Slamming induced pressure and forces on marine structures Sun.pdfSlamming induced pressure and forces on marine structures. Hui Sun, Sectionof shiphydrodynamicsand stability, DNV (PhDstudent

Slamming induced pressure and forces on marine structures

Hui Sun, Section of ship hydrodynamics and stability, DNV

(PhD student in CeSOS from Aug 2003 to July 2007,

post doctor in CeSOS from July 2007 to June 2011,

Supervised by Prof. O.M. Faltinsen)

∗ Background∗ Water entry of 2D rigid body

∗ Symmetric∗ Asymmetric

∗ Water entry of an elastic cylindrical shell∗ Forced oscillations of 2D ship sections∗ Study on ships at high speed

∗ Planing vessel in calm water∗ Forced heave and pitch in calm water ∗ Planing vessels in head sea∗ Semi-displacement ships in steady and unsteady motions

∗ Slamming on a body in waves--- application of a numerical wave tank

∗ Summary

2

Outline

3

Background

∗ Potential flow theory: inviscid, incompressible, irrotational

∗ Fully nonlinear free surface conditions with gravity considered;

∗ Boundaries discretized into straight line elements and linear approximation of physical values on each element;

∗ Regriding and smoothing of the free surface

∗ To cut the thin jet and thin sprays (Zhao & Faltinsen, 1993; Lu,He& Wu, 2000)

∗ To simulate the flow separation from knuckles (Zhao et al., 1996)

∗ To simulate the flow separation from a curved body surface

4

A 2D boundary element method

∗ Water entry of a wedge with constant speed

∗ Free water entry of a circular cylinder

∗ Free water entry of a wedge section

∗ Free water entry of a bow-flare section

∗ Asymmetric water entry of a bow-flare section

∗ Free water entry of an elastic shell

5

Water entry problems

6

Water entry of a wedge with constant speed

0 20 40 60-2

-1

0

1

2

z/(V

t)

y/(Vt)

β=4o

BEM SIM.

-1,0 -0,5 0,0 0,5 1,0

0

200

400

600

β=4o

BEM SIM.

p/(0

.5ρV

2 )

z/(Vt)

β = 4˚

0,0 2,5 5,0 7,5 10,0-5,0

-2,5

0,0

2,5

5,0

z/(V

t)

y/(Vt)

β=20O

BEM SIM.

-1,0 -0,5 0,0 0,5 1,00

5

10

15

20

p/(0

.5ρV

2 )

z/(Vt)

β=20O

BEM SIM.

β = 20˚

0 1 2 3-1,5

-1,0

-0,5

0,0

0,5

1,0

1,5

z/(V

t)

y/(Vt)

β=45O

BEM SIM.

-1,0 -0,5 0,0 0,5 1,00

1

2

3

4

p/(0

.5ρV

2 )

z/(Vt)

β=45O

BEM SIM.

β = 45˚

A circular cylinder, buoyancy = weight,V0 = 2.955m/s, D = 0.11m

Photos:Greenhow & Lin

(1983)

Green lines:BEM results

t = 0.015s, 0.090s,

0.110s, 0.200s

0

200

400

600

800

1000

1200

0 0.05 0.1 0.15 0.2

Time (s)

Vertical force (N/m)

8

Free water entry of a wedge(Greenhow and Lin, 1983)

(a)(c)

(d)

(b)

Free water entry of a rigid wedge with deadrise 30˚ and V0 = 1.55 m/s

-0.01 0.00 0.01 0.02 0.03 0.04 0.05-100

0

100

200

300

400

Vertical force (N)

Time (s)

Exp. BEM

0,00 0,01 0,02 0,03 0,04 0,05-0,02

0,00

0,02

0,04

0,06

0,08

0,10

0,12

0,14

P

ress

ure

(bar

)

Time (s)

P1 P2 P3 P4 P5

Free water entry of a rigid bow-flare section V0 = 2.43 m/s

-0.02 0.00 0.02 0.04 0.06 0.08-100

0

100

200

300

400

Vertical force (N)

Time (s)

Exp. BEM

11

0,00 0,02 0,04 0,06 0,08

0,00

0,05

0,10

0,15

0,20

0,25

P

ress

ure

(bar

)

Time (s)

Exp. BEM CIPP1

0,00 0,02 0,04 0,06 0,08

0,00

0,05

0,10

0,15

0,20

0,25

P

ress

ure

(bar

)

Time (s)

Exp. BEM CIPP2

0,00 0,02 0,04 0,06 0,08

0,00

0,05

0,10

0,15

0,20

0,25

P

ress

ure

(bar

)

Time (s)

Exp. BEM CIPP3 P4

12

Asymmetric water entry of bow-flare ship section θ=20.3° and h = 0.03m (V0=0.75m/s)

-0.05 0.00 0.05 0.10 0.15 0.20

0

100

200

300

Vertical force (N)

Time (s)

Exp. BEM CIP

-0.05 0.00 0.05 0.10 0.15 0.20-200

-150

-100

-50

0

50

Horizontal force (N)

Time (s)

Exp. BEM CIP

0.0 0.1 0.2

0.00

0.05

0.10

0.15

0.20

0.0 0.1 0.2

0.00

0.05

0.10

0.15

0.20

0.0 0.1 0.2

0.00

0.05

0.10

0.15

0.20

0.0 0.1 0.2

0.00

0.05

0.10

0.15

0.20P1

Pressure on the impact side (bar)

Time (s)

P2

Time (s)

P3

Time (s)

P4

Time (s)

0.0 0.1 0.2-0.02

0.00

0.02

0.04

0.06

0.08

0.10

0.0 0.1 0.2-0.02

0.00

0.02

0.04

0.06

0.08

0.10

0.0 0.1 0.2-0.02

0.00

0.02

0.04

0.06

0.08

0.10

0.0 0.1 0.2-0.02

0.00

0.02

0.04

0.06

0.08

0.10P1

Pressure on the leeward side (bar)

Time (s)

P2

Time (s)

P3

Time (s)

P4

Time (s)

-0.10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25

t = 0.10s t = 0.12s t = 0.17s

θ = 20.3o

t = 0.05s t = 0.08s t = 0.09s

y (m)

-0.10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25

t = 0.10s t = 0.12s t = 0.17s

θ = 20.3o

t = 0.05s t = 0.08s t = 0.09s

y (m)

-0.10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25

t = 0.10s t = 0.12s t = 0.17s

θ = 20.3o

t = 0.05s t = 0.08s t = 0.09s

y (m)

-0.10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25

t = 0.10s t = 0.12s t = 0.17s

θ = 20.3o

t = 0.05s t = 0.08s t = 0.09s

y (m)

-0.10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25

t = 0.10s t = 0.12s t = 0.17s

θ = 20.3o

t = 0.05s t = 0.08s t = 0.09s

y (m)

-0.10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25

t = 0.10s t = 0.12s t = 0.17s

θ = 20.3o

t = 0.05s t = 0.08s t = 0.09s

y (m)

-0.10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25

t = 0.10s t = 0.12s t = 0.17s

θ = 20.3o

t = 0.05s t = 0.08s t = 0.09s

y (m)

-0.10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25

t = 0.10s t = 0.12s t = 0.17s

θ = 20.3o

t = 0.05s t = 0.08s t = 0.09s

y (m)

Arai and Matsunaga (1989)’s experimentsθ=22.5°

-0.4 -0.2 0.0 0.2 0.4 0.6 0.8-0.4

-0.2

0.0

0.2

0.4

0.6

0.8(a)

z (m

)

y (m)

t = 0.0495 s

Secondary impact

Air cavity

P-6

-0.4 -0.2 0.0 0.2 0.4 0.6 0.8-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6(b)

z (m

)

y (m)

Air cavity

0.00 0.05 0.10 0.152.5

3.0

3.5

4.0

4.5

0.00 0.05 0.10 0.150.0

1.0

Pressure (Bar)

Time (s)

P-9

0.0

1.0 P-8

0.0

1.0 P-6

0.0

1.0 P-40.0

1.0 P-3

0.0

1.0P-2

BEM Experiments

Speed (m/s)

2. Hydroelasticity

3. Air cavity

1. Secondary impact

Water entry of a cylindrical shell

V

o

COG

Cylindrical shell

Free surface

z

y

BEM versus von Karman’s theory

0.000 0.005 0.010 0.015 0.020 0.025-1500

-1000

-500

0

500

1000

1500

2000Strain (x106)

Time (s)

Experiment BEM von Karman

27

Velocities by coupled and uncoupled solutions

0.000 0.005 0.010 0.015 0.020 0.025-5

-4

-3

-2

-1R

igid

-bod

y ve

loci

ty (

ms-1

)

Time (s)

Coupled Uncoupled

Forced oscillations of 2D ship sections

28

29

∗ Planing vessel in calm water

∗ Hydrodynamic forces on planing vessels in forced unsteady motions

∗ Dynamic responses of planing vessels in head sea

30

Study of planing vessels

2D+t theory for steady motions

1x Ut=

Earth-fixedcross-plane

Ut = t0

t = t1

t = t2

V

V U τ=

x1

Gravity effectsComparing free surface elevations

FnB = 2.5 and FnB=5.0

0.0 0.2 0.4 0.6 0.8 1.0-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

y%

z% / B

/ B

0.0 0.2 0.4 0.6 0.8 1.0-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

y%

/ Bz%

/ B

Gravity effects--- Comparing vertical force distriutions

FnB = 2.5 and FnB=5.0

0 1 2 3 40.00

0.02

0.04

0.06

0.08

x%x%x%

Remaining force

/ B

0 1 2 3 40.00

0.02

0.04

0.06

0.08

F3

(2D)/(0.5ρU2B)F3

(2D)/(0.5ρU2B)F3

(2D)/(0.5ρU2B)

/ B

Hydrostatic force

0 1 2 3 40.00

0.02

0.04

0.06

0.08

/ B

(c)(b)(a)

Total force

2D+t theory for unsteady motions

12345678

U

12345678

Added mass coefficients

0.8 1.0 1.2 1.4 1.6 1.8 2.0

-0.5

0.0

0.5

1.0

1.5

2.0 EXP. NUM. 3D Corr.A

33

A53

A

35

A55

Added mass coefficients

ω(B/g)1/2

Damping coefficients

0.8 1.0 1.2 1.4 1.6 1.8 2.0-4

-3

-2

-1

0

1

2

3

4

Damping coefficients

ω(B/g)1/2

EXP. NUM. 3D Corr.

B33

B

53

B35

B

55

Decomposition of the total velocity potential

Φ = φI + φ

Total velocity potential

Incident waves

Disturbance potential

( )00

coskzaI

ge t kx

ζϕ ωω

= −

Original 3D problem for the total Φ

Decomposition of Φ

3D problem for the disturbance potential φ

Slender body assumption and small pitch angle

2D problems for the disturbance potential φ in Earth fixed cross planes

Model tests by Fridsma(1969)---Configuration A

∗ Beam B: 9 inches (0.2286m)

∗ Length L: 5B

∗ Deadrise angle: 20 degree

∗ Trim angle in calm water: 4 degree

∗ Mean wetted length-beam ratio: 3.6

∗ Length Froude number: U/(gL)1/2=1.19

∗ Incident waves:

amplitude ζa=0.0555B

wave length λ/L=1.0, 2.0,3.0,4.0,5.0, 6.0

ζa=0.0555B, λ/L=3.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0-0.020.00

0.02

Pitch (degree)

Heave (m)

Time (s)

Acc. atbow(g)

Acc. atCOG(g)

F5*

F3*

0.0 0.5 1.0 1.5 2.0 2.5 3.0

-202

0.0 0.5 1.0 1.5 2.0 2.5 3.00.05

0.10

0.0 0.5 1.0 1.5 2.0 2.5 3.0

-0.020.000.02

0.0 0.5 1.0 1.5 2.0 2.5 3.0-0.30.00.3

0.0 0.5 1.0 1.5 2.0 2.5 3.0-0.50.00.5

Configuration A

2D+t theory for a semi-displacement ship in steady motions

1x Ut=

Earth-fixedcross-plane

Ut = t0

t = t1

t = t2

V

V U τ=

x1

Keuning’s model

Length L = 2.0 m

Beam B = 0.25 m

Draft D = 0.0624 m

Froude number

Fn = U/(gL)1/2=1.14

Trim angle

1.62 degree

43

Free surface flow around Keuning’s model in steady flow at Fn=1.14Trim angle=1.62o

y (m)

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

z (m

)

-0.1

0.0

0.1

0.2 Free surfaceHull surface

0.0 0.5 1.0 1.5 2.0

-100

-50

0

50

100

Distance from stern (m)

Sectionalverticalforce (N/m)(withouthydrostaticForce)

Faltinsen & Zhao: Nonlinear 2D+t without separation

Sun & Faltinsen : Nonlinear 2D+t with separation

Experiments

There is a very rapidundetected change in the verticalforce at the stern

The total verticalforce at the sternis zero

Dynamic vertical force distribution.Steady flow at Fn=1.14. Trim angle=1.62o

ω = 13 rad/s

0.0 0.5 1.0 1.5 2.0

33

-30

-20

-10

0

10

20

30

40

Distance from stern (m)

Sectional heave added mass coefficients. Fn=1.14.

a33 (kg/m)

Sun& Faltinsen : Nonlinear 2D+t inthe time domain

Experiments

ω = 13 rad/s

0.0 0.5 1.0 1.5 2.0-100

0

100

200

300

400

Distance from stern (m)

Sectional heave damping coefficients. Fn=1.14.

b33 (kg/m) Sun& Faltinsen : Nonlinear 2D+t inthe time domain

Experiments

Added mass coefficients compared with Faltinsen&Zhao (1991)’s results

ω =5 rad/s

X0-distance from stern (m)

0.0 0.5 1.0 1.5 2.0

a 33(

kg/m

)

-100

-50

0

50

100

Faltinen &Zhao:Nonlinear steady flow and linear unsteady flow

Damping coefficients compared with Faltinsen&Zhao (1991)’s results

ω = 5 rad/s

X0-distance from stern (m)

0.0 0.5 1.0 1.5 2.0

b 33 (k

g/(s

m))

-100

0

100

200

300

400

Faltinen &Zhao:Nonlinear steady flow and linear unsteady flow

49

A numerical wave tank

h

y z

Damping zone

L Ld

Vwm

Damping zone Wave generation

γ γ

50

Horizontal force on a circular cylinder in waves with H = 0.087m,T = 1.084s.

51

Vertical force on a circular cylinder in waves with H = 0.087m,T = 1.084s.

1. H. Sun, Odd M. Faltinsen (2013) A Nonlinear numerical wave tank and its applications. Proceedings of 32nd International Conference on Ocean, Offshore and Arctic Engineering, OMAE2013-10087.

2. H. Sun, Odd M. Faltinsen (2012) Hydrodynamic Forces on a semi-displacement ship at high speed. Applied Ocean Research. Vol. 34, pp 68-77. doi:10.1016/j.apor.2011.10.001.

3. H. Sun, Odd M. Faltinsen (2011) Hydrodynamic Forces on High-Speed Ships in Forced Vertical Motions. Proc. 11th International Conference on Fast Sea Transportation (FAST 2011), Honolulu, Hawaii, USA, September 2011.

4. H. Sun, Odd M. Faltinsen (2011) Predictions of porpoising inception for planing vessels. Journal of Marine Science and Technology. Vol. 16, n. 3, pp270-282. DOI : 10.1007/s00773-011-0125-2.

5. H. Sun, Odd M. Faltinsen (2011) Dynamic motions of planing vessels in head sea. Journal of Marine Science and Technology. Vol. 16, n. 2, pp 168-180. DOI : 10.1007/s00773-011-0123-4.

6. H. Sun, Odd M. Faltinsen (2010) Numerical study of planing vessels in waves. In: Int. Conference on Hydrodynamics, Shanghai, China, 11-15 October, 2010.s

7. H. Sun, Odd M. Faltinsen (2010) Numerical study of a semi-displacement ship at high speed. In: Proc. 29th Inter. Conf. on Ocean, Offsh. Arctic Eng., Shanghai, China, June 2010 (OMAE 2010).

8. H. Sun, Odd M. Faltinsen (2009) Water entry of a bow-flare ship section with roll angle. Journal of Marine Science and Technology. v 14, n 1, p 69-79.

9. H. Sun, Odd M. Faltinsen (2007), The influence of gravity on the performance of planing vessels in calm water. Jouranl of Engineering Mathematics, Vol 58, pp 91-107.

10. H. Sun, Odd M. Faltinsen (2007) Porpoising and Dynamic Behavior of Planing Vessels in Calm Water. Proc. of the 9th Int. Conf. on Fast Sea Transportation. Shanghai, China, Oct. 23-27, 2007(FAST 2007).

11. H. Sun, Odd M. Faltinsen (2007). Asymmetric water entry of a Bow-flare ship section with roll angle. Proc. of IUTAM Symposium on Fluid-Structure Interaction in Ocean Engineering. Hamburg, Germany, July 23-27, 2007.

12. H. Sun (2007) A Boundary Element Method Applied to Strongly Nonlinear Wave-Body Interaction Problems. Ph.D. thesis in Norwegian University of Science and Technology, Trondheim, Norway.

13. H. Sun, Odd M. Faltinsen (2007) Hydrodynamic forces on a planing hull in forced heave or pitch motions in calm water. The 22nd Int. Wrokshop on Water Waves and Floating Bodies, April, 2007, Plitvice, Croatia.

14. H. Sun, Odd M. Faltinsen (2006), Water impact of horizontal circular cylinders and cylindrical shells. Applied Ocean Research. Vol. 28,299-311.15. H. Sun, Odd M. Faltinsen (2006), A numerical study of the hydrodynamic forces on heaving bow-flare ship cross-sections. 7th Int. Conference on

Hydrodynamics, Ischia, Italy, October.16. H. Sun, Odd M. Faltinsen (2006), The fluid-structure interaction during the water impact of a cylindrical shell. 4th Int. Conference on

Hydroelasticity in Marine Technology, Wuxi, China.

52

References:

1. Aarsnes JV (1996) Drop test with ship sections – effect of roll angle. Report 603834.00.01. Norwegian Marine Technology Research Institute, Trondheim, Norway.

2. Arai M, Matsunaga K (1989) A numerical and experimental study of bow flare slamming. Journal of Society Naval Architecture Japan. 166 (in Japanese).

3. Arai M, Miyauchi T (1998) Numerical study of the impact of water on cylindrical shells, considering fluid-structure interactions. In: Practical Design of Ships and Mobile Units. Editors: M.W.C. Oosterveld and S.G. Tan. London and New York: Elsevier Applied Science. pp59-68.

4. O.M. Faltinsen, R. Zhao, Numerical Prediction of ship Motions at High Forward Speed, Phil. Trans. R. Soc. Lond., 334 (1991) 241-252.

5. Greenhow M, Lin WM (1983) Nonlinear free surface effects: experiments and theory. Report No. 83-19 Department of Ocean Engineering, MIT.

6. Lu, C.H., He, Y.S., Wu, G.X. (2000)Coupled analysis of nonlinear interaction between fluid and structure during impact. Journal of Fluids and Structructures. Vol. 14, 127-146.

7. Troesch AW (1992) On the hydrodynamics of vertically oscillating planing hulls. J. Ship Res.36, 317-331.

8. Zhao R, Faltinsen OM, Aarsnes JV (1996) Water entry of arbitrary two-dimensional sections with and without flow separation. In: Proc. Twenty-first Symposium n Naval Hydrodynamics, Trondheim, Norway, 1996.

9. Zhao R, Faltinsen OM (1993) Water entry of two-dimensional bodies. J. Fluid Mech. 246, 593-612.10. Zhu XY, Faltinsen OM, Hu CH (2005) Water entry loads on heeled ship sections. Proc. 16th Int.

Conf. on Hydrodynamics in Ship Design, Gdansk, Poland.

53

References:

∗ Water entry problems:

∗ symmetric and asymmetric water entry

∗ Water entry of elastic body

∗ Water entry and exit in the forced oscillations

∗ 2D+t method used to solve the seakeeping problems

∗ for planing vessels

∗ semi-displacement vessels

∗ Numerical wave tank applications

54

Summary

∗Thank you for your attention!

55