Modeling of solidification of molten metal droplet during atomization
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I.
II.
INTRODUCTION
DURING gas atomization, a liquid stream of molten metal is impinged and atomized by a number of high pressure atomization gas jets to form a spray of droplets. The droplets subsequently either solidify to become metal powder to be collected or deposit onto a collector to form a spray deposit.[1–14] The droplet, powder, and spray-deposit characteristics are all influenced by the solidification of the droplets during flight. All the previous models of droplet solidification were based on the traditional concept of steady-state nucleation during solidification of the molten droplets.[15–19] However, during atomization, the cooling rate, and thus the solidification rate, of the molten metal droplets is very high, which gives very little time for the nucleation event to happen. In the present work, the concept of transient nucleation,[20] instead of the steady-state nucleation, is considered to model such short nucleation events during solidification of the atomized droplets. A mathematical model is formulated to describe the solidification behaviors of an atomized droplet during flight, in terms of nucleation temperature, recalescence temperature, nucleation position, solid fraction at nucleation temperature, and droplet temperature and velocity. The effects of the atomization gas flow patterns are also presented. Several of the assumptions used in the present work would be specific to atomizing nozzle designs or atomizer tower shape and the interactions between the two, which are a severe limitation to the atomization process. However, the present work has left aside the complication brought by these limitations and concentrated on the simpler situation, which is easier to study. Y.H. SU, Graduate Student, and C.-Y.A. TSAO, Associate Professor, are with the Department of Materials Science and Engineering, National Cheng Kung University, Tainan, 701, Taiwan. Manuscript submitted March 1, 1996.
METALLURGICAL AND MATERIALS TRANSACTIONS B
FORMULATIONS OF THE MODEL
Figure 1 shows the flow chart of the formulations of the model. Four formulations, namely, the atomization gas velocity decay formulation, momentum formulation, energy formulation, and nucleation temperature formulation, are required to complete the model. These are discussed in Sections A through D. A. Atomization Gas Velocity Decay Formulation Once the atomization gas leaves the exit of the atomizer nozzle, it enters, at a great velocity, an environment where the surrounding gas is relatively stagnant. The resulting drag forces create turbulence around the atomization gas jet, which causes a decay of the velocity of atomization gas away from the exit of the atomizer nozzle. Three types of gas velocity decay formulations are used in this study: [19,21,22]
~ ! ~ ! ~ !
Vg 5 Vge exp 2
Z Zc1
[1]
2
Vg 5 Vge
Z 12 Zc2
[2]
3
Vg 5 Vge
Zc3 Z 1 Zc3
[3]
Grant et al. have shown that the axial gas velocity decaying with distance could be approximated by an exponential-decayed function,[19] as shown by Eq. [1], in which the constant ZC1
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