Transient Conjugate Heat Transfer Numerical Simulation in Superfluid Helium. Issue 1 (March 2020) - Vitrano, A
Abstract: Computational simulations of superfluid helium are needed in order to improve the cooling system design of superconducting magnets in particle accelerators and to achieve a better understanding of the transient phenomena during magnet quenches. A conjugate heat transfer numerical model based on the C++ toolbox OpenFOAM [1] is implemented to three-dimensional case studies involving superfluid helium and heating sources. The governing equations of the solver are modified according to the Kitamura's model [2], a simplified version of the two-fluid model developed by Khalatnikov [3]. This simplified model is based on the assumption that the thermo-mechanical effect term and the Gorter-Mellink mutual friction term prevail on the others in the superfluid component momentum equation. Simulations are performed with the thermal conductivity function of superfluid helium both from theory [4] and the formulation used by Sato [5], who normalized the function according to a different conductive heat flux exponential coefficient determined from data analysis. An empirical calculation of the Kapitza conductance [6] is adopted in order to simulate the thermal resistance at the interface between helium and solids. Steady-state and transient simulations are compared to experimental data available in the literature. For such purpose, data are used from Van Sciver's experiment in a helical coil [7] and a rectangular cross-section channel experiment conducted at CEA Paris-Saclay. The experiments comprised heaters and multiple temperature probes situated at different locations to track the temperature distribution and evolution of the superfluid helium state.