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
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