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TECHNICAL PAPERS

Low-Gravity Sloshing in an Axisymmetrical Container Excited in the Axial Direction

[+] Author and Article Information
M. Utsumi

Machine Element Department, Research Institute, Ishikawajima-Harima Heavy Industries Company, Ltd. (IHI), 3-1-15 Toyosu, Koto-ku, Tokyo 135-0061, Japan

J. Appl. Mech 67(2), 344-354 (Jan 20, 2000) (11 pages) doi:10.1115/1.1307500 History: Received April 23, 1998; Revised January 20, 2000
Copyright © 2000 by ASME
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References

Abramson, H. N., ed., 1966, “The Dynamic Behavior of Liquids in Moving Containers,” NASA SP-106.
Bauer,  H. F., and Siekmann,  J., 1971, “Dynamic Interaction of a Liquid with the Elastic Structure of a Circular Cylindrical Container,” Ing. Arch., 40, pp. 266–280.
Dodge,  F. T., and Garza,  L. R., 1967, “Experimental and Theoretical Studies of Liquid Sloshing at Simulated Low Gravity,” ASME J. Appl. Mech., 34, pp. 555–562.
Peterson,  L. D., Crawley,  E. F., and Hansman,  R. J., 1989, “Nonlinear Fluid Slosh Coupled to the Dynamics of a Spacecraft,” AIAA J., 27, pp. 1230–1240.
Satterlee, H. M., and Reynolds, W. C., 1964, “The Dynamics of the Free Liquid Surface in Cylindrical Containers Under Strong Capillary and Weak Gravity Conditions,” Technical Report LG-2, Department of Mechanical Engineering, Stanford University, Stanford, CA.
Tong,  P., 1967, “Liquid Motion in a Circular Cylindrical Container With a Flexible Bottom,” AIAA J., 5, pp. 1842–1848.
Chu,  W. H., 1970, “Low-Gravity Fuel Sloshing in an Arbitrary Axisymmetric Rigid Tank,” ASME J. Appl. Mech., 37, pp. 828–837.
Concus, P., Crane, G. E., and Satterlee, H. M., 1969, “Small Amplitude Lateral Sloshing in Spheroidal Containers Under Low Gravitational Conditions,” NASA CR-72500.
Dodge,  F. T., and Garza,  L. R., 1970, “Simulated Low-Gravity Sloshing in Spherical, Ellipsoidal, and Cylindrical Tanks,” J. Spacecr. Rockets, 7, pp. 204–206.
Dodge,  F. T., Green,  S. T., and Cruse,  M. W., 1991, “Analysis of Small-Amplitude Low Gravity Sloshing in Axisymmetric Tanks,” Micrograv. Sci. Technol., 4, pp. 228–234.
Hung,  R. J., and Lee,  C. C., 1992, “Similarity Rules in Gravity Jitter-Related Spacecraft Liquid Propellant Slosh Waves Excitation,” J. Fluids Struct., 6, pp. 493–522.
Yeh,  C. K., 1967, “Free and Forced Oscillations of a Liquid in an Axisymmetric Tank at Low-Gravity Environments,” ASME J. Appl. Mech., 34, pp. 23–28.
Utsumi, M., 1989, “The Meniscus and Sloshing of a Liquid in an Axisymmetric Container at Low-Gravity,” Sloshing and Fluid Structure Vibration, D. C. Ma, J. Tani, S. S. Chen, and W. K. Liu, eds., ASME, New York, pp. 103–113.
Utsumi,  M., 1998, “Low-Gravity Propellant Slosh Analysis Using Spherical Coordinates,” J. Fluids Struct., 12, pp. 57–83.
Seliger,  R. L., and Whitham,  G. B., 1968, “Variational Principles in Continuum Mechanics,” Proc. R. Soc. London, Ser. A, 305, pp. 1–25.
Neu,  J. T., and Good,  R. J., 1963, “Equilibrium Behavior of Fluids in Containers at Zero Gravity,” AIAA J., 1, pp. 814–819.
Coney, T. A., and Salzman, J. A., 1971, “Lateral Sloshing in Oblate Spheroidal Tanks Under Reduced and Normal Gravity Conditions,” NASA TN D-6250.

Figures

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Axisymmetrical container and coordinate systems
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Shape of meniscus for various Bond numbers and dimensionless z-coordinates of contact line
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Dimensionless eigenfrequency ω=ω*ch* (ω* is the dimensional eigenfrequency, ωch* is the characteristic frequency given by ωch*=(g*/b*)1/2)
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Dimensionless eigenfrequency ω=ω*ch* for the case Bo=0 (ω* is the dimensional eigenfrequency, ωch* is the characteristic frequency given by ωch*=[σ*f*(b*)3]1/2
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Comparison of the present and the previous results for the meniscus shape (78 percent, 50 percent, and 25 percent filling levels for Bo=1 and Bo=2; θc=5 deg; •, present analysis; – analysis by Dodge et al. 10
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Comparison of the present and the previous results for the eigenfrequency. (a) –, present analysis and theoretical prediction by Concus et al. 8 both for θc=0 deg; •, experiment by Coney and Salzman 17. (b) –, present analysis; •, experiment by Dodge and Garza 9.
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Dimensionless magnitude of liquid surface displacement |ζ| at (θ,φ,t)=(θ̄,0,10π/ω)
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Coefficient of excitation term Q in modal Eq. (56) normalized by its critical value Qcr
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Characteristic root s1 normalized by dimensionless eigenfrequency ω
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Results for the case Bo=0; (a) dimensionless magnitude of liquid surface displacement |ζ| at (θ,φ,t)=(θ̄,0,10π/ω); (b) coefficient of excitation term Q in modal Eq. (56) normalized by its critical value Qcr; (c) characteristic root s1 normalized by dimensionless eigenfrequency ω
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Virtual displacement δRM cos γM in direction normal to the meniscus M considered for derivation of Eq. (A1)
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Influence of contact angle on the eigenfrequency
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Value of 1/M, where M is area of meniscus
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Eigenfrequency shown as a function of the ratio [liquid volume]/[container volume] within the range zC≤1.9

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