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RESEARCH PAPERS

An Isothermal Finite Difference Model for Droplet Spread in the Spraying of Hot Die Surfaces With Water-Based Graphite Lubricants

[+] Author and Article Information
L. Yang

Department of Industrial, Welding, and Systems Engineering, The Ohio State University, 1971 Neil Avenue, 210 Baker Systems, Columbus, OH 43210

R. Shivpuri1

Department of Industrial, Welding, and Systems Engineering, The Ohio State University, 1971 Neil Avenue, 210 Baker Systems, Columbus, OH 43210shivpuri.1@osu.edu

1

Corresponding author.

J. Manuf. Sci. Eng 129(5), 874-884 (Jan 16, 2007) (11 pages) doi:10.1115/1.2752525 History: Received February 09, 2006; Revised January 16, 2007

Dilute sprays are used in hot die processing to lubricate and cool the die surface prior to forming of the part. These sprays are often stochastic in nature with fine droplets that are randomly deposited at high velocities. Consequently, the spraying mechanism is difficult to measure and to model. This paper presents a simple isothermal deterministic model for the spreading of droplets on hot die surfaces. This model is based on the volume of fluid (VOF) finite difference approach. The lubricant properties for this model are inverse calculated from simple experiments using various lubricant dilution ratios. Using similarity principles, the model is validated by comparing it with results from single droplet experiments with different droplet diameters and deposition speeds. It is found that for dilute suspensions the isothermal assumption is valid for surface temperatures where no-steam forms and that a simple linear relationship exists in the logarithmic scale between the spread factor and the droplet Weber number.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

The cylindrical coordinate description of lubricant droplet on a solid surface

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Figure 2

The boundary conditions of free moving surface

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Figure 3

Schematic of the experiment setup for single droplet experiments

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Figure 4

The configuration and meshing of the simulation

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Figure 5

Simulation results of lubricant 1:1 with 4-mm-diameter droplet at impact velocity of 10cm∕s

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Figure 6

Simulation results of lubricant 1:1 with 4-mm diameter droplet at impact velocity of 100cm∕s

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Figure 7

Experimental results of ξmax versus TD:We=27

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Figure 8

Experiment and simulation results of lubricants, ξmax versus Re

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Figure 9

Experiment and simulation results of lubricants, ξmax versus We

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Figure 11

Experiment and simulation results of lubricants, log(ξmax) versus log(We)

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Figure 12

Typical values of the VOF function F in the droplet model

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Figure 13

The fractional area and volume ratios Af and Vf

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Figure 10

Experiment and simulation results of lubricants, log(ξmax) versus log(Re)

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