Methodology for sloshing induced slamming loads and response Olav Rognebakke Det Norske Veritas AS Post doc. CeSOS 2005-2006 1
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 2
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 3
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 4
Impact areas onboard LNG tanks Transverse Sway and roll induced Longitudinal Surge and pitch induced Low filling Consider CCS in this area for tank filling from 10%H 40%H 5 High filling Consider CCS in this area for tank filling from 40%H 70%H High filling considered critical
Physical effects and scaling of impact loads Impact location Reynolds number: No Froude number: Yes Surface tension: No Ullage pressure and air cushions (Euler number):? Compressibility in the liquid:? Boiling:? Hydroelasticity:? Tank roof Tank roof Chamfer knuckle Upper hopper knuckle Keel CL Transverse BH Chamfer Impact location Keel 6
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 7
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 8
Square and rectangular base tank Multi-modal method developed for 3D flow Experimental campaigns using MClab and Marintek sloshing rig 9 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
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 11
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 12
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 13
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 14
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 15
Flat impact 16 Wagner s type impact analysis method can be used Nonlinear BEM with local slamming solution Occurs during transient start-up High local pressures
Local vertical jet flow and high curvature free surface 17 The free surface has a local high curvature before impact A high speed jet shoots upwards and hits in the corner Localized pressure peak
Impacts with air pockets An air pocket is often trapped in the tank corner Compressibility of air results in oscillating pressure 18
Theoretical description of tank roof impact with air cavity Free surface Wetted roof Air cavity y 0 a t b t Continuity of pressure Tank wall x Image flow 19 Linear adiabatic pressure-density relationship in air cavity Velocity potential φ for the liquid flow due to impact Vortex distribution from a to a
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 Particular solution of Vertical velocity vortex density b p V ( x) V x b 2 b 0 w 1 I ( ) dx d 2 p ( x) x 1.4 pa t 2 a 2 b 1 0 w sign( x) d 2 2 2 2 2 1.4 p 2 2 2 2 a t a b b C x C dx b b x a x a x x 20 Mean air cavity volume
Pressure (kpa) Oscillation period = resonance period for air cavity Experiments 1 +2 Theory Experimental oscillations are highly damped Time (s) 21 Damping caused by air leakage
Results Experimental case: f 80Hz 22
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 23
Experimental study of hydroelastic impact Harmonic tank motion Flexible aluminium plate in upper right corner Rectangular tank Rigid steel frame 24
Strain measurements on flexible panel Calibrated as cantilever beam 25
26 Pressure measurements on tank top
High speed camera 300 or 1000 fps Time of each frame is recorded synchronization with other measurements 27
Typical elastic impact response Large elastic deformation of aluminium plate Lowest mode damping at about 7% of critical damping 29
Hydroelastic sloshing induced impact Beam model Generalized coordinate Mode shape 30 d a d a M A A M dz 2 2 a m m 2 mm mm 2 km 2 m mmam pexc dt k m dt b Slamming pressure dv 2 2 2 2R pexc c z z V dt c z 2 2 m
Beam model Velocity potential written as where Normal velocities expressed as a Fourier-series in z Strains are found from the curvature of the beam 31
Numerical results Tank geometry and elastic plate properties as in the presented experimental study Two lowest modes are included 32
Calculated strains Aluminium plate with impact modeled by V(t)=0.5-5t m/s and R=0.5m 33 Calculated eigenfrequencies are 99.3 and 413Hz for the two modes
Comparison between measured and calculated strains Measured Measured Calculated Measured Calculated 34
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 35
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 36 36
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 37 37
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 38
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 39
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 40
41 Thank you for your attention
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 42