Geoffrey Deliège

The eggshell approach for the computation of electromagnetic forces in 2D and 3D

The expressions of the material derivative of differential forms in the language of vector analysis are introduced. These formulae allow us to describe naturally the electromechanical coupling, and the coupling term appears to be a volume integral. A general approach to compute forces is then proposed, which takes that fact into consideration. The method is applicable in 2D and 3D with dual formulations. Numerical evidences of its efficiency are given.

Coupled thermo-magnetic simulation of a foil-winding transformer connected to a nonlinear load

Foil-winding power transformers contain compact sets of flat conductors having a large aspect ratio. Modeling the eddy currents in the individual foils is therefore difficult and requires completely meshed conductors, especially when the influence of the thermal field on the local conductivity is considered. Coupled 2D magnetic and thermal models of a 30 kVA transformer having 50 secondary foils are presented. In the thermal model, thin layer elements or equivalent anisotropic materials are used to model the insulation material between the conductors. The coupled problem is solved for the steady-state and transient case. A novel method will be introduced to solve the transient coupled problem using time steps, much larger than the magnetic subproblems time constants.

On algebraic multigrid methods derived from partition of unity nodal prolongators

This paper is concerned with algebraic multigrid for finite element discretizations of the divgrad, curlcurl and graddiv equations on tetrahedral meshes with piecewise linear shape functions. First, an edge, face and volume prolongator are derived from an arbitrary partition of unity nodal prolongator for a tetrahedral fine mesh, using the formulas for edge, face and volume elements. This procedure can be repeated recursively. The implied coarse topology and the normalization of the prolongators are analysed. It is proved that the range spaces of the nodal prolongator and of the derived edge, face and volume prolongators form a discrete de Rham complex if these prolongators have full rank. It is shown that on simplicial meshes, the constructed edge prolongator is a generalization of the Reitzinger–Schoberl prolongator. The derived edge and face prolongators are applied in an algebraic multigrid method for the curlcurl and graddiv equations, and numerical results are presented. Copyright

Crank-Nicolson Scheme for Solving Low Mach Number Unsteady Viscous Flows Using an Implicit Preconditioned Dual Time Stepping Technique

The aim of this paper is to simulate low Mach number unsteady viscous flows using a density-based finite volumes solver. This kind of solver is known to encounter some difficulties to simulate low Mach number flows in which the density is almost constant. Convergence fails or accuracy decreases when the speed of sound is much greater than the fluid velocity. Local preconditioning methods intend to solve this problem by altering the time derivative terms of the Navier-Stokes equations in order to artificially modify the speed of sound, improving the convergence and accuracy in the case of low Mach number steady flows [1], [4].

3D h-phi finite element formulation for the computation of a linear transverse flux actuator

A finite element analysis of a permanent magnet transverse flux linear actuator is presented. In this application where we need a small model (for optimisation purposes) as well as a high accuracy on the computed force, we propose to combine several models with different levels of size and complexity, in order to progressively elaborate an accurate, but nevertheless tractable, model of the system.

Finite element modeling of an electrostatic painting device

The system of coupled equations describing an electrostatic painting device is solved. The design of an efficient resolution strategy is discussed, and time integration schemes for the steady-state solution of the convection equation are compared.

A hybrid high speed electrical micromachine for micro scale power generation

This paper presents a methodology for the optimization of a new type of high speed electrical micromachine for micro scale power generation. The micromachine is integrated into the compressor of a microturbine which operates at 500,000 rpm. Because of the high energy density of fuel, the turbine-generator combination exceeds the limitations of batteries and smoothes the way for high power or long endurance applications. The micromachine is optimized for a mechanical output power of 100 W within the dimensions of the turbine. Special attention is paid to the problems caused by high speed operation and their influence on the design of the machine

Accuracy analysis of the thrust force in 2D‐3D finite element models

Purpose – The purpose of this paper is to analyse the accuracy of the thrust force of a linear actuator computed with different finite elements models.Design/methodology/approach – A series of 2D and 3D models corresponding to different levels of approximation of the original problem are considered. A reliable error estimator based on dual magnetostatic formulations is used.Findings – A 3D model does not necessarily ensure more accurate results than a 2D model. Because of limitations on the number of mesh elements, the discretisation error in 3D can be of the same order of magnitude as the error introduced by the 2D approximation.Originality/value – The results emphasise the need to consider errors arising from different simplifications with respect to one another, in order to avoid improvements of the model increasing the complexity but not improving the accuracy of the results.