Methodology for sloshing induced slamming loads and response

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

7

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

11

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

13

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

16

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

17

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

18

Impacts with air pockets

• An air pocket is often

trapped in the tank

corner

• Compressibility of air

results in oscillating

pressure

19

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

20

• 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

21

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

22

Results

Experimental case: f ≈ 80Hz

23

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

24

Experimental study of hydroelastic impact

Harmonic tank motion

Rectangular tank

Rigid steel frame

Flexible aluminium plate in

upper right corner

25

Strain measurements on flexible panel

• Calibrated as cantilever beam

26

Pressure measurements on tank top

27

High speed camera

• 300 or 1000 fps

• Time of each frame is

recorded – synchronization

with other measurements

29

Typical elastic impact response

• Large elastic deformation of aluminium plate

• Lowest mode damping at about 7% of critical damping

30

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

31

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

32

Numerical results

• Tank geometry and elastic plate properties as in the

presented experimental study

• Two lowest modes are included

33

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

34

Comparison between measured and calculated strains

Measured

Calculated

Calculated Measured

Measured

35

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

38

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

39

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

40

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

41

Thank you for your attention

42

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