,

Artificial surface boundary conditionArtificial surface boundary condition

(13)(13)

(15)(15)

(14)(14)0on0),(2

zQPG

zg

xUi W

e

Side wall effect on the unsteady waveSide wall effect on the unsteady wave

Fn=0.2 , KL=2.0 (Fn=0.2 , KL=2.0 (=0.283)=0.283) Fn=0.2 , KL=1.3 (Fn=0.2 , KL=1.3 (=0.23)=0.23)

Computational grids of Series-60 Computational grids of Series-60 utilized in Hybrid Methodutilized in Hybrid Method

Coupled added mass and damping coefficients Coupled added mass and damping coefficients for heave and pitch for Series-60 (Cb=0.6) at Fn=0.2for heave and pitch for Series-60 (Cb=0.6) at Fn=0.2

Wave exciting forces and moment Wave exciting forces and moment for Series-60 (Cb=0.6) at Fn=0.2, for Series-60 (Cb=0.6) at Fn=0.2, =180 degs.=180 degs.

Added mass and damping coefficients Added mass and damping coefficients for heave and pitch for Series-60 (Cb=0.8) at Fn=0.2for heave and pitch for Series-60 (Cb=0.8) at Fn=0.2

Contour plot of heave radiation wave for Series-60 (Cb=0.8)Contour plot of heave radiation wave for Series-60 (Cb=0.8)at Fn=0.2, KL=1.32, at Fn=0.2, KL=1.32, =0.23=0.23

Perspective view of heave radiation wave for Perspective view of heave radiation wave for Series-60 (Cb=0.8)Series-60 (Cb=0.8)

at Fn=0.2, KL=1.32, at Fn=0.2, KL=1.32, =0.23=0.23

• In the low frequency range, the experimental data will be affected by the side wall effects In the low frequency range, the experimental data will be affected by the side wall effects of the towing tank. The obtained experimental data needs to be carefully validated, before of the towing tank. The obtained experimental data needs to be carefully validated, before we utilize them as an index of validation the computation codes. A simple time domain we utilize them as an index of validation the computation codes. A simple time domain simulation was applied to make clear the side wall effect and it was confirmed that the simulation was applied to make clear the side wall effect and it was confirmed that the unsteady wave, measured at unsteady wave, measured at =0.23, was not contaminated by the reflected wave from the =0.23, was not contaminated by the reflected wave from the side wall. Therefore, we can utilize this experimental data for the validation of the side wall. Therefore, we can utilize this experimental data for the validation of the computation codes.computation codes.

• It was developed a new hybrid method, which combines the advantages of the It was developed a new hybrid method, which combines the advantages of the desingularized Rankine panel method for the high frequency range and and the Green desingularized Rankine panel method for the high frequency range and and the Green function method for the low frequency range. The predicted hydrodynamic forces by this function method for the low frequency range. The predicted hydrodynamic forces by this method, are in good agreement with experiments for a wide frequency range. The method, are in good agreement with experiments for a wide frequency range. The importance of the steady wave field on hydrodynamic forces is demonstrated through importance of the steady wave field on hydrodynamic forces is demonstrated through numerical results for the added mass, damping coefficients and the wave exciting forces.numerical results for the added mass, damping coefficients and the wave exciting forces.

• The hybrid method is able to estimate in good accuracy the unsteady waves for both, high The hybrid method is able to estimate in good accuracy the unsteady waves for both, high and low frequency range. It was shown that fully nonlinear formulation, used in this study, and low frequency range. It was shown that fully nonlinear formulation, used in this study, was necessary in order to capture the influence of the steady wave field in high accuracy. was necessary in order to capture the influence of the steady wave field in high accuracy. The influence of the steady wave field is revealed especially in the downstream region of the The influence of the steady wave field is revealed especially in the downstream region of the ship.ship.

Conclusions Conclusions Hybrid MethodHybrid Method

Y

Z

X

Hull discretization for the fast Hull discretization for the fast shipship

NNHH=1007=1007

-0.030

-0.020

-0.010

0.000

0.010

0.020

0.030

-1.5-1-0.500.51

x/L

h/L

Linear ship-sideLinear center-lineNonlinear ship-sideNonlinear center-line

F.P.

A.P.

Linear C W =0.620 . 10 -3

Nonlinear C W =0.907 . 10 -3

Experiment C W =1.053 . 10 -3

Steady wave distributions along ship-side at Fn=0.6Steady wave distributions along ship-side at Fn=0.6

-0.030

-0.020

-0.010

0.000

0.010

0.020

0.030

-1.5-1-0.500.51

x/L

h/L

Linear ship-sideLinear center-lineNonlinear ship-sideNonlinear center-line

F.P.

A.P.

Linear C W =0.698 . 10 -3

Nonlinear C W =1.027 . 10 -3

Experiment C W =1.251 . 10 -3

Improved hull formImproved hull formInitial hull formInitial hull form

Improved hull form

-0.005 -0.004 -0.003 -0.002 -0.001 0 0.001 0.002 0.003 0.004 0.005

Initial hull form

/LNonlinear computation

Steady wave contour plots, Fn=0.6Steady wave contour plots, Fn=0.6

ZX

Y

cp: -0.06 -0.05 -0.04 -0.02 -0.01 0.00 0.01 0.02 0.04 0.05 0.06

Linear computation

Nonlinear computation

ZX

Y

cp: -0.06 -0.05 -0.04 -0.02 -0.01 0.00 0.01 0.02 0.04 0.05 0.06

Linear computation

Nonlinear computation

Initial hull formInitial hull form

Improved hull formImproved hull form

Steady pressure distributions on hull, Fn=0.6Steady pressure distributions on hull, Fn=0.6

-1 0 1x/L

0

0.2

0.4

0.6

0.8

y/L

-0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25

Diffraction wave - initial hull form

-1 0 1x/L

0

0.2

0.4

0.6

0.8y/

L-0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25

Diffraction wave - improved hull form

Diffraction wave - Diffraction wave - 77/A/A

at Fn=0.6, at Fn=0.6, /L=0.5, /L=0.5, =180º and t=0=180º and t=0

End of PresentationEnd of Presentation

Thank you!Thank you!