3D CFD Transient Numerical Simulation of Superfluid Helium

Abstract

Numerical simulations of superfluid helium are necessary to design the next generation of superconducting accelerator magnets at CERN. Previous studies have presented the thermodynamic equations implemented in the Fluent CFD software to model the thermal behavior of superfluid helium. Momentum and energy equations have been modified in the solver to model a simplified two-fluid model. In this model, the thermo-mechanical effect term and the Gorter-Mellink mutual friction term are the dominant terms in the momentum equation for the superfluid component. This assumption is valid for most of superfluid applications. Transient thermal and dynamic behavior of superfluid helium has been studied in this paper. The equivalent thermal conductivity in the energy equation is represented by the Gorter-Mellink term and both the theoretical and the Sato formulation of this term have been compared to unsteady helium superfluid experiments. The main difference between these two formulations is the coefficient to the power of the temperature gradient between the hot and the cold part in the equivalent thermal conductivity. The results of these unsteady simulations have been compared with two experiments. The first one is a Van Sciver experiment on a 10 m long, and 9 mm diameter tube at saturation conditions and the other, realized in our laboratory, is a 150×50×10 mm rectangular channel filled with pressurized superfluid helium. Both studies have been performed with a heating source that starts delivering power at the beginning of the experiment and many temperature sensors measure the transient thermal behavior of the superfluid helium along the length of the channel.