Mathematical modeling and calculation of heating and melting of particles of the polymeric powder in flow channel of the sprayer

Heating and melting of particles of polymeric powder in the central flow channel of spraying gun is investigated. Mathematical models of these processes taking into account convective and radiative-convective heat interaction of particles with environment is represented. Relations for calculating the temperature of the particles depending on the longitudinal coordinate, time of flight, operating and design parameters as well as thermophysical characteristics of the particles material and environment are given.


Introduction
When applying polymeric powdered materials (compositions) for retaining powder particles on the treated surface it is preheated to a temperature that ensures melting of the particles at the point of contact with the surface. Particles charging, their deposition on the electrode with subsequent melting and formation of the coating is also produced. In the case of flame spraying the powder particles are fed in the high temperature jet of the fuel combustion products. Thus the probability of material destruction on the particle surface and as a result appearance of the coating imperfections is high [1,2]. In order to prevent the mentioned undesirable circumstances, taking into account the high thermal inertia of the material of sputtering polymeric powders it is appropriate to carry out heating and melting of the particles stage-by-stage: first in the proportioning feeder then in the first section of the central flow channel of the sprayer by convection through the dividing wall. After that in the second section in the area of direct contact of powder-air mixture with the gases heated up to high temperature the melting of the powder particles should be carried out mainly through the radiant heat exchange.
First section of flow channel of the sprayer consists of a central annular channel of length 1 l with a helical insert wherein the powder-air mixture is moving and a peripheral annular channel of the same length with a hot gaseous medium flowing in it. In fact, this section represents a recuperative tube-intube heat exchanger. Second section is a tube of length 2 l its inner diameter coincides with the diameter of the peripheral annular channel of the first section. Outer surface of this tube like outer surface of the tube of first section is thermally insulated. In the tube of the second section powder-air mixture and heated gaseous medium (air, fuel combustion products) covering the mixture flow are moving at different speeds. When considering nonisothermal flow of mediums in the cavities of these sections it is assumed that mediums are incompressible and in the first section powder-air mixture is homogeneous. Cylindrical coordinate system ,, rz  is introduced; its axis 0z is directed along a symmetry axis of the concentric tubes.

First section of flow channel
Initial system of equations describing the motion of powder-air mixture in the central annular channel consists of differential equations of conservation of momentum, mass, energy and dependency of powder-air mixture density on the temperature.
At the first section equations of this system are averaged and supplemented by closing phenomenological relations.
In order to find formulas suitable for engineering calculations, the system of averaged equations is simplified as much as possible using the following assumptions. Turbulent nonisothermal flow of the mixture in the channel is considered quasi-stationary, terms containing z coordinate derivatives in the equations of conservation of momentum and continuity are neglected, change of the heat flow density in the longitudinal direction is assumed to be small compared to the change in the radial direction [3].
Thus obtained problem is solved with regard to the weight-average temperature of the mixture where 01 t is the average temperature of the powder-air mixture at the inlet to the annular channel,  t is the average density, specific heat capacity, speed of the mixture flow rate, inlet temperature of the heated gas in the peripheral annular channel. In the general case the density, heat capacity, average speed of the gas flow rate in the considered channels are close, 12 SS  . Taking this into consideration, assuming 0 It follows that if We can see that temperature ; p t , p T is the temperature of the particle surface, C  is the convective heat exchange coefficient of the particle surface,