CFD Application for Added Resistance Computation

CFD Application for Added Resistance Computation

2012 International Research Exchange Meeting of Ship and Ocean Engineering (SOE) in Osaka

Kyung-Kyu Yang1, Jae-Hoon Lee(2)1, Bo-Woo Nam1,2 and Yonghwan Kim1

1Seoul National UniversityDepartment of Naval Architecture & Ocean Engineering

2Korea Institute of Ocean Science and TechnologyOcean Plant Research Division

21 December, 2010Osaka, Japan

Background

21Jameson (2008)

< Airplane Design1 > < Resistance > < Seakeeping >

Inertia Dominant

Large-AmplitudeShip Motion withBreaking WaveLocal ImpactWake…

State of the Art

C. Hu et al.

(Kyushu Univ.)

D.G.Dommermuthet al.

(SAIC)

J. Yang et al.

(Univ. of Iowa)

P. Queutey et al.(ECN)

R. Löhner et al.

(George Mason Univ.)

H. Miyata et al.

(Univ. of Tokyo)

Y. Kim et al.(SNU)

Discretization(Convective term)

CIP 3rd QUICK 3rd QUICK / WENO

Improved Gamma Galerkin QUICK MC Limiter

Body Motion

IBMParticle

IBMTriangle panel

IBMTriangle

panel

Mesh Deformation ALE

Overlapping Grid

IBMTriangle

panel

Free Surface

THINC (VOF) CLSVOF CLSVOF VOF VOF

Density Function(QUICK)

THINC (VOF)

Reference

2008 ONR2010 IWWWFB

2007 NSH2008 ONR2010 ONR

2008 ONR2009 JCP

2007 Computer & Fluids2010 ONR

2007 Int. J. Numer. Meth. Fluids2007 NSH

2003 JMST2005 JMST 2011 IWSH

Remark LESLESGhost Fluid Method

RANSCompressive face reconstruction

RANS

3

Moving complex body Highly distorted free-surface High-Reynolds number (turbulence) Multi-scale problem (large aspect ratio) Huge computational cost

Numerical Methods

Fluid Flow SolverFVM + Fractional stepMC limiterCartesian gridFree surface capturing

(THINC / WLIC)Solid Body TreatmentTriangular surface mesh → Volume fractionLevel-set + Angle weighted pseudo-normal Immersed boundary method

4

1.0solid

1.0air

1.0water

Flow Chart

5

- THINC/WLIC2

- Fractional Step Method

*

** *

1

1 **1

1

1 **1

0

1

1

1 1

nn n

bn

nn

n

nn

u u u u n dSt

u u f dVt

u u p ndSt

p ndS u ndSt

11

1/2

0

1 tanh2

ii

i

ut

x xF x

x

1van Leer (1977); 2Xiao (2005), Yokoi (2007)

- Monotonized Cetral Limiter1

1/2 1/2

1max 0, min 2 , , 22

/ / /i i

rr r

r q x q x

Flow Chart (cont.)

6

Level-set

H

(Smoothed Heaviside function)

,s tT

2, ,Q s t s t T P

, 0,0Q s t Minimum value of Q(s,t) is occurred at…

Eberly (2008)

Example – S175 Containership

7< Triangular surface mesh (upper) and calculated density function (lower) of S175 containership >

3

3 3ˆ 1 bodyu u U

bodyU3

,i ju1,i ju

, 1i jv

,i jv

3 ,i ju1,i ju

, 1i jv

,i jv

Improvement of Body Representation

8

3 3 3 3 3u u v wa b c d

3u

3v

A

B

A B

3 1.0 3 0.95

Linear Restoring Coefficients

9

33 3, ,

255 3

, ,

3, ,

calculated target

target

% 100

i ji j k ksurf

i j ii j k ksurf

displacement i j ki j k ksurf

C g x y

C g x y xc

V x y z

C CError

C

Grid Index

Err

or(%

)

0 1 2 3 4 5 6-1

0

1

2

3

4

5

6

7

8

C33C55Displacement

Index Nx * Ny * Nz △xmin/L △ymin/L △zmin/L

1 153*113*107 0.040 0.0060 0.0040

2 202*117*118 0.030 0.0055 0.0030

3 264*121*122 0.020 0.0050 0.0020

4 264*121*131 0.020 0.0050 0.0015

5 284*121*131 0.018 0.0050 0.0015

Incident Wave Simulation

10

λ/Δx = 10 λ/Δx = 20 λ/Δx = 40

A/Δz = 2

A/Δz = 4

A/Δz = 8

A/Δz = 16

10; 40; 10 ~ 20A xz x z

Grid Generation

11L: ship length, B: ship breadth, T: ship draught, λ: wave length, A: wave amplitude, h: tank depth

/ 40/ 20

/ 10

xx z

A z

1 / 1.04 ~ 1.08i ix x (expansion ratio)

/ 75L x

20By

Incident Wave Region

Exciting Force and Hydrodynamic Coefficients

12

(L/g)1/2A

33/

B33

(L/g

)1/2 /

1 2 3 4 5 60

0.5

1

1.5

2

2.5

3

0

0.5

1

1.5

2

2.5

3

A33,Exp.(Journee,1992)A33,PresentB33,Exp.(Journee,1992)B33,Present

/L

X5

/k a

C55

0 0.5 1 1.5 2 2.50

0.2

0.4

0.6

0.8

1

Exp.(Journee,1992)Present

time(sec)

3/A

5/k

A

5 10 15-1.5

-1

-0.5

0

0.5

1

1.5

-1.5

-1

-0.5

0

0.5

1

1.5

HeavePitch

time(sec)

Fx,F

z(N

)

My

(Nm

)

5 10 15-60

-40

-20

0

20

40

60

-60

-40

-20

0

20

40

60

HeavePitchSurge

Wigley III Motion

13

/L 5

L/2A

0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

2.5

3

Exp. (Journee, 1992)w/o averagew/ average

Wigley III Motion (cont.)

14

/L

3/A

0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

2.5

3

Exp. (Journee, 1992)w/o averagew/ average

S175 Containership

15

/L 5

/kA

0 0.5 1 1.5 2 2.50

0.4

0.8

1.2

1.6

2

Exp. (Fonseca, 2004)w/o average, H/=1/40w/ average, H/=1/40

midfinecoarse

S175 Containership (cont.)

16

/L

3/A

0 0.5 1 1.5 2 2.50

0.4

0.8

1.2

1.6

2

Exp. (Fonseca, 2004)w/o average, H/=1/40w/ average, H/=1/40

midfinecoarse

kA 5

/kA

0 0.045 0.09 0.135 0.180

0.4

0.8

1.2

1.6

Exp.(O'Dea et al.,1992)WISH 2.1(Kim et al.,2008)Present

Nonlinear Response (λ/L = 1.0)

17

kA

3/A

0 0.045 0.09 0.135 0.180

0.4

0.8

1.2

1.6

Exp.(O'Dea et al.,1992)WISH 2.1(Kim et al.,2008)Present

kA

3/A

0 0.045 0.09 0.135 0.180

0.4

0.8

1.2

1.6

Exp.(O'Dea et al.,1992)WISH 2.1(Kim et al.,2008)Present

kA 5

/kA

0 0.045 0.09 0.135 0.180

0.4

0.8

1.2

1.6

Exp.(O'Dea et al.,1992)WISH 2.1(Kim et al.,2008)Present

Nonlinear Response (λ/L = 1.2)

18

Added Resistance

19

Time (sec)

Fx(N

)

5 10 15-2

0

2

4

6

8

10

12

Time (sec)

Fx(N

)

5 10 15 20 25 30 350

1

2

3

4

5

6

R_steady

R_wave

R_addedR_wave R_steady

time(sec)

Fx

30 35 40 45 50 55 60-4E+06

-2E+06

0

2E+06

4E+06

6E+06

8E+06

1E+07

CoarseMidFineFine_dyFine_dxFine_dxdz

Grid Convergence Test (S175)

20

Half Body L/∆x B/∆y A/∆z ∆x/∆z Nx Ny Nz Total

Coarse 37.5 14.5 5.9 10.0 180 55 102 1,009,800

Mid 50.0 19.4 7.8 10.0 209 59 110 1,356,410

Fine 75.0 29.0 11.7 10.0 266 64 121 2,059,904

Fine_dy 75.0 40.0 11.7 10.0 266 76 121 2,446,136

Fine_dx 100 29.0 11.7 7.5 291 64 121 2,253,504

Fine_dxdz 100 29.0 16.7 10.7 291 64 170 3,166,080

S175 – Fixed vs. Free

21

< λ/L = 0.5 >

< λ/L = 1.0 >

Wigley III – Surge Force Signal

22

time(sec)

Fx

2 4 6 8 10 12 14 16 18-2

0

2

4

6

8

10

12

14

16

18

w/o averagew/ averagew/o average (steady)w/ average (steady)

Added Resistance (Wigley III)

23

/LR

/gA

2 B2 /L

0 0.5 1 1.5 2 2.5

0

15

30

45

60

Exp. (Journee, 1992)w/o averagew/ average

/L

R/

gA2 B

2 /L

0 0.5 1 1.5 2 2.5

0

15

30

45

60

Exp. (Journee, 1992)w/o averagew/ average

/LR

/gA

2 B2 /L

0 0.5 1 1.5 2 2.5

0

5

10

15

20

Exp. (Fujii, 1975)Exp. (Nakamura, 1977)w/o averageFree Motion

midfinecoarse

fine2finemidcoarse

Added Resistance (S175)

24

/L

R/

gA2 B

2 /L

0 0.5 1 1.5 2 2.5

0

5

10

15

20

Exp. (Fujii, 1975)Exp. (Nakamura, 1977)w/o averageFree MotionFixed

mid_dxmid_dzmid_dycoarse

Conclusions In order to consider a three-dimensional complex body in a

Cartesian-grid, a level-set-based algorithm was successfullyimplemented.

Numerical results of wave excitation force, hydrodynamiccoefficients, and ship motion responses show that reasonablepredictions can be obtained by using the newly developed code.

In order to increase the order of accuracy of body representation,cell face values are taken into account when calculating the volumefraction of a solid body. This small modification affected theprediction of added resistance, especially if a ship has very thinplate-like bow shape.

The added resistance is more sensitive to the grid spacing than theship motion response and it is found that at least 10 grid pointsshould be used within the wave amplitude while the ratio ∆x to ∆z ismaintained less than 20 in the incident wave region.

25

Q & A

26