Perspective from the Comet: Modeling water and gas species under variable gravity

NASA is developing life-support technology for manned missions, using plants to provide supplemental food and improve air quality. It is a challenge to design a medium that allows oxygen and carbon dioxide to exchange between plant roots and cabin atmosphere, while simultaneously supplying roots with water, without significant gravitational body forces to move water around. As a precursor to medium design, a simulator was developed with the intention of characterizing plant uptake, water redistribution, and gas-species movement under microgravity. The numerical formulation uses liquid pressure and dissolved-gas mass fractions as state variables, calculating gas pressure assuming equilibrium between dissolved and gaseous states. Part of the simulator-testing program included comparison with observations from columns subjected to sequences of parabolas flown by a KC-135 ``Vomit Comet'', in which acceleration repeatedly changed between 0 and 1.8 G within seconds. The parabolic flight path requires specific tensiometer orientation relative to the aircraft axes to minimize post-flight correction of data. The simulator considers liquid- and gas-phase flow, diffusion of gas species in both the bulk gas phase and as a dissolved species in the liquid, and thermal redistribution. Alternation between 0 and 1.8 g redistributes water from a more-or-less uniform distribution throughout the medium to having a sharp water table in seconds, which is challenging numerically for the coarse media being characterized. The initial formulation was unable to negotiate the sequence of water redistributions in a mass-conservative simulation. A robust, mass-conservative approach fully honoring the retention relationship was developed by linearly approximating the derivative near the discontinuity in capacitance as the gas phase disappears, which was found to be extremely effective in minimizing iterations and thus allowing large time steps. This approach should be useful in other situations with sharp discontinuities in capacitance, such as freezing soils. The particular choice of state variables requires tight convergence criteria to maintain mass balance during redistribution events. In the formulation, capillary pressure is calculated as the difference between gas and liquid pressures, which are almost identical near saturation hence are subject to roundoff error. It is hypothesized that using partial capillary pressure for the dissolved-gas state variables may provide a more robust formulation.