Identification of a dynamic reduced model for heat convection with tationary flows
Résumé
Model Reduction techniques are designed to extract, from the knowledge of an initial detailed model, a low dimensioned one: the Reduced Model (RM). For several years, the Modal Identification Method bas been developed in our laboratory. Starting from the structure of Partial Differential Equations of the physical system, a structure is defined for the RM. Its parameters are then identified through the resolution of an optimization problem. In this paper, an advection diffusion problem is studied: forced heat convection is considered with an incompressible, stationary, laminar 2-D flow. Therefore, thermal properties of the fluid are not temperature dependent, so the velocity field is independent of the temperature field. The system under consideration is a channel flow over a backward facing step. A time-varying heat flux density is applied upstream of the step. On this example are shown the principles of the identification method in two ways. The first is the identification of a non linear reduced model, relative to Navier-Stokes equations, that can reproduce, very quickly, the computation of the steady velocity field in a given range of Reynolds numbers. The second application is the identification of a thermal transient reduced model, relative to the energy equation, that can compute the temperature field evolution.