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A number of analytical models predicting the size distribution of particles during atomization of Al-based alloys by N_{2}, He and Ar gases were compared. Simulations of liquid break up in a close coupled atomizer revealed that the finer particles are located near the center of the spray cone. Increasing gas injection pressures led to an overall reduction of particle diameters and caused a migration of the larger powder particles towards the outer boundary of the flow. At sufficiently high gas pressures the spray became monodisperse. The models also indicated that there is a minimum achievable mean diameter for any melt/gas system.

In metal spray forming, the atomization parameters define the size of the powders to be deposited on the substrate. The size of the particles and their position inside the spray affect their cooling histories and the solid fraction on the preform. The quality of the end product depends very much on porosity, grain size and distribution of intermetallic phases in the powder, all of which are in turn a function of the cooling histories of the powder particles in flight. It, therefore, follows that information on the dynamic behaviour of the drops is needed for an accurate prediction of the shape and quality of the preform or the mean diameter and the microstructure of the powder collected. A first major step in this direction is the prediction of the liquid break up mechanisms during gas atomization.

In gas atomization a liquid metal stream is perturbed by a number of high velocity gas jets and is broken up into fine drops [

This study presents a comparison of principal analytical models used in engineering practice, addressing primary and secondary break up. The models have been applied to the atomization of Al melts. In a previous study of He atomized Al alloys [

The first algorithm considered is based on the Surface Wave Formation (SWF model) theory and has been explained in [_{c}, is defined as:

where σ is the liquid surface tension; C_{D} is the drag coefficient; ρ_{g} is the gas density and U_{r} is the relative velocity between the liquid and the gas phase. The SWF model utilizes a force balance criterion to calculate the critical amplitude for specific gas and metal properties above which stripping of the tip of the crest or detachment of the liquid column occurs. In this way, the fastest growing wavelength is related to a critical amplitude and for every crest with an amplitude exceeding the critical one, the diameter and volume of the ring-shaped ligament are also determined. The SWF model of secondary break up—

where m_{p} is the mass of the particle being transported, U_{p} is the velocity of the particle, A is the area of the particle seen by the gas flow and g is the gravitational acceleration.

The second model is based on a drop break up criterion, termed the Weber model, which is based on observations made by Hinze [_{we})_{c}, through the expression:

Any drop exceeding the critical size is instantaneously broken into fragments of the critical diameter. The number of fragments is equal the ratio of mass of the initial drop to that of the critical size. In practise, the actual value of the critical Weber number first needs to be evaluated for a particular melt/gas system and for a given set of injection parameters by trial and error. Afterwards, that critical value can be used for any other set of conditions for that particular system.

An analytical model for drop break up originally presented by Wolf and Andersen [_{c} is assumed. The gas pressures necessary to cause either a hollow bag or a stripping break up were calculated. The pressure for the hollow bag mechanism, P_{b}, is given by Equation (4), while the pressure necessary for the stripping mode, P_{s}, is given by Equation (5):

The pressure that is positive and larger between Equations (4) and (5) was selected to be the driving force of the disintegration. The displacement of an assumed outer layer of the drop in respect to the undisturbed position of its free surface was then calculated. If at any time the displacement was found to be equal or larger than the diameter of the initial drop, the outer layer was broken into fragments with dimensions, y, L and W, given by Equations (6), (7) and (8), respectively:

where μ_{l} is the dynamic viscosity of the melt; for liquid Al, μ_{l} is taken to be 1.0 mPa·s. The diameter of each drop, D_{s}, produced in this manner is given by the expression:

and the number, N_{s}, of drops produced was expressed as:

by dividing the volume of the stripped layer by the volume of the assumed drops formed by its collapse.

Finally, the empirical Lubanska equation [_{m}, to the processing parameters of atomization:

where C_{L} is a numerical constant ranging from 40 to 50; ν_{l} and ν_{g} are the liquid and gas kinematic viscosities; respectively, D_{o} is the initial diameter of the melt and N_{we} is the Weber number defined as:

In the current study, the kinematic viscosity of liquid Al at 1100 °C was taken to be 3.10 × 10^{−7} m^{2}/s, while the kinematic viscosities of N_{2}, He and Ar at 20 °C were 1.51 × 10^{−5}, 1.17 × 10^{−4} and 1.34 × 10^{−5} m^{2}/s, respectively.

Primary atomization,

Atomization Pressure : 150 psi (1.03 MPa);

Ambient Pressure : 14 psi (0.096 MPa);

Initial Melt Column Radius : 0.001 m;

Initial Melt Exit Velocity : 1 m/s;

End of break up calculations 0.4 m downstream of atomizer.

The behavior of the atomization models was studied as a function of the injection pressure and type of gas. The parameter considered was the Sauter D_{32} particle size for which the overall and localized-radial values were calculated.

_{2}, He and Ar, respectively, on the overall D_{32} size for liquid Al. The Lubanska equation predicts finer particles for Ar than for He up to a pressure of 150 psi, above which the trend is reversed, in par with experimental evidence for the two gases [_{32} size with increasing pressure. In addition the models predict that He produces the finest powders under any atomization pressures. In addition, N_{2} yields coarser particles compared to Ar. The Weber model is not sensitive to the changes in the injection pressure of He.

Effect of the type of atomizing gas on the overall D_{32} particle size for Al (_{2}; (

The radial distribution of particle sizes is shown in _{2},

Predicted radial variation of the D_{32} size for Al-N_{2} at (

Predicted radial variation of the D_{32} size for Al-He at (

Predicted radial variation of the D_{32} size for Al-Ar at (

Increasing gas pressure with a fixed initial melt velocity amounts to an increasing gas to melt mass flux ratio, and as expected the Lubanska expression predicts a continuous decrease in drop sizes as do the three break up models, e.g., see

The effect of the gas pressure on the D_{32} size can be understood by inspection of

The predicted break up events in two phase flows by the SWF, Weber and WA models, revealed that the radial distribution of particle sizes was that fine particles existed near the center axis and coarser ones with increasing distance from the center. At sufficiently high injection pressures a monodisperse spray of fine powders was produced, with the coarse particles being pushed to the outer edge of the flow. At very high gas pressures, break up reached a saturation point in the center of the flow and there was no detectable radial gradient of particle sizes. Helium was found to produce the finest particles under any set of atomization conditions with nitrogen producing the coarsest ones. Due to its inherent affinity with Kelvin-Helmholtz theory, the SWF model offers enhanced insight regarding the radial distribution of particle sizes, which the rest of the models lack. The WA model offers some accountability towards radial distribution of sizes but due to the deterministic nature of the twin break up mechanism on which it operates, it has a bias towards monodisperse particle distributions.