Droplet solidification and gas-droplet thermal coupling in the atomization of a Cu-6Sn alloy
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I.
INTRODUCTION
TO produce quality spray deposits and powders and to optimize the spray-forming process, i.e., to reduce overspray, it is necessary to know the temperature and/or the solidified fraction of droplets as a function of size, spray location, and spray-process parameters. There have been numerous efforts to simulate droplet cooling in melt sprays;[1] however, these efforts have not been in agreement with experimental results. This is in part because of the difficulty in verifying model predictions and because accurate data of many spray parameters are lacking and not easy to obtain. An indirect approach to determining the thermal state of droplets in the spray is to calculate the droplet cooling rate using measured cell spacings from powders sampled throughout the spray. One of the basic prerequisites to using this approach is that the dependency between cooling rate and cell spacing must be reliably established. Although the Bridgeman method may be used to generate a reliable relationship between cell spacing and cooling rates,[2] by virtue of the small sample ingot diameter and the lack of macrosegregation, numerous ingot samples must be made in order to have a wide-range coolingrate measurement. This can be very time consuming. A newer approach was adopted in this work by using the impulse atomization technique.[3] As a result, a reliable, quantitative and controlled cell-spacing vs cooling-rate model can be used along with innovative diagnostics and sampling in both gas and impulse atomization to provide AXEL V. FREYBERG, Scientific Assistant (Dipl. Ing. Student), MARKO BUCHHOLZ, Scientific Assistant (Postdoctoral Student), Institut für Werkstofftechnik, and VOLKER UHLENWINKEL, Manager of Collaborative Research Program “Spray Forming,” are with the University of Bremen, 28359 Bremen, Germany. HANI HENEIN, Professor and Director, is with the Advanced Materials and Processing Lab., University of Alberta, Edmonton, AB, Canada T6G 2G6. Contact e-mail: [email protected] Manuscript submitted May 16, 2001. METALLURGICAL AND MATERIALS TRANSACTIONS B
unique insight into the thermal history of droplets in the melt spray in gas atomization. This article will present such an approach, applied to the atomization of a Cu-6Sn binary alloy. II. MATHEMATICAL MODELING A. Droplet Cooling Model The solidification cooling rate of a droplet was determined using a model described in detail by Wiskel et al.[3] using the Whitaker[5] correlation for the Nusselt number (Nu): Nu ⫽ 2.0 ⫹ (0.4 Re0.5 ⫹ 0.06 Pr0.67)Pr0.4 ⭈ (ma /ms)0.25 [1] where Nu is the Nusselt number; Re and Pr are the Reynolds and the Prandtl numbers, respectively; and ma and ms are the dynamic viscosities of the fluid at the ambient and at the surface temperature of the particle, respectively. We also considered radiation in the cooling history of the droplet. Thus, the overall heat-transfer coefficient (hT) consists of convective (hconv) and radiative (hrad) components: hT ⫽ hconv ⫹ hrad ⫽
Nu kG (T 4 ⫺ T a4 ) ⫹ s D T ⫺ Ta
[2]
where kG is the cond
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