A three-dimensional stochastic model to simulate thermal plasma spraying and coating formation was developed. The model is capable of predicting the variation of coating porosity, average thickness and roughness as a function of process parameters. The model assumes that particle speed, diameter, temperature, and impact point are given by their respective distribution functions. The spread factor of the splat after droplet impact is calculated from an analytical model in which it is related to the impact process parameters and particle material properties. Since the time required for a droplet to spread and solidify is much less than the average time between depositions of two particles, it is assumed that they impact on the substrate sequentially and that no two particles land at the same time. Previous rules are improved to specify the splat shape as a function of droplet impact conditions, which reveals that splat shape is sensitive to the offset distance between the center points of the two splats interacting with each other.

Two possible sources of porosity formation are considered: one is curling up at the edges of splats due to thermal stresses; the other is incomplete filling of voids under unmelted particles during deposition.

The curling up mechanism is investigated with respect to different coating materials and impact conditions. Experimental images and numerical simulations are studied to help understanding the effect of impact conditions and material properties to the curling up size. These studies show that curling up location and curling up angle are sensitive to the droplet initial temperature, the substrate preparation and temperature, the droplet coefficient of thermal expansion, and the impact velocity. A simplified analytical model is then derived and applied to calculate the curling up angle according to different impact conditions and substrate temperatures.

  We use a three-dimensional droplet deposition model to simulate the impact of different liquid droplets on an unmelted droplet and to evaluate the void under the unmelted droplet caused by incomplete filling by molten droplets. The simulations were used to develop rules to simulate incomplete filling under unmelted particles.

The effect of partial melting of thermally-sprayed particles on coating formation is considered. A one-dimensional heat conduction model is applied to calculate the fraction of each particle melted. A partially melted particle is then considered to consist of a completely melted portion which spreads out as a splat and a solid core which keeps its spherical shape after impact. The coating build-up rules are modified to include such unmelted particles.

A three-dimensional Cartesian grid is used to define the computational domain and to track the shape and position of the coating surface. The structure of the coating is defined using the variable known as volume-of-fluid f, and f throughout the coating is updated after each droplet is deposited. The quality of modeled coating microstructure is evaluated by three parameters: porosity, average thickness and roughness.