NUMERICAL MODELLING OF HEAT TRANSFER DURING IMPACT OF A MOLTEN DROPLET ON A SURFACE

. SPH-based numerical technique for modelling of impact of molten drops on a surface with heat transfer and phase transitions effects is proposed. Computational algorithm uses SPH with procedure of restoring of particle consistence and variational approach to calculation of acceleration field. Also, boundary algorithm for free and contact surfaces in 3D setting are developed.


Introduction
In plasma coating techniques metal powder is heated to a molten state and the flow of drops is directed onto the surface of tool. Molten droplets spread out over the surface, cool and solidify during interaction. The particles solidify to form a coating deposit on the substrate's surface. It is important to have a clear understanding of the physics of process and to have a models of droplet impact on the surface of substrates for better control of the generation of splats and the structure of coating. Experiments are used to get a link between factors related to droplet impact and final morphology and quality of coating, but this is an expensive way. Numerical models are more preferable for prediction of coating quality and properties, but it need a good computational model, able to treat high deformation, liquid flow and solidification, heat transfer and contact interaction of droplet and surface. Important side is ability to make modeling in 3D, because of significant loose of information in simplified 2D-setting.

Computational Method
To calculate the parameters of splats, various approximation methods are used with different degrees of simplification. So, the representation of drops in the form of the equivalent cylinders provides a way to semi-analytical solution of the problem. Computational fluid dynamics or numerical method of solid mechanics lead to computer aided physical modeling in 3D setting.
In this paper we propose the use of smooth particle method (SPH) [1], adapted to the modeling of the deformation process of the liquid droplet with a phase transition at crystallization in a large range of speeds.
Basis of SPH approximation is equation where h is smoothing parameter, which define a radius of fluency for points, x x -is a space coordinate, W -smoothing function. Spatial derivatives are defined via: , , Corresponding to (2) particle approximation is written as: -radius-vector, approximated function value, mass and density at k-th point.
Equation (3) have C 0 -consistency [2] near surfaces and boundaries and at non-uniform particle distribution, and for restoring particle consistency special approaches needed. According [2], a test vector-function is introduced in form: Approximation of test function (1) and its derivatives (2) can be found with C 0consistency, but due to the fact that this values are known, this approximation can be used to construct correction procedure and restore particle consistency. Let's define : Matrix of approximations for this function at n-th point, found via uncorrected SPH approximation (3) Now, corrected approximation of function f(x) value or its derivatives can be found, if we build full matrix of uncorrected approximations (3) and apply correction matrix (7): For calculation of flow of liquid and solid phases, approximation (8) applied to lagrangian of system: where k v k v -is particle speed, k u -is internal energy (per mass). In both phases (liquid and solid) internal energy change can be written in form: As it shown at fig. 1, solidification of melted material starts at contact surface approximately 140 ns after contact and significant fragmentation of droplet due to high initial speed is observed. Energy conservation during calculation doesn't exceed 0.1 %, full change of momentum doesn't exceed 0.01 %.