Scientific developments

The research work carried out by the Numerical Tools and Methods team revolves around two themes. The first theme deals with the numerical resolution of Maxwell’s equations in a quasi-static regime and the development of a model of ferromagnetic materials to be implanted in the calculation codes for electromagnetic fields. The second theme deals with the design by optimisation of complex systems.

Development of numerical methods

The numerical methods studied are quite specific in the national and international community, e.g.

• The quantification of uncertainties that involves studying the influence of the variability of the input data (constitutive equations of materials or the geometry) of a numerical model on the quantities of interest. This makes it possible, for example, to assess the impact of manufacturing processes on the performance of an electrical machine.
• The estimation of numerical errors that involves working out the errors introduced by the spatial and temporal discretisation on the solution given by the numerical model.
• The reduction of models where techniques (POD, PGD, etc.) are applied to reduce the number of unknowns of the numerical model with the aim of not only reducing computation times but also taking into account a large number of parameters simultaneously. This can be very useful when sizing an electric machine, for example.

Estimator cards in A-φ (right) and T-Ω (left) formulations for an eddy current non-destructive testing application

Code_Carmel as a tool for investigation, capitalisation and dissemination

Since 1994, the team has been developing an electromagnetic field calculation code based on the finite element method: code_Carmel. Since 2008, this code has been jointly developed with EdF R&D as part of the LAMEL joint laboratory.

The results of the research on numerical methods are capitalised in code_Camel, which makes it a tool with unique features, such as the quantification of uncertainties, the estimation of errors, the projection of solutions, etc. This code changes in the Salome free environment and naturally makes it possible to carry out « multiphysics » studies using solution projection tools.

The code_Carmel code is also used as an investigative tool in the context of various theses or studies. These studies relate to electrotechnical devices such as rotating (asynchronous, synchronous, with magnets and/or coils) and linear electrical machines, energy transport cables, MEMS, the human body, etc.

Calculation of the distribution of local forces in a claw alternator

Finally, the code Carmel code is also a tool for circulating the team’s know-how. Training courses can be set up for industrialists and academics.

Modelling and characterisation of ferromagnetic materials

Work using significant experimental characterisation means (Epstein square, Single Sheet Tester, thermal enclosure, etc.) to develop loss calculation models in soft and hard ferromagnetic materials, are inserted in code_Carmel.

Density of iron losses (W/m3) in a three-phase transformer (1/4 of the transformer)

These experimental means are supplemented by mock-ups of specific measurements in order to study the variability of the electrical and magnetic properties following the impact of the manufacturing processes. The experimental data can then be used to extract the statistical laws relating to the properties of materials.