Magnetic positive propellant positioning (MP3) of cryogenic propellants in spacecraft tanks may outperform existing technologies and, unlike some of the competing technologies, MP3 can be an adaptive management system that optimizes performance for the entire mission profile. Surface Evolver, (SE), a public domain program that seeks minimum energy configurations for modeled systems, provided a foundation on which to build a computational simulation to begin investigating the promise of MP3. Energies modeled include surface tension, potential energy due to background acceleration, and the change in potential energy due to the presence of a fluid in a magnetic field. A detailed development of these models is presented as well as specific expressions that other researchers can use with SE to study MP3. Verification and validation of the comprehensive model has been performed using several “known” solutions, three of which are reported herein: a constant gradient, a current carrying wire, and a dipole magnetic field. The computational tool is then used to study the ability of a magnet to retain a pool of LO2 about it when subjected to background acceleration. Results from this study, presented herein, indicate the promise of MP3 for adaptive cryogenic propellant management systems for future spacecraft and fuel depot applications.
A direct minimization technique for finding minimum energy configurations for beam buckling and post-buckling problems with constraints
