Multiphase Heat Transfer and Fluid Flow
Professor Roger H. Rangel --
Jean-Pierre Delplanque --
An existing model of the deformation and solidification of a single
droplet impinging on a cold surface (Fig.
1) has been revised and improved. The original model (Fig. 2) is based on a two dimensional
axisymmetric flow approximation of the velocity field, the Neumann
solution to the one-dimensional Stefan solidification problem, and an
integral mechanical energy balance. The improved model features a more
appropriate velocity field which satisfies the no-shear boundary
condition at the free surface, and an accurate derivation of the
dissipation term from the mechanical energy equation. This equation is
solved numerically(Fig. 3).
Comparisons of the original and the improved models are performed.
Results show that the original model over-estimates the final splat
size by about 10%. The discrepancy is more pronounced at larger Weber
numbers, where viscous effects dominate (Fig. 4).
The effects of the Weber
number, the Reynolds numbers, and the solidification parameter are
investigated through detailed numerical calculations (Figs. 5 and 6). Two regimes of
spreading/solidification have been identified. If Re/We is small, the
process is one of dissipation of the incident droplet kinetic energy;
whereas for large values of Re/We the process can rather be
characterized as a transfer between kinetic and potential energy (Fig. 7). In the latter case, the
variations of the final splat size versus the solidification constant
exhibit a non-monotonic behavior. This indicates that, for a given
material, the deposition process can be optimized. Correlations
relating the final splat size to the process parameters are given.
- Schematic of the problem.
- Coordinate system definition
(after Madejski, 1976).
- Correlation of the final splat size with
Re and We as derived from the improved model
in the non-solidifying case (K=0).
- Relative error between the final
splat size predicted in the non-solidifying
case (K=0) by Madejski's and that obtained with
the improved model.
- Final splat size
vs. We and K
for Re=400 and Re=400,000.
- Final splat size
vs. Re and K
for We=5 and We=500.
- Energy Distribution history. Effect of We
(Re=400 and K=0.02).
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Jean-Pierre Delplanque -
- December 1994
Last update - January 1996