Comparaison des schémas numériques de discrétisation des premier et second ordre

Abstract

This study concerns the flow of a Newtonian and incompressible fluid in a horizontal cylindrical duct uniformly heated at the wall. The associated heat transfer modes are mixed convection in the fluid and conduction in the wall. Thermophysical fluid properties are thermo-dependant. A three dimensional numerical simulation is conducted, The finite volumes method with a second order scheme in time and space is adopted to resolve this problem, Two different heating conditions are considered: strenght of electrical current of 45 an 65 Amperes which correspond to two various Graschof numbers: Gr=244492 and 510000. The other control parameters such Reynolds and Prandtl numbers are fixed constant: Re=606 and Pr=8. The transversal secondary flow in a cross section is induced by a bouyancy effect along the duct. In a cross straight section, two contra-rotative cells are observed. These rolls are separated by the median vertical plane. The center of these rolls moves downward when the axial coordinate increases. The major points of this work consist first at a qualitative and a quantitative comparison between the results obtained by the first and the second order schemes, then a comparison with experimental results is achieved. It is to be noted that, qualitatively the first and the second order schemes give similar results but quantitatively the results obtained by the first order scheme are closer to the experimental results. These differences induce more important discrepancies of the axial Nusselt number. This is due to the fact that the second order scheme needs a more refined mesh than the first order on one hand and on other hand in the experimental results the uncertainties and the heat losses are not known. Taking into account these comments could reduce the difference between the obtained results.