Challenges in Hydrodynamic Analysis of VLFS

M.Ohkusuohkusu@jamstec.go.jp

Workshop on Very Large Floating Structures for the FutureTrondheim 28-29 October 2004

Challenges

• Non-uniformity

• Station-keeping

• Consequence of small failure

• Local phenomena

• Small global rigidity

X

Y

hd Fluid beneath the platform

Fluid without the platform above

Thin plate type:

x

Frequency of resonance of 1D vibration: Eqs of vibration

Eq. of wave number

b-b

R i I

Thin plate type:

g /h

Complex frequency of resonance for a plate

D /gh4 2 104 ,b /h 50

(Meylan 2003)

Energy of plate vibration (Meylan 2003)

D /gh4 2 104 ,b /h 50

Transmission T and reflection R coefficients of a plate (Meylan 2003)

D /gh4 2 104 ,b /h 50

Reflection coefficient is zero at

2kbn

x

y

b-b

Frequency of resonance of 2D vibrationPeriodic in Y direction

Thin plate type:

x

y

b-b

ky k(real) : progressive wave impossible

ky k(real) : trapped-modeno incident wave

x

y

b-b

ky k(real) : progressive wave impossible

ky k(real) : trapped-modeno incident wave

Complex frequency of resonance (2nd symmetric mode)(Tkhacheva 2000 )

k2 ky

k2 ky

Complex frequency of resonance (2nd asymmetric mode)(Tkhacheva 2000 )

Geometrical optics approach

K K

K

K

plate

water

Parabolic approximation

Deflection of a Platein Oblique Waves at 65.2deg Less Than the Critical Angle(shallow water)

Comparison of Analyticaland Numerical Solutions

Analytical

Numerical

Analytical

Deflection:

Numerical

Ray approach

Full numerical ( Ohmatsu )

Oblique incidence ( Takagi )

Section y/B=0.5

0.0

0.1

0.2

0.3

0.4

0.00 0.25 0.50 0.75 1.00x/L

aa Ray Theory

3-D Cal. by Ohmatsu

Hierarchical Interaction Theory (Kashiwagi)Hierarchical Interaction Theory (Kashiwagi)

A trouble: Fictitious bodies must not penetrate each other

Float array

Wave Pattern around a column-supported VLFSWave Pattern around a column-supported VLFS

N=32X160(d/a=2)N=32X160(d/a=2)N=16X80(d/a=1)N=16X80(d/a=1)In a wave of L/λ=32.59 coming from upper rightIn a wave of L/λ=32.59 coming from upper right

Experiment (Kashiwagi)Experiment (Kashiwagi)

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6-180

-90

0

90

180

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.60.0

1.0

2.0

3.0

4.0

Phase (deg.)

Ks

Between No.13 & No.14 Calculation Experiment

d/a=2, s/a=2, =0 deg.

Wave Amplitude ||/A

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6-180

-90

0

90

180

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.60.0

1.0

2.0

3.0

4.0

Phase (deg.)

Ks

Between No.15 & No.16 Calculation Experiment

d/a=2, s/a=2, =0 deg.

Wave Amplitude ||

/A

Wave elevation between floats

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6-180

-90

0

90

180

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.60.0

1.0

2.0

3.0

4.0

5.0

Phase (deg.)

Ks

Column No.1(upwave end) Calculation Experiment

d/a=2, s/a=2, =0 deg.

Surge Force |Ex|/gA(a

2 )

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6-180

-90

0

90

180

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.60.0

0.2

0.4

0.6

0.8

1.0

Phase (deg.)

Ks

Column No.1(upwave end) Calculation Experiment

d/a=2, s/a=2, =0 deg.

Heave Force |Ez|/gA(a

2 )

Wave exciting surge & heave forcesWave exciting surge & heave forces

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6-180

-90

0

90

180

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.60.0

1.0

2.0

3.0

4.0

5.0

Phase (deg.)

Ks

Column No.15(downwave side)

Calculation Experiment

d/a=2, s/a=2, =0 deg.

Surge Force |Ex|/gA(a

2 )

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6-180

-90

0

90

180

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.60.0

0.2

0.4

0.6

0.8

1.0

Phase (deg.)

Ks

Column No.15(downwave side)

Calculation Experiment

d/a=2, s/a=2, =0 deg.

Heave Force |Ez|/gA(a

2 )

Wave exciting surge & heave forcesWave exciting surge & heave forces

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

Ks

Fx/0.5gA2D

Column No.9 inside(almost center)

Calculation Experiment

d/D=2, s/D=1, =0 deg.

Steady Steady Force

Steady Wave Drift Force ; inside(left) & outside (right)Steady Wave Drift Force ; inside(left) & outside (right)

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

Ks

Fx/0.5gA2D

Column No.9 outside(almost center)

Calculation Experiment

d/D=2, s/D=1, =0 deg.

Steady Surge Force

x

y

b-b

ky k(real) : progressive wave impossible

ky k(real) : trapped-modeno incident wave

Complex frequency of resonance (2nd symmetric mode)(Tkhacheva 2000 )

k2 ky

k2 ky

Complex frequency of resonance (2nd asymmetric mode)(Tkhacheva 2000 )

Geometrical optics approach

K K

K

K

plate

water

Parabolic approximation

Deflection of a Platein Oblique Waves at 65.2deg Less Than the Critical Angle(shallow water)

Comparison of Analyticaland Numerical Solutions

Analytical

Numerical

Analytical

Deflection:

Numerical

Ray approach

Full numerical ( Ohmatsu )

Oblique incidence ( Takagi )

Section y/B=0.5

0.0

0.1

0.2

0.3

0.4

0.00 0.25 0.50 0.75 1.00x/L

aa Ray Theory

3-D Cal. by Ohmatsu

Hierarchical Interaction Theory (Kashiwagi)Hierarchical Interaction Theory (Kashiwagi)

A trouble: Fictitious bodies must not penetrate each other

Float array

Wave Pattern around a column-supported VLFSWave Pattern around a column-supported VLFS

N=32X160(d/a=2)N=32X160(d/a=2)N=16X80(d/a=1)N=16X80(d/a=1)In a wave of L/λ=32.59 coming from upper rightIn a wave of L/λ=32.59 coming from upper right

Experiment (Kashiwagi)Experiment (Kashiwagi)

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6-180

-90

0

90

180

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.60.0

1.0

2.0

3.0

4.0

Phase (deg.)

Ks

Between No.13 & No.14 Calculation Experiment

d/a=2, s/a=2, =0 deg.

Wave Amplitude ||/A

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6-180

-90

0

90

180

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.60.0

1.0

2.0

3.0

4.0

Phase (deg.)

Ks

Between No.15 & No.16 Calculation Experiment

d/a=2, s/a=2, =0 deg.

Wave Amplitude ||

/A

Wave elevation between floats

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6-180

-90

0

90

180

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.60.0

1.0

2.0

3.0

4.0

5.0

Phase (deg.)

Ks

Column No.1(upwave end) Calculation Experiment

d/a=2, s/a=2, =0 deg.

Surge Force |Ex|/gA(a

2 )

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6-180

-90

0

90

180

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.60.0

0.2

0.4

0.6

0.8

1.0

Phase (deg.)

Ks

Column No.1(upwave end) Calculation Experiment

d/a=2, s/a=2, =0 deg.

Heave Force |Ez|/gA(a

2 )

Wave exciting surge & heave forcesWave exciting surge & heave forces

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6-180

-90

0

90

180

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.60.0

1.0

2.0

3.0

4.0

5.0

Phase (deg.)

Ks

Column No.15(downwave side)

Calculation Experiment

d/a=2, s/a=2, =0 deg.

Surge Force |Ex|/gA(a

2 )

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6-180

-90

0

90

180

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.60.0

0.2

0.4

0.6

0.8

1.0

Phase (deg.)

Ks

Column No.15(downwave side)

Calculation Experiment

d/a=2, s/a=2, =0 deg.

Heave Force |Ez|/gA(a

2 )

Wave exciting surge & heave forcesWave exciting surge & heave forces

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

Ks

Fx/0.5gA2D

Column No.9 inside(almost center)

Calculation Experiment

d/D=2, s/D=1, =0 deg.

Steady Steady Force

Steady Wave Drift Force ; inside(left) & outside (right)Steady Wave Drift Force ; inside(left) & outside (right)

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

Ks

Fx/0.5gA2D

Column No.9 outside(almost center)

Calculation Experiment

d/D=2, s/D=1, =0 deg.

Steady Surge Force