The Effect of Tank Geometry on Sloshing Forces

Abstract

The geometry of the impact surface is as effective as the wave shape in the change of sloshing forces. The wave shape depends on the shape of the tank, oscillation frequency coinciding with the natural frequencies of the tank under sloshing motion. This study compares the surface deformations and pressures on the lateral walls that occur during oscillation along one axis at the same oscillation frequency between a rectangular tank and a chamfered tank of similar dimensions. The pressure distribution on the surfaces due to sloshing was measured for both tanks over a wide range of oscillation frequencies. From experiments, free surface deformations were monitored in the resonant and non-resonant regions, and the impact effects of the waves were compared. While maximum pressures were measured in the resonant regions of both tanks, pressures decreased at other oscillation frequencies. The sloshing of the tanks changed the wave shapes based on the geometry of the chamfered tank and also caused lower measurements at the same pressure measurement points at similar oscillation/natural frequency ratios.

Keywords

• Liquid sloshing
• Rectangular tank
• Chamfered tank
• pressure measurement
• free surface tracking.

Tank Geometrisinin Çalkantı Kuvvetlerine Etkisi

Öz

Çalkantı kuvvetlerinin değişiminde dalga formu kadar, çarpma yüzeyinin geometrisi de etkilidir. Dalga form ise çalkantı hareketinde; tankın şekline, salınım frekansının tankın doğal frekanslarıyla çakışmasına bağlı olarak değişir. Bu çalışmada benzer boyuttaki dikdörtgen ve pahlı tankın aynı salınım frekansındaki tek eksende salınım esnasında meydana gelen yüzey deformasyonları ve yanal yüzeylerde oluşturduğu basınçların karşılaştırılması yapılmıştır. Geniş salınım frekans aralığındaki çalkantı sebebiyle yüzeylerde oluşan basınç dağılımı her iki tank için ölçülmüştür. Serbest yüzey deformasyonları rezonans ve rezonans dışı bölgelerde takip edilerek dalgaların çarpma etkileri karşılaştırılmıştır. Her iki tankta da rezonans bölgelerinde maksimum basınçlar ölçülürken diğer salınım frekanslarında basınçlar düşmüştür. Tankların benzer salınım-doğal frekans oranlarındaki çalkantıları, pahlı tankın geometrisi yardımıyla dalga formlarını değiştirdiği gibi aynı basınç ölçüm noktalarında da daha az ölçülmesi sebep olmuştur.

Anahtar Kelimeler

• Sıvı Çalkantısı
• dikdörtgen tank
• pahlı tank
• basınç ölçümü
• serbest yüzey takibi.

References

1. AlMashan, N., Neelamani S. and Al-Houti, D. (2021). Experimental investigations on wave impact pressures under the deck and global wave forces and moments on offshore jacket platform for partial and full green water conditions. Ocean Engineering, 234, 109324.
2. Bredmose, H., Bullock G. N. and Hogg, A. J. (2015). Violent breaking wave impacts. Part 3. Effects of scale and aeration. J. Fluid Mech., 765, 82–113.
3. Bredmose, H., Peregrine D. H. and Bullock, G. N. (2009). Violent breaking wave impacts. Part 2: modelling the effect of air. J. Fluid Mech., 641, 389–430.
4. Bullock, G. N., Obhrai, C., Peregrine D. H. and Bredmose H. (2007). Violent breaking wave impacts. Part 1: Results from large-scale regular wave tests on vertical and sloping walls. Coastal Engineering, 54, 602–617.
5. Chella, M. A., Torum A. and Myrhaug, D. (2012). An Overview of Wave Impact Forces on Offshore Wind Turbine Substructures. Energy Procedia, 20, 217 – 226.
6. Cuomo, G., Allsop W., Bruce T. and Pearson J. (2010). Breaking wave loads at vertical seawalls and breakwaters. Coastal Engineering, 57, 424–439.
7. Cuomo G., Piscopia R. and Allsop W. (2011). Evaluation of wave impact loads on caisson breakwaters based on joint probability of impact maxima and rise times. Coastal Engineering, 58, 9–27.
8. Ding, S., Wang G. and Luo G. (2020). Study on sloshing simulation in the independent tank for an icebreaking LNG carrier. International Journal of Naval Architecture and Ocean Engineering, 12, pp. 667-679.

9. Faltinsen O. M. and Timokha, A. N. (2009). “Sloshing”, Cambridge University Press.
10. Graczyk M. and Torgeir M. (2008). A Probabilistic Assessment of Design Sloshing Pressure Time Histories in LNG Tanks. Ocean Engineering, 35 (8–9), 834–55.
11. Kim, S. Y., Kim, Y., Park J. J. and Kim, B. (2017). Experimental Study of Sloshing Load on LNG Tanks for Unrestricted Filling Operation. Journal of Advanced Research in Ocean Engineering, 3 (1), 041-052.
12. Kisacik, D., Troch P. and Van Bogaert, P. (2012). Description of loading conditions due to violent wave impacts on a vertical structure with an overhanging horizontal cantilever slab. Coastal Engineering, 60, 201–226.
13. Korkmaz, F. C. (2022). Damping of sloshing impact on bottom-layer fluid by adding a viscous top-layer fluid. Ocean Engineering, vol. 254, 111357.
14. Korkmaz, F. C., Yigit, K. and Güzel, B. (2021). Experimental Study on Sloshing Reduction Effects of Baffles. El-Cezeri , 8 (3), 1149-1157.
15. Lee, J., Ahn, Y., Kim, J., Kim, Y., Yang, K. K., Yi S. I. and Noh, M. H. (2021). Observation on sloshing flow and hydrodynamic pressures on cylindrical liquefied natural gas tank with swash bulkhead. Proc IMechE Part M: J Engineering for the Maritime Environment, 235 (1), 30–40.
16. Lee, D. H., Kim, M. H., Kwon, S. H., Kim J. W. and Lee, Y. B. (2007). A Parametric Sensitivity Study on LNG Tank Sloshing Loads by Numerical Simulations. Ocean Engineering, 34 (1), 3–9.
17. Lugni, C., Brocchini M. and Faltinsen, O. M. (2010). Evolution of the air cavity during a depressurized wave impact. II. The dynamic field. Physics of Fluids, 22, 056102.
18. Lugni, C., Miozzi, M., Brocchini M. and Faltinsen O. M. (2010). Evolution of the air cavity during a depressurized wave impact. I. The kinematic flow field. Physics of Fluids, 22, 056101.
19. Lu, Y., Zhou, T., Cheng, L., Zhao W. and Jiang, H. (2018). Dependence of critical filling level on excitation amplitude in a rectangular sloshing tank. Ocean Engineering, 156, 500–511.
20. Nasar, T., Sannasiraj S. A. and Sundar V. (2009). Wave-induced sloshing pressure in a liquid tank under irregular waves. Proceedings of the Institution of Mechanical Engineers, Part M: Journal of Engineering for the Maritime Environment, 223 (2), 145-161.
21. Sauret, A., Boulogne, F., Cappello, J., Dressaire E. and Stone, H. A. (2015). Damping of liquid sloshing by foams. Physics of Fluids, 27, 022103.
22. Song, Y. K. Chang, K. A., Ryu Y. and Kwon, S. H. (2013). Experimental study on flow kinematics and impact pressure in liquid sloshing. Exp Fluids, 54, 1592.
23. Souto-Iglesias, A., Botia-Vera E. and Bulian, G. (2012). Repeatability and two-dimensionality of model scale sloshing impacts. in: Proceedings of the Twenty Second International Society of Offshore and Polar Engineering Conference, Rhodes, Greece.
24. Souto-Iglesias, A., Bulian G. and Botia-Vera, E. (2015). A set of canonical problems in sloshing. Part 2: Influence of tank width on impact pressure statistics in regular forced angular motion. Ocean Engineering, 105, 136–159.
25. Thiagarajan, K. P., Rakshit D. and Repalle, N. (2011). The air–water sloshing problem: Fundamental analysis and parametric studies on excitation and fill levels. Ocean Engineering, 38, 498–508.
26. Topliss, M. E., Cooker M. J. and Peregrine, D. H. (1992). “Pressure oscillations during wave impact on vertical walls”. Publ by ASCE, New York, NY, United States, 2, 1639–1650.
27. Tosun, U., Aghazadeh, R., Sert C. and Ozer, M. (2017). Tracking free surface and estimating sloshing force using image processing. Experimental Thermal and Fluid Science, 88, 423-433.
28. Xue, M. A., Jiang, Z., Hu Y. and Yuan, X. (2017). Numerical Study of Porous Material Layer Effects on Mitigating Sloshing in a Membrane LNG Tank. Ocean Engineering, 218, 108240.
29. Zou, C. F., Wang, D. Y., Cai Z. H. and Li, Z. (2015). The effect of liquid viscosity on sloshing characteristics. J Mar Sci Technol, 20, 765–775.