MSMechanical SciencesMSMech. Sci.2191-916XCopernicus GmbHGöttingen, Germany10.5194/ms-6-127-2015An analysis of the particulate flow in cold spray nozzlesMeyerM.meyerm@tcd.ieLupoiR.The University of Dublin, Trinity College, Department of Mechanical &
Manufacturing Engineering, Parsons Building, Dublin 2, IrelandM. Meyer (meyerm@tcd.ie)11August20156212713619February201528May201525June2015This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://ms.copernicus.org/articles/6/127/2015/ms-6-127-2015.htmlThe full text article is available as a PDF file from https://ms.copernicus.org/articles/6/127/2015/ms-6-127-2015.pdf
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.
Introduction
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
onto substrates of other metals or alloys.
An alternative to conventional deposition technologies, such as Laser
Cladding , Plasma and Flame Spray
is Cold Spray (CS). This method is free of
melting and therefore avoids the unwanted effects of those techniques which
operate under high temperature levels . High pressure gas
is accelerated in a converging-diverging supersonic nozzle to velocities in
the order of 1000 ms-1. The coating material is injected as
powder into the nozzle and accelerated by the gas flow. As the powder
particles strike against a substrate placed at a distance from the nozzle
exit, they deform plastically and bond with the substrate material.
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
. Despite the simple design and working principle, the
flow characteristics are very complex, e.g. due to trans- and supersonic
velocities, boundary layer instability, turbulence, and particularly the
presence of multiple phases. The rapid change that the flow variables undergo
from the inlet to the outlet of the nozzle is the most critical factor.
This complexity makes the nozzle dynamics sensitive to manufacturing
inaccuracies . In addition, numerical methods are in
general not tailored for all the present local flow situations, e.g. the
increased particle volume fraction in the throat region or the high pressure
gradients in combination with extreme shear flow. Therefore, investigations
often focus on specific aspects of the flow field independently.
For example, published a numerical investigation about the
effects that gas operating conditions, particularly pressure and temperature,
have on the flow field. discussed the outcome of
1-D-nozzle calculation in comparison to 2-D axi-symmetric simulations and
found measured velocities in an intermediate range between those theoretical
approaches. A more application-related question was asked by
, who analysed the gas flow of a jet that impinges onto a
mask. They tracked non-interacting particles that were released in the nozzle
exit in order to find how they move through the mask. In contrast,
observed at the impingement region how the impact velocity
increases due to the change of the shock system as the substrate size is
changed. A work by concentrates on the gas phase as well,
which is a good approximation, since it is dealt with nano-particles. Others,
like , were interested in numerical nozzle comparisons, but
rather depending on the mixing conditions in the pre-chamber where the
carrier and process gas streams join. Similarly, recently
examined the effect of a variation of the injection pressure on the gas flow
field on the one hand, but also on the dispersion of the particulate phase on
the other. It was found, that the dispersion is strongly increased with
enhanced injection pressure. It was also found by that the
injection point as well has a significant effect on the particle dynamics,
especially on the thermal conditions. Because the temperature has a major
influence on the process efficiency, were engaged with the
numerical modelling of heat transfer within the nozzle and substrate. In a
similar manner, developed a 3-D-model that is also mainly
concerned with the heat transfer between the nozzle, the fluid and the
substrate. Interestingly, to point out the importance of turbulence
treatment, a k-ε-turbulence model resulted in over-predicted
temperatures of the gas, which could be drastically improved by a
model-calibration. Numerical works that focus on the particle behaviour were
for example conducted by , who were interested in the
differences between under-expanded and over-expanded jets, using a variety of
particle sizes. investigated recently how the particle
velocity depends on the type of carrier gas, which was calculated with a
simple particle tracking technique. The velocity error was of the order of
10 % in this regard. again considered in a different
context the interaction between particles during the deposition process, thus
influencing the deformation of the particles upon impact, not considering any
fluid dynamic effects.
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 Lagrangian particle tracking. In addition, a more
complex approach is discussed, a 2-way-coupled Lagrangian method
with stochastic particle collisions, and applied to one of the nozzles,
thereby comparing the outcomes at different particle loadings. It is found
that conventional numerical methods can be inherently limited for the
identification of the performance trends.
Experimental procedure and results
The general set-up for the CS process is shown in Fig. . The
experiments were conducted utilizing a nitrogen type CS apparatus with an open loop
powder feeder. The handling system was capable of delivering a working
pressure of up to 3 MPa. A load cell read the powder mass flow rate,
while a flow meter measured the gas flow rates in both the powder feeder line
and the main line, where a gas heater was installed. This component was used
to generate a higher inlet temperature, i.e. nozzle exit speed. Titanium
powder (CP-grade 2, -45 µm size, spherical) was injected in the
subsonic region of the nozzle and deposited onto 50 mm diameter tubes
(Al 6082-T6) using three nozzles in order to assess their DE performance.
The geometrical details of the nozzles can be seen in Fig. .
Correspondent values of the three designs (N1, N2, N3) are summarized in
Table . Ai and Ae represent the inlet
and exit cross-sectional area, respectively. Lc and
Ld are the length of the converging and diverging sections of the
nozzles and A* quantifies the cross-sectional throat area. For all test
runs the same processing conditions were applied, i.e. the substrate was
placed at a stand-off distance of 40 mm from the nozzle exit. The
inlet pressure and temperature were set to 3 MPa and 350 ∘C
in order to reach the desired velocity regimes, the powder feed rate was
measured to be 55±9gmin-1.
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 . Comparing N1 and
N3, the DE of 16.3 % is almost doubled to a value of 33.3 %, despite
the processing conditions remaining constant. Although their overall design
is different, nozzle N2 and N3 exhibit similar DE values that correspond to
the identical cross sectional throat area. A theoretical analysis was carried
out so as to identify the key parameters to unravel the scientific reasons of
the experimental outcomes.
Uncoupled simulation
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
k-ε-turbulence model with standard wall functions. The choice
of this type of model was based on its common application in CS and the
solution of the variables of interest experienced a negligible change when
compared against non-equilibrium wall functions. Gravitational forces were
considered negligible. The governing equations are according to
:
∂∂xi(ρui)=0∂∂xi(ρuiuj)=-∂P∂xi+∂τij∂xi∂∂xi(ρeui)=-∂Pui∂xi+∂(ujτij-qi)∂xi∂∂xi(ρkui)=∂∂xjμ+μtσk∂k∂xj+Gk+Gb-ρε-YM+Sk∂∂xi(ρεui)=∂∂xjμ+μtσε∂ε∂xj+C1εεk(Gk+C3εGb)-C2ερε2k+Sε
In Eqs. ()–(), ρ, u, P, e, τ,
and q denote the gas density, velocity, static pressure, internal energy,
viscous stress tensor, and conductive heat flux. k is the turbulent kinetic
energy, ε the eddy dissipation rate, while all other quantities
are model-specific constants and source terms. Due to compressibility, a
density-based solver was used with a second-order discretisation. The
structured mesh was developed to suit the respective flow phenomena with a
size of approx. 120 000 elements and tested to provide a mesh-independent
solution for the gas phase. It was refined in the near-wall region to capture
the boundary layer flow appropriately. The use of standard wall functions
requests a wall-adjacent cell hight of no smaller than y+=15-30 as it
should not be placed in the viscous sub-layer. The flow variables,
particularly the shear stress and the heat flux, tend to degrade otherwise.
However, a sufficient number of grid points are required to resolve the
boundary layer. Therefore, the mesh was designed for y+ values between 20
and 80. The throat radius was resolved with 110 points in the flow direction
for a sufficient resolution of the flow gradients. Likewise the resolution at
the nozzle exit was kept slightly refined in order to capture the shear layer
of the jet. The cell size in the nozzle exit region was tested to be
sufficiently fine to capture the shock pattern, i.e. with a change in
solution due to mesh refinement less than 1 %. However, adaptive mesh
refinement is an option for future work in order to optimise the shock
resolution. This is particularly important for smaller particles
(≈ 1 µm) with shorter response times than in this study.
Figure shows the mesh at the nozzle inlet and throat as well as
at the exit.
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 (p0=3MPa, T0=350∘C). The outlet pressure was defined to be atmospheric
pressure, sufficiently far downstream from the actual nozzle exit. An
adiabatic no-slip boundary condition was applied to the nozzle wall.
Figure illustrates the computational domain and boundaries.
Table summarises the respective boundary conditions.
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 µm
diameter in the model) was released in the inlet zone and further described
in a frame of reference that moves with the particle, solving the particle
equations based on the local fluid properties. Nevertheless, the change of
the gas state variables due to momentum and energy transfer to the particles
is not taken into account, as it would require a two-way coupled multiphase
model. This one-way coupling is often used in CS simulations, because it
provided acceptable results under set conditions .
Mostly, it is claimed that this simplification is justified due to high
Stokes numbers St and low momentum interaction parameters
Πmom. In this manner, after obtaining a
converged solution for the gas phase, particles are injected into the
converging part of the nozzle. Their trajectories are calculated according to
the force balance per unit particle mass given by Eq. ().
dupdt=FD(u-up)
Here, the time differential is induced by the motion of the reference frame,
but does not imply an unsteady tracking, since the solution is the same for
every particle that is exposed to the flow at that specific position.
u and up are the local velocity vectors of fluid
and particle respectively. FD is a drag force term, that is based
on the relative Reynolds number, see Eq. (), with particle
diameter dp.
Re=ρdp‖up-u‖μ
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 presents the gas velocity profiles along the axial
position for the different nozzle designs N1 to N3. The gas phase
acceleration is most intense in the transonic region. Each profile shows the
typical alternating pattern for over-expanded flows downstream of the nozzle.
In all three nozzle types the gas reaches similar maximum values, although
the acceleration in the transonic region differs.
Figure shows a comparison of representative velocity profiles for
single particle injections (at the nozzle centre line) in all nozzle design configurations. Since the accelerating drag
force is directly related to the relative velocity of the fluid, it increases
dramatically in the transonic region and reduces in the diverging section due
to the fading gas expansion, as can be seen in Fig. . Since
particle and gas speeds are still of different levels at the nozzle exits
Ae, some slight acceleration is maintained downstream of those
points. The shock pattern does not significantly affect the 45 µm
particles because of their relatively high inertia. Interestingly, the all
particles show very similar profiles and maximal velocities of approximately
595 ms-1 or 63 % of the carrier gas speed.
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 . Since the impact velocity is the main driver for DE as
experimental conditions were not changed, this fundamental mismatch can only
be explained through the fact that the modelling approach neglects important
aspects of the process physics: it does not account for any gas-particle and
particle–particle interactions. The phase coupling is therefore shown to
play a more decisive role in CS nozzle dynamics.
Comparison of titanium particle velocity profiles along the nozzle axis (uncoupled).
Coupled simulation
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 A* and a lower gas flow
rate. A work published by provides this claim with
further theoretical explanation. In this case, the inter-phase relations were
modelled in a more sophisticated manner, using an Eulerian approach.
Accordingly, both the fluid and the particulate phase were modelled as
immiscible, interacting continua in the same reference frame. The authors
showed a significant decrease in gas velocity at the exit due to the gain in
momentum of the particulate phase as the loading was increased. This suggests
significant interactions, at least on a theoretical level. A limit of this
type of model is the dependency of its validity on relatively high particle
density and uniform distribution.
The same authors contributed with another publication
that is focused on the simulation of the shock pattern in the jet using a
two-way coupled Lagrangian approach. It was found that flow patterns
could be predicted with high accuracy, including effects of high particle
loading in the jet. Using a particle size distribution of mostly small
particles (< 10 µm), the calculated exit velocities were
within the error range of the measurements. According to the authors, this
agreement originated from the complex RSM turbulence model and the two-way
phase coupling.
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 gmin-1. The numerical
modelling was adjusted as follows. The gas phase was modelled and solved as
described above, but using a re-normalisation group (RNG)
k-ε-turbulence model as it amends the turbulent dissipation at different
length scales and was successfully used in gas-particle flows .
In terms of particle injection, apart from the feed rate no changes were
made. Nonetheless, the two-way coupling corresponds to an unsteady tracking
of particles and produces additional source terms in
Eqs. ()–(). Likewise, the particle balance
Eq. () is expanded by an additional force, that depends on the
details of the coupling, including the concepts of virtual mass, turbulence
coupling, Saffman lift, and stochastic particle–particle collisions, as well
as a correction for high pressure gradients which plays a role in the
vicinity of shock waves. Consequently, the solution requires an iteration for
both the discrete and the continuous phase.
Figure shows the volume fraction distribution in the throat
region of nozzle N1 for the two loading cases of 16 and
64 gmin-1. Local maximum values are as high as 2.8 % and
occur around the centreline, since less space is present for the gas phase.
These maxima can be found more frequently in the case of higher loading, but
the maximum particle density does not increase measurably. Therefore, higher
loadings apparently tend to cause the formation of lump-like spots of high
volume fraction if the model accounts for particle particle-interactions.
Nevertheless, the higher the particle volume fraction, the more likely
collisions become. In this study, it is not observed how this evolution takes
place with time while moving downstream through the flow field. This can
cause some effect on the velocity observations and motivates a time-dependent
solution. A time-averaging of the local particle behaviour could give a more
general answer of its impact on the gas velocity.
Comparison of gas Mach number along axial position (coupled).
Comparison of titanium particle velocity profiles along axial position (coupled)
Figures and show the velocity and Mach number
profiles of nitrogen along the nozzle axis for all three particle feed rates
and the unladen gas flow. It can be seen, that the velocity profiles are
similar in the region of the throat and in the shock-expansion pattern of the
jet. However, in the diverging section, the gas velocity decreases
considerably with increasing particle feed rate, as more momentum is
transferred to the discrete phase. Also, the Mach number profile shows a
drastic reduction compared to the pure gas flow, although the differences
between the three loading cases are comparatively small. A Mach number drop
within the last section of the divergent part of the nozzle can be observed
for the pure gas flow, which diminishes with increasing feed rate.
Interestingly, the gas velocity at the highest particle feed shows a
different, more fluctuating trend as compared to the others, especially in
regions of dense flow. These fluctuations indicate the importance of the
turbulence coupling.
In Fig. the analogous velocity profiles for the particles are
shown. Here, the curve depicts the averages over intervals of 100 particles
each considering an overlap of 40 %. In this manner, the respective data
is reduced to a meaningful representation of the local velocity magnitude. As
can be seen, the velocity profiles are similar in the throat region, while
the final velocity in fact decreases with increasing feed rate by 8.9 %
for the present model. Velocities in the converging nozzle section appear to
be the highest for the maximum feed rate which can be explained by a more
dominant influence of particle–particle interactions that lead to local
velocity maxima. It should be mentioned that the presented analysis neglects
information about the velocity direction and hence the particle distribution.
The radial gas velocity profiles for three different axial positions are
shown in Fig. . The first location with x=30mm
corresponds to the nozzle throat, x=100mm is a central position
of the diverging section and finally x=211mm is just downstream
of the nozzle exit. For this comparison, the radial position is normalised by
the local internal nozzle radius. It can be seen how the velocity profiles
evolve from an accelerating flow characterised by boundary layers to a fully
developed flow. In shock dominated flow at the nozzle exit, the pure carrier
gas does not differ much from the loaded cases. However, the gas velocity
reduces particularly in the vicinity of the centreline inside the nozzle. The
figure shows that increasing the loading does not affect the gas phase as
much as injecting 16 gmin-1 titanium in the first place.
Figures and compare the according radial particle
velocity distributions at the nozzle throat and nozzle exit respectively. The
different loading cases are compared against each other and represented by
both the individual particles in the vicinity of the axial position and a
second order polynomial fit. The first set, corresponding to the nozzle
throat, shows homogeneously distributed particles for all cases, which agrees
with the gas velocity profile. Because of the higher collision rate, the
velocity level spreads out with increasing loading and the mean velocity
raises. At the nozzle exit, the particles at 16 gmin-1 exhibit a
strong accumulation around the centreline. For the medium loading, this
accumulation can still be seen, but the dispersion and the number of low
speed particles have increased measurably. At 64 gmin-1, the
particles are spread over all radii with a near-to-constant velocity range,
which is slightly lower than in the more dilute cases. The coupled model
hence shows an important effect of mass loading on the particle dynamics.
These are results at an instant of time, therefore the time-averaging of
particle dynamics could possibly show the effects more clearly.
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 gmin-1. The simulated particle
velocity at the substrate stand-off distance (x=0.25m)
consequently drops by 4.4 % to 511.9 ms-1. According to
, the DE for aluminium particles in heated air can
experience a 65 % decrease, as the particle velocity is reduced by
9.21 % to 505 ms-1. Transferring this trend to the
corresponding simulation results, the 4.4 % decrease in particle velocity
can be roughly estimated to cause a drop in DE of 31.1 %. As described in
previous sections, the actual reduction of DE is as high as 51.05 %.
Therefore, these results show a plausible tendency, however the magnitude is
rather underestimated. A reason is the use of data from experiments with a
different material and unequal parameters in this argumentation. The enhanced
modelling is nonetheless a major improvement in face of the uncoupled
Lagrangian simulation, where the decrease in DE was predicted to be 0 %.
However, in a work by the particle velocities were still
considerably overestimated in a validation against experimental data despite
a two-way coupling. It was reasoned mainly that this was due to the limits of
the k-ε-turbulence model, although the realizable formulation
was used that has improved performance for the jet spreading rate. However,
particularly the dispersion of the particles was not captured sufficiently.
Additionally, showed that the deposition strongly depends on
the particle injection process. These aspects represent another direct link
between the geometry and the deposition efficiency. Taking the findings of
the present study into account, the validity of more elaborately coupled
modelling is therefore not only a question of design, gas operating
conditions and particle feed rate, but also of local conditions, such as
turbulence and particle distribution. This makes further development of more
advanced methods and their validation necessary. It could be suggested to
make use of a Reynolds-stress model (RSM) that was successfully applied in CS
applications in good agreement with experimental observations
.
Conclusions
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 k-ε-turbulence model and a
one-way coupled discrete phase model. The computed results showed very
similar velocity profiles for both phases in all nozzles. The variations in
nozzle performance were therefore not numerically reproducible.
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.
Acknowledgements
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
References
Champagne, V.: The cold spray materials deposition process, Woodhead
Publishing Limited, Cambridge CB21 6AH, England, 2007.
Champagne, V. K., Helfritch, D. J., Dinavahi, S. P. G., and Leyman, P. F.:
Theoretical and Experimental Particle Velocity in Cold Spray, J. Therm. Spray
Techn., 20, 425–431, 2010.
Easter, G.: Thermal Spraying – Plasma, Arc and Flame Spray Technology,
Wexford College Press, Palm Springs, CA, 2008.
FLUENT: FLUENT Manual, FLUENT Inc., Lebanon, NH, 2012.
Fu, Y., Wang, T., and Gu, C.: Experimental and numerical analyses of
gas-solid-multiphase jet in cross-flow, Proceedings of the Institution of
Mechanical Engineers, Part G: Journal of Aerospace Engineering, 227, 61–79,
2012.
Han, T., Gillispie, B. A., and Zhao, Z. B.: An Investigation on Powder
Injection in the High-Pressure Cold Spray Process, J. Therm. Spray Techn.,
18, 320–330, 2009.
Kuroda, S., Watanabe, M., Kim, K., and Katanoda, H.: Current status and
future prospects on warm spray technology, J. Therm. Spray Techn., 20,
653–676, 2011.
Lee, M.-W., Park, J.-J., Kim, D.-Y., Yoon, S. S., Kim, H.-Y., James, S. C.,
Chandra, S., and Coyle, T.: Numerical Studies on the Effects of Stagnation
Pressure and Temperature on Supersonic Flow Characteristics in Cold Spray
Applications, J. Therm. Spray Techn., 20, 1085–1097, 2011.
Li, C.-J. and Yang, G.-J.: Relationships between feedstock structure,
particle parameter, coating deposition, microstructure and properties for
thermally sprayed conventional and nanostructured WC Co, Int. J. Refract.
Met. H., 39, 2–17, 2013.
Li, S., Muddle, B., Jahedi, M., and Soria, J.: A Numerical Investigation of
the Cold Spray Process Using Underexpanded and Overexpanded Jets, J. Therm.
Spray Techn., 21, 108–120, 2011a.
Li, W.-Y., Yin, S., Guo, X., Liao, H., Wang, X.-F., and Coddet, C.: An
Investigation on Temperature Distribution Within the Substrate and Nozzle
Wall in Cold Spraying by Numerical and Experimental Methods, J. Therm. Spray
Techn., 21, 41–48, 2011b.
Lupoi, R.: Current design and performance of cold spray nozzles: experimental
and numerical observations on deposition efficiency and particle velocity,
Surf. Eng., 30, 316–322, 2014.
Park, J.-J., Lee, M.-W., Yoon, S. S., Kim, H.-Y., James, S. C., Heister,
S. D., Chandra, S., Yoon, W.-H., Park, D.-S., and Ryu, J.: Supersonic Nozzle
Flow Simulations for Particle Coating Applications: Effects of Shockwaves,
Nozzle Geometry, Ambient Pressure, and Substrate Location upon Flow
Characteristics, J. Therm. Spray Techn., 20, 514–522, 2010.
Partes, K. and Sepold, G.: Modulation of power density distribution in time
and space for high speed laser cladding, J. Mater. Process. Tech., 195,
27–33, 2008.
Pattison, J., Celotto, S., Khan, A., and O'Neill, W.: Standoff distance and
bow shock phenomena in the Cold Spray process, Surf. Coat. Tech., 202,
1443–1454, 2008.
Pattison, J. A.: Cold Gas Dynamic Manufacturing, Ph.D. thesis, Darwin
College, University of Cambridge, Cambridge (UK), 2006.
Pawlowski, L.: The Science and Engineering of Thermal Spray Coatings, Wiley,
New York, NY, 1995.
Samareh, B. and Dolatabadi, A.: Dense Particulate Flow in a Cold Gas Dynamic
Spray System, J. Fluid. Eng.-ASME, 130, 81702-1–81702-11, 2008.
Samareh, B., Stier, O., Lüthen, V., and Dolatabadi, A.: Assessment of CFD
Modeling via Flow Visualization in Cold Spray Process, J. Therm. Spray
Techn., 18, 934–943, 2009.
Sova, A., Doubenskaia, M., Grigoriev, S., Okunkova, A., and Smurov, I.:
Parameters of the Gas-Powder Supersonic Jet in Cold Spraying Using a Mask,
J. Therm. Spray Techn., 22, 551–556, 2013.
Sova, A., Grigoriev, S., Kochetkova, A., and Smurov, I.: Influence of powder
injection point position on efficiency of powder preheating in cold spray:
Numerical study, Surf. Coat. Tech., 242, 226–231, 2014.Suo, X., Yin, S., Planche, M.-P., Liu, T., and Liao, H.: Strong effect of
carrier gas species on particle velocity during cold spray processes, Surf.
Coat. Tech., pp. 1–4, 2014.
Tabbara, H., Gu, S., McCartney, D. G., Price, T. S., and Shipway, P. H.:
Study on Process Optimization of Cold Gas Spraying, J. Therm. Spray Techn.,
20, 608–620, 2010.
Tang, W., Liu, J., Chen, Q., Zhang, X., and Chen, Z.: The effects of two gas
flow streams with initial temperature and pressure differences in cold
spraying nozzle, Surf. Coat. Tech., 240, 86–95, 2014.
Yin, S., Wang, X.-F., Li, W.-Y., and Xu, B.-P.: Numerical Investigation on
Effects of Interactions Between Particles on Coating Formation in Cold
Spraying, J. Therm. Spray Techn., 18, 686–693, 2009.
Yin, S., Wang, X.-F., Li, W.-Y., and Li, Y.: Numerical Study on the Effect of
Substrate Size on the Supersonic Jet Flow and Temperature Distribution Within
the Substrate in Cold Spraying, J. Therm. Spray Techn., 21, 628–635, 2011.
Yin, S., Liu, Q., Liao, H., and Wang, X.: Effect of injection pressure on
particle acceleration, dispersion and deposition in cold spray, Comp. Mater.
Sci., 90, 7–15, 2014.
Zahiri, S. H., Phan, T. D., Masood, S. H., and Jahedi, M.: Development of
Holistic Three-Dimensional Models for Cold Spray Supersonic Jet, J. Therm.
Spray Techn., 2014.