Determination of thermophysical properties and boundary conditions of direct chill-cast aluminum alloys using inverse me
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. INTRODUCTION
IN the direct-chill (DC) casting of nearly rectangular rolling-sheet ingots and extrusion billets of aluminum alloys, a stationary temperature distribution gradually develops in the solidifying strand.[2] During cooling, the metal experiences a high nouniform thermal gradient, which results in differential thermal contraction and high stress levels partially relieved by creep. In this process, two distinct zones of cooling can be distinguished: the first one is due to the direct contact of the melt with the mold and the second one is associated with the water spray underneath. This leads to the formation of a thin solid shell that remains nearly parallel to the mold in between the two cooling zones. This thin shell bends inward under the high local thermal gradient, while the influence of the metallostatic pressure can be neglected.[3] An accurate description of the heat-transfer characteristics at the surface of the ingot in run conditions is important in many respects, for example, for a better understanding of the development of surface segregation and exudation.[4] It is also an essential input for thermomechanical models aimed at computing ingot distortions and stresses.[5] The DC casting of aluminum alloys has been the subject of considerable development in recent decades, mostly as a result of an improved understanding of the heat flow involved. Yu[6] studied the heat-transfer mechanisms by quenching preheated probes in water. He showed that, in the case of DC casting, the ingot cooling rate highly depends on boiling water phenomena. Four mechanisms were distinguished by Incropera and de Witt,[7] depending on the target surface temperature: unstable film boiling, film boiling, J.-M. DREZET, Senior Scientist, and M. RAPPAZ, Professor, are with the Laboratoire de Me´tallurgie Physique, Ecole Polytechnique Fe´de´rale ¨ N is with the de Lausanne, CH-1015 Lausanne, Switzerland. G.-U. GRU Research and Development Centre, VAW Aluminum AG, D-53014 Bonn, Germany. M. GREMAUD is with Calcom SA, CH-1015 Lausanne, Switzerland. Manuscript submitted August 18, 1999. METALLURGICAL AND MATERIALS TRANSACTIONS A
nucleate boiling, and convection. Weckman and Niessen[8] built a numerical model based on the finite-element method to compute the steady-state temperature field in DC-cast AA6063 billets. Using a combination of theories involving nucleate boiling, forced convection, and film cooling, these authors developed a method to calculate the external boundary conditions associated with the casting configuration. Nevertheless, the authors showed that direct application of the theoretical coefficients would produce substantial errors, especially in the region where heat transfer is dominated by nucleate boiling. Grandfield et al.[9,10] discussed the heattransfer mechanisms in the water jet and falling water film, with special attention paid to the boiling modes. They pointed out that, under normal steady-state conditions, nucleate boiling is the dominant phenomenon, but some areas of unstable film boiling can exis
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