Double phase transition numerical modeling of superfluid helium for fixed non-uniform grids

A thermo-fluid dynamic numerical model for the simulation of the first-order and second-order phase transitions in superfluid helium (He II) is presented. The model is based on a Finite Volume Method algorithm for transient multidimensional problems. The method is also intended to simulate the conjugate heat transfer between helium and solids, which required the implementation of customized boundary conditions to replicate the Kapitza resistance and superfluid partial slip. The implemented governing equations for He II constitute an advanced version of an existing single-fluid model, which is herein newly derived with a more generalized conductive heat power law. The vapor-He I phase change is addressed through an explicit calculation of the volume fractions of the helium mixture and by introducing surface tension forces. An algorithm for fixed non-uniform orthogonal grids is conceptualized to deal with the lambda transition. The model is validated against data collected during clamped heat flux experiments in a rectangular cross-section channel of a high aspect ratio. The experiments were conducted both above and below the lambda temperature at atmospheric pressure with the channel in horizontal and vertical positions. The comparison with the data showed satisfactory agreement in the temperature profiles