Frequencies and total force response in rigid cylindrical tanks comparted into sectors by vertical walls and excited in translation to study liquid sloshin

Abramson, H. N.

Garza, L. R.

Kana, D. D.

English

NASA Technical Reports Server

S O U T H W E S T  R E S E A R C H  I N S T I T U T E  
8500 Culebra Road, San Antonio 6,  Texas 
Department of Mechanic a1 Sciences 
Engineering Analysis Section 
SOME NOTES ON LIQUID SLOSHING 
H. Norman Abramson 
Luis R. Garza 
Daniel D. Kana 
Technical Report No. 1 
Contract No. NAS8- 1555 
SwRI Project No. 6-1072-2 
Prepared for 
National Aeronautics and Space Administration 
Huntsville, Alabama 
George C. Marshall Space Flight Center 
15  February 1962 
APPROVED: 
H. Norman Abramson, Director 
Department of Mechanical Sciences 
https://ntrs.nasa.gov/search.jsp?R=19660006482 2020-03-16T21:40:41+00:00Z
INTRODUCTION 
As one relatively simple means of avoiding dynamic coupling 
between sloshing of liquid propellants and automatic control system 
response, or elastic body response, i t  has been suggested that propellant 
tanks be compartmented so  as tu rdiae ur otherwise ii-iodify the zcrxzl  
sloshing frequencies. There is  also the possibility of an overall reduction 
in the total force response a s  a result of phasing of the liquid motions in 
different compartments. 
clustered tank configurations (over that for  a single tank of the same 
Frequencies a r e  a lso increased in the case of 
capacity), but the weight penalty is more severe and additional complica- 
tions may be introduced through other dynamic coupling effects 
The present paper gives some resul ts  of experimental studies of 
frequencies and total force response in rigid cylindrical tanks compart- 
mented into sectors  by vertical wal ls  and excited in translation. These 
data a re  correlated with theoretical values, where available. Some theo- 
retical  values for  cylindrical tanks with annular c ros s  -sections are also 
shown for comparative purposes. The experimental equipment and proce = 
dures are similar to those employed in ( l ) c x s  
Numbers in parentheses refer  to the References given at the end 
of the paper. 
-,, 
i _ I  
TANK CONFIGURATIONS 
---l--- -  -  uic V C L  L L L c a A  w a & & v  GALCIILU &I V A A I  uUu. - .A*- 
surface to the tank bottom. 
is a s  shown in Figure 1. 
The direction of the translational excitation 
LIQUID NATURAL F R E Q U E N C I E S  
It is well-known that the liquid natural frequencies in  a cylindrical 
tank are virtually independent of liquid depth for  h / d  3 1. 
values of liquid natural frequencies, in te rms  of the dimensionless param- 
e te r  
h / d  >/ 1. 
f rom ( 2 - 5 )  and the results of the present study. 
and quarter tank configurations have their lowest natural frequencies 
considerably above that for  the uncompartmented tank; but the eighth (45O 
sec tor )  tank has a very much higher value than any of the other configura- 
tions, Of course, as the liquid depth decreases (h/d L 1)  the natural  f re -  
cuencies also decrease,  but the relative values for the various configura- 
tions remain essentially unchanged ( F i g .  2 ) .  As shown in Table 1, there 
Table 1 gives 
, 
I w:d/a, for  the various compartmented tank configurations for  
The data, partly theoretical and partly experimental, is  taken 
It is noted that the half 
, 
3 
is  some difference between theoretical (4) and experimental values of the 
natural irequency parameter f o r  the quarter tank. 
The annular tank (4,5) exhibits an unusual variation of natural 
frequencies of the outer ring compartment with diameter ratio k. The 
lowest natural frequency (for h/d 1) remaifis a~~bstant ia l?y the same o r  
. .  siightiy iess  than for the uncorriljariiiieiiied tarik, reach ing  a XIEIZ~ILZ. 
value of 2 w ,d /a  of approximately 2. 0 a t  k = 0. 8. On the other hand, the 
second resonant mode (again for h /d  7 1)  shows a very large increase 
in frequency, reaching a maximum value of 0 t d / a  of more than 30. 0 at 
k = 0.8. 
the single case of k = 0. 5, is shown in  Figure 2. 
The variation of these frequencies with depth for  h / d  e 1, for 
The frequency variations 
f o r  the inner cylindrical tank are,  of course, the same as for  an uncom- 
partmented tank, based on the appropriate inner tank diameter. 
The essential effect of sector compartmentation i s  to ra i se  the 
lowest liquid frequency and to introduce new resonant frequencies, as 
shown in Table 1. The lower frequencies, corresponding to resonances 
of various sector combinations, a r e  generally not widely separated. 
_I 
Because of the weight penalty associated with increasing numbers 
of sectors,  consideration has also been given to effects of wall perfora- 
tion. F o r  a quarter tank with perforated sector walls of 2370 opening, it 
was found that the essential  effect w a s  to provide sector fluid exchange 
resulting in an effective geometrical configuration intermediate between 
4 
the uncompartmented tank and the solid wall quarter tank. 
ferent  sector resonances a r e  blended into one, as  a consequence of the 
liquid interchange. 
size be maintained relatively small in order  that the lowest resonant 
frequencies do not. decrease to the order  of those of the uneornpartmented 
tank. 
e te r  
on perforation hole diameter*. The value of the natural frequency param- 
e t e r  is  seen to vary f rom between 5. 0 and 6. 0, corresponding to the solid 
wall quarter tank (RNH+ 0),  to somewhat more than 3. 0, approximately 
the value fo r  the uncompartmented tank (R + oo), The transition zone 
i s  clearly dependent upon the excitation amplitude and probably on liquid 
depth (for h /d  e 1) as well. 
The two dif- 
However, it is also required that the perforation hole 
This effect i s  shown in Figure 3 where the satura? frzqueixy pararn- 
2 o ,d/a is plotted against an equivalent Reynolds Number ( l ) ,  based 
NH 
FORCED VIBRATION RESPONSE 
Experimental data for total force response in uncompartmented, 
half, and quarter tanks with solid walls a r e  shown in Figure 4 in te rms  of 
force magnitude and phase versus excitation frequency. Similar data is 
The experimental data of Figure 3 was obtained for  a tank with 
d = 14.4 in. ,  perforation hole sizes of 0. 020 and 0. 078 in. , and 
with water and methylene chloride a s  tes t  liquids. 
.L *,- 
5 I I 
1 , shown in Figure 5 fo r  an uncompartmented tank and for a quarter tank 
with both solid and perforated walls. It can readily be seen that a slightly I 
greater amount of total force damping results f rom using perforated walls, 
compared to solid sector walls, and that all of these provide some ampli- 
tude damping over the non-compartmented tank. 
Results similar to those shown in Figures 4 and 5 have been ob- 
tained for  various other liquid depths (h/d < 1)  and excitation amplitudes, 
but a r e  not presented in this paper in the interests of brevity. 
Calculated values of total force response in annular tanks a r e  
given in (5). Fo r  quarter tanks, the appropriate equations for  total force 
response are given in (4), but calculated results a r e  not yet available. 
DISCUSSION 
In general, one may come to several  conclusions regarding the 
effects of tank sectorization, although these a re  not clear-cut and lead at 
times to conflicting opinions regarding the advantages of such compart- 
mentation. F i r s t ,  compartmentation by sectors  leads to higher resonant 
frequencies (the increase becomes very large for  sector angles less  than 
90°), and in the case of solid sector walls a t  least  the lowest frequencies 
a r e  not very widely separated (Fig .  4). 
holes of proper size may serve the purpose of weight reduction and at  the 
Perforation of the sector walls by 
6 
same time provide for liquid interchange between sectors  which blends the 
two lowest liquid resonant frequencies into one; however, the effects of 
perforation on the creation of turbulence in the liquid may be undesirable 
fo r  certain types of propellants. 
damping provided by compartmentation, while sigrrificarit, is ce r t a idy  
much iess  than can be obtained through iiiole ciistsrrrarji r i n g  Safflz 
arrangements and probably involves greater weight penalties. 
Finally, the amount of force amplitude 
The attractiveness of the annular tank resides in the wide separa- 
tion between freqeuncies of the inner and outer compartments and in the 
fact  that phasing of the liquid motions between the two compartments 
results in a lower total force. Values of the diameter ratio 0. 5 c k 
give not only the widest separation of frequencies but also almost equal 
fluid masses  in the two compartments so that force cancellation i s  maxi- 
mized. 
0. 9 
Thus, it appears that final selection of a tank configuration must  
depend on the overall vehicle dynamics; in some cases  i t  may be sufficient 
to provide adequate force damping by means of ring baffles, while in others 
i t  may be more desirable to modify the propellant sloshing frequencies by 
compartmentation. But, in either case,  an analysis of the overall vehicle 
dynamics must  be undertaken which includes some representation of the 
effects of the sloshing liquid. 
employed in such dynamic analyses (6);  appropriate models for quarter 
and annular tanks a r e  given in (4, 5). 
Equivalent mechanical models a r e  often 
1. 
2. 
3. 
4. 
5. 
6. 
7 
REFERENCES 
Abramson, H. N . ,  and Ransleben, G. E. ,  Jr.,  !'Simulation of Fuel  
Sloshing Characteristics in Missile Tanks by U s e  of Small Models, 
ARS Journal, _. 30, 7, pp. 603-612, July 1960. 
Unpublished data, The Martin Company, Baltimore, 1960. 
Bauer, H. , IIDynamics of Liquid Propellant Vehicles, ONR / M A  
Symposium on Structural  Dynamics of High Speed Flight, pp. 319- 
355, Los Angeles, California, April 1961. 
Bauer, H., "Theory of the Fluid Oscillations in a Circular Cylin- 
dr ical  Ring Tank Partially Fil led With Liquid, I '  NASA Tech. Note 
D-557 (December 1960). 
Abramson, H. N . ,  Chu, W. H., andRansleben, G. E . ,  J r . ,  
"Representation of Fuel Sloshing in  Cylindrical Tanks by an 
Equivalent Mechanical Model," ARS Journal, 31, - 12, pp. 1697- 
1705, December 1961. 
TABLE 1. VALUES O F  LIQUID NATURAL FREQUENCY 
PARAMETER W:d/a FOR VARIOUS TANK 
CONFIGURATIONS FOR h / d  8 1 
Lowest Second 
Tank Configuration Natural Frequency Natural Frequency 
theory experiment the o r  y expe rime nt 
Unc ompartmented 3. 68)": 
-- Haif - e - -  
Quarter  (9  ~Osec to r  6.1'' 
Eighth (45Osector) ---- 
Annular (k = 0.2) 3.4O 
Annular (k = 0. 5 )  2.7* 
Annular (k = 0.8) 2 .20  
3.6)": 10.66** 
5. iu ---- 
5.0" 7. 6+tv 
7.7& - - - -  
9.9O ---- 
- - - -  13. l o  
---- 31.6' 
Notes: 
* -I- 
** 
0 
0 0  
t 
tt 
a 
A a  
V 
0 
first mode normal sloshing resonance 
second mode normal sloshing resonance 
in-phase resonance (exp., Ref. 2 )  
out-of-phase resonance (exp., Ref. 2 )  
sector 2 , 4  resonance 
sector 1 , 3  resonance 
sector 1 , 5  resonance (exp., Ref. 3) 
sector 3,7 resonance (exp., Ref. 3) 
theoretical values (Ref. 4 )  
outer (ring) tank resonance (theory, Ref. 5)  
- 
-EXCITATION X,' 
(a) UNCOMPARTMENTED TANK !b! HALF TANK 
- 
EXCITATION X, 
(c) QUARTER (90° SECTOR) TANK (d) EIGHTH (45O SECTOR) TANK 
(e) ANNULAR TANK (k  = di /d) 
FIGURE 1. TANK CONFIGURATIONS 
I€ 
14 
ii 
IC 
a 
6 
4 
2 
0 
0.2 0.4 0.6 0.8 I .o 1.2 
LIQUID DEPTH h/d 
FIGURE 2. VARIATION IN LIQUID NATURAL FREQUENCIES WITH 
LIQUID DEPTH FOR VARIOUS TANK CONFIGURATIONS 
(THEORETICAL VALUES) 
I! 
0 
0 
0 
0- - 
0 
0 
9 
0 
8 
a 
W c 
a 
I i 
I 
-I- 
T 
I E 
r--rl-- 
\ \  
I I 
 
rr) 
Ir) 
. 
\ 
\ 
4 1 
i i  
I 


Some Notes on Liquid Sloshing in Compartmented Cylindrical Tanks Technical Report No. 1

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server