Effect of property variations on the operation of phase separators for superfluid helium

Many low-gravity space missions have used porous plugs to keep He II in a dewar while venting the vaporized gas to space. The operational state of a He II phase separator is determined by the interplay of several competing physical processes. It appears that one of these phenomena has not been included in past published models of a separator. When He II flows through a porous material that sustains a thermal gradient, large pressure maxima and moderate temperature maxima occur in the profiles. The transition of the superfluid component to the normal component causes the maxima. The ratio of the density of the two components is a thermodynamic property and the transition between the components adjusts the ratio to the local value of the pressure and temperature. This can be a large effect with the pressure maxima reaching ten times the saturation pressure. We present a model for a He II phase separator, similar to previous models, but with the property variation process included. We derive formulas that show the conditions when the effect is significant and the extent of the changes from constant property models. The property variation phenomenon is modeled using a modified Green's function approach with step functions. It is iterative on the pressure, temperature and velocity profiles starting with the constant property profiles. This process generates a power series expansion of the pressure, temperature and velocity profiles. Two iterations are sufficient for nearly all applications. The predictions of the model are compared with reported measurements and the agreement is good.