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

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.