In this paper the Finite Element Method (FEM) is presented for mass/volume gauging of a fluid in a tank subjected to zero or microgravity conditions. In this approach first mutual capacitances between electrodes embedded inside the tank are measured. Assuming the medium properties the mutual capacitances are also estimated using FEM approach. Using proper non-linear optimization the assumed properties are updated by minimizing the mean square error between estimated and measured capacitances values. Numerical results are presented to validate the present approach

Deshpande, Manohar D.

Doiron, Terence a.

NASA Technical Reports Server

Analysis sf fluid gauge sensor for zero or microgravity conditions using Finite Element 
Method 
Source of Acqu~sltlon 
NASA Goddard Space Right Cellter 
Manohar D. Deshpande* and Terence A, Doiron 
NASA Goddard Space Flight Center, Greenbelt, MD, USA 
manohar.d.deshpande @nasa.gov 
Abstract: In this paper the Finite Element Method (FEM) is presented for mass/volume gauging 
of a fluid in a tank subjected to zero or microgravity conditions. In this approach first mutual 
capacitances between electrodes embedded inside the tank are measured. Assuming the medium 
properties the mutual capacitances are also estimated using FEM approach. Using proper non-lin- 
ear optimization the assumed properties are updated by minimizing the mean square error 
between estimated and measured capacitances values. Numerical results are presented to validate 
the present approach. 
Introduction: For future space explorations, an existence of an orbiting "gas station" supplying 
liquid hydrogen and oxygen to space crafts on their way to Moon, Mars, and other planets will 
make the future space missions more efficient and sustainable. These so called orbiting gas sta- 
tions are envisioned to be able to store liquid hydrogen, oxygen, and other necessary liquids 
required for space travels. One of the important advantages of having such orbiting gas stations 
will be avoiding necessity of lifting heavy fuel loads out of the earth's gravity for long duration 
missions. For construction of such orbiting gas stations, efficient and cost effective methods to 
store, supply and transfer these cryogenic liquids in adverse orbital environments are essential. 
Once these propellants liquids are stored in an orbital storage facility robust and reliable methods 
to measure the liquid fuel quantities in these storages are also essential. In low gravity orbital 
environment an accurate measurement of liquid contents in these tanks becomes problematic 
because of liquid in the tank is always unsettled, sloshing, not wall bounding, and flowing. Tradi- 
tional ground based mass and volume gauging techniques [l-21 such as liquid level estimation 
using mechanical floats, Capacitance theory, Frequency Modulated Continuous Wave Radar 
(FMCW) techniques, and ultrasonic sensors fails in a zero gravity conditions due to uncertain 
behavior of liquids. In the recent past there have been attempts to apply these techniques to esti- 
mate liquid quantities in tanks subjected to zero gravity conditions [2-31. These techniques espe- 
cially those using electromagnetic waves employed in mass gauging have important 
shortcomings. In these techniques a change in electromagnetic characteristic such as a shift in 
resonance frequency is used to estimate mass of liquid in tank However, due to the large size of 
storage tanks and existence of large number of higher order modes, electromagnetic field strength 
in side the tank varies in a random fashion. Hence, presence of in-homogeneity in the medium 
due to the liquid uncertainty makes it almost impossible in a deterministic way to relate amount of 
resonant frequency shifts to the liquid contents. In the mass gauges that estimate liquid quantities 
from measuring the amount of microwave energy absorptions, it is assumed that the electric field 
intensity is uniform in the medium. However, a random distribution of liquid inside microwave 
cavity (storage tank) causes to generate standing waves and hence assumption of an uniform field 
intensity may not achieve desire accuracy in the estimation. 
In this paper the FEM approach is presented for masslvolume gauging of a fluid in a tank sub- 
jected to zero or rnicrogravity conditions. For masslvolume gauging the tank is assumed to be 
https://ntrs.nasa.gov/search.jsp?R=20070032094 2019-08-31T01:10:38+00:00Z
embedded evenly/randornly with multiple rods. In the presence of liquid inside the tanks, muma1 
capacitances between the rods are measured. Also using the FEM the mutual capacitances 
between the rods are estimated assuming the medium properties. Dielectric profile of medium 
inside the tank is then estimated using standard optimization procedcre which will minimize the 
mean square error between the estimated and measured values of the mutual capacitances. From 
the knowledge of dielectric profile the volume of the liquid inside the tank can be estimated. The 
method suggested in this paper uses the electromagnetic principles (as has been used by earlier 
approaches) to develop a mass gauging system for microgravity conditions. However, in the pro- 
posed approach we take into account the random liquid distribution in the storage tank while esti- 
mating its responses. This makes the measurement system more robust and reliable under all 
conditions compared to the existing systems. 
Theory: Electrical Capacitance Tomography: Figure 1 shows an arrangement of various com- 
ponents placed in a cryogenic tank to measure liquid quantities stored in the tank under micro- 
gravity conditions. This arrangement consists of number of thin metallic electrodes printed on 
inside surface of the tank. In order to avoid stray capacitance effect an electric field screen is 
inserted between the tank surface and electrodes as shown in Figure 1. 
Electrodes 
Eiec@ic Field 
Figure 1: Electrical capacitance 
tomography for 
mass/voulmegauging 
in microgravity conditions 
Data Acquisition 
&Processing 
A pair from these electrodes is selected and mutual capacitance between the pair is measured by 
activating one and grounding the other electrode while other remaining electrodes may be free 
potential points. This will create N(N - 1)/2 independent pair combinations where N is total 
number of electrodes. These independent mutual capacitances Cij, where i and j are equal to 
1,  2, 3 ,  ..N . can be used to extract the dielectric profile of the medium inside the tank using the 
following procedure. These mutual capacitances can also be estimated using the expressions 
CVe = Q, /Vi  (1) 
Q,, the total charge collected by j'" electrode when V j  voltage is applied to the irh electrode 
and all other electrodes being grounded is obtained through 
where gi is the potential distribution when ith electrode is excited by voltage Vi and all other 
electrodes grounded, Tj  is the closed contour enclosing the jth electrode, is the dielectric con- 
stant of medium surrounding the jth electrode, and 2 is the unit normal to the electrode con- 
tour. The electric potential gi appearing in (2) can be obtained by solving Laplace's equation 
Above equation is solved using the FEM approach by discretizing the medium into tetrahedrons. 
Numerical values of zero or one are assigned to each tetrahedron. Tetrahedron with value one 
corresponds to presence of liquid inside it. Where as a tetrahedron with zero value corresponds to 
presence of liquid inside it. Initially this assignment is arbitrary since the liquid distribution is 
unknown. With this assumed liquid distribution the mutual capacitances can be estimated. The 
mean squared error defined as Error(0)  = 7~ J  is minimized using nonlinear 
i j 
optimization procedure [4]. A liquid distribution that gives the error below some predetermined 
small value is most probable distribution from which liquid volume and mass can be estimated. 
Numerical Results: For numerical validation a multi-electrode geometry embedded in an inho- 
mogeneous media, as shown in Figure 2 is considered 
Figure 2: Geometry of four sensor 
electrodes embedded in a 
stratified media. 
In this case we assume that the mutual capacitances between the sensor electrodes are known 
(obtained either through an experiment or through a numerical simulation). However, the media 
in which these sensor electrodes are embedded is assumed to be completely unknown. Using a 
non-linear optimization procedure and following the procedure described above medium parame- 
ters are estimated and are shown in Figure 3. 
I Dielectric Constant of 3rd Layer 
I 1 3 5 7 9 11 13 15 17 19 Number of Iteration 
I 1 3 5 7 9 11 13 15 17 19 Wmber of Iteration I 
, 
Figure 3: Estimated medium parameters 
Conclusion: A finite element method approach has been presented for mass/volume gauging of a 
fluid stored in a cryogenic tank subjected to zero gravity or microgravity conditions. By embed- 
ding metal electrodes inside the tank measurement of mutual capacitances is performed. Also 
using the finite element approach the mutual capacitances are estimated as a function of dielectric 
profile of medium inside the tank. Using a appropriate non-linear optimization, most probable 
dielectric profile is estimated by minimizing the mean square error between measured and esti- 
mated capacitances. Numerical results are also presented to validate present approach. 
References 
[I] R. J. Hansman Jr, and J. S. Meserole, "Fundamental limitations on low gravity fluid gauging 
technologies imposed by orbital mission requirements," AIAA/ASME/SAE/ASEE, 24th Joint 
PropulsionConference, July 11-13> 1988,Boston, Massachsetts. 
[2] Mathew. E. Moran, "Liquid hydrogen sensor considerations for space exploration," NASA/ 
TM-2006,214264, May 2006. 
[3] Neil T. Van Dresar and James D. Siegwarth, "Reference gauging system for a small-scale liq 
uid hydrogen tank, " NASAITM-2003-212455, July 2003. 
[4] Baginski, ME.; Faircloth, D.L.; Deshpande, M.D. "Comparison of two optimization tech 
niques for the estimation of complex pemittivities of multilayered structures using waveguide 
measurements,; Microwave Theory and Techniques, IEEE Transactions on, Volume 53, Issue 
10, Oct. 2005 Page(s):325 1 - 3259 


Analysis of Fluid Gauge Sensor for Zero or Microgravity Conditions using Finite Element Method

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