The shape formation of ferrofluid under magnetic field has been considered to be one of most difficult problems to analyze. In this paper we present a numerical implementation of the level set method for the equilibrium shape calculation of ferrofluid under magnetic field. The magnetic-fluid coupled system has an extremum value of electromagnetic system energy. When the system is composed of magnetic permeable material and current sources, the system energy is a maximum at the equilibrium state. The level set method is adopted for shape capturing since it can easily handle shape variations of fluid including topological changes such as merging, splitting, and even disappearing of connected material regions. The velocity field for the level set method is calculated using a shape derivative of continuum sensitivity analysis that is derived by employing the material derivative concept. The numerical results for a model problem of some ferrofluid on a glass plate show that the level set method works well for the ferrofluid shape formation.
Most electrical machines like motor, generator and transformer are symmetric in terms of magnetic field distribution and mechanical structure. In order to analyze these problems effectively, many coupling techniques have been introduced. This paper deals with a coupling scheme for open boundary problem of symmetric and periodic structure. It couples an analytical solution of Fourier series expansion with the standard finite element method. The analytical solution is derived for the magnetic field in the outside of the boundary, and the finite element method is for the magnetic field in the inside with source current and magnetic materials. The main advantage of the proposed method is that it retains sparsity and symmetry of system matrix like the standard FEM and it can also be easily applied to symmetric and periodic problems. Also, unknowns of finite elements at the boundary are coupled with Fourier series coefficients. The boundary conditions are used to derive a coupled system equation expressed in matrix form. The proposed algorithm is validated using a test model of a bush bar for the power supply. And the each result is compared with analytical solution respectively.
In this paper a new coupling method for efficient and simple analysis of single phase induction motor is presented. The circuit representation of both the stator winding and each conducting rotor loop (composed of rotor bar and end ring segment) is used in conjunction with the distribution of magnetic flux linkage instead of inductance matrix. The flux linkage is calculated using air-gap flux density distributions driven by unit currents in the stator windings and rotor bars. The field distribution of one turn of a coil is calculated by FEM and the result is used to calculate total flux linkage by employing a coordinate transformation. The numerical results give good agreement with prior literature. The method is particularly effective in analyzing the effect of the number of rotor bars.
In this paper, a method for numerical simulation of the shape of a ferrofluid under external magnetic fields and the gravitational field is presented. The final shape is determined by an equilibrium condition of energy in a coupled system of electromagnetic fields and ferrofluid in the presence of gravity. The shape of the ferrofluid is captured by using the level set technique. The velocity field is calculated using continuum shape sensitivity analysis based on the material derivative concept. The numerical algorithm is implemented with a standard finite element procedure and tested on a shaping problem of ferrofluid located under an electromagnet. The numerical results showed that the proposed algorithm and numerical techniques are feasible and effective means of calculating ferrofluid shape variation under magnetic fields and the gravitational force.
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