Experimental and theoretical investigation of the effect of screens on sloshing

Transcription

1 1 Experimental and theoretical investigation of the effect of screens on sloshing Reza Firoozkoohi Trondheim, 28 May 2013

2 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 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 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 5 Solidity ratio: Sn (2) (1) Solidity ratio (Sn) : For h/l=0.4: Screen(1): Sn= Screen(2): Sn=0.6825

6 6 Tools 1. Experiments 2. Analytical modeling based on multimodal method

7 7 Experiments; setup Harmonic forcing motion:s: Measured parameter: Response at 1 cm distance from vertical walls

8 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 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 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 11 Quasi-Linear modal theory vs. Experiments Experiments QL theory

12 12 Quasi-Linear modal theory vs. Experiments Experiments QL theory

13 13 Quasi-Linear modal theory vs. Experiments Experiments QL theory Compartmentation

14 14 Quasi-Linear modal theory vs. Experiments Experiments QL theory Nonlinear effects

15 15 Experimental results Sn= Sn= Sn= Sn= Sn= Sn= Sn= Sn= ,

16 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

17 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 18 Responses for , Secondaryresonance Soft-spring behavior Sn_ Sn_ Sn_ Sn_ Sn_ Sn_ Sn_ Sn_

19 19 Secondary resonance Secondary resonance : Experiments :1 st Fourier, : 2 nd Fourier :Theory

20 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 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 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 23 Special free-surface effects Wave breaking 0.01, 0.4, , 1

24 24 Jet through screen openings 0.01, 0.4, , 1.48

25 25 Run-up on the screen with liquiddetachment 0.01, 0.4, 0.9,

26 26 Unequal responses in compartments 0.01, 0.4, 0.94,

27 27 Unequal responses in compartments Initial condition (damping)

28 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 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 30 Concluding remarks Solidity ratio of minimum response is amplitude dependent , Quasi-linear modal method captures expertimtns Very small forcing amplitude Finite water depth Nonlinear adaptive modal method captures secondary resonance for

31 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, June 25, , pp Beijing: International Society of Offshore and Polar Engineers.

32 32 Thanks for your time and attention!