Two fluid model for thermal stratification in the Apollo cryogenic oxygen tanks

It is observed on Apollo flights that for oxygen densities greater than 42 lb/cu ft the heater operation time to achieve a desired pressure rise is half that which would be required if the energy were uniformly dispersed. A two fluid model was developed to describe this effect of stratification on the tank's pressurization behavior. The increase in pressure rise rate is attributed to compression of the bulk fluid in response to expansion of the heated fluid adjacent to the heater. It is assumed that during the heating operation the adjacent fluid retains nearly all the heater energy and has no mass interaction with the bulk fluid. The hot fluid temperatures predicted by the model are in reasonable correspondence with the observed heater temperatures. The model indicates that the fraction of the fluid interacting with the heater increases with decreasing density, from less than 0.1% at full tank to roughly 1% at 50% quantity, the lowest quantity at which stratification effects on pressure are observed.