Implementation of the superfluid helium phase transition using finite element modeling: Simulation of transient heat transfer and He-I/He-II phase front movement in cooling channels of superconducting magnets

In the thermal design of high magnetic field superconducting accelerator magnets, the emphasis is on the use of superfluid helium as a coolant and stabilizing medium. The very high effective thermal conductivity of helium below the lambda transition temperature significantly helps to extract heat from the coil windings during steady state and transient heat deposition. The layout and size of the helium channels have a strong effect on the maximum amount of heat that can be extracted from the porously insulated superconducting cables. To better understand the behavior of superfluid helium penetrating the magnet structure and coil windings, simulation based on a three dimensional finite element model can give valuable insight. The 3D geometries of interest can be regarded as a complex network of coupled 1D geometries. The governing physics is thus similar for both geometries and therefore validation of several and different 1D models is performed. Numerically obtained results and published experimental data are compared. Once the viability of the applied methods is proven, they can be incorporated into the 3D geometries. Not only the transport properties in the bulk of the helium are of interest, but also the strong non-linear behavior at the interfaces between solids and superfluid helium (Kapitza conductance) is important from an engineering point of view, since relatively large temperature jumps may occur here. In this work it is shown how He-II behavior in magnet windings can be simulated using COMSOL Multiphysics. 1D models are validated by experimental results taken from literature in order to improve existing 2D and 3D models with more complete physics. The examples discussed include transient heat transfer in 1D channels, Kapitza conductance and sub-cooling of normal liquid helium to temperatures below the lambda transition in long channels (phase front movement).