A mathematical model of the spray deposition process
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I. INTRODUCTION A L T H O U G H numerous property improvements have been demonstrated to result from rapid solidification, commercialization has been limited, due to the difficulty involved in the production of bulk shapes and also to the oxide formation almost always associated with the particulate nature of the products of processing. [1 11,~9,421 However, the recently developed spray deposition techniques, such as Osprey and the liquid dynamic compaction process, appear capable of producing dense, fine-grained, bulk specimens directly from the melt and with a minimum of oxidation. ~2-221 Significant property improvements have been demonstrated to result from these processes in several alloy systems. L16-22~ The spray deposition process consists of two steps: first, a molten metal stream is fragmented by means of high speed gas jets; the resulting droplet dispersion is then collected onto a suitably designed substrate, [23,24,261 which may or may not be cooled, but generally is. Figure 1 is a schematic representation of a typical spray deposition process. Figure 16 shows the SD set-up at the University of California, Irvine. The spray formed during the atomization stage is rapidly quenched by the moving gas, so that the thermal conditions of the spray at the moment of impact with the deposit are determined by the amount E. GUTIERREZ-MIRAVETE, Curriculum Chair and Assistant Professor, Department of Metallurgy, The Hartford Graduate Center, 275 Windsor Street, Hartford, CT 06120; also Research Affiliate, Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139. E.J. LAVERNIA is Assistant Professor, Department of Mechanical Engineering, University of California at Irvine, Irvine, CA 92717; formerly, Research Associate, Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139. G.M. TRAPAGA, Graduate Student, J. SZEKELY, Professor of Materials 9 Engineering, and N.J. GRANT, Professor of Metallurgy, are at Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139. Manuscript submitted April 8, 1987. METALLURGICAL TRANSACTIONS A
of energy extracted from the drops by the gas. It should be noted that the thermal history of the preform is the result of the combined effects of the enthalpy content of the impinging spray, the heat loss from the top surface, and the rate of heat extraction by the underlying substrate. Since the structure and properties of the deposit are related to the thermal conditions during solidification, it is of interest to have some means of estimating heat transfer rates during spray deposition. The objective of this work is to obtain a better quantitative understanding of the process while using only a minimum of mathematics. In the sequel, the formulation of the mathematical model of the spray deposition process is presented first; followed by a discussion of the main simplifying assumptions used in the model. The second half of the paper includes
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