0
Research Papers: Fluid-Structure Interaction

Standing Gravity Waves in a Horizontal Circular Eccentric Annular Tank

[+] Author and Article Information
Mohammad Nezami

Assistant Professor
Department of Mechanical Engineering,
Firoozkooh Branch,
Islamic Azad University,
Firoozkooh, Iran

Atta Oveisi

School of Mechanical Engineering,
Iran University of Science and Technology,
Tehran, Iran
e-mail: atta.oveisi@gmail.com

Mohammad Mehdi Mohammadi

School of Mechanical Engineering,
Iran University of Science and Technology,
Tehran, Iran

1Corresponding author.

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received February 21, 2013; final manuscript received February 22, 2014; published online April 28, 2014. Assoc. Editor: Samir Ziada.

J. Pressure Vessel Technol 136(4), 041301 (Apr 28, 2014) (9 pages) Paper No: PVT-13-1038; doi: 10.1115/1.4026978 History: Received February 21, 2013; Revised February 22, 2014

Standing gravity waves in half-full horizontal cylindrical containers with eccentric tube are analyzed using the linear theory of water waves. The problem solution is obtained by the method of conformal coordinate transformation, leading to standard truncated matrix Eigen-value problem from which fluid motion characteristics (Eigen-frequencies and wave modes) are calculated. The effects of tube eccentricity and radius ratio upon the three lowest antisymmetric and symmetric sloshing frequencies and the associated hydrodynamic pressure mode shapes are examined. Also, convergence of the adopted approach with respect to the eccentricity condition, and radius ratio is discussed. Accuracy of the present analysis is checked by comparison with the known results of the limiting cases.

FIGURES IN THIS ARTICLE
<>
Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.

References

Ibrahim, R. A., 2005, Liquid Sloshing Dynamics: Theory and Applications, 2nd ed., Cambridge University Press, New York.
Veldman, A. E. P., Gerrits, J., Luppes, R., Helder, J. A., and Vreeburg, J. P. B., 2007, “The Numerical Simulation of Liquid Sloshing on Board Spacecraft,” J. Comput. Phys., 224(1), pp. 82–99. [CrossRef]
Monti, R., 2002, Physics of Fluids in Microgravity, 1st ed., CRC Press, Boca Raton, FL.
Antar, B. N., and Nuotio-Antar, V. S., 1994, Fundamentals of Low Gravity Fluid Dynamics and Heat Transfer, 1st ed., CRC Press, Boca Raton, FL.
Hubert, C., 2003, “Behavior of Spinning Space Vehicles With Onboard Liquids,” Proceedings 2003 Flight Mechanics Symposium, NASA, pp. 1–14.
Romero, J. A., Ramirez, O., Fortanell, J. M., Martinez, M., and Lozano, A., 2006, “Analysis of Lateral Sloshing Forces Within Road Containers With High Fill Levels,” Proc. Inst. Mech. Eng., Part D, 220, pp. 302–312. [CrossRef]
Dai, L., and Xu, L., 2006, “A Numerical Scheme for Dynamic Liquid Sloshing in Horizontal Cylindrical Containers,” Proc. Inst. Mech. Eng., Part D, 220, pp. 901–918. [CrossRef]
Wu, C. H., and Chen, B. F., 2009, “Sloshing Waves and Resonance Modes of Fluid in a 3D Tank by a Time-Independent Finite Difference Method,” Ocean Eng., 36(6–7), pp. 500–510. [CrossRef]
Wu, G. X., 2007, “Second-Order Resonance of Sloshing in a Tank,” Ocean Eng., 34(17–18), pp. 2345–2349. [CrossRef]
Liu, D., and Lin, P., 2009, “Three-Dimensional Liquid Sloshing in a Tank With Baffles,” Ocean Eng., 36(2), pp. 202–212. [CrossRef]
Budiansky, B., 1960, “Sloshing of Liquids in Circular Canals and Spherical Tanks,” J. Aerosp. Sci., 27, pp. 161–173. [CrossRef]
McCarty, J. L., and Stephens, D., 1960, Investigation of the Natural Frequencies of Fluids in Spherical and Cylindrical Tanks, National Aeronautics and Space Administration, Washington, DC.
Moiseev, N. N., and Petrov, A. A., 1966, “The Calculation of Free Oscillations of a Liquid in a Motionless Container,” Adv. Appl. Mech., 9, pp. 91–154. [CrossRef]
McIver, P., 1989, “Sloshing Frequencies for Cylindrical and Spherical Containers Filled to an Arbitrary Depth,” J. Fluid Mech., 201, pp. 243–257. [CrossRef]
Kobayashi, N., Mieda, T., Shibata, H., and Shinozaki, Y., 1989, “A Study of the Liquid Slosh Response in Horizontal Cylindrical Tanks,” ASME J. Pressure Vessel Technol., 111(1), pp. 32–38. [CrossRef]
Evans, D. V., and Linton, C. M., 1993, “Sloshing Frequencies,” Q. J. Mech. Appl. Math., 46(1), pp. 71–87. [CrossRef]
Popov, G., Sankar, S., Sankar, T. S., and Vatistas, G. H., 1993, “Dynamic of Liquid Sloshing in Horizontal Cylindrical Road Containers,” Proc. Inst. Mech. Eng., Part C, 207(2), pp. 399–406. [CrossRef]
Papaspyrou, S., Karamanos, S. A., and Valougeorgis, D., 2004, “Response of Half–Full Horizontal Cylinders Under Transverse Excitation,” J. Fluids Struct., 19(7), pp. 985–1003. [CrossRef]
Karamanos, S. A., Patkas, L. A., and Platyrrachos, M. A., 2006, “Sloshing Effects on the Seismic Design of Horizontal–Cylindrical and Spherical Industrial Vessels,” ASME J. Pressure Vessel Technol., 128(3), pp. 328–340. [CrossRef]
Patkas, L., and Karamanos, S. A., 2007, “Variational Solutions of Externally-Induced Sloshing in Horizontal-Cylindrical and Spherical Vessels”. ASCE J. Eng. Mech., 133(6), pp. 641–655. [CrossRef]
Zhou, H., Li, J. F., and Wang, T. S., 2008, “Simulation of Liquid Sloshing in Curved-Wall Containers With Arbitrary Lagrangian–Eulerian Method,” Int. J. Numer. Methods Fluids, 57(4), pp. 437–452. [CrossRef]
Lakis, A. A., Bursuc, G., and Toorani, M. H., 2009, “Sloshing Effect on the Dynamic Behavior of Horizontal Cylindrical Shells,” Nucl. Eng. Des., 239(7), pp. 1193–1206. [CrossRef]
Gedikli, A., and Erguven, M. E., 2003, “Evaluation of Sloshing Problem by Variational Boundary Element Method,” Eng. Anal. Boundary Elem., 27(9), pp. 935–943. [CrossRef]
Abramson, H. N., 1969, “Slosh Suppression,” NASA Technical Report No. SP-8031, National Aeronautics and Space Administration.
Strandberg, L., 1978, “Lateral Stability of Road Tankers,” VTI Report No. 138A, Vol. 1, Sweden.
Cho, J. R., Lee, H. W., and Kim, K. W., 2002, “Free Vibration Analysis of Baffled Liquid-Storage Tanks by the Structural-Acoustic Finite Element Formulation,” J. Sound Vib., 258(5), pp. 847–866. [CrossRef]
Gavrilyuk, I., Lukovsky, I., Trotsenko, Yu., and Timokha, A., 2006, “Sloshing in a Vertical Circular Cylindrical Tank With an Annular Baffle. Part 1: Linear Fundamental Solutions,” J. Eng. Math., 54(1), pp. 71–88. [CrossRef]
Biswal, K. C., Bhattacharyya, S. K., and Sinha, P. K., 2006, “Nonlinear Sloshing in Partially Liquid Filled Containers With Baffles,” Int. J. Numer. Methods Eng., 68(3), pp. 317–337. [CrossRef]
Modaressi-Tehrani, K., Rakheja, S., and Stiharu, I., 2007, “Three-Dimensional Analysis of Transient Slosh Within a Partly-Filled Tank Equipped With Baffles,” Veh. Syst. Dyn., 45(6), pp. 525–548. [CrossRef]
Maleki, A., and Ziyaeifar, M., 2008, “Sloshing Damping in Cylindrical Liquid Storage Tanks With Baffles”. J. Sound Vib., 311(1–2), pp. 372–385. [CrossRef]
Chantasiriwan, S., 2009, “Modal Analysis of Free Vibration of Liquid in Rigid Container by the Method of Fundamental Solutions,” Eng. Anal. Boundary Elem., 33(5), pp. 726–730. [CrossRef]
Hasheminejad, S. M., and Aghabeigi, M., 2009, “Liquid Sloshing in Half-Full Horizontal Elliptical Tanks,” J. Sound Vib., 324(1–2), pp. 332–349. [CrossRef]
Yan, G., Rakheja, S., and Siddiqui, K., 2009, “Baffle Design Analysis for a Road Tanker: Transient Fluid Slosh Approach,” SAE Int. J. Commer. Veh., 1(1), pp. 397–405.
Yan, G. R., Rakheja, S., and Siddiqui, K., 2010, “Analysis of Transient Fluid Slosh in Partly-Filled Tanks With and Without Baffles,” Int. J. Heavy Veh. Syst., 17(3/4), pp. 359–379. [CrossRef]
Pal, P., 2012, “Slosh Dynamics of Liquid-Filled Rigid Containers: Two-Dimensional Meshless Local Petrov-Galerkin Approach,” J. Eng. Mech., 138(6), pp. 567–581. [CrossRef]
Dutta, S., and Laha, M. K., 2000, “Analysis of the Small Amplitude Sloshing of a Liquid in a Rigid Container of Arbitrary Shape Using a Low-Order Boundary Element Method,” Int. J. Numer. Methods Eng., 47(9), pp. 1633–1648. [CrossRef]
Wolfram, S., 1991. Mathematica: A System for Doing Mathematics by Computer, second edition, Addison Wesley, Boston, MA.
Faltinsen, O. M., and Timokha, A. N., 2010, “A Multimodal Method for Liquid Sloshing in a Two-Dimensional Circular Tank,” J. Fluid Mech., 665, pp. 457–479. [CrossRef]
Aghabeigi, M., Mohammadi, M. M., and Hasheminejad, S. M., 2010, “Standing Gravity Waves in a Horizontal Circular Annular Tank,” 13th Annual & 2nd International Fluid Dynamics conference, Shiraz University, Shiraz, Iran.

Figures

Grahic Jump Location
Fig. 1

Geometry of the problem

Grahic Jump Location
Fig. 2

Conformal coordinate transformation

Grahic Jump Location
Fig. 3

Variation of the wave motion frequencies with radii ratio and eccentricity parameter

Grahic Jump Location
Fig. 4

Compartmentalization of the fluid region by streamlines

Grahic Jump Location
Fig. 5

The first five wave modes of the liquid

Grahic Jump Location
Fig. 6

First three antisymmetric (n = 1, 3, 5) and three symmetric (n = 2, 4, 6) dimensionless sloshing frequencies as a function of the radius ratio, r1/r2, and eccentricity e

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In