Study of resonant oscillations of an ideal fluid in a cylindrical tank is used to obtain a better understanding of fuel sloshing in large liquid booster. More realistic structural design criteria may be formulated when the dynamic response of the liquid in a cylindrical tank can be predicted analytically

Di Maggio, O. D.

Salzman, R. N.

English

NASA Technical Reports Server

November 1967
	 Brief 67-10439 
NASA TECH BRIEF	 1 
NASA Tech Briefs are issued to summarize specific innovations derived from the U.S. space program, 
to encourage their commercial application. Copies are available to the public at 15 cents each 
from the Clearinghouse for Federal Scientific and Technical Information, Springfield, Virginia 22151. 
Study Made of Large Amplitude Fuel Sloshing 
F_
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To obtain a better understanding of fuel sloshing 
in large liquid boosters, such as the Saturn vehicle, 
a study was made of resonant oscillations of an ideal 
fluid in a cylindrical tank. Although a linear theory 
predicts satisfactory results away from resonance, a 
nonlinear theory is required at or near resonance. 
Prior to this study only limited information was avail-
able on fluid motions due to forcing frequencies at or 
near resonance. 
The study utilized a perturbation procedure. The 
velocity potential apd wave profile were expanded 
in one-third powers of the exciting amplitude. The 
constant pressure condition and the kinematic free 
surface condition were combined into one equation 
valid on the free surface. The arbitrary constants 
which are determined by removing the secular terms 
from the third order solution contain an additional 
"depth correction" term. Analytical expressions have 
been obtained for the wave amplitude, the force and 
moment on the tank walls, and the displacement of 
the center of mass for both the planar mode and the 
nonpianar or rotary slosh mode. 
One conclusion of this study has been that the non-
linearities of the system tend to make the liquid in 
the planar mode behave as a soft spring for large 
depths and a hard spring for all depths. The quanti-
tative engineering results obtained are curves of wave
amplitude, force, moments, and c.g. displacement ver-
sus the frequency parameter. These curves are non-
dimensional and may be adapted to any tank with this 
geometry. 
It is believed that more realistic structural design 
criteria may be formulated when the dynamic response 
of the liquid in a cylindrical tank can be predicted 
analytically. 
Note: 
Additional details are contained in: Finite Ampli-
tude Liquid Oscillations H. Forced Resonant Oscilla-
tions, by 0. D. DiMaggio and R. N. Salzman, SID 
65-853-1, North American Aviation, Inc., June 1966. 
Copies of this report are available from: 
Technology Utilization Officer 
Marshall Space Flight Center 
Huntsville, Alabama 35812 
Reference: B67-10439 
Patent status: 
Inquiries about obtaining rights for the commer-
cial use of this invention may be made to NASA, 
Code GP, Washington, D. C. 20546. 
Source: 0. D. DiMaggio and R. N. Salzman

of North American Aviation, Inc.

under contract to

Marshall Space Flight Center 
(MFS-12381) 
Category 03 
This document was prepared under the sponsorship of the National	 Government assumes any liability resulting from the use of the 
Aeronautics and Space Administration. Neither the United States 	 information contained in this document, or warrants that such use 
Government nor any person acting on behalf of the United States 	 will be free from privately owned rights.
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Study made of large amplitude fuel sloshing

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