Resolution of linear inverse forced convection problems using model reduction by the Modal identification Method: application to turbulent flow in parallel-plate duct
Résumé
Inverse Heat Convection Problems have received attention only recently. They usually involve the use of a high order model corresponding to the spatial discretization of the domain. In this numerical study, the possibility to quickly solve such a problem with a low order model is analysed. The proposed method can be applied to any forced convection problem, whatever the geometry, as far as it is linear. Starting from a Detailed Model (DM) of the system, the Modal Identification Method is applied to build a Reduced Model (RM), which can be used to solve the inverse problem. The inversion procedure is sequential and requires non iterations. The function specification method is used to stabilize the inverse problem. An illustrative applications is given. Turbulent forced convection is considered, with a hydrodynamically fully developed, thermally developing, incompressible, turbulent flow of a newtonian and constant property fluid inside a parallel-plate duct. Axial conduction in the flow is neglected. Two wall heat flux densities, varing with time, are estimated from the knowledge of stimulated transient temperature measurements inside the fluid. When solving the inverse problem with RM instead of DM, a drastic reduction of computing time is obtained (with a reduction factor up to 11,000 in the present study), without significant loss of accuracy. Effects of functional form of the unknowns, sensors number and position, measurement error, on the accuracy of estimates are examined.