Transient thermal regime trough the constitutive matrix applied to asynchronous electrical machine using the cell method

Abstract

In this paper, a new constitutive matrix for thermal conduction in transient thermal regime is developed and tested. We use cell method as a numerical method that is included in finite formulation methodology. The constitutive matrix defines through the cell method the behavior of solids when they are under a thermal potential. We have demonstrated that this matrix is equivalent to the electrical conduction constitutive matrix in steady state. We have applied this constitutive matrix to thermal analysis of asynchronous electric machines in transient regime. This constitutive matrix has been validated with comparisons based on finite element method. In finite formulation, the physical laws governing the electromagnetic fields and the physical thermal phenomena are expressed in integral formulation. The final algebraic equation system is tailored directly without discretizing of the differential equations. This is an important advantage because we omit a complex differential formulation and the discretization of the respective equations.

New Thermal-Conductivity Constitutive Matrix in Fourier’s Law for Heat Transfer Using the Cell Method

“…In the present section, we obtain the analytical formulation of the matrix [M τ ] that has been developed to improve the results obtained with [M λ ]. In a steady state, and without internal heat sources, the equation of energy balance without mass transfer [10][11][12][13] is in the CM,…”

“…Monzón-Verona [12][13] analyzed the temperature distribution in a conductor disk in a transitory regime. The disk is in motion in a stationary magnetic field generated by a permanent magnet, and so the electric currents induced inside it generate heat.…”

“…Three methodologies have been formulated previously in order to obtain the constitutive thermal matrix. These methods are those by Tonti [16], Bullo [21][22], and the method proposed by Specogna [14], for problems of electrical conduction, which we have adapted to thermal conduction [10][11][12][13].…”

“…Dual barycentric cell complexes are used for both space and time domains, the latter inducing a Crank-Nicolson time integration scheme. In the present work, we propose the finite formulation (FF) [10][11][12][13][14][15], as well as the Cell Method (CM), [16,17] as an associated numerical method to analyze the numerical models proposed. In this methodology, we work with the global magnitudes associated with space-oriented elements such as volumes, surfaces, lines, and points of the discretized space, as well as to temporal elements, instead of the field magnitudes associated with independent variables with spatial and temporal coordinates [16][17][18][19][20].…”

“…González [12,13] developed a new constitutive matrix ([M λ ]) for thermal conduction in a transient thermal regime using CM. He demonstrates that this matrix is equivalent to the electrical conduction constitutive matrix in a steady state, and applies this constitutive matrix to the thermal analysis of asynchronous electric machines in a transient regime.…”