Modeling of the Dynamics of a Slug of Liquid Oxygen in a Magnetic Field and Experimental Verification

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This study presents the theoretical basis for the dynamics of a slug of liquid oxygen in a quartz tube when displaced by a pulsed magnetic field. The theoretical model calculated slug movement by balancing the forces due to magnetism, pressure, and damping and was verified with experimental data for a slug 1.3 cm long and 1.9 mm in diameter. During the experiments, the hidden slug length and damping factor were unknown, but quantifiable through the numerical solution. The hidden slug length accounted for the mass of LOX which cannot be seen during the experiment and was calculated as 10-14.5 cm. The damping factor was an empirical augmentation to represent increased damping from various phenomena and was calculated as 5.76-6.3. The experiments generated damped pressure waves of 6-8 Hz with maximum amplitudes of 0.8-1.3 kPa. Outside these ranges, the model indicated that the oscillation frequency decreased logarithmically with the hidden slug length, and the maximum amplitude decreased logarithmically with the damping factor. Measurement uncertainties of the visible length and slug initial position (0.8 mm) were also evaluated for their effects on the frequency and amplitude of the oscillations. The visible slug length did not seem to significantly affect the pressure waves, but the initial position strongly altered the amplitudes and mean of the oscillations. The predictive model matched the experiment well and could be used to design advanced flow control systems for cryogenic applications.

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