Fluid flow, heat transfer, and solidification of molten metal droplets impinging on substrates: Comparison of numerical
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INTRODUCTION
T H E R E has been a growing interest in spray forming as a technique for the production of "near net shapes," that is, tubes, rods, or sheets from a molten metal spray that is made to impact onto a cooled substrate. ~1-7] As discussed in previous review articles, the focal point of this research has been the evaluation of the properties of the deposit formed. [71 In terms of process analysis, the main interest has concerned the cooling of the metal droplets during their passage and during the actual formation of the deposit. ]s-13J Most previous investigators adopted the "so-called" continuum approach, in which the effect of the individual droplets impinging onto the surface was averaged over a finite spatial and time domain; this time domain was large compared to the droplet size or the time of impaction, spreading, and solidification of the individual droplets. As discussed in an earlier article, t131 this continuum approach, while appealing due to its mathematical simplicity, cannot address important processing questions regarding the role of droplet size and impaction velocity on the properties of the deposit formed. The work described in this article has been undertaken with the object G. TRAPAGA, Postdoctoral Associate, and J. SZEKELY, Professor, are with the Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA, 02139. E.F. MATTHYS, Professor, is with the Department of Mechanical and Environmental Engineering, University of California-Santa Barbara, 93106. J.J. VALENCIA, formerly Postdoctoral Researcher with UCSB, is Principal Technical Staff with Metalworking Technology, Inc., Johnstown, PA 15904. This article is based on a presentation made in the symposium "Spray Processing Fundamentals: Coating and Deposition" presented as part of the 1990 TMS Fall Meeting, October 9, 1990, in Detroit, MI, under the auspices of the TMS Synthesis and Analysis in Materials Processing Committee. METALLURGICAL TRANSACTIONS B
of examining the droplet impaction process in detail, with full attention to both the fluid flow and the associated heat-transfer and solidification phenomena. The purely fluid flow aspects of this problem have been addressed in a previous article, 1~41where the authors calculated the spreading of an isothermal droplet upon impaction onto a solid substrate. While this previous mathematical modeling effort has been helpful in the quantitative description of the process, it has been verified experimentally only to a limited extent. Indeed, the only quantitative verification has been through a comparison with the previously reported measurements of Madejski l~51 and Savic and Boult. fl61 Nevertheless, the theoretical predictions appear to have been consistent with the qualitative picture that has been articulated for the spray forming and plasma spraying operations by several investigators. [14] The purpose of this article is to study some fundamental aspects involving heat transfer and solidification of the droplet impingement processes an
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