R. WANG et al.: INFLUENCE OF SPRAY DISTANCE ON THE POROSITY OF Ni-BASED AMORPHOUS COATINGS ...
217–224
INFLUENCE OF SPRAY DISTANCE ON THE POROSITY OF
Ni-BASED AMORPHOUS COATINGS: NUMERICAL SIMULATION
AND EXPERIMENT
VPLIV RAZDALJE NAPR[EVANJA NA POROZNOST AMORFNE
PREVLEKE NA OSNOVI NIKLJA: NUMERI^NA SIMULACIJA IN
EKSPERIMENT
Rui Wang, Deming Wang, Nianchu Wu
*
Liaoning Petrochemical University, School of Mechanical Engineering, Fushun 113001, P.R. China
Prejem rokopisa – received: 2023-09-20; sprejem za objavo – accepted for publication: 2024-02-27
doi:10.17222/mit.2023.1002
The influence of injection distance on the porosity of Ni-based amorphous coatings (AMCs) prepared with a high-velocity air
fuel (HVAF) process is discussed based on a numerical analysis and experimental methods. A computational fluid dynamics
model was established to demonstrate the gas flow field and behavior of particles in flight at different spraying distances during
HVAF spraying. When analyzing the changes in the particle velocity and temperature, the spraying distance is less than 30 μm.
The velocity and temperature changes of small particles have a significant impact, and the optimal spray distance (350 mm) for
obtaining a low porosity coating is predicted. The calculation was validated experimentally by producing a Ni-based AMC with
a low porosity (1.87 %) that was manufactured using the predicted HVAF optimal spraying distance.
Keywords: Ni-based amorphous coating, porosity, HVAF, computational simulation, spray distance
V ~lanku je opisan vpliv razdalje napr{evanja na poroznost amorfnih prevlek na osnovi niklja (Ni) izdelanih s postopkom zelo
hitrega napr{evanja v me{anici kurilnega plina (propana) in zraka (HVAF; angl.: high-velocity air fuel). Raziskavo so izvedli s
pomo~jo eksperimentalnih in numeri~nih metod. Razvili so model temelje~ na ra~unalni{ki dinamiki fluidov (teko~in) zato, da
so lahko predstavili polje pretakanja plinov in obna{anje delcev med njihovim letom proti podlagi pri razli~no izbranih razdaljah
napr{evanja s postopkom HVAF. Z simulacijami in analizami sprememb hitrosti ter temperature delcev so ugotovili, da je
najmanj{a mo`na razdalja napr{evanja 30 μm. Spremembe hitrosti in temperature majhnih delcev delcev mo~no vplivajo na
debelino prevleke. Ugotovili so, da je optimalna razdalja napr{evanja 350 mm za izdelavo prevlek z majhno poroznostjo (1,87
%). Izra~une so ovrednotili in potrdili z eksperimentalnimi preizkusi izdelave prevlek z majhno poroznostjo, ki so jih izdelali z
izbranim HVAF postopkom pri izra~unani optimalni razdalji napr{evanja.
Klju~ne besede: amorfna prevleka na osnovi Ni, postopek napr{evanja v me{anici propana in zraka (HVAF), ra~unalni{ka
simulacija, razdalja napr{evanja
1 INTRODUCTION
Because of their high glass-transition temperature
and excellent corrosion resistance, Ni-based amorphous
alloys show ultra-high strength and high thermal stabil-
ity.
1
Generally, Ni-based amorphous alloys are made into
thin strips, powders and wires with small diameters.
Therefore, the glass-forming ability limits the use of
amorphous alloys as structural materials. However,
amorphous coatings based on Ni-based metallic glass
systems prepared on a substrate with different methods
can overcome this drawback.
Nowadays, there are several methods used for pro-
ducing amorphous coatings, such as the laser cladding
and thermal spray-based techniques. It is reported that
Ni-based amorphous alloy coatings were successfully
applied onto metal parts, and these coatings have the best
corrosion resistance compared with the properties of
crystalline substrates.
2,3
In laser cladding, coatings are
typically complex structures composed of amorphous,
nanocrystalline and metal compound phases. Amorphous
powder is completely melted by laser cladding, and then
cooled down and solidified to form a coating. However,
the amorphous content in a coating is extremely rare, and
the thermal stress and residual stress in the coating can
easily lead to cracking during rapid cooling.
4,5
In addi-
tion, some amorphous metal coatings were prepared
within a Ni-based alloy system, mainly through plasma
spraying and high-velocity oxygen fuel (HVOF) spray-
ing.
6,7
HVAF and HVOF are similar spraying processes,
but the difference is that in the former air is used instead
of oxygen. Considering that high-speed particles can
produce dense coatings,
8
HVAF is a good candidate for
preparing Ni-based amorphous alloy coatings. However,
fully amorphous Ni-based coatings have been difficult to
achieve with HVAF so far.
Porosity is one of the most important parameters for
determining the quality of thermal sprayed coatings, be-
cause it can significantly affect mechanical and chemical
magnetism and thermal conductivity, and has a signifi-
Materiali in tehnologije / Materials and technology 58 (2024) 2, 217–224 217
UDK 669.24:669.058.67 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 58(2)217(2024)
*Corresponding author's e-mail:
wunianchu@163.com (Nianchu Wu)

cant impact on the conductivity of a coating material.
9–11
The velocity and temperature of particles colliding with
the substrate affect the structure of the deposit, which
strongly affects the porosity of an HVOF sprayed coat-
ing.
12,13
Many numerical and experimental studies show
that the spraying distance is also related to the particle
velocity and temperature.
14,15
Therefore, spraying dis-
tance is an important parameter that affects the final
porosity of HVOF thermal sprayed coatings.
16
We can
optimize the spraying distance through repeated experi-
ments. Although this method is expensive, it is reliable.
The effect of spraying distance on the porosity of an
HVOF thermal sprayed WC-12 % Co coating was stud-
ied using a numerical computational fluid dynamics
(CFD) simulation.
15
The speed and temperature of small
particles depend on the spraying distance. However,
there are few experiments about the effect of the spray-
ing distance on the porosity of HVAF sprayed Ni-based
AMCs. Therefore, it is very important to study the rela-
tionship between the spraying distance and coating po-
rosity during HVAF spraying of Ni-based AMCs by
combining the CFD simulation and experiments.
In our study, an Ni
53
Nb
20
Ti
10
Zr
8
Co
6
Cu
3
(at.%) amor-
phous alloy is used as the thermal spraying material be-
cause this alloy exhibits an excellent glass-forming abil-
ity.
17
Through a CFD simulation, the effect of injection
distance on the characteristics of Ni-based amorphous
particles during injection was studied. Using the best
spraying distance predicted by the simulation, Ni-based
AMCs with low porosity were prepared with HVAF ther-
mal spraying.
2 MATHEMATICAL MODELING
2.1 HVAF thermal spray gun model and the boundary
Figure 1 shows the detailed grid of the AK06 spray
gun. The numerical methods and mathematical models
are applied to a propane-fueled 2-D geometry. There are
82331 units and 83235 nodes in the whole domain. The
grids around the free jet area, the air-fuel inlet and the
nozzle have been successively refined to accurately cap-
ture the characteristics of the flame flow. Table 1 shows
the spray parameters for HVAF sprayed Ni-based AMCs.
The distance between the base plate and the nozzle outlet
is (300, 350 and 400) mm, respectively. We use a carrier
gas to introduce powder particles downstream of the noz-
zle.
18
The variation range of the particles injected into
the nozzle is 15–55 μm. The other parameters are set, as-
suming that the inlet temperatures of both the pro-
pane-air inlet and the particle inlet are 300 K, and that
the wall of the spray gun is at a constant temperature of
300 K. The pressure far field and pressure outlet bound-
aries should be applied to the external area. Finally, the
atmospheric pressure is set to 1.01 KPa.
Table 1: HVAF spray parameters for Ni-based AMCs
air pres-
sure
(Psi)
propane
pressure
(Psi)
nitrogen
pressure
(Psi)
chamber
pressure
(Psi)
feed rate
(g/min)
traverse
velocity
(mm/s)
spray
distance
(mm)
90.4 94.8 76.0 74.3 30 500 300
90.4 94.8 76.0 74.3 30 500 350
90.4 94.8 76.0 74.3 30 500 400
2.2 Gas flow model
The "realizable k- model" is widely used in the
HVAF simulation. The governing equations for the 2-D
model in a Cartesian tensor are defined below:
19
Mass conservation equation:
∂
∂
∂
∂
  tx
u
i
i
+= ()0 (1)
Momentum conservation:
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
t
u
x
uu
p
xx x
u
i
j
ij
ij
ij
j
() ()
() (


+=
=+ +−
eff
 ij
u
,,
)
 (2)
Energy transport equation:
[]
∂
∂
∂
∂
∂
∂
∂
∂
t
E
x
uEp
x
k
T
x
u
i
i
jj
ii j
() )
)
 

++ =
=+
⎛ ⎝ ⎜ ⎜ eff eff
⎞ ⎠ ⎟ ⎟ + S
h
(3)
   
ij
j
i
i
j
i
i
ij
u
x
u
x
u
x
)
eff eff eff
=+
⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ −
∂
∂
∂
∂
∂
∂
2
3
(4)
R. WANG et al.: INFLUENCE OF SPRAY DISTANCE ON THE POROSITY OF Ni-BASED AMORPHOUS COATINGS ...
218 Materiali in tehnologije / Materials and technology 58 (2024) 2, 217–224
Figure 1: Computational grid and boundary conditions used in the HVAF model: a) internal domain, including the combustion chamber and the
convergent-divergent nozzle, b) external domain

where the effective thermal conductivity is:
kk
c
t
eff
pt
=+
  (5)
2.3 Combustion model
There are complex chemical reactions between hy-
drocarbons and air in an HVAF chamber. They include a
large number of basic reactions, and the atoms have
strong thermal vibrations. The combustion products may
decompose due to a high temperature and high pres-
sure.
20
Therefore, it is necessary to simplify the complex
combustion chamber reaction. In this study, a stoichio-
metric calculation of each product was completed using
the chemical balance code developed by Gordon and
McBride. The chemical reactions in our model are as fol-
lows:
C
3
H
8
+4.762O
2
+0.014N
2
 0.47CO+2.553CO
2
+
+0.009H+0.129H
2
+3.843H
2
O+0.027NO+0.002O+
0.037OH+0.026O
2
(6)
The eddy dissipation model is applied to the reaction.
This approach is based on the solution of the transport
equations for species mass fractions. It is assumed that
the turbulence controls the reaction rate rather than the
calculation of the Arrhenius chemical kinetics. The net
rate of production for species i due to reaction r is given
by the smaller of the two equations below:
RM A
k
Y
M
iii ,,,
min
rrw
R
R, r w,R
=
⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ 
  (7)
RM A B
k
Y
M
iii
j
j
N
,,,
,
min
rrw
P
P
rw , R
=
⎛ ⎝ ⎜ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ⎟ ∑
∑

  (8)
2.4 Particle models
Using the Navier-Stokes equation, the gas is consid-
ered as the continuous phase, and the dispersed particle
phase is solved by tracking a large number of liquid
droplets. In addition to calculating the heat and mass
transfer to the gas phase, the trajectories of these discrete
phase entities are also calculated.
When Cartesian coordinates are used, the motion
equation of the particles in the x direction can be written
as the force balance, and the inertia of liquid droplets is
equal to the force acting on the particles. The basic equa-
tion of particles is as follows:
18
d
d
p
pp
2
D
p
u
t d
C
uu F
x
=− +
1
24
  Re
()
The following formula is the energy equation for a
single particle, ignoring the radiation heat transfer:
21
mC
T
t
hA T T
pp
p
pgp
d
d
=− ()
where the material characteristic parameters of the
Ni-based amorphous powders used in this study are as
follows: p
= 8200 kg/m
3
and c
p
= 400 J/(kg·K).
3 EXPERIMENTAL PROCEDURE
The material used in this work is an
Ni
53
Nb
20
Ti
10
Zr
8
Co
6
Cu
3
(at. %) alloy. It is prepared by
melting an appropriate amount of high-purity elements
in a water-cooled copper crucible in an argon atmosphere
with titanium absorption by an electric arc. Amorphous
ribbons were fabricated using a Bühler melt spinner
(Hechingen, Germany) and the copper wheel was rotat-
ing at a speed of 40 m/s. After heating to about 1473 K
with a tightly coupled annular nozzle, the amorphous
powder is prepared by the atomization of high-purity ar-
gon under a dynamic pressure of 7 MPa, with a size of
15–55 μm. Atomized powders are screened based on a
traditional sieve analysis and divided into different parti-
cle size ranges. We select (100 × 40 × 5) mm 304 type
stainless steel plate as the base. The
Ni
53
Nb
20
Ti
10
Zr
8
Co
6
Cu
3
AMC is prepared using the AK07
HVAF thermal spraying system by Kermetico. Table 1
shows detailed spraying parameters of the HVAF pro-
cess.
The microstructures of the powder and coating can be
detected with scanning electron microscopy (Quanta
600). The band and coating are analyzed with X-ray dif-
fraction (XRD) with a monochromatic Cu-K
 radiation
(k = 0.1542 nm) on a Rigaku D/max 2400 diffractometer
(Tokyo, Japan). Due to its simplicity, accessibility and
ability to measure porosity, the image analysis technol-
ogy has become a popular method to determine the po-
rosity of thermal sprayed coatings.
22,23
There is a high
contrast between dark holes and coating material with
high reflectivity so that porosity can be clearly detected
in SEM micrographs by analyzing the images. They are
analyzed using Image Pro Plus 6.0 software to evaluate
the porosity. To ensure data accuracy, 20 random and
non-overlapping SEM image fields are taken for each
sample. All images are taken under the same parameters
(such as acceleration voltage, working distance, resolu-
tion and magnification).
4 RESULTS AND DISCUSSION
4.1 Gas dynamics for different spray distances
Figures 2 and 3 show the relationship between differ-
ent injection distances (300, 350, 400) mm and the pre-
dicted pressure, gas temperature and gas velocity of the
flame along the centerline. When air and propane are
transported to the combustion chamber, a chemical reac-
tion occurs between the two substances, which converts
them into high-temperature and high-pressure gases. The
generation of a supersonic flame flow is inseparable
from the flow of the high-pressure gas through a re-
stricted nozzle. The gas pressure in the combustion
R. WANG et al.: INFLUENCE OF SPRAY DISTANCE ON THE POROSITY OF Ni-BASED AMORPHOUS COATINGS ...
Materiali in tehnologije / Materials and technology 58 (2024) 2, 217–224 219

chamber is about 7 KPa, and the pressure in the barrel is
less than 1.0 KPa; the pressure fluctuation near the gun
outlet is shown in Figures 2a, 2d and 2g and Figures 3a,
3d and 3g. The fluctuation of the flame pressure at the
nozzle outlet is caused by a periodic over-expansion of
the air flow and subsequent re-concentration above and
below the atmospheric pressure.
24
In general, (Figures 2b, 2e and 2h and Figures 3b,
3e and 3h) the gas temperature in the combustion nozzle
and chamber rises sharply and reaches a peak near the
nozzle outlet. Notably, the higher centerline temperature
is about 2000 K. On the outside of the spray gun, the ef-
fect of the spray distance on the temperature is zero. Fig-
ures 2c, 2f and 2i and Figures 3c, 3f and 3i show the
R. WANG et al.: INFLUENCE OF SPRAY DISTANCE ON THE POROSITY OF Ni-BASED AMORPHOUS COATINGS ...
220 Materiali in tehnologije / Materials and technology 58 (2024) 2, 217–224
Figure 2: a), d), g) Contours of gas pressure, b), e), h) gas temperature and c), f), i) gas velocity magnitude for different spray distances (300,
350, 400) mm
Figure 3: Calculated contours of the flame and gas characteristics along the centerline: a), d), g) gas pressure (Pa), b), e), h) gas temperature (K),
c), f), i) gas velocity magnitude (m/s) at different spray distances (300, 350, 400) mm

centerline axial gas velocities plotted against the axial
distance. The speed variation trend in the C-D nozzle
and cylinder is gradually increasing. At the nozzle outlet,
due to the spiral of the expansion compression wave out-
side the nozzle, the expansion compression wave veloc-
ity presents a sharp increase trend, and then it decreases.
After five diamond impacts, the ambient air slows down
as it reaches the centerline.
4.2 Effect of the spray distance on the particle velocity
and temperature
Figures 4a, 4c and 4e show the function of particle
velocity as a function of distance along the centerline
when the spray distance varies (300, 350, 400) mm. Ac-
cording to the experimental data, the particle size has a
significant impact on the acceleration and deceleration
behavior of particles. Small-sized particles (15 μm) can
reach a very high speed (nearly 700 m/s) during flight.
However, as their momentum inertia is small, the speed
of small particles is much lower than that of large parti-
cles. The acceleration of larger particles is slower, and
they can reach their maximum speed when they hit the
substrate. The axial velocity of particles as a function of
the particle size is shown in Figure 4g. As shown in the
figure, the smaller the particle size, the faster is its speed.
Figures 4b, 4d and 4f show the predicted tempera-
ture of the particles with nine different diameters at the
jet’s centerline for different spray distances (300, 350,
400) mm. Small-sized particles (15 μm) take a short time
to heat to the melting point, and they can completely
melt during flight. However, after a long flight, they may
eventually be in a liquid-solid coexistence state, or even
completely in a solid state. For small particles, it is ex-
tremely easy to change their temperature due to their
small thermal inertia. For large-sized particles e.g. (45,
50, 55) μm, the acceleration and heating time are longer,
and their temperature distribution becomes almost aver-
age.
Figures 4g and 4h show the axial particle velocity
and temperature at spray distances of (300, 350 and 400)
mm for the particle size of 15–55 μm. It can be seen that
the axial particle velocity and temperature at impact in-
crease with the spray distance for the particle size of
15–55 μm. Due to a short spray distance, particles of sev-
eral microns can be completely melted. The spray dis-
tance is short, and even particles of a few microns can
melt completely. However, as the spray distance in-
creases, they do not melt completely, but they partially
melt, or even remain solid when impinging on the sub-
strate, as they solidify due to the effect of temperature
decay on the free jet. Typically, the change in the spray
distance affects small particles (less than 30 μm), and the
impact on large particles is greater than that on small
particles. This is because with a rapid increase in the
spray distance, the velocity and temperature of small par-
ticles impacting the substrate significantly decrease.
However, the velocity and temperature of large particles
decrease slowly as the spray distance increases.
The two most important factors that determine the
porosity of HVAF coatings are the particle velocity and
temperature.
25,26
The change in the particle velocity is
usually related to the improvement of splash deforma-
tion, but has little effect on porosity. The melting behav-
ior of particles depends on the particle temperature,
which is the key for a low porosity and dense coating.
27,28
When the temperature of the powder is between the soli-
dus temperature and liquidus temperature (T
m
and T
L
)of
the Ni-based amorphous material, the best thermal spray-
ing effect is obtained. At the spray distance of 350 mm,
particles mostly melt during flight because their temper-
ature is between T
m
= 1302 K and T
L
= 1338 K, as shown
in Figure 4h. Thus, the computational results of this
work show that the optimal spray distance is 350 mm for
the Ni-based AMCs.
29
R. WANG et al.: INFLUENCE OF SPRAY DISTANCE ON THE POROSITY OF Ni-BASED AMORPHOUS COATINGS ...
Materiali in tehnologije / Materials and technology 58 (2024) 2, 217–224 221
Figure 4: Effect of spray distance (300, 350, 400) mm on: a), c), e)
particle velocity and b), d), f) particle temperature for a particle size of
15–55 μm, g) predicted particle axial velocity and h) temperature at
spray distances of (300, 350, 400) mm for the particle size of
15–55 μm

4.3 Experimental validation
The Ni-based AMCs were prepared using the powder
with three spray distances (350, 400, 450) mm to verify
the simulation results. Figure 5 shows a SEM image of
the Ni
53
Nb
20
Ti
10
Zr
8
Co
6
Cu
3
feedstock powder. In an argon
environment, most particles produced with gas atomiza-
tion are spherical or near-spherical. Although some parti-
cles are attached to small satellites, most particles have a
smooth surface and good fluidity. Figure 6 shows the
XRD patterns of the deposited coating of atomized pow-
der, Ni
53
Nb
20
Ti
10
Zr
8
Co
6
Cu
3
melt-spun ribbon and spray
powder of various particle sizes. The diffusion mode and
an absence of any peak related to the crystalline phase
indicate that they are completely amorphous.
Figure 7 shows the cross-sectional structures and
surface morphologies of different Ni-based AMCs. In
Figure 7c, the surface morphology shows that at the
spraying distance of 400 mm the coating is not com-
pletely melted during the spraying process. In Figure 7a,
the surface morphology of the coating applied at the
spraying distance of 300 mm shows that the coating is
completely melted. Therefore, at the spraying distance of
350 mm, an almost completely dense coating is obtained
(Figure 7d), with a porosity as low as 1.87 %. As the
spraying distance increases, the porosity of the coating
increases to 3.50 % with the spraying distance of 300
mm (Figure 7e) and it is as high as 4.96 % when the
spraying distance is 400 mm (Figure 7f). These results
imply that the porosity of an HVAF coating is largely de-
pendent on the spraying distance and that the densest
coating can be obtained using the spraying distance of
350 mm.
5 CONCLUSIONS
The effect of the spraying distance on the porosity of
Ni-based AMCs during HVAF thermal spraying was
studied by means of a predictive simulation, and was
R. WANG et al.: INFLUENCE OF SPRAY DISTANCE ON THE POROSITY OF Ni-BASED AMORPHOUS COATINGS ...
222 Materiali in tehnologije / Materials and technology 58 (2024) 2, 217–224
Figure 5: SEM image of Ni
53
Nb
20
Ti
10
Zr
8
Co
6
Cu
3
alloy powder
Figure 6: XRD patterns for different Ni
53
Nb
20
Ti
10
Zr
8
Co
6
Cu
3
dis-
tances (300, 350, 400 mm)
Figure 7: a), c), e) SEM micrographs of the as-sprayed surfaces and b), d), f) cross-sections show the general characteristics of the three HVAF
coatings made from different spray distances (300, 350, 400) mm

verified with experiments. The flight behavior of
Ni-based amorphous alloy powder particles during
HVAF spraying was studied using computational fluid
dynamics (CFD). According to the prediction results, the
static pressure of combustion products in the combustion
chamber can reach 7 KPa, and the flame temperature can
reach 2000 K. The particle size strongly affects the tem-
perature and velocity of the particles. Spraying distance
significantly affects the particles with a size of less than
30 μm, changing their velocity and temperature. When
the temperature of the powder is kept between the soli-
dus and liquidus temperatures of the Ni-based amor-
phous alloy, the optimal thermal spraying distance is 350
mm. Using this optimized spraying distance, we ob-
tained a low-porosity Ni-based AMC.
Notation
A
p
surface area of the particle
C
D
drag coefficient
c
p
specific heat of the particle
d
p
particle diameter
E enthalpy
F
x
additional acceleration
h heat transfer coefficient
k thermal conductivity
k
eff
effective thermal conductivity
m
p
mass of the particle
Re Reynolds number
S
h
chemical reaction source energy
T temperature
T
g
gas temperature
T
p
particle temperature
u velocity
u
i
velocity in the i-direction
u
p
particle velocity
x
i
coordinate in the i-direction
A constant in eddy dissipation model = 4.0
B constant in eddy dissipation model = 0.5
k kinetic energy, m
2
/s
2
M
w,i
molecular weight of species i
M
 ,R
molecular weight of reactant R
M
 ,j
molecular weight of reactant j
N number of chemical species in the system
p pressure, Pa
R
i,r
net rate of production of species i due to reaction r
v
i,r
stoichiometric coefficient for reactant i in reaction r
Y
P
mass fraction of product P
Y
R
mass fraction of a particular reactant, R
Greek letters
 Kronecker symbol
μ viscosity
μ
t
turbulent viscosity
 density
 deviatoric stress tensor
Subscripts
g gas
i,j coordinate indices
p particle
 turbulence dissipation rate, m
2
/s
3
Acknowledgements
This work was supported by the Educational Com-
mission of the Liaoning Province of China under Grant
No. L2020021, Natural Science Foundation of the
Liaoning Province under Grant No. 2022-MS-364 and
Fushun Revitalization Talents Program under Grant No.
FSYC202107011.
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