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TECHNICAL PAPERS: Melting and Freezing

Melting and Resolidification of a Substrate Caused by Molten Microdroplet Impact

[+] Author and Article Information
D. Attinger, D. Poulikakos

Laboratory of Thermodynamics in Emerging Technologies, Institute of Energy Technology, Swiss Federal Institute of Technology (ETH), 8092 Zurich, Switzerland

J. Heat Transfer 123(6), 1110-1122 (Mar 20, 2001) (13 pages) doi:10.1115/1.1391274 History: Received November 09, 2000; Revised March 20, 2001
Copyright © 2001 by ASME
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References

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Haferl, S., Zhao, Z., Giannakouros, J., Attinger, D., and Poulikakos, D., 2000, “Transport Phenomena in the Impact of a Molten Droplet on a Surface: Macroscopic Phenomenology and Microscopic Considerations: Part I—Fluid Dynamics,” in Annual Review of Heat Transfer, C. L., Tien, ed., Vol. XI, Begell House, NY, pp. 65–143.
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Figures

Grahic Jump Location
Schematic of the problem of interest showing axisymmetric droplet coordinate definition and melted domain (dashed line)
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Details of a typical mesh used. The first layer of the substrate has a dimensionless thickness of 0.01 and its conductivity can be tuned for simulating interfacial resistance to heat transfer. The droplet, substrate and interface domain are indicated by the symbols 1, 2, and 3.
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(a) Temporal evolution of the Z-axis contact point for the baseline case, for different temporal and spatial discretizations; and (b) temporal evolution of the melted volume VM for the baseline case, for different temporal and spatial discretizations.
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Droplet shape and phase change location as a function of the dimensionless time for the baseline case
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Temporal evolution of the melted volume VM for different values of the superheat parameter SHP, corresponding to initial substrate temperatures of 180, 181, and 182°C
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Temporal evolution of the melted volume VM for different values of the impact velocities. The velocities ranging from 1 to 2 m s−1 correspond to Reynolds and Weber numbers in the interval (250.6; 501.3), respectively (1.9;7.61).
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Temporal evolution of the melted volume VM for different values of the Biot number. The case with an infinite Biot number is the case without thermal contact resistance between the splat and the substrate, and the four subsequent cases correspond to interfacial heat transfer coefficient values of 107,106,105, and 104 Wm−2 K−1.
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Maximum melted volume VM as a function of the impact velocity for five different superheat parameter SHP in case of an infinite Biot number
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Droplet shape and interface between the drop and substrate material as a function of the dimensionless time for the baseline case. Details (a) and (b) show the instantaneous flow pathlines corresponding to τ=0.4 and 1.0.
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Experimental cross-section of a solidified 3.5 mm steel droplet on a steel substrate 3 compared with two numerical models, (b, conduction model of Zarzalejo et al., 3) and (c,d present study). The horizontal line crossing figures (a, b, and c) denotes the substrate surface. The maximum substrate melting location visible as a darker line in (a) is approximated by a heat-diffusion based model (b), 3), with a heat conductivity artificially increased for convection, and by the numerical model developed in the present study (c,d). Oscillations of the phase change front around approximately R=0.2 explain the formation of the shoulders circled in the cross section (a), since the envelope of the instantaneous phase change fronts defines the maximum substrate melting location (c). With permission from Springer-Verlag for frames (a) and (b).
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Droplet shape, instantaneous velocity distribution and flow pathlines corresponding to the simulation in Fig. 10 (c,d). The dimensionless time is indicated, and the length of the horizontal arrow in the first frame corresponds to a dimensionless velocity of 1.

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