Cold Spray is a novel technology for the application of coatings onto a variety of substrate materials. In this method, melting temperatures are not crossed and the bonding is realized by the acceleration of powder particles through a carrier gas in a converging-diverging nozzle and their high energy impact over a substrate material. The critical aspect of this technology is the acceleration process and the multiphase nature of it. Three different nozzle designs were experimented under constant conditions and their performance simulated using Computational Fluid Dynamics tools. The Deposition Efficiency was measured using titanium as feedstock material and it was shown that it decreases with the cross-sectional throat area of the nozzle. Computational results based on a one-way coupled multiphase approach did not agree with this observation, while more sophisticated modelling techniques with two-way couplings can partially provide high-quality outcomes, in agreement with experimental data.

New required standards and tolerances come along with an increasing demand of
enhanced surface properties, making a new generation of coating technologies
necessary and capable of applying high quality layers of advanced materials

An alternative to conventional deposition technologies, such as Laser
Cladding

The ratio of particle mass that is deposited successfully over the particle
mass fed into the nozzle is called Deposition Efficiency (DE). It is evident
that DE strongly depends on the impact velocity of the particles

This complexity makes the nozzle dynamics sensitive to manufacturing
inaccuracies

For example,

Summarising, no studies so far deeply consider particle–particle interaction during the injection and acceleration, although the mixing conditions in the dense throat region and particle dispersion are found to be important in several studies. Several studies found the particle size to have important effects, even within not fully coupled phases, nevertheless, no investigation of the particle loading on the velocity distribution was conducted. There are no conclusive studies which link experimentally measured DE against nozzle design and their relationship at theoretical level.

This forms the starting point for the present study. In order to begin with the integration of all important modelling aspects, this work generates a connection between the particle loading and performance parameters, for example depending on different nozzle designs and operating conditions.

In this regard, experiments when depositing titanium onto aluminium tubes,
are compared to numerically computed multiphase flows and discussed taking
into account the features of the most widely used numerical approach, the
1-way-coupled

The general set-up for the CS process is shown in Fig.

The geometrical details of the nozzles can be seen in Fig.

Set-up of the Cold Spray process.

Geometry of the Cold Spray nozzle.

The measured feedstock powder mass flow enables the direct calculation of DE.
The respective results are summarised in Table

In this section, a widely used approach is applied to all three nozzle
geometries in order to survey its capabilities regarding an estimate of the
experimentally detected behaviour. Therefore, the three cases were simulated
with ANSYS Fluent v14.0. An initial analysis of this study was reported by

The operating fluid nitrogen was set to be an ideal gas. The problem was
reduced from a three dimensional to an 2-D-axi-symmetric flow. The
Navier–Stokes equations for mass, momentum, and energy of the gas phase were
solved for a steady state. Moreover, the equations were used in their
Reynolds-averaged form and, consequently, extended by a

Geometrical details of the nozzles.

Comparison of deposition efficiencies.

In Eqs. (

Computational mesh at the nozzle inlet, throat and exit.

Geometry of computational domain and boundaries.

A pressure inlet boundary condition was applied to the nozzle inlet and set
to the same values as in the experiments (

Boundary conditions for the axisymmetric calculation.

Concerning the particle phase modelling, a one-way coupled Lagrangian
approach was chosen. In this respect, each particle (45

It can be seen, that the modelled acceleration of the particle is mainly influenced by the relative velocity and particle size.

Comparison of nitrogen velocity profiles along the nozzle axis.

Figure

Figure

Not only the simulated gas phase, but also the particulate material behaves
in similar ways regardless of the considered design changes. However, in
reality, the deposition performances are entirely different as reported in
Table

Comparison of titanium particle velocity profiles along the nozzle axis (uncoupled).

If a significant fluid-particle interaction is present, it must have larger
effects in N1 than in N2 and N3. The reason is a higher volume fraction of
the particulate phase, originating from the smaller

The same authors contributed with another publication

Volume fraction of particles in the throat region.

Comparison of nitrogen velocity profiles along axial position (coupled).

The latter approach is chosen in this study in order to compare different
operating conditions. The inaccuracy of previously discussed models go back
to the dependency of gas and particle dynamics on local particle loading and
volume fraction. Therefore, the respective effects can be investigated if the
only parameter that is changed is the particle feed rate, keeping the
geometry constant. Since nozzle N1 is the design with the smallest
restriction cross-section, it was chosen for this part of the study. It was
investigated using the same gas flow conditions but varying particle feed
rates from 0 to 16, 32, and through to 64

Figure

Comparison of gas Mach number along axial position (coupled).

Comparison of titanium particle velocity profiles along axial position (coupled)

Figures

In Fig.

The radial gas velocity profiles for three different axial positions are
shown in Fig.

Figures

Comparison of gas velocity profiles along radial position (coupled)

Comparison of titanium particle velocity profiles along radial position at the nozzle throat (coupled)

Comparison of titanium particle velocity profiles along radial position at the nozzle exit (coupled)

It is difficult to compare these results to the experimental data in default
of directly measured velocities. In particular, a model to link the
calculated velocities to DE is not available yet, because of a vast amount of
practical influences. However, an attempt can be made to compare the
calculated changes in velocity to the measured changes in DE as follows.
Reducing the cross-sectional throat area of N3 to N1 by half, causes an
increase in particulate loading. This is analogous to doubling the particle
feed rate in N1 from 32 to 64

However, in a work by

In this work, the deposition performances of three different De
Laval nozzle designs under constant process conditions were investigated and
explained by comparing them to numerical results. Titanium was deposited onto
aluminium 6082-T6 tubes. It was found that the N1 nozzle, with the smallest
throat cross-sectional area, performs the worst in terms of DE. Numerical
simulations were performed based on fluid dynamic observations, using steady
axisymmetric equations with a

The insufficiency of the inter-phase coupling was derived as the main reason, as the comparison with more sophisticated modelling in literature showed. Using a two-way coupled discrete phase model, the effect of increased particle feed rate and hence density on the velocity distributions of both phases was shown to be noticeable for nozzle N1. However, the large number of factors, in relation to the nozzle design, the extreme changes in velocity, and volume fraction makes overall theoretical predictions difficult. Another important factor is the turbulence model, which is derived as another reason for uncertainty. These initial studies will require further development stages in this regard to achieve full validation.

The authors wish to express their gratitude to FP7 – Marie Curie (project acronym: SSAM) for the valuable support in developing the work presented in this article. Edited by: M. Cotterell Reviewed by: R. Clarke and one anonymous referee