Bitter magnet modeling: reproduce experimental data using Feel++

[jermuzet]

In early June, at LNCMI Grenoble, an internal Bitter insert was replaced by a new Bitter manufactured in the laboratory. Several tests were carried out and we tried to reproduce the results with a thermo-magnetic model using Feel++.

A Bitter insert is a stack of copper alloy plates with insulators between the plates to create a helicoidal current path. Small holes are drilled to allow water to flow through the magnet and cool it, and tie rods are inserted to ensure good electrical contact between each plate. On an LNCMI site, Bitter magnets consist of two Bitter inserts, one internal and one external.

Fig1. The picture shows the previous internal Bitter insert after disassembly and replacement by the newly manufactured insert.

The static thermo-magnetic model used to model our Bitters consists of a system of differential equations. Firstly, the electromagnetism of the magnets is described by Maxwell's equations in the form of the A-V formulation. Then, the heat and the cooling of the Bitters by water are described by the heat equation with Robin boundary conditions. Coupling is effected by the Joule effect generated by electromagnetism, which increases the temperature, which in turn modifies the electrical properties of the inserts.

To reproduce experimental conditions, the current flowing through the Bitters and the initial temperature are imposed, and the resulting magnetic field is measured, along with the Bitters' output voltage and power. Axi-symmetric coordinates geometry is used to model the two Bitter magnets, with slits inside the inserts to represent the passage of water through the magnet. The > Coefficient Form PDE Feel++ toolbox is used for the simulation of the thermo-magnetic model.

Fig2. Comparison of data from multiple simulations for several imposed currents ranging from 20,000 to 0 amperes with experimental results. This includes data for magnetic field, power, flow and voltage in the Bitter magnet.

Our model simulates the thermo-magnetic behavior of Bitter inserts with a margin of error of around 5%. We still have the option of adding different types of cooling model and fit to better reproduce the reality of cooling in Bitter inserts.