The response of low-gravity propellant sloshing is analyzed for the case where an axisymmetrical container is exposed to axial excitation. Spherical coordinates are used to analytically derive the characteristic functions for an arbitrary axisymmetrical convex container, for which time-consuming and expensive numerical methods have been used in the past. Numerical results show that neglecting the surface tension results in the underestimation of the magnitude of the liquid surface oscillation. The reason for this is explained by the influences of the Bond number and the liquid filling level on the critical value of the coefficient of the excitation term in the modal equation, above which the oscillation is destabilized, and on the characteristic root of the destabilized system. [S0021-8936(00)01502-6]

Issue Section:
Technical Papers
Keywords:
surface tension, vibrations, eigenvalues and eigenfunctions
Topics:
Containers, Displacement, Excitation, Gravity (Force), Sloshing, Surface tension, Variational principles
1.
Abramson, H. N., ed., 1966, “The Dynamic Behavior of Liquids in Moving Containers,” NASA SP-106.
2.
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
.
3.
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
.
4.
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
.
5.
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.
6.
Tong
,
P.
,
1967
, “
Liquid Motion in a Circular Cylindrical Container With a Flexible Bottom
,”
AIAA J.
,
5
, pp.
1842
–
1848
.
7.
Chu
,
W. H.
,
1970
, “
Low-Gravity Fuel Sloshing in an Arbitrary Axisymmetric Rigid Tank
,”
ASME J. Appl. Mech.
,
37
, pp.
828
–
837
.
8.
Concus, P., Crane, G. E., and Satterlee, H. M., 1969, “Small Amplitude Lateral Sloshing in Spheroidal Containers Under Low Gravitational Conditions,” NASA CR-72500.
9.
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
.
10.
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
.
11.
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
.
12.
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
.
13.
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.
14.
Utsumi
,
M.
,
1998
, “
Low-Gravity Propellant Slosh Analysis Using Spherical Coordinates
,”
J. Fluids Struct.
,
12
, pp.
57
–
83
.
15.
Seliger
,
R. L.
, and
Whitham
,
G. B.
,
1968
, “
Variational Principles in Continuum Mechanics
,”
Proc. R. Soc. London, Ser. A
,
305
, pp.
1
–
25
.
16.
Neu
,
J. T.
, and
Good
,
R. J.
,
1963
, “
Equilibrium Behavior of Fluids in Containers at Zero Gravity
,”
AIAA J.
,
1
, pp.
814
–
819
.
17.
Coney, T. A., and Salzman, J. A., 1971, “Lateral Sloshing in Oblate Spheroidal Tanks Under Reduced and Normal Gravity Conditions,” NASA TN D-6250.
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