An effort is under way to develop capacitive sensors for measuring the masses of cryogenic fluids in tanks. These sensors are intended to function in both microgravitational and normal gravitational settings, and should not be confused with level sensors, including capacitive ones. A sensor of this type is conceptually simple in the sense that (1) it includes only one capacitor and (2) if properly designed, its single capacitance reading should be readily convertible to a close approximation of the mass of the cryogenic fluid in the tank.

Consider a pair of electrically insulated electrodes used as a simple capacitive sensor. In general, the capacitance is proportional to the permittivity of the dielectric medium (in this case, a cryogenic fluid) between the electrodes. The success of design and operation of a sensor of the present type depends on the accuracy of the assumption that to a close approximation, the permittivity of the cryogenic fluid varies linearly with the density of the fluid. Data on liquid nitrogen, liquid oxygen, and liquid hydrogen, reported by the National Institute of Standards and Technology, indicate that the permittivities and densities of these fluids are, indeed, linearly related to within a few tenths of a percent over the pressure and temperature regions of interest. Hence, ignoring geometric effects for the moment, the capacitance between two electrodes immersed in the fluid should vary linearly with the density, and, hence, with the mass of the fluid.

The Inner Electrode of the Capacitor is tapered so that along with the horizontal-plane cross-sectional area, the capacitance per unit height of the electrodes varies with height.
Of course, it is necessary to take account of the tank geometry. Because most cryogenic tanks do not have uniform cross sections, the readings of level sensors, including capacitive ones, are not linearly correlated with the masses of fluids in the tanks. In a sensor of the present type, the capacitor electrodes are shaped so that at a given height, the capacitance per unit height is approximately proportional to the cross-sectional area of the tank in the horizontal plane at that height (see figure). This shaping should ensure that the contribution of the fluid at each height to the overall capacitance is proportional to the density of fluid at that height, whether the fluid is pulled down by normal gravitation or becomes stratified in microgravitation.

The feasibility of this sensor concept was demonstrated in an experiment in which a simple cylindrical capacitor was immersed in liquid nitrogen and capacitance readings were taken and correlated with mass readings as the liquid nitrogen boiled off. The results of this experiment, taken together with theoretical calculations, have been interpreted as signifying that suitably designed sensors of this type can be expected to yield mass readings accurate to within about one percent of their full-scale values.

This work was done by Mark Nurge and Robert Youngquist of Kennedy Space Center. For further information, access the Technical Support Package (TSP) free on-line at under the Computers/Electronics category.

This invention is owned by NASA, and a patent application has been filed. Inquiries concerning nonexclusive or exclusive license for its commercial development should be addressed to the Technology Programs and Commercialization Office, Kennedy Space Center, (321) 867-8130. Refer to KSC-12457.

NASA Tech Briefs Magazine

This article first appeared in the September, 2003 issue of NASA Tech Briefs Magazine.

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