Numerical simulation of solidification of molten aluminum alloys in cylindrical molds
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INTRODUCTION
A. Background Casting is the most common method of mass producing industrial components in a desired shape. It allows economical fabrication of geometrically intricate components. As casting provides design flexibility, metallurgical versatility, and economic benefits, it remains as a fundamental and vital technology for the industry. Although the casting process has been used for several centuries, it involves a host of complex phenomena that are still not thoroughly understood. To date, casting remains a highly empirical technology, and production of new castings requires an expensive, time-consuming, trial-anderror diagnostic approach. The dominant phenomena are heat transfer and fluid motion, which control micro- and macrosegregation, phase selection, grain size, shape, porosity, and quality of the final product. The mathematical modeling of solidification of molten alloys is extremely important for producing defect free castings. The bulk of the engineering components are produced via solidification of molten alloys by a variety of processes, such as gravity casting in sand molds or permanent molds, pressure die casting for thin wall complex shapes, squeeze casting for producing fiber-reinforced metal matrix composites as well as thick wall complex shapes, and investment casting for high-temperature resistance gas turbine engine blades. The transition from molten alloy to solidified casting is achieved via the extraction of heat by the mold or die, which accounts for several of the important processes at the microscopic level, such as nucleation and growth of crystals, solute diffusion, formation of microsegregation, and microporosity, and at the macro level, such as channel segregation, shrinkage porosity (primary and secondary pipe formation), hot tearing, and cold shuts. In order to design the process for an industrial application, a thorough understanding of the heat and fluid flow are essential. The J.N. REDDY, Oscar S. Wyatt Chair in Mechanical Engineering, is with the Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843-3123. W.J. MASCARENHAS, Development Engineer, is with Technalysis, Indianapolis, IN 46268. G.S. REDDY, Scientist, is with the Defense Metallurgical Laboratory, Kanchanbagh P.O., Hyderbad (A.P.) 500 258, India. Manuscript submitted September 13, 1991. METALLURGICAL TRANSACTIONS B
information gained from both experiments and numerical simulation helps in the proper designing of the process. The formation of equiaxed dendritic structure, the eutectic structure in castings, I1'2"31and fluid flow and heat transfer in castings t4,51have been modeled in some recent studies. Porosity is predicted in some of the castings based on the ratio of temperature gradient and square root of cooling rateJ 6-~~ Several reviews are available on thermal aspects of solidification; t11-2~ however, the numerical methods dealing with the nonlinearities are not very well addressed. The main objective of this study is to bridge this gap by presenting the finite el
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