Modeling of spray-formed materials: Geometrical considerations
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INTRODUCTION
SPRAY forming is a manufacturing technique in which partially solidified metal droplets are dispersed upon a substrate to produce an almost fully dense material in tonnage quantities. Available studies show that the thermal and solidification conditions that are present during spray forming promote several desirable characteristics, such as microstructural refinement,[1,2,4,5] extended solubility,[1,4] and, in some cases, the appearance of nonequilibrium phases.[1] For the production of near-net-shape deposits, the droplet size and spatial distribution are of interest because the deposit shape resembles the spatial distribution of droplet mass arriving at the deposition surface. The droplet size and spatial distribution are related to the type of atomizer used and to operating variables. In the atomization of metals, circular gas jet nozzles represent a type of atomizer that is commonly used. Therefore, there exists a limitation in that the droplet mass distribution exhibits a Gaussian distribution centered about the spray axis. To that effect, specific experimental arrangements have been taken to approach a variety of geometries, including rings, billets, tubes, and cylinders, while using circular atomizers. Experimental and simulation efforts have been conducted on the geometry of plates[7–11] and tubes.[12] However, threedimensional growth during buildup of round billets leads to complexities in the required control protocols, as a result of transient phenomena that develop under certain conditions. One example of such transient phenomena is described in the literature as a shadowing effect,[14] which leads to the formation of columnar porosity.[6] Exploring the optimal Y.J. LIN, Graduate Student, and E.J. LAVERNIA, Professor, Department of Chemical and Biochemical Engineering and Materials Science, and J.E. BOBROW, Professor, Department of Mechanical and Aerospace Engineering, are with the University of California Irvine, Irvine, CA 926972575. D.R. WHITE, Principal Engineering Specialist, is with the Materials Systems Reliability Department, Ford Research Laboratory, Dearborn, MI 48121-2053. Manuscript submitted August 2, 1999. METALLURGICAL AND MATERIALS TRANSACTIONS A
processing parameters through experimentation is time-consuming and not economical. Hence, computer simulation is a useful approach to investigating the formation and development of round billets.[15] Several mathematical models have been developed to calculate the growth of round billets.[13–22] These models aim at the selection of optimal processing parameters, the design of spray-forming chambers and plants, and the investigation of the thermal transfer. In related studies, Frigaard et al. formulated a mathematical model to investigate the growth dynamics of sprayformed billets.[14,19–21] In their model, a partial differential equation describing the average motion of a billet’s surface is formulated. Numerical solution of the partial differential equation is then implemented to study both transient billet growth and steady-stat
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