Eur. Phys. J. Appl. Phys. (2013) 61: 10602 DOI: 10.1051/epjap/2013120434 THE EUROPEAN PHYSICAL JOURNAL APPLIED PHYSICS Regular Article Transient axisymmetric FVM analysis of electodynamic levitation devices Abd El-hamid Mabrouk 1, a , Ahmed Cheriet 1 , Mouloud Feliachi 2 , and Ala-eddine Lakhdari 1 1 Laboratoire LGEB, Universit´ e de Biskra, 07000 Biskra, Alg´ erie 2 IREENA-IUT de Saint-Nazaire, Universit´ e de Nantes, PRES-L’UNAM, 44600 Saint-Nazaire Cedex, France Received: 1 October 2012 / Received in final form: 11 December 2012 / Accepted: 2 January 2013 Published online: 31 January 2013 – c  EDP Sciences 2013 Abstract. In this paper a transient finite volume model for electrodynamic levitation devices analysis has been developed. Both electromagnetic and mechanical equations are time stepped and coupled to give the dynamic characteristic of the motion. Furthermore, the nonconforming mesh technique is introduced to take movement into account. To check the efficiency and accuracy of the transient finite volume method (FVM) model, the Team Workshop Problem 28 is used. 1 Introduction In electrodynamic levitation system, levitation is obtained by the repulsive force between an incident magnetic field and an induced one on a movable body [1]. Since the mechanical motion couples with the electromagnetic phe- nomena together, and the eddy current does not distribute uniformly in the solid conductor, the transient electromag- netic field analysis coupled with motion is required [2]. The finite element method has been demonstrated as an effective tool for the transient field analysis [3, 4]. Nevertheless the implementation of such models is fairly complicated. During the past few years, the finite volume method (FVM) has proved its effectiveness in the solution of different kinds of electromagnetic problems. The FVM achieves a compromise between robustness of computation and facilities of implementation [5, 6]. The discretization of devices which contains moving parts must be carefully handled. Small displacements cause a distortion of the mesh, which leads in general to a reduction of mesh quality. Large displacements require fre- quent remeshing of the whole device, due to continuously changing the position of moving parts. The unknowns on the new mesh have to be related to the unknowns on the previous mesh, this therefore causing some perturbation on the final solution [7]. In a previous work, we have devel- oped a suitable technique based on nonconforming mesh associated to the FVM [5]. In this paper, a transient finite volume model for elec- trodynamic levitation devices has been developed. The displacement of the moving part is simulated thanks to the use of nonconforming mesh technique. To check the efficiency and accuracy of the developed model, the Team a e-mail: h mabrouk@rocketmail.com Workshop Problem 28 is analyzed. The numerical results obtained with the proposed model are then compared to measurements. 2 Analyzed method 2.1 Governing equations By using Euler’s scheme, the axisymmetric governing electromagnetic equation to solve is: ∂ ∂z  ν r ∂A * ∂z  + ∂ ∂r  ν r ∂A * ∂r  -  σ r A * - A *0 Δt  = -J sθ in Ω, (1) A * = 0 in Γ. (2) In this formulation, A * = rA θ and A *0 are the modi- fied magnetic vector potential at times t + Δt and t, re- spectively. σ is the electric conductivity, J sθ is the source current density and ν is the magnetic reluctivity. The Dirichlet condition is considered by equation (2). To analyze the dynamic behavior of the device, the follow- ing mechanical motion equation is considered: m¨ z =F Z , (3) where m and ¨ z are, respectively, the mass and the ac- celeration of the levitated item. The total force F z in equation (3) includes the gravity force and the applied electromagnetic force F m : F m =  Ω J ×B. (4) 10602-p1