1 Experimental and theoretical investigation of the effect of screens on sloshing Reza Firoozkoohi Trondheim, 28 May 2013
2 Outline of this presentation Part 1: Definition of the problem Part 2: Very small forcing amplitude sloshing Quasi-linear modal theory vs. Experiments Part 3: Small forcing amplitude Experiments, nonlinear effects and adaptive modal theory Part 4: Conclusions
3 Part 1: Definition of the problem Part 2: Very small forcing amplitude sloshing Quasi-linear modal theory vs. Experiments Part 3: Small/relatively large forcing amplitude Experiments, nonlinear effects and adaptive modal theory Part 4: Conclusions
4 The problem How do screens change the steady-state resonant sloshing in a two-dimensional rectangular tank as a function of: Forcing motion : Forcing amplitude: ; is length of the tank Forcing frequency: ; Mean water depth: Mean free surface Solidity ratio: Slat screen (Solidity ratio )
5 Solidity ratio: Sn (2) (1) Solidity ratio (Sn) : For h/l=0.4: Screen(1): Sn=0.4725 Screen(2): Sn=0.6825
6 Tools 1. Experiments 2. Analytical modeling based on multimodal method
7 Experiments; setup Harmonic forcing motion:s: Measured parameter: Response at 1 cm distance from vertical walls
8 Experiments; Important physical parameters The first three sloshing natural frequencies in a clean tank Large solidity ratios are included Very small and small forcing amplitudes The effect of nonlinearity of free surface How resonant frequencies are modified
9 Part 1: Definition of the problem Part 2: Very small forcing amplitude sloshing Quasi-linear modal theory vs. Experiments Part 3: Small forcing amplitude Experiments, nonlinear effects and adaptive modal theory Part 4: Conclusions
10 Quasi-Linear modal theory Linear free-surface condition Continuous horizontal velocity at the screen openings Zero velocity at screen slats Quadratic pressure drop at the screen: Antisymmetric modes affected by screen responsible for screen-caused damping Symmetric modes are not modified
11 Quasi-Linear modal theory vs. Experiments Experiments QL theory
12 Quasi-Linear modal theory vs. Experiments Experiments QL theory
13 Quasi-Linear modal theory vs. Experiments Experiments QL theory Compartmentation
14 Quasi-Linear modal theory vs. Experiments Experiments QL theory Nonlinear effects
15 Experimental results 30 25 20 15 10 5 Sn=0.4725 Sn=0.6825 Sn=0.7863 Sn=0.83875 Sn=0.89125 Sn=0.91375 Sn=0.93625 Sn=0.95125 0 0.8 1 1.2 1.4 1.6 1.8 2, 0.89125 0.91375
16 Quasi-Linear theory and experiments; summary Resonance behavior is quantitatively captured for For very large response near is predicted due to free-surface nonlinearity Minimum response occurs for 0.89125 0.9137
17 Part 1: Definition of the problem Part 2: Very small forcing amplitude sloshing Quasi-linear modal theory vs. Experiments Part 3: Small forcing amplitude Experiments, nonlinear effects and adaptive modal theory Part 4: Conclusions
18 Responses for 20 15 10, 0.7863 Secondaryresonance Soft-spring behavior Sn_0.4725 Sn_0.6825 Sn_0.7863 Sn_0.8387 Sn_0.8912 Sn_0.9137 Sn_0.9363 Sn_0.9512 5 0 0.72 0.92 1.12 1.32 1.52 1.72 1.92 2.12
19 Secondary resonance Secondary resonance : Experiments :1 st Fourier, : 2 nd Fourier :Theory
20 Nonlinear adaptive modal method Free-surface nonlinearity couples symmetric and anti-symmetric modes; many modes are included (20 modes) Asymptotic ordering of generalized coordinates depend on the frequency Screen-caused damping terms affect equations for anti-symmetric modes Linear damping terms,, should be introduced into the modal equations to achieve steady-state responses
21 Nonlinear adaptive modal method M1 M2 M3 M4 M1:[1,3,5,2,4] M2:[1,5,7,9,2,4] M3:[1,5,7,9,11,13,4] M4:[1,5,7,9,11,13,15,4,6]
22 Nonlinear adaptive modal theory; summary Quantitatively captures secondary resonance due to the presence of screen for Generally, results at secondary resonant frequencies are sensitive to linear damping for symmetric modes
23 Special free-surface effects Wave breaking 0.01, 0.4, 0.4725, 1
24 Jet through screen openings 0.01, 0.4, 0.8913, 1.48
25 Run-up on the screen with liquiddetachment 0.01, 0.4, 0.9,
26 Unequal responses in compartments 0.01, 0.4, 0.94,
27 Unequal responses in compartments Initial condition (damping)
28 Part 1: Definition of the problem Part 2: Very small forcing amplitude sloshing Quasi-linear modal theory vs. Experiments Part 3: Small forcing amplitude Experiments, nonlinear effects and adaptive modal theory Part 4: Conclusions
29 Concluding remarks Screen causes extra secondary resonance of higher sloshing modes for 0.01, 0.4 Amplitudes of Wave breaking Screen-caused jet flows 0.01( 0.4) can lead to: Run-ups on the screen accompanied with liquid detachment Unequal responses
30 Concluding remarks Solidity ratio of minimum response is amplitude dependent 0.001 0.8913 0.927, 0.01 0.7863 Quasi-linear modal method captures expertimtns Very small forcing amplitude Finite water depth Nonlinear adaptive modal method captures secondary resonance for
31 References Faltinsen, O. M., & Timokha, A. N. (2009). Sloshing. Cambridge University Press. Faltinsen, O. M., Firoozkoohi, R., & Timokha, A. N. (2011), "Effect of central slotted screen with a high solidity ratio on the secondary resonance phenomenon for liquid sloshing in a rectangular tank" Physics of Fluids, 23 (6), 13. Faltinsen, O. M., Firoozkoohi, R., & Timokha, A. N. (2011), "Steady-state sloshing in a rectangular tank with a slat-type screen in the middle:quasilinear modal analysis and experiments", Physics of Fluids, 23 (4), 19. Firoozkoohi, R., & Faltinsen, O. M. (2010), "Experimental and numerical investigation of the effect of swash bulkhead on sloshing", 20th International Offshore and Polar Engineering Conference, ISOPE-2010, June 20, 2010 - June 25, 2010. 3, pp. 252-259. Beijing: International Society of Offshore and Polar Engineers.
32 Thanks for your time and attention!