Stabilized finite element method for heat transfer and turbulent flows inside industrial furnaces

The development of efficient methods to understand and simulate conjugate heat transfer for multi-components systems appears in numerous engineering applications and still a need for industrials, especially in the case of the heat treatment of high-alloy steel by a continuously heating process inside industrial furnaces. The thermal history of the load and the temperature distribution in the furnace are critical for the final microstructure and the mechanical properties of the treated workpieces and can directly determined their final quality in terms of hardness, toughness and resistance. The main objectives of this thesis is then to understand and better model the heat treatment process at the same time in the furnace chamber and within the workpieces under specified furnace geometry, thermal schedule, parts loading design, initial operation conditions, and performance requirements. The Computational Fluid Dynamics (CFD) simulation provides a useful tool to predict the temperature evolution and such processes. In the first part of this work, various stabilized finite element methods required for computing the conjugate heat transfer and the incompressible flows are proposed and analyzed. Two turbulence models, the k-epsilon and the Large Eddy Simulations (LES) models were introduced and used to simulate and take into account the complex turbulent flows inside the furnace chamber. The effect of thermal radiation was appropriately accounted for by means of a volumetric model known as the P1-model. In the latter part of this work, a multidomain approach referred as the immersed volume method (IVM) is introduced and applied to treat the fluid-solid interactions. It is based on the use of an adaptive anisotropic local grid refinement by means of the level-set function to well capture the sharp discontinuities of the fluid-solid interface. The proposed method showed that it is well suited to treat simultaneously the three modes, convective, conductive and radiative heat transfer that may interfere in both the fluid part and the solid part using anisotropic finite element meshes.

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