A fast 1D model of active magnetic regeneration with a compressible working fluid.

We present a 1D model of an active magnetic regenerator (AMR) with a compressible heat transfer fluid that increases calculation speed without compromising accuracy. Compressible heat transfer fluids have previously been shown to be difficult to handle numerically. The presented model alleviates this by assuming that the momentum transfer within the AMR cycle takes place much faster than heat transfer during the blowing stages of the cycle. We show that this leads to an ordinary differential equation for the pressure, that can be solved in conjunction with the thermal energy equations for the solid and fluid parts of the regenerator. Considering a test case of an AMR with helium as the heat transfer fluid we show that the presented model has a maximum deviation in pressure of 5% and an average deviation of 0.4% compared to a reference model that solves fully for the pressure. Finally, we show that the presented model is stable to much higher Courant–Friedrichs–Lewy (CFL) numbers than the reference model, where the CFL number governs the time step in the model. This leads to an increase in computational speed of two orders of magnitude of the presented model, reducing the computation time from ∼ 105 s to ∼ 103 s for moderate mass flow rates.