On the order reduction of the radiative heat transfer model for the simulation of plasma arcs in switchgear devices

Abstract

An approach to derive low-complexity models describing thermal radiation for the sake of simulating the behavior of electric arcs in switchgear systems is presented. The idea is to approximate the (high dimensional) full-order equations, modeling the propagation of the radiated intensity in space, with a model of much lower dimension, whose parameters are identified by means of nonlinear system identification techniques. The low-order model preserves the main structural aspects of the full-order one, and its parameters can be straightforwardly used in arc simulation tools based on computational fluid dynamics. In particular, the model parameters can be used together with the common approaches to resolve radiation in magnetohydrodynamic simulations, including the discrete-ordinate method, the P-N methods and photohydrodynamics. The proposed order reduction approach is able to systematically compute the partitioning of the electromagnetic spectrum in frequency bands, and the related absorption coefficients, that yield the best matching with respect to the finely resolved absorption spectrum of the considered gaseous medium. It is shown how the problem's structure can be exploited to improve the computational efficiency when solving the resulting nonlinear optimization problem. In addition to the order reduction approach and the related computational aspects, an analysis by means of Laplace transform is presented, providing a justification to the use of very low orders in the reduction procedure as compared with the full-order model. Finally, comparisons between the full-order model and the reduced-order ones are presented.

Optimal Band Selection for the Calculation of Planck Mean Absorption Coefficients

“…This objective function describes the difference between the spectral and the band averaged solution, in particular the energy source/sink term due to radiation transfer. Alternatively, the radiative intensity could be used to define the objective function as well [6]. Based on the variation of ∆F ν due to varying band limits, the procedure is able to determine an optimal set of band limits.…”

“…To address these questions, numerical optimization procedures have been developed to find an optimal number and distribution of the bands [5,6]. In this paper, we apply the optimization procedure as introduced in [5,7] to a specific mixture of SF 6 and copper vapor.…”

Reduced order models for thermal radiative transfer problems based on moment equations and data-driven approximations of the Eddington tensor

“…Furthermore, several data-based ROMs have been developed to date for the nonlinear problems of radiative transfer considered here. Dimensionality along the frequency variable has been formulated with the POD for SP 1 radiative heat transfer calculations [79], and for radiative heat transfer in plasma applications using an optimization problem [80]. ROMs for thermal analysis of spacecraft have been created with POD-Galerkin and trajectory piecewise-linear methods [81].…”

Reduced Order Models for conduction and radiation inside semi-transparent media via the Modal Identification Method

“…In the field of electronics, Fagiano and Gati [7] developed an approach to build ROMs for thermal radiation from plasma arcs in switchgear devices. The heat radiation problem is first modelled as a Linear Parameter Varying (LPV) full order model with one input (black-body intensity), one output (radiation intensity), three parameters (temperature, pressure, gas composition), and a large number of internal states (one for each considered frequency of the electromagnetic spectrum.…”