Simplified numerical model for steady-state He II forced flow

Abstract

The main objective of this study is to reproduce the heat and mass processes in He II forced flows in steady-state condition using a modified simplified two-fluid model with an open source CFD environment. The model is derived from the so-called two-fluid model by assuming that the dominant terms in the superfluid momentum equation are the thermo-mechanical, the Gorter-Mellink mutual friction and the pressure gradient terms. From this simplification, a new system of equations describing the heat and mass transfer in He II is obtained with a conventional continuity equation, a modified momentum equation for the total fluid, and an energy equation revealing the unique counter-flow heat transport mechanism as in other simplified models, but here with the addition of the pressure gradient effect in He II. The model has been validated and compared with other models available in the literature, such as the original two fluid model and simplified models, as well as experimental data. Our model has been implemented using the OpenFOAM software and we have demonstrated here its good accuracy with experimental results and shorter computational time by 2-6% compared to the two-fluid model.