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

Abstract

In the frame of characterization of thermophysical properties of semi-transparent gray media for which radiative transfers can be modelled by P1 approximation, the present study deals with development, construction and validation of conducto-radiative linear reduced order models (ROMs) explicitly parametrized by thermal conductivity and effective absorption coefficient. As variations of temperature are assumed to be limited in magnitude (about a few tenths of K) in the considered applications, the radiative contribution is linearized in the ROM formulation. ROMs are built through the Modal Identification Method (MIM): once their general form has been derived, they are identified using Particle Swarm Optimization and Ordinary Least Squares, from simulations coming from a nonlinear reference model. In the presented application, the latter is a two-dimensional axisymmetric unsteady model designed to model a “flash-type” experiment. The chosen range of values for thermal conductivity and effective absorption coefficient includes the values usually found for polymethyl methacrylate (PMMA). In comparison with the reference model, the computing time is considerably reduced with limited loss of accuracy.