N. WU et al.: NUMERICAL INVESTIGATION OF HVAF-SPRAYED FE-BASED AMORPHOUS COATINGS
677–688
NUMERICAL INVESTIGATION OF HVAF-SPRAYED Fe-BASED
AMORPHOUS COATINGS
NUMERI^NE RAZISKAVE S POSTOPKOM HVAF NAPR[ENIH
AMORFNIH PREVLEK NA OSNOVI @ELEZA
Nianchu Wu
*
, Tingting Li, Jingbao Lian
Liaoning Petrochemical University, School of Mechanical Engineering, Fushun, China
Prejem rokopisa – received: 2022-09-29; sprejem za objavo – accepted for publication: 2022-10-25
doi:10.17222/mit.2022.636
A numerical analysis was performed to predict the effect of the convergent section geometry of a gun nozzle on the high-veloc-
ity air-fuel (HVAF) thermal spray Fe-based amorphous coating (AC) process. A computational fluid dynamics model was ap-
plied to investigate the gas-flow field and the behavior of in-flight particles at nozzle entrance convergent section length ranging
from 28 mm to 56.8 mm and different shapes of the Laval nozzle convergent section (a straight line and Vitosinski convergence
curve). On the one hand, the change in the gas-flame flow characteristics for the Vitosinski curve shows a uniform and stable
flame compared with the straight-line curve in the convergent section. The straight-line curve shape of the Laval nozzle conver-
gent section has a higher particle temperature compared with the Vitosinski-curve shape of the Laval nozzle convergent section.
The particle dwell time for the straight-line curve shape of the Laval nozzle convergent section is longer than that for the
Vitosinski curve shape of the Laval nozzle convergent section. On the other hand, the nozzle entrance convergent section length
obviously affects the particle temperature, and the particle dwell time increases with the increasing nozzle entrance convergent
section length. By analyzing both the melt status of the particles and particle velocity, the optimal gun configuration (0.7 V) pro-
ducing low-porosity coatings was predicted. These calculations were experimentally verified by producing a low-porosity
(1.37 %) Fe-based AC, fabricated with HVAF using the predicted optimal gun configuration.
Keywords: Fe-based amorphous coatings, high-velocity air fuel, computational simulation, nozzle
Numeri~na analiza je bila uporabljena za napoved u~inka konvergentnega profila {obe na pu{ki, uporabljeni pri postopku zelo
hitrega termi~nega napr{evanja amorfnih prevlek na osnovi `eleza s plinsko me{anico propan (C3H8)-zrak (HVAF; angl.:
High-Velocity Air Fuel). Za raziskavo je bil uporabljen ra~unalni{ki model na osnovi dinamike fluidov in obna{anje znotraj
plinske me{anice lete~ih delcev na vhodu {obe s konvergentnim profilom dol`ine od 28 mm do 56,8 mm in razli~no obliko
konvergentnega dela Lavalove {obe (ravna linija in konvergen~na ukrivljenost po Vitosinskem). Sprememba pretoka plinske
me{anice oziroma lastnosti plamena pri uporabi Vitosinskijeve krivulje je pokazala enovit in stabilen plamen v primerjavi z
uporabo ravne linije v konvergentnem delu {obe. Pri izbiri ravne linije oblike konvergentnega profila Lavalove {obe so dosegli
vi{je temperature delcev v primerjavi z Lavalovo {obo, ki je imela Vitosinskijev profil ukrivljenosti. ^as zadr`evanja delcev v
primeru ravne linije konvergentnega profila Lavalove {obe je bil dalj{i kot pri Lavalovi {obi z ukrivljenostjo po Vitosinskem. Po
drugi strani pa so ugotovili, da vstopna dol`ina konvergentnega dela {obe o~itno vpliva na temperaturo delcev in ~as zadr`evanja
delcev, ki je nara{~al s pove~evanjem dol`ine konvergentnega profila. Z analiziranjem stanja raztaljenih delcev in njihove
hitrosti so lahko pri optimalni konfiguraciji {obe pu{ke za napr{evanje (0,7 V) napovedali izdelavo prevleke z majhno
poroznostjo. Te izra~une so tudi eksperimentalno potrdili z izdelavo nizko porozne amorfne prevleke (1,37 %) na osnovi `eleza
pri ra~unalni{ko napovedani optimalni konfiguraciji {obe za HVAF.
Klju~ne besede: amorfne prevleke na osnovi `eleza, postopek HVAF, ra~unalni{ka simulacija, {oba
1 INTRODUCTION
Fe-based amorphous coatings (ACs) are promising
for applications in the military and nuclear industry, oil
and gas industry and manufacturing due to their excel-
lent corrosion resistance, wear resistance and neu-
tron-absorption ability.
1
The high-velocity air-fuel
(HVAF) thermal spray technique is frequently used to
fabricate Fe-based ACs.
2–4
During a HVAF spray pro-
cess, porosity defects in the coating are inevitable, sig-
nificantly influencing the corrosion behavior.
5
In the
HVAF spray process, both the particle temperature and
particle velocity attained in flight are the determining
factors for porosity defects. The particle heating and ac-
celeration can be efficiently controlled by changing the
Laval-nozzle geometry. Therefore, the Laval nozzle is an
important part of a HVAF thermal spray gun, affecting
the quality of the coating.
Nowadays, the nozzle gun used for the HVAF ther-
mal spray process is a Laval nozzle, which consists of a
convergent section and a divergent section. The influence
of the nozzle geometry on the thermal spray process was
studied experimentally. The change in the entrance con-
vergent section length of the gun nozzle had a significant
effect on the deposition efficiency, microstructure, and
hardness of the HVOF-sprayed Al
2
O
3
–40 w/% TiO
2
coat-
ings.
6
The effect of nozzle configuration on the perfor-
mance of WC-based coatings was also studied experi-
mentally. Matikainen et al.
7
studied the effect of nozzle
configuration on the tribological properties of
HVAF-sprayed WC-CoCr coatings. Their results showed
Materiali in tehnologije / Materials and technology 56 (2022) 6, 677–688 677
UDK 621.924.9.024 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 56(6)677(2022)
*Corresponding author's e-mail:
wunianchu@163.com (Nianchu Wu)

that the particle melting and average particle velocity can
be efficiently controlled by changing the nozzle geome-
try from cylindrical to convergent–divergent, resulting in
an improvement in the density and microstructure of a
coating. Lyphout et al.
8
studied mechanical and wear
properties of WC-CoCr coatings for different nozzles
varying in length. Their results showed that increasing
the length of a nozzle leads to an improvement in the
microhardness and abrasion wear resistance of a coating.
In another study by Kumar et al.,
9
it was shown that the
AK06 HVAF gun with different nozzle configurations
can also change average particle velocities. The effect of
nozzle configuration on the deposition, microstructural
features, hardness and sliding wear behavior of HVAF-
sprayed WC-CoCr coatings was evaluated. Fine and
coarse feedstock powders were found to be sensitive to
the type of nozzle used, while no major difference was
observed in the coatings from powders with a medium
size sprayed with different nozzles.
10
Among all of the
above studies, none studies the influence of the nozzle
configuration effect on the quality of Fe-based ACs.
The nozzle geometry, which influences the combus-
tion gas dynamics, is one of the most important parame-
ters in a thermal spray process. To date, the influence of
the nozzle configuration on a thermal spray process has
been investigated by computational fluid dynamics simu-
lations. Numerical simulation has investigated the effect
of increasing the throat diameter and the nozzle entrance
converging section on the HVOF-sprayed Al
2
O
3
–40 w/%
TiO
2
coatings. When increasing the entrance convergent
section length of a nozzle, the particle temperature in-
creases, but the particle velocity slightly decreases.
6
As
the diameter of the nozzle throat is increased, the loca-
tion of the Mach shock disc moves backward from the
nozzle exit into the HVOF system.
11,12
Recently, for the
WC-12Co coatings deposited by a HVAF spray process,
it has been further found that a reduction in the Laval
nozzle throat diameter increases the particle velocity and
does not obviously affect the particle temperature. A re-
duced Laval nozzle divergent angle causes an increase in
the particle temperature and velocity. The longer the
length of the Laval nozzle divergent part, the higher is
the temperature of the particles.
13
However, only few
studies have focused on the convergent-section geometry
(the length and curve shape) of the gun nozzle design for
HVAF-sprayed Fe-based ACs to improve their density
and properties. The shape of the convergent curve affects
the uniformity of the nozzle outlet airflow and a good
convergent part can improve the stability and uniformity,
reducing the turbulence of the flow field. Therefore, it is
necessary to design the shape and size of the convergent
section geometry of the gun nozzle for a HVAF spray
process in order to gain high-density Fe-based ACs.
In this research, the effect of the convergent section
geometry of a gun nozzle on the characteristics of the
flame flow and in-flight Fe-based amorphous particles
during HVAF spraying was studied using CFD simula-
tions. The convergent section geometry of a gun nozzle
includes the nozzle entrance convergent section length
and shape of the Laval nozzle convergent section (a
straight line and Vitosinski convergence curve). Using
the optimal gun configuration, predicted via this simula-
tion, a Fe-based AC with a low porosity was fabricated
during a HVAF thermal spray process.
2 MATHEMATICAL MODELING
2.1 Boundary conditions and grid meshing
Figure 1 shows the detailed mesh of an AK07 spray
gun. Numerical methods and mathematical models were
applied to the propane-fueled 2-D geometry. There are
85 680 cells and 86 664 nodes in the whole domain. The
sensitive area grid, including the free jet region, air-fuel
inlet, and the grids around the nozzle, has been succes-
sively refined to accurately capture the characteristics of
the flame flow. The Laval nozzle geometric parameters
can be varied in the following two aspects:
1) the length of the Laval nozzle convergent section,
2) the curve shape of the Laval nozzle convergent
section.
Table 1 shows the spray parameters for HVAF-
sprayed Fe-based ACs. Table 2 lists six different lengths
N. WU et al.: NUMERICAL INVESTIGATION OF HVAF-SPRAYED FE-BASED AMORPHOUS COATINGS
678 Materiali in tehnologije / Materials and technology 56 (2022) 6, 677–688
Figure 1: a) Schematic diagram of the AK07 spray gun with computa-
tional grid and boundary conditions used in the HVAF model: b) inter-
nal domain, including the combustion chamber and the convergent-di-
vergent nozzle, c) external domain

of the Laval nozzle convergent section and two kinds of
shape of the Laval nozzle convergent section (a straight
line and Vitosinski convergence curve), which are di-
vided into eight cases for calculation and discussion. Par-
ticles in a size-range of 10–50 μm are injected into the
nozzle. The physical properties of the Fe-based amor-
phous powder can be given as follows:  = 7701 kg/m
3
and C = 680.5 J/(kg·K). The walls of the spray gun are
all assumed to be at a constant temperature of 300 K.
The pressure far field and pressure outlet boundary are
applied at the external domain. Finally, the atmospheric
pressure is assumed to be 1010 Pa.
Table 2: Different lengths (L) of the Laval nozzle convergent part and
shape of the Laval nozzle convergent part for HVAF thermal spray
Fe-based ACs
Case
Variable
Length
(mm)
Shape
0.4-S
28
Straight line
0.4-V Vitosinski convergence curve
0.6-S
42.6
Straight line
0.6-V Vitosinski convergence curve
0.7-S
49.7
Straight line
0.7-V Vitosinski convergence curve
0.8-S
56.8
Straight line
0.8-V Vitosinski convergence curve
2.2 Gas-flow model
The "realizable k- model" is used extensively in the
HVAF simulation. The governing equations for the 2-D
model in the Cartesian tensor are defined below:
14
Mass conservation Equation (1):
∂
∂
∂
∂
p
tx
v
i
i
+= ()  0 (1)
Momentum conservation Equation (2):
∂
∂
∂
∂
∂π
∂
∂
∂
∂
∂
t
v
x
vv
xx x
v
i
j
ij
ij
ij
j
i
() ()
() (


+=
=+ +
eff
 v
j
)
(2)
Energy transport Equations (3) and (4):
[]
∂
∂
∂
∂
∂
∂
∂
∂
t
E
x
vHp
x
k
T
x
v
i
i
j
eff
j
ii j
() ( )
()

 ++ =
=+
⎛ ⎝ ⎜ ⎜ eff
⎞ ⎠ ⎟ ⎟ + S
h
(3)
()  
ij
j
i
i
j
i
i
ij
v
x
v
x
v
x
eff eff eff
=+
⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ −
∂
∂
∂
∂
∂
∂
2
3
(4)
Effective thermal conductivity Equation (5):
kk
c
eff
pt
t
=+
  (5)
where x
i
is the coordinate in the i direction, v is the ve-
locity, i and j are the coordinate indices, v
i
is the veloc-
ity in the i-direction, is the density, ij
is the deviatoric
stress tensor, H is the enthalpy, p is the particle, k
eff
is
the effective thermal conductivity, T is the temperature,
S
h
is the chemical reaction source energy, μ is the vis-
cosity, is the Kronecker symbol, C
p
is the specific heat
of the particle.
2.3 Combustion model
In practice, the chemical reactions between hydrocar-
bon and air in the HVAF chamber are extremely com-
plex, not only because they consist of a large number of
elementary reactions, but also because the combustion
products may decompose at high temperature and pres-
sure due to the strong thermal vibration of atoms.
15
Therefore, it is necessary to simplify the chemical reac-
tions in the combustion chamber. In this study, the chem-
ical equilibrium code developed by Gorden and McBride
is used to calculate the stoichiometry of each product.
The chemical reaction considered in our model is as fol-
lows:
C
3
H
8
+ 4.762O
2
+ 0.014N
2
 0.447CO + 2.553CO
2
+ 0.009H + 0.129H
2
+
3.843H
2
O + 0.027NO + 0.002O + 0.047OH + 0.026O
2
An eddy dissipation model is used to solve this
global reaction. This approach is based on the solution of
transport equations for species mass fractions. The reac-
tion rates are assumed to be controlled with the turbu-
lence rather than a calculation of the Arrhenius chemical
kinetics. The net rate of production for species i due to
reaction r is given by the smaller of Equations (6) and
(7) below:
RM A
k
Y
M
ir ir i
R
Rr R
,,,
,,
min =
⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ 
    (6)
RM A B
k
Y
M
ir ir i
P
P
jr j
j
N
,,,
,,
min =
⎛ ⎝ ⎜ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ⎟ ∑
∑

    (7)
N. WU et al.: NUMERICAL INVESTIGATION OF HVAF-SPRAYED FE-BASED AMORPHOUS COATINGS
Materiali in tehnologije / Materials and technology 56 (2022) 6, 677–688 679
Table 1: HVAF spray parameters for Fe-based ACs
Air pressure
(kPa)
Propane pres-
sure (kPa)
Nitrogen pres-
sure(kPa)
Chamber pres-
sure (kPa)
Feed rate
(g/min)
Traverse veloc-
ity (mm/s)
Spray distance
(mm)
Particle size
(μm)
623.286 653.622 524.001 512.280 30 500 180 20–30

2.4 Particle models
The gas is treated as a continuum phase by solving
the Navier-Stokes equations, while the dispersed particle
phase is solved by tracking a large number of droplets.
The trajectories of these discrete phase entities are com-
puted in addition to the heat and mass transfer to the gas
phase.
The equation of motion for the particles in the x di-
rection (using Cartesian coordinates) can be written as a
force balance that equates the droplet inertia with the
forces acting on the particle. The basic equations for a
particle are Equations (8) and (9).
16
d
d
p
pp
D
p
v
t d
C
vv a =− +
18
24
2
  Re
() (8)
The energy equation for a single particle, neglecting
the heat transfer via radiation, is as follows:
17
mc
T
t
kA T T
pp
p
pgp
d
d
=− () (9)
where v
p
is the particle velocity, d
p
is the particle diame-
ter, C
D
is the drag coefficient, Re is the Reynolds num-
ber, a is the acceleration, m
p
is the mass of the particle,
T
p
is the particle temperature, k is the coefficient of heat
transfer, A
p
is the surface area of the particle, T
g
is the
gas temperature. The density of a Ni-based amorphous
alloy is 8200 kg/m
3
and the specific heat is
400 J/(kg·K).
3 EXPERIMENTAL PART
The Fe-based AC composition is (Fe 54.5, Cr 18.4,
Mn 2, Mo 13.9, W 5.8, B 3.2, C 0.9 and Si 1.3) w/%. A
316 stainless steel plate with dimensions of
(100 × 50 × 5) mm was used as the substrate. The
Fe-based AC was fabricated using an AK07 HVAF ther-
mal spray system from Kermetico Company. Detailed
spraying parameters for the HVAF process are shown in
Table 1.
The microstructure of the powders and coatings were
examined with SEM (Quanta 600). An X-ray diffraction
(XRD) analysis of the powders and coatings was con-
ducted on a Rigaku D/max 2400 diffractometer (Tokyo,
Japan) with monochromated Cu·K radiation. Porosity
can be easily detected with SEM micrographs during an
image analysis due to a high degree of contrast between
the dark pores and more highly reflective coating mate-
rial. Porosity was evaluated by analyzing the SEM mi-
crographs with the Image-Pro-Plus 6.0 software.
4 RESULTS AND DISCUSSION
4.1 Gas dynamics for different Laval-nozzle conver-
gent-section designs
Simulated contours of the pressure, velocity magni-
tude and temperature in both the internal and external
fields for different gun configurations from Table 2
(0.4 S, 0.6 S, 0.7 S, 0.8 S, 0.4 V, 0.6 V, 0.7 V, 0.8 V) are
shown in Figures 2–4. In order to investigate the
gas-flow characteristics, the distributions of pressure, ve-
locity and temperature at the center line of the HVAF
thermal spray gun for different gun configurations
(0.4 S, 0.6 S, 0.7 S, 0.8 S, 0.4 V, 0.6 V, 0.7 V, 0.8 V) are
shown in Figures 5 and 6. The air and propane are in-
jected into the combustion chamber, undergoing a chem-
ical reaction. The high-pressure gas flow through the
constrained nozzle gives rise to a supersonic flame flow.
As the thermal energy generated by combustion is con-
verted into kinetic energy through the convergent–diver-
gent nozzle, the high pressure in the combustion cham-
ber decreases and the gas velocity inside the nozzle
increases continuously. The fluctuations in the flame
pressure at the barrel exit are created periodically by the
overexpanding flow, subsequently re-converging above
and below the atmospheric pressure.
18
The velocity at the
throat can reach the velocity of sound, and at the exit of
the divergent section it reaches two times the velocity of
sound. Four diamond waves appear at the nozzle exit,
which then gradually decay until they disappear. In addi-
tion, the gas temperature increases sharply within the
N. WU et al.: NUMERICAL INVESTIGATION OF HVAF-SPRAYED FE-BASED AMORPHOUS COATINGS
680 Materiali in tehnologije / Materials and technology 56 (2022) 6, 677–688
Figure 2: Calculated contours of the gas pressure for different gun
configurations

N. WU et al.: NUMERICAL INVESTIGATION OF HVAF-SPRAYED FE-BASED AMORPHOUS COATINGS
Materiali in tehnologije / Materials and technology 56 (2022) 6, 677–688 681
Figure 4: Calculated contours of the gas temperature for different gun
configurations
Figure 3: Calculated contours of the gas velocity magnitude for dif-
ferent gun configurations and insets showing the convergent section of
the nozzle gun
Figure 5: Calculated contours of the flame and gas characteristics along the centerline for the nozzle entrance convergent section length: a) and
d) gas pressure, b) and e) gas temperature, c) and f) gas velocity

combustion nozzle and reaches its peak near the exit of
the nozzle. There are four noticeable hollow circles in
the core of the free jet. The temperature curve shows
damping oscillation.
Below we discuss the effect of the increasing conver-
gent section length of the nozzle on the gas flame flow
characteristics. As shown in Figure 6, there are four sec-
tions of the HVAF thermal spray process, that is, the
chamber (A), the convergent section (B), the divergent
section (C) and the atmosphere (D). The length of the
convergent part (ranging from 28 mm to 56.8 mm) has
no effect on the initial chamber pressure, gas velocity
and temperature. And with the increasing length of the
convergent part, the location of the Mach shock disc
moves backward from the nozzle exit (see Figure 5).
There are shock waves of equal magnitude at the gun
outlet as the length of the convergent part is increasing.
Next, the effect of the shape (a straight line or Vito-
sinski curve) of the nozzle on the gas flame flow charac-
teristics is discussed. The Vitosinski-curve variation is
smoother than that of the straight line. Consequently the
change in the gas flame flow characteristics (pressure,
velocity and temperature) for the Vitosinski curve shows
a uniform and stable flame compared with the
straight-line curve (see Figures 3 and 6) in the conver-
gent section. In addition, we can see that the Vitosinski
curve falls flat at the throat after a sharp decline. For the
Vitosinski curve, the diameter gradient at the far end of
the throat is larger than that of the nozzle, while the ra-
dius change at the front part of the convergent section is
relatively flat. However, the gas velocity and temperature
increase a little for the nozzle with a straight-line curve
compared with those of the nozzle with a Vitosinski
curve. Meanwhile, the effect of the increasing nozzle en-
trance convergent section length on the gas flame flow
characteristics is also discussed. The gas pressure, veloc-
ity and temperature remain the same when the HVAF
nozzle entrance convergent section length ranges from
28 mm to 56.8 mm (see Figure 5).
4.2 Effect of the Laval nozzle convergent section de-
sign on the particle velocity and temperature
Numerical simulation results on the effect of the in-
creasing nozzle entrance convergent section length (from
28 mm to 56.8 mm) on the particle velocity and particle
temperature for the same particle sizes (10 μm and
50 μm) and two kinds of curve shape of the Laval nozzle
convergent section (a straight line and Vitosinski conver-
gence curve) are given in Figures 7 and 8, respectively.
The results show that the particle velocity for the straight
line and Vitosinski convergence curve increases slightly
with the increasing nozzle entrance convergent section
length. That is, the change in the nozzle convergent sec-
tion length has a weaker effect on the particle velocity.
However, as shown in Figure 8, the increasing nozzle
entrance convergent section length leads to a significant
increase in the axial particle temperature for particle
sizes of 10 μm and 50 μm. When the nozzle entrance
convergent section length increases from 28 mm to
56.8 mm, the increased amplitude of the particle temper-
ature is about 200 K. The reason for this is the fact that
the particles stay in the flame flow for a longer time to
gain more heat. Therefore, the particle velocity and tem-
N. WU et al.: NUMERICAL INVESTIGATION OF HVAF-SPRAYED FE-BASED AMORPHOUS COATINGS
682 Materiali in tehnologije / Materials and technology 56 (2022) 6, 677–688
Figure 6: Calculated contours of the flame and gas characteristics along the centerline of the Laval nozzle convergent straight line and Vitosinski
convergence curve: a) and b) gas pressure, c) and d) gas velocity, e) and f) gas temperature

N. WU et al.: NUMERICAL INVESTIGATION OF HVAF-SPRAYED FE-BASED AMORPHOUS COATINGS
Materiali in tehnologije / Materials and technology 56 (2022) 6, 677–688 683
Figure 7: Predicted particle axial velocity for the nozzle entrance convergent section length
Figure 8: Predicted particle axial temperature for the nozzle entrance convergent section length

perature impacting the substrate can be adjusted by
changing the nozzle entrance convergent section length.
Figure 9 illustrates the particle velocity and tempera-
ture curves for the centerline with different shapes of the
Laval nozzle convergent section (a straight line and
Vitosinski convergence curve) and the same particle
sizes (10 μm and 50 μm). In Figures 9a and 9b, the par-
ticle velocity for the Vitosinski curve shape of the Laval
nozzle convergent section is a little higher than that for
the straight-line curve shape of the Laval nozzle conver-
gent section. In contrast, compared with the Vitosinski
curve shape of the Laval nozzle convergent section, the
straight-line shape of the Laval nozzle convergent sec-
tion has a higher particle temperature (see Figures 9c
and 9d). Thus, compared with the nozzle entrance con-
vergent section length, the curve shape of the Laval noz-
zle convergent section has a weaker effect on the particle
velocity and temperature.
4.3 Particle melting behavior for different Laval nozzle
convergent section designs
In the HVAF spray process, an increase in the particle
temperature and in-flight velocity is not always benefi-
cial for the deposition of particles. And more important,
it is related to the melt status of the particles. The melt-
ing index (MI) is used to characterize the melt status of
the particles. MI is defined as the ratio of the dwell time
of particle to the time required to melt one in-flight parti-
cle, to indicate the molten state of a particle in a particle
jet. A higher MI signifies a better melt status. A low MI
reflects partial melt or unmelted conditions. A MI calcu-
lation is presented in Equation (10):
MI
k
h/ B i
TTt
d
=⋅
+
⋅
−⋅
24 1
14
2
 fg
sm fly
() Δ
(10)
where T
s
is the particle temperature, T
m
is the particle
melting point (1 404 K), k is the thermal conductivity of
liquid (40 W/(m·K
–1
), h
fg
is the latent heat
(26 7000 J/Kg), Bi is the Biot number defined as hd/k
where d is the particle diameter (30 μm), h is the heat
transfer coefficient (6 000 J/Kg),  t
fly
is the particle
dwell time and v is the particle velocity. The particle ve-
locity and particle temperature can be observed in Fig-
ures 7 and 8. Figure 10 shows the particle dwell time
( t
fly
) along the centerline for different shapes of the
Laval nozzle convergent section (a straight line and
Vitosinski convergence curve) and the nozzle entrance
convergent section length L (from 28–56.8 mm) for the
same particle sizes (10 μm and 50 μm). It can be seen
that the particle dwell time gradually increases with the
increasing nozzle entrance convergent section length.
And for the same nozzle entrance convergent section
length, the particle dwell time for the straight-line shape
of the Laval nozzle convergent section is longer than
N. WU et al.: NUMERICAL INVESTIGATION OF HVAF-SPRAYED FE-BASED AMORPHOUS COATINGS
684 Materiali in tehnologije / Materials and technology 56 (2022) 6, 677–688
Figure 9: Predicted values for different curve shapes of the Laval nozzle convergent sections and particle sizes: a) and b) particle axial velocity,
c) and d) temperature

N. WU et al.: NUMERICAL INVESTIGATION OF HVAF-SPRAYED FE-BASED AMORPHOUS COATINGS
Materiali in tehnologije / Materials and technology 56 (2022) 6, 677–688 685
Figure 11: MI along the centerline for different nozzle entrance convergent configurations and for particle sizes of 10–50 μm
Figure 10: Particle dwell time along the centerline for different nozzle entrance convergent configurations (0.4 S, 0.8 S, 0.4 V, 0.8 V) and for par-
ticle sizes of 10 μm and 50 μm

that for the Vitosinski-curve shape of the Laval nozzle
convergent section.
To sum up, the MI along the centerline with different
nozzle entrance convergent configurations (0.4 S, 0.8 S,
0.4 V, 0.8 V) for the same particle sizes (10 μm and
50 μm) can be observed in Figure 11. Particles of the
large size (50 μm) may not reach the melting point, re-
maining in the solid state during the entire flight. Parti-
cles of the small size (10 μm) may be heated to the melt-
ing point in a short time and be fully melted during the
flight, finally hitting the substrate in the solid state.
When particles of a medium size (20 μm and 30 μm)
reach the substrate, they are in a semi-molten state
(where both the liquid and solid coexist). Particles with
the size of 20 μm are the first to melt completely and be
eventually in the state of coexistence between the liquid
and solid after a long enough distance. The melt status of
the particles is the key to creating low porosity and dense
coatings.
19,20
The optimum thermal spraying occurs when
the particles reach the substrate in a semi-molten state. It
can be seen in Figure 11 that the melt status of the parti-
cles for the nozzle entrance convergent configuration of
0.7 V and 0.6 S might be mostly a semi-molten state. It
is clear that an increase in the particle velocity signifi-
cantly improves the coating density. As shown in Figure
7, the particle velocity, impacting the nozzle entrance
convergent configuration of 0.7 V is a little larger than
the particle velocity, impacting the nozzle entrance con-
vergent configuration of 0.6 S. Thus, we found that the
optimal nozzle entrance convergent configuration for the
Fe-based ACs is 0.7 V.
4.4 Experimental validation
To validate the simulations, Fe-based amorphous
coatings were fabricated using powders and two gun
configurations (0.7 V, 0.4 S). The XRD patterns of the
atomized powder and the as-deposited coatings for each
gun configuration (0.7 V, 0.4 S) are shown in Figure 12.
The diffuse pattern and the absence of any peaks associ-
ated with crystalline phases indicate that they are fully
amorphous. The structures of cross-sections and the sur-
N. WU et al.: NUMERICAL INVESTIGATION OF HVAF-SPRAYED FE-BASED AMORPHOUS COATINGS
686 Materiali in tehnologije / Materials and technology 56 (2022) 6, 677–688
Figure 13: SEM micrographs of the HVAF coatings for 0.4 S and 0.7 V gun configuration: a) and b) as-sprayed surface, c) and d) cross-section
Figure 12: XRD patterns for the atomized powder and HVAF-sprayed
ACs (0.4 S and 0.7 V configuration)

face morphologies of different Fe-based ACs are shown
in Figure 13. The surface morphology reveals that with
the gun configuration of 0.4 S the powder was not fully
melted during spraying (Figure 12a). Thus, the porosity
of the coating applied at the gun configuration of 0.4 S is
2.71 % (Figure 12c). However, the coating applied at the
gun configuration of 0.7 V was almost fully melted (see
Figures 12b and 12d). An almost fully dense coating
with a porosity of approximately 1.37 % was obtained at
the gun configuration of 0.7 S, which is lower than that
for the gun configuration of 0.4 S. Thus, dense Fe-based
AMs can be obtained using the gun configuration of
0.7 V.
5 CONCLUSIONS
The effect of the convergent section geometry of a
gun nozzle on the HVAF thermal spray Fe-based AC
process was investigated using predictive simulations
and verified via an experiment. CFD was used to investi-
gate the gas-flow field and the behavior of in-flight parti-
cles at the nozzle entrance convergent section length
ranging from 28 mm to 56.8 mm and different shapes of
the Laval nozzle convergent section (a straight line and
Vitosinski convergence curve). The main findings are
summarized as follows:
1) For the gas-flow field, the length of the convergent
part (ranging from 28 mm to 56.8 mm) does not affect
the initial chamber pressure, gas velocity or temperature.
The change in the gas flame flow characteristics at the
Vitosinski curve shows a uniform and stable flame com-
pared with the straight line of the convergent section. In
addition, the gas velocity and temperature increase
slightly more for the nozzle with a straight-line curve
than for the nozzle with a Vitosinski curve.
2) For the in-flight flow field, the change in the noz-
zle convergent section length has a weaker effect on the
particle velocity. However, the nozzle entrance conver-
gent section length leads to a significant increase in the
axial particle temperature. That is, the longer the length
of the nozzle entrance convergent section, the higher is
the particle temperature. The particle velocity at the
Vitosinski-curve shape of the Laval nozzle convergent
section is a little higher than that at the straight-line
shape of the Laval nozzle convergent section. And the
straight-line shape of the Laval nozzle convergent sec-
tion causes a higher particle temperature compared with
the Vitosinski-curve shape of the Laval nozzle conver-
gent section. In addition, the particle dwell time in-
creases with the increasing nozzle entrance convergent
section length, and the particle dwell time at the
straight-line shape of the Laval nozzle convergent sec-
tion is higher than that at the Vitosinski-curve shape of
the Laval nozzle convergent section.
3) The optimal nozzle entrance convergent configura-
tion is 0.7 V because the melt status of the particles is a
mostly semi-molten state and the particle velocity at im-
pact is high. Using this optimized gun configuration (0.7
V), we obtained low-porosity (1.37 %) Fe-based ACs.
Acknowledgements
This work was supported by the Natural Science
Foundation of Liaoning Province under Grant No.
2022-MS-364, Educational Commission of Liaoning
Province of China under Grant No. L202002, and
Fushun Revitalization Talents Program under Grant No.
FSYC202107011.
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