Pressure sensor network for measuring liquid dynamic response in flight including fuel tank acceleration, liquid slosh amplitude, and fuel depth monitorin

Powell, C. A., Jr.

Stephens, D. G.

English

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INSTRUMENT FOR MEASURING THE DYNAMIC BEHAVIOR OF LIQUIDS 
Piled Jan. 26, 1968 2 Sheets-Sheet 1 
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INSTRUMENT FOR MEASURING THE DYNAMIC BEHAVIOR QF LIQUIDS 
Filed Jan. 26, 1968 2 Sheets-Sheet 2 
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INVENTORS 
DAVID G. STEPHENS 
CLEMANS A. POWELL, JR. 
atente 
An instrument to  determine the dynamic behavior of 
liquid in a tank including a pipe fixed to the tank and 
extending throughout its height. An inlet of the pipe 
allows liquid to enter the pipe. A tube placed inside the 
pipe carries a plurality of pressure transducers, one being 
exposed to  the liquid in the tank, a second exposed to 
liquid within the pipe, and a third located at the end of 
the tube below the other transducers. Outputs from the 
transducers are computed and indicate the simultaneous 
acceleration of the tank, the amplitude of liquid slosh 
in the tank, and the depth of liquid in the tank. 
The invention described herein was developed by em- 
ployees o fthe United States Government and may be 
manufactured and used by or for the Government for 
governmental purposes without the payment of any royal- 
ties thereon or therefor. 
This invention relates to  an instrument which measures 
the dynamic behavior of liquid in a tank ana more par- 
ticularly to an instrument which will measme dynamic 
behavior of liquid in a fuel tank subjected to flight 
conditions. 
Several methods have been used for studying slosh 
characteristics of a liquid under laboratory conditions; 
however, these techniques are not generally applicable to 
a Iiquid-propellant fuel tank under flight conditions. 
Prior art methods of observing the dynamic behavior 
of liquids in a tank include observing either physically or 
photographically. Although these arrangements are gen- 
erally satisfactory for static observation, they are not par- 
ticularly adaptable to flight conditions. If photography is 
utilized, mechanism to recover the photograph is also 
necessary resulting in expensive, involved equipment. 
Furthermore, since the fuel tank is seldom, if ever re- 
covered, additional equipment is necessary to  relay the 
results of the pictures. Television systems also involve 
substantial. equipment and require larger power supplies, 
all of which are not generally desirable on space missions. 
Certain types of electronic equipment have also been 
utilized to provide information regarding liquid behavior, 
but this equipment has not proved to be generally suitable 
for use in closed systems such as a fuel tank since they 
require frequent replacement and calibration, and are 
particularly susceptible to corrosion and breakage due to 
the slosh of the liquid within the tank. 
The idea of sensing the acceleration of bodies which 
float on the surface of the liquid has also been oontem- 
plated; however, due to the freedom of motion of these 
floats, precise measurements are extremely difficult if not 
impossible. 
The invention here under consideration overcomes the 
abovementioned problems by providing transducers actu- 
ated by the behavior of liquid at various levels. The out- 
puts from the transducers are conveyed through a protec- 
tive system to the exterior of the fuel tank wherein the 
information is read and interpreted. 
It is therefore an object of this invention to provide 
an instrument for measuring the dynamic behavior of 
liquid. 
A further object of this invention is to provide an 
instrument for measuring the slosh amplitude of liquid in 
a fuel tank. 
Another object of the invention is to  provide an instru- 
ment for measuring the acceleration of the fuel tank. 
A further object of the invention is to provide instru- 
mentation for measuring the dynamic behavior of liquid in 
An additional object of the invention is to provide 
instrumentation for mapping the entire surface behavior 
of liquid in a fuel tank. 
Still another object of the invention is to provide an 
15 instrument which will measure the depth of liquid in a fuel 
tank, as well as acceleration and slosh amplitude. 
Yet another object of the invention is to provide an 
instrument for determining the dynamic behavior of a 
liquid which is of durable construction, not subject to 
20 corrosion, is simple to  operate and maintain, and that is 
readily adapted to use in a fuel tank of a liquid-propellant 
launch vehicle. 
These and other objects and advantages of the invention 
will become more apparent upon reading the specification 
25 in conjunction with the accompanying drawings. 
In the drawings: 
FIG. 1 is a cross sectional view of a fuel tank section 
showing the instrument for measuring the dynamic be- 
havior of liquid in the tank as it is associated with the 
FIG. 2 is a cross sectional view taken along the section 
lines 11-11 of FIGUKE 1, illustrating the positioning of 
certain of the transducers utilized in the instrument; 
FIG. 3 is a cross sectional view taken along the sec- 
35 tional lines 111-111 of FIG. 1, showing another trans- 
ducer and its position in the instrument; 
FIG. 4 is a plan view showing schematically the posi- 
tioning of instruments utilized in mapping the dynamic 
behavior of the entire surface of liquid in a tank; and 
FIG. 5 is a diagram showing the wave form outputs 
from the various transducers utilized in the insirument. 
Referring now more specscally to the details of the 
invention, FIG. 1 illustrates the instrument assembly 
designated generally by the reference numeral 10. 
The assembly 10 is shown in conjunction with a tank 
or fuel tank 11 containing liquid or fuel 12. It should be 
understood, however, that the invention has application 
to any body of liquid, for example, measuring the 
dynamic behavior of the ocean. The fuel tank El, for 
50 purposes of illustration, has the general configuration of 
a fuel tank which might be utilized in a liquid-propellant 
launch vehicle. Such tanks have a depth or height which 
is usually several times the diameter of the tank, due to 
the design of the overall vehicle. It is to be understood, 
55 however, that the invention has application to tanks of 
various sizes and shapes. 
The dotted line transversing tank 11 is  associated with 
the reference numeral 13 and illustrates the quiescent 
liquid level in the fuel tank, the line 14 representing a 
60 possible surface profile under slosh conditions. Both of 
these lines are shown to facilitate the description and 
understanding of the invention. 
The instrument, designated generally by the reference 
numeral 19, includes a pipe 20 which extends from the 
65 top to the bottom of the tank. The pipe 20 has a leg 21 
which projects at an angle normal thereto along the 
bottom of the tank. A portion of the extremity of the 
pipe is turned up and left open providing an inlet 22. 
Liquid within the tank is thus free to enter inlet 22 and 
70 seek the quiescent level 13 within the pipe 20. FIGURE 1 
shows onIy a portion of a tank and therefore only a 
portion of the pipe 20. Although not shown, brackets or 
10 a fuel tank at all levels of fuel in the tank. 
30 tank; 
40 
45 
3,473,379 
clamps of conventional design would be secured to the 
side of the tank and to the pipe in a conventional manner 
to maintain the pipe in the proper position with respect 
to the tank. The pipe 20 may also be formed of a series 
of sections joined by couplings, such as the coupling 23, 
shown in FIGURE 2. The coupling 23 has an offset clo- 
sure 24 and an opening 25 to accommodate transducers, 
to be explained more fully hereinafter. 
Disposed within the pipe 20 is a tube 28 which is gen- 
erally concentric with the pipe. The top of the tube 28 
would be connected to the tank I?. in a manner such that 
leads carried by the tube might pass through the wall of 
the tank to equipment. The lower extremity of the tube 
extends to a position adjacent the bottom of the tank. The 
tube 28 is also formed in sections being joined by a 
cross-shaped union 29. The union 29 is positioned in the 
tube 28 such that one arm of the union projects into the 
offset closure 24 of pipe coupling 23, and the other arm 
thereof projects through the couplings outlet 25. 
Differential pressure transducer 32 is connected to the 
union 29 in a conventional manner such as by welding 
or a thread connection. The transducer 32 is of conven- 
tional design having a diaphragm and strain gage arrange- 
ment, this type of transducer being available commercial- 
ly. A pressure transducer 35 is  connected to the other 
arm of the union 29 and is of the same type as trans- 
ducer 32. Another transducer 40 is located in the lower 
end of tube 28 and is also of the same type as the trans- 
ducers 32 and 35. Leads 33, 36, an$ 42 from transducers 
32, 35 and 40, respectively, travel through the tube 28 
to the exterior of the fuel tank carrying the outputs from 
the strain gages forming a part of the various transducers. 
These leads are connected to an amplifier 45, which is 
in turn connected to a computer 47, the output of which 
may be fed to a recorder 49 and/or telemetry equipment 
50. The amplifier, computer, recorder and telemetry equip- 
ment are of a conventional design and many types of 
each device may be obtained commercially. 
The pipe 20 contains gas at the ullage pressure, which 
is the pressure of gas between the liquid and the top of 
the container. 
Additional transducers may be placed at different levels 
throughout the length of the pipe 20. For example, the 
points 34 and 38 (FIG. 1 )  represent additional trans- 
ducers which may be placed along the pipe. It is to be 
understood that these transducers might be placed at in- 
tervals from the top to the bottom of the pipe to gather 
information on the dynamic behavior of the liquid in the 
tank at all levels, this being necessary as the liquid is 
consumed and drained from the tank. 
FIG. 5 illustrates diagrammatically that instrumenta- 
tion may be placed at  various points about the tank in 
order to sense the behavior of the entire surface of the 
liquid. Thus, an instrument similar to the 
might be placed at each qu 
additional instruments 55, 
FIG. 5 of the drawings. These instruments would be 
similar in construction to the instrument 19. 
OPERATION 
In describing the operation, it is assumed that the in- 
strument 19 is positioned in a tank and that liquid is at 
some level in the tank essentially as shown in FIG. 1. 
The liquid in the tank will seek a level and have a quiescent 
level line such as 13 under static conditions. The liquid 
will also enter the inlet 22 and fill the pipe 20 to the 
quiescent level line. The liquid in pipe 20 will remain at 
the quiescent level even under slosh conditions. 
I t  is believed to be clear from viewing FIGS. 1-3 that 
the transducer 32 is subjected to the liquid within the 
pipe 20, that the transducer 35 is subjected to  the liquid 
within the tank, and that transducer 40 is subjected to 
the liquid in the pipe 20 at a Iower level. 
Assuming that liquid is agitated, for example, by shak- 
ing in a static test, or movement of the entire tank as a, 
5 
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36 
40 
45 
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60 
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73 
result of launch, various outputs are provided from the 
transducers. The diagram shown in FIG. 5 illustrates the 
output from each of the transducers. The output from the 
transducer 32 corresponds with the tracing P-E, the out- 
put from the transducer 35 corresponds with the tracing 
P-2, and the output from the transducer 40 correspond 
with the tracing P-3. It is apparent from FIG. 5 that the 
reading from the transducers subjected to the liquid with- 
in the pipe remains substantially constant at a given level 
of liquid. The transducer subjected to the liquid in the 
tank, however, provides a fluctuating output as shown by 
tracing P-2. With these relationships, it has been found 
that the difference between tracing P-3 and P-9 is pro- 
portional to the tank acceleration, and is therefore in- 
dicative of the acceleration of the tank and liquid. It has 
further been found that output P-3 is proportional to the 
depth of liquid in the tank and is therefore indicative of 
the quiescent liquid level in the tank. The difference be- 
tween tracings P-2 and P-l is proportional to the liquid 
amplitude and is therefore indicative of the degree of 
slosh. Utilizing known hydrodynamic relationships, the 
acceleration, depth of liquid and slosh amplitude can be 
determined. This is accomplished by the computer 47, the 
output of which is recorded under static test conditions, 
or under flight conditions may be recorded and relayed 
by telemetry equipment. 
The hydrodynamic relationship is represented by the 
equation 
where: 
Po ullage pressure 
p fluid density, slugs/ft.3 
g longitudinal acceleration field, ft./sec.2 
7 
a tank radius, ft. 
h height of quiescent fluid surface, ft. 
maximum wave height above quiescent free surface 
at  the tank walls, Et. 
wl fundamental slosh frequency 
d1.841 pa-1 tanh 1.841 ha-',, rad/sec. 
z distance from-quiescent free surface (positive direc- 
With the outputs from the various tsansducers, it is a 
simple matter to solve for the acceleration (g). the slosh 
amplitude (q), and the depth ( h ) ,  with the aid of Equa- 
tion l. 
Simplified instrumentation can be utilized to determine 
slosh amplitude if the liquid depth, acceleration, and trans- 
ducer location are known such as in laboratory testing. A 
single pressure transducer, such as transducer 35, is 10- 
cated at a known distance below the quiescent liquid level. 
The transducer is subjected directly to  the liquid in the 
tarik. The pressure fluctuations sensed by the transducer 
are directly proportional to the amplitude of slosh. Thus 
by properly calibrating the transducer, the output thereof 
will provide a direct reading of slosh amplitude. 
From the above description of the invention, the many 
advantages thereof are believed to be readily apparent. 
The instrument is believed to  be the only device of its 
type which will provide acceleration, slosh amplitude and 
depth data of a dynamic liquid which is itself being con- 
veyed in a flight vehicle. The instrument is rugged in con- 
struction, is of a simple. design readily adapted for use 
in a fuel tank, and is constructed so as to withstand the 
buffeting of moving liquid and resists its corrosive effect. 
The instrument has also proven to be extremely accurate 
and has few parts of minimum weight, thereby being par- 
ticularly adapted for space flight application. 
While a preferred embodiment of tha invention has 
been described, it will be understood that modifications 
a& improvements may be made thereto. 
tion downward), ft. 
3,413,359 
What is claimed as new d desired to be secured by 
. An assembly for measuring the dynamic behavior of 
Letters Patent of the United States is: 
liquid or the like comprising: 
a body of liquid; 
a pipe extending into the liquid and being open to said 
liquid; 
first pressure sensing transducer means positioned in 
said pipe and being subjected to the liquid therein; 
second pressure sensing transducer means subjected to 
the liquid surrounding the pipe; 
a tube containing gas at ambient pressure extending 
into said liquid; 
third pressure sensing transducer means sealingly lo- 
cated on the end of the tube and subjected to said 
liquid at a depth greater than said f is t  and second 
transducers; 
means responsive to the outputs of said first, second 
and third transducer means for calculating the 
quiescent surface level of the liquid, the amplitude 
of slosh from said level, and the acceleration of the 
liquid body. 
2. An assembly for measuring the dynamic behavior 
of liquid or  the like as in claim I wherein the tube is 
housed within the pipe. 
3. An assembly for measuring the dynamic behavior 
of liquid or the like as in claim 1 wherein said first and 
second transducers are located on the same, level and 
said third transducer is located below said first and sec- 
ond transducers. 
4. An assembly for measuring the dynamic behavior 
of liquid or the like as in claim 1 wherein the dzerence 
between the outputs of the first and third transducers is 
indicative of the liquid body acceleration. 
5. An assembly for measuring the dynamic behavior 
of liquid or the like as in claim 1 wherein the difference 
between the outputs of the first and second transducers is 
indicative of slosh amplitude. 
6. An assembly for measuring the dynamic behavior 
of liquid or the like as in claim 1 wherein said means for 40 References Cited 
comparing outputs of the transducers includes an ampli- UNITED STATES PATENTS 
fier and computer; and recorder and telemetering means 2,921,469 1/1960 Newton _ _ _ _ _ _ _ _ _ _ _  73-301 
for storing and transmitting liquid behavior data from 3,114,381 12/1963 Klose et al. 73-299 
the computer. 
of liquid or the like. as in claim 1 wherein the output of 
the third transducer means is indicative of the quiescent 
45 3,269,187 811966 Perino -____________- 73-398 
3,371,534 3/1968 Akeley _ _ _ _ _ _ _ _ _ _ _ _ _ _  73-299 
7. An assembly for measuring the dynamic behavior 3,364,466 1/1968 Stine _ _ _ _ _ _ _ _ _ _ _ _  340-179 
liquid is in a tank; and additional transducers are located 
at different levels in the tank to provide outputs at all levels 
of liquid in the tank. 
9. An assembly for measuring the dynamic behavior of 
liquid or the like. as in claim I wherein the body of liquid 
is in a tank, and a plurality of pipes are located at sev- 
eral different positions about the perimeter of the tank, 
each pipe including first, second and third pressure sens- 
ing transducers to map all surface movement within the 
tank. 
IO. An assembly for measuring the, dynamic behavior 
of liquid or the like comprising: 
a tank having a depth substantially greater than its 
a pipe carried by the tank extending from the top to 
said pipe having a leg extending at an angle therefrom 
an inlet formed in the leg allowing liquid to enter 
a tube positioned within said pipe; 
opposing first and second pressure sensitive transducer 
means mounted on said tube; 
one of said transducers extending through an aperture 
in said pipe and being subjected to the liquid in said 
tank; 
the other transducer being subjected to liquid in said 
pipe; 
a third pressure sensitive. transducer sealingly fixed to 
the bottom of said tube; 
computer means; 
leads from said first, second and third transducer means 
passing through said tube and being connected to 
said computer means; and 
said computer means being responsive to the outputs 
of said first, second and third transducer means for 
determining acceleration of the tank, depth of liquid 
and amplitude of liquid slosh. 
diameter; 
the bottom of the tank; 
along the bottom of the tank; 
ib 
20 the pipe; 
25 
30 
35 
LOUIS R. PRINCE, Primary Examiner liquid level. 
of liquid or the like as in claim 1 wherein the body of 50 DANIEL 
8. An assembly for measuring the dynamic behavior 
YASICH~ Assistant Examiner 


Instrument for measuring the dynamic behavior of liquids Patent

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