1
Methodology for sloshing induced
slamming loads and
response
Olav Rognebakke
Det Norske Veritas AS
Post doc. CeSOS 2005 - 2006
2
Presentation overview
• Physics of sloshing and motivation
• Sloshing in rectangular containers
• Coupling with ship motions
• Sloshing induced impacts at high filling ratios
• Hydroelastic effects
• Design load methodology
3
Physics of sloshing
• Resonant, violent free surface
flow
• Nonlinear standing waves for
high filling h/l>0.25
• Travelling bore for shallow
water h/l<0.15
• Very low damping in smooth
containers
• Well represented by potential
flow
4
Marine applications
• Sloshing induced impacts
are of concern for transport
of liquefied natural gas,
LNG, in membrane type
ships
• Extreme impact loads have caused severe damage and
filling ratios between 10% and 70% of the tank height are
barred during transit
• Hydroelastic effects may occur due to deformation of both
the insulation boxes and supporting steel structure
• Sloshing in stiffened cargo tanks may lead to fatigue and
permanent deformations. Partly covered by class rules
5
Impact areas onboard LNG tanks
Transverse
• Sway and roll induced
Longitudinal
• Surge and pitch induced
Consider CCS in this area for tank filling
from 10%H – 40%H
Consider CCS in this area for tank filling
from 40%H – 70%H
Low
filling
High
filling
High filling
considered critical
6
Physical effects and scaling of impact
loads
• Reynolds number: No
• Froude number: Yes
• Surface tension: No
• Ullage pressure and air
cushions (Euler number): ?
• Compressibility in the liquid: ?
• Boiling: ?
• Hydroelasticity: ?
Keel
Tank roof
Chamfer
Impact location
CL
Keel
Tank roof
Upper hopper
knuckle
Chamfer knuckle Transverse
BH
Impact
location
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Presentation overview
• Physics of sloshing and motivation
• Sloshing in rectangular containers
• Coupling with ship motions
• Sloshing induced impacts at high filling ratios
• Hydroelastic effects
• Design load methodology
8
Sloshing in rectangular containers
• Multi-modal model including damping term used for
nonlinear standing wave sloshing flow
• Significant damping due to sloshing induced impacts
• Impact model developed to remove energy from system
• Iterative solver
9
Square and rectangular base tank
• Multi-modal method developed for 3D flow
• Experimental campaigns using MClab and Marintek
sloshing rig
Swirling - special feature of three-dimensional flow in square base
tank, vertical circular tank or spherical tank
10
Flow types in square based tank with
longitudinal excitation. Effect of fluid depth
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Presentation overview
• Physics of sloshing and motivation
• Sloshing in rectangular containers
• Coupling with ship motions
• Sloshing induced impacts at high filling ratios
• Hydroelastic effects
• Design load methodology
12
Coupling with ship motions
• Experimental and numerical study
• Internal flow: Multi-modal approach or linear model
• External flow: BEM based on Rankine sources, viscous
effects as empirical nonlinear drag
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Large coupling effects
• Sensitive to level of damping in internal model
• Fluid volume large part of total displacement
• Regular waves and steady-state results
• Takes long time to build up around resonance
• Limited effect for irregular waves
14
Presentation overview
• Physics of sloshing and motivation
• Sloshing in rectangular containers
• Coupling with ship motions
• Sloshing induced impacts at high filling ratios
• Hydroelastic effects
• Design load methodology
15
Experimental study of high filling
sloshing induced impacts
• Setup
– 2-D tank
– Rectangular
– Regular oscillatory
motion
• Instrumentation
– High speed video –
1250 fps
– Pressures measured
with 19.2kHz
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Flat impact
• Wagner’s type impact analysis method can be used
• Nonlinear BEM with local slamming solution
• Occurs during transient start-up
• High local pressures
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Local vertical jet flow and high curvature free
surface
• The free surface has a
local high curvature
before impact
• A high speed jet shoots
upwards and hits in the
corner
• Localized pressure peak
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Impacts with air pockets
• An air pocket is often
trapped in the tank
corner
• Compressibility of air
results in oscillating
pressure
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Theoretical description of tank roof impact
with air cavity
y
x b t a t
0
Free surface
Tank wall
Continuity of pressure
Air cavity
Image flow
Wetted roof
• Linear adiabatic pressure-density relationship in air cavity
• Velocity potential φ for the liquid flow due to impact
• Vortex distribution from –a to a
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• The singular integral equation for the vortex density gives
analytical solutions
• A solution of the homogeneous part of the equation is
needed
• This solution is proportional to a constant C(t)
• A differential equation for the constant C(t) is obtained by
satisfying the continuity equation for the air cavity
2
2
2
22 2 2 2 2 2 2 2
0
0
1d d
1.4 2( )
1 ( )d d
( )
1
)
.4
(
b b
w
a
p
b a
b b
w
a
I
b
p
a
x xp t
sign xC x C x
p tb x a x a x x
xV x V x
b
Vertical velocity
Mean air cavity volume
Particular solution of
vortex density
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Experiments
1 +2
Theory
Time (s)
Pre
ssure
(kP
a)
Oscillation
period =
resonance
period for
air cavity
Experimental
oscillations
are highly
damped
Damping caused by air leakage
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Results
Experimental case: f ≈ 80Hz
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Presentation overview
• Physics of sloshing and motivation
• Sloshing in rectangular containers
• Coupling with ship motions
• Sloshing induced impacts at high filling ratios
• Hydroelastic effects
• Design load methodology
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Experimental study of hydroelastic impact
Harmonic tank motion
Rectangular tank
Rigid steel frame
Flexible aluminium plate in
upper right corner
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Strain measurements on flexible panel
• Calibrated as cantilever beam
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Pressure measurements on tank top
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High speed camera
• 300 or 1000 fps
• Time of each frame is
recorded – synchronization
with other measurements
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Typical elastic impact response
• Large elastic deformation of aluminium plate
• Lowest mode damping at about 7% of critical damping
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Hydroelastic sloshing induced impact
2
2 exc
22
2
d dd
d d
m m
a
mm mm km m m mm
k m b
m
a aM A A M z
ta p
t
2 2 2
2 2
2exc
dV Rp c z z V
dt c z
Beam model
Generalized coordinate Mode shape
Slamming pressure
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Beam model
• Velocity potential written as
• Normal velocities expressed as a Fourier-series in z
• Strains are found from the curvature of the beam
where
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Numerical results
• Tank geometry and elastic plate properties as in the
presented experimental study
• Two lowest modes are included
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Calculated strains
• Aluminium plate with impact modeled by V(t)=0.5-5t m/s
and R=0.5m
• Calculated eigenfrequencies are 99.3 and 413Hz for the
two modes
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Comparison between measured and calculated strains
Measured
Calculated
Calculated Measured
Measured
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Presentation overview
• Physics of sloshing and motivation
• Sloshing in rectangular containers
• Coupling with ship motions
• Sloshing induced impacts at high filling ratios
• Hydroelastic effects
• Design load methodology
36 36
LNG impact load characteristics
• Highly nonlinear base flow implies that irregular, realistic
tank excitation is required
• Very large variability in impact loads, and a large number
of impacts are needed to get converged statistics
• Cargo Containment System has relevant failure modes
down to a scale of 10-1 meters
• Large spatial variations of impact pressures on this scale
• Impact temporal scale of 10-2 seconds or less
37 37
LNG impact load characteristics
• The spatial scales of the tank are typically about
50x40x30m
• Rapid changes are important for hydroelastic dynamic
effects and must be captured
• This implies excessive simulation / model test times
Pure FVM / VOF type CFD modelling is not possible in the
forseeable future
Practical hybrid methods with local solutions are required
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Design load methodology
• Model tests with large pressure sensor clusters and 200+
hours full-scale irregular motion realizations
• The larger part of the sloshing events occur
at relatively low sea states
• A full long-term approach is needed
• Assess annual probability of exceedance
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Summary and conclusions
• Multi-modal method is validated for rectangular base tanks
• Damping impact model helps improve the prediction of
integrated dynamic forces on the tank
• Nonlinear sloshing effects matter to accurately predict
coupling with ship motions. Correct estimate of internal
damping is important
• Impact models including air cushioning and hydroelastic
effects allow for detailed study of scale effects
• Design for acceptable risk of sloshing impacts implies
extensive model test campaigns and long-term assessment
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Acknowledgements
• Truly great years carrying out interesting and rewarding
work with world class researchers
– Prof. Odd M. Faltinsen
– Prof. Alexander Timokha
– Prof. Marilena Greco
• Fantastic colleagues at Marintek and NTNU facilitating the
experiments
– Unique culture where different professions collaborate to achieve
high quality, innovative and flexible solutions
• Great inspiration and support from Dr. Rong Zhao
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Thank you for your attention
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References
• Rognebakke, O. F. and Faltinsen, O. M., (2006), Hydroelastic sloshing
induced impact with entrapped air, 4th International Conference on
Hydroelasticity in Marine Technology, 10-14 September, Wuxi, China
• Rognebakke, O. F. and Faltinsen, O. M., (2005), Sloshing induced impact
with air cavity in rectangular tank with a high filling ratio, 20th
International Workshop on Water Waves and Floating Bodies, Svalbard,
Norway
• Faltinsen, O. M. and Rognebakke, O. F. and and Timokha, A. N., (2005),
Resonant three-dimensional nonlinear sloshing in a square base basin. Part
2. Effect of higher modes, J. Fluid Mech., 523, pp. 199-218
• Faltinsen, O. M. and Rognebakke, O. F. and and Timokha, A. N., (2005),
Classification of three-dimensional nonlinear sloshing in a square-base tank
with finite depth, J. Fluids and Structures, V 20, Issue 1, pp. 81-103
• Rognebakke, O. F. and Faltinsen, O. M. (2003), Coupling of Sloshing and
Ship motions, J. Ship Research, Vol. 47, No. 3, pp. 208-221
• Rognebakke, O. , Opedal, J. A. and Ostvold, T. K., (2009), Sloshing Impact
Design Load Assessment, ISOPE, 21-26 June, Osaka, Japan