D. WANG et al.: OPTIMIZATION OF Al-BASED AMORPHOUS COATINGS BY WARM SPRAYING BASED ON ...
819–832
OPTIMIZATION OF Al-BASED AMORPHOUS COATINGS BY
WARM SPRAYING BASED ON A NUMERICAL SIMULATION
AND A RESPONSE-SURFACE METHODOLOGY
OPTIMIZIRANJE AMORFNIH PREVLEK NA OSNOVI Al,
IZDELANIH S TOPLIM NAPR[EV ANJEM; NUMERI^NA
SIMULACIJA IN METODOLOGIJA ODGOVORA POVR[INE
Deming Wang, Tingting Li, Nianchu Wu
*
School of Mechanical Engineering, Liaoning Petrochemical University, Fushun 113001, PR China
Prejem rokopisa – received: 2024-07-17; sprejem za objavo – accepted for publication: 2024-10-24
doi:10.17222/mit.2024.1247
Al-based fully amorphous coatings with low porosity were prepared using a warm-spraying technology by combining numerical
simulations and a response-surface methodology (RSM). The influences of spraying parameters (reactant flow rate, oxygen/fuel
(O/F) ratio, coolant flow rate, and spraying distance) on the particle temperature and velocity were investigated using numerical
simulation methods. On this basis, the response-surface equations for temperature and the velocity of the particles were estab-
lished using the Box-Behnken Design (BBD) methods. The RSM was used to analyze the influence of the interactions between
the spraying parameters on the temperature and the velocity of the particles. The optimum spraying parameters (OSP) predicted
by the response optimizer were 0.012047 kg/s for the reactant flow rate, 0.011034 kg/s for the coolant flow rate, 2.7 for the O/F
ratio, and 142 mm for the spraying distance. According to the OSP, the Al-based fully amorphous coatings with a porosity of
0.08% were obtained by warm-spraying experiments. This work provides guidance for the production of Al-based fully amor-
phous coatings with low porosity using warm spraying.
Keywords: Al-based amorphous coatings, warm spraying, numerical simulation, response-surface methodology
Popolne amorfne prevleke na osnovi Al z majhno poroznostjo so avtorji pripravili s tehnologijo toplega napr{evanja.
Optimizacijo postopka so izvedli s kombinacijo numeri~nih simulacij in metodologije odgovora povr{ine (RSM; angl.: response
surface methodology). Ugotavljali so vpliv parametrov napr{evanja (hitrosti pretoka reaktivnega plina, razmerje med kisikom in
raaktivnim plinom (O/F; angl.: oxygen/fuel), hitrostjo pretoka ohlajevanlnega sredstva in razdaljo od {obe do mesta/povr{ine
napr{evanja) na temperaturo delcev in njihovo temperaturo z uporabo metod numeri~nih simulacij. Na tej osnovi so avtorji z
uporabo BBD (angl,; Box-Behnken Desigen) metod postavili ena~be za odziv (odgovor) povr{ine na temperaturo in hitrost
delcev. RSM so uporabili za analizo vpliva interakcij med parametri napr{evanja na temperaturo in hitrost delcev. Napovedali so
optimalne parametre napr{evanja (OSP; angl.: optimum spraying parameters) z optimizatorjem odziva in sicer: 0,012047 kg/s za
pretok reaktivnega (zgorevalnega) plina, 0,011034 kg/s za pretok ohlajevalnega plina, za O/F razmerje 2,7 in za oddaljenost
napr{evanja 142 mm. V skladu z OSP so avtorji s prakti~nimi preizkusi toplega napr{evanja izdelali amorfne prevleke na osnovi
Al s poroznostjo 0,08%. Ta raziskava po mnenju avtorjev predstavlja koristne napotke za izdelavo popolnih amorfnih prevlek na
osnovi Al z nizko poroznostjo s postopkom toplega napr{evanja.
Klju~ne besede: amorfne prevleke na osnovi Al, toplo napr{evanje, numri~na simulacija, metodologija odgovora povr{ine
1 INTRODUCTION
Al-based amorphous coatings (AMCs) have broad
application prospects in the fields of marine equipment,
petrochemicals, and aerospace due to their excellent cor-
rosion and wear resistance.
1–4
However, porosity and
crystalline phase structures are inevitably generated in
the preparation of Al-based AMCs.
5
The presence of po-
rosity and crystalline phase structures reduces the corro-
sion and wear resistance of Al-based AMCs.
6
Therefore,
it is necessary to find a suitable spraying process to pre-
pare Al-based fully AMCs with low porosity.
Recently, the spraying processes used to produce
Al-based AMCs include laser cladding,
7,8
cold spray -
ing,
9–11
and thermal spraying.
12–18
T a ne ta l .
7
synthesized
Al
85
Cu
10
Zn
5
AMCs by laser cladding under water-cool-
ing conditions. However, there is sedimentation of
nanocrystallines and intermetallic phases in the coatings
due to the lower cooling rates. Jin et al.
11
prepared
Al
86
Ni
8
Co
1
La
1
Y
2
Gd
2
AMCs via cold spraying. Neverthe-
less, the Al-based amorphous alloy particles are easily
crystallized during flight inside the cold spray gun. For
thermal spraying, Cheng et al.
14
produced Al-Ni-Ti
AMCs by arc spraying. Gao et al.
17
prepared
Al
86
Ni
6
Y
4.5
Co
2
La
1.5
AMCs by high-velocity air-fuel
spraying. Zhou et al.
18
sprayed Al
81
Ni
10
Ti
9
AMCs using
plasma spraying. However, most of the Al-based amor-
phous alloy particles are completely molten or even
over-molten in the thermal spraying process. As for
warm spraying, it was developed based on the sin-
gle-stage, high-velocity, oxygen-fuel (HVOF) thermal
spray system.
19
The essence of the warm-spray system is
to control the flame flow temperature by adding coolant
of different mass flow rates to the mixing chamber.
20
Materiali in tehnologije / Materials and technology 58 (2024) 6, 819–832 819
UDK 544.022.6:676.017.62 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek Mater. Tehnol.
*Corresponding author's e-mail:
wunianchu@163.com (Nianchu Wu)

Based on the process characteristics mentioned above,
the warm-spraying technique can maintain particle tem-
perature in the range 850–1400 K and particle velocity in
the range 620–1160 m/s.
20
Since the special construction
of the warm-spray gun, the deposition temperature of
particles is lower than that of other thermal spraying pro-
cesses at the same particle velocity.
21
Therefore, warm
spraying becomes a potentially ideal method to prepare
the Al-based fully AMCs with low porosity.
To prepare Al-based fully AMCs with low porosity,
there is a need to optimize the warm-spraying process to
obtain the OSP. Thus, it is crucial to choose an appropri-
ate optimization method. Presently, the methods used to
optimize the spraying processes include design of experi-
ments (DOE),
22–31
numerical simulation,
32–36
and machine
learning (ML).
37–40
In the DOE methods, two-level facto-
rial design,
23–25
the Taguchi method,
26–28
and RSM
29–31
are
widely employed. Among them, the number of experi-
ments for the two-level factorial design approach in-
creases geometrically with the number of factors.
22
The
Taguchi method is limited to single-response assemblies
and is incapable of handling multi-response systems.
24
Compared with the two-level factorial design and the
Taguchi method, the RSM has fewer experiments and
can intuitively observe the effects of factor interactions
on the response variable through 3D surfaces.
30
In the
meantime, RSM can also obtain the OSP by analyzing
the contours of the response surface.
31
For numerical
simulation methods, due to revealing the complex reac-
tions and fluid physics in the spraying process, numeri-
cal simulation methods were used to conduct many stud-
ies on the thermal spraying process.
32–36
Nevertheless,
numerical simulation methods can only investigate sin-
gle-factor variations and cannot consider the effects of
multi-factor interactions on the response variables. As a
result, the combination of numerical simulation and
RSM becomes a novel approach for optimizing the
spraying process to obtain OSP. Ren et al.
33
prepared
WC–12Co coatings with low porosity using the HVOF
spraying process based on combining numerical simula-
tion and RSM. Chen et al.
35
predicted OSP by combining
numerical simulation and RSM and prepared WC–12Co
coatings with high corrosion and wear resistance using
HVOF spraying experiments. However, the study for
combining numerical simulation and RSM to predict
OSP is rarely reported in terms of the warm-spraying
process. Li et al.
36
only studied the sensitivity of the
warm-spraying process parameters to particle-deposition
temperature and velocity based on numerical simulation
and RSM. Therefore, the combination of numerical sim-
ulation and RSM has research value for optimizing the
parameters of the warm-spraying process. As for ML ap-
proaches, it is the scientific investigation of algorithms
and statistical models used by computer systems to carry
out particular missions.
38
However, the applicability and
accuracy of the ML approaches are strongly affected by
he data size and it is tedious work to obtain enough in -
formation about the data. In summary, it is important to
prepare Al-based fully AMCs with low porosity using
warm-spraying technology by combining numerical sim-
ulation and RSM.
In this study, the process parameters for the produc-
tion of Al-based AMCs by warm spraying were opti-
mized by combining numerical simulation and RSM.
The influences of the spraying parameters (reactant flow
rate, O/F ratio, coolant flow rate, and spraying distance)
on the particle temperature and velocity were investi-
gated using numerical simulation methods. Moreover,
the RSM was used to analyze the influence of the inter-
actions between the spraying parameters on the particle
temperature and velocity and to predict the OSP. Accord-
ing to the OSP, the Al-based fully AMCs with low poros-
ity were prepared using warm-spraying experiments.
2 MATHEMATICAL MODELLING AND
EXPERIMENTAL METHODS
2.1 Mathematical modelling
Figure 1 depicts the structure and dimensions of the
warm-spray system. A is the propylene and oxygen inlet,
B is the coolant inlet, and C is the carrier gas and particle
inlet. The computational areas of the numerical simula-
tion include the combustion chamber (I), convergent noz-
zle (II), mixing chamber (III), converging-diverging
(C-D) nozzle (IV), barrel (V), and free jet region (VI).
Figure 2 illustrates the computational grids and
boundary conditions for the warm-spray gun model.
Since the warm-spray gun is an axisymmetric structure,
only half of the two-dimensional computational region is
modeled. During the modeling process, the whole com-
putational area is meshed using the quadrilateral struc-
tural cell. There are 93,160 cells, 187,780 faces, and
94,621 nodes in the entire computational domain. The
D. WANG et al.: OPTIMIZATION OF Al-BASED AMORPHOUS COATINGS BY WARM SPRAYING BASED ON ...
820 Materiali in tehnologije / Materials and technology 58 (2024) 6, 819–832
Figure 1: Schematic of structure and dimensions for the warm-spray system

grids of the fuel-oxygen inlet, C-D nozzle, and free jet
regions are encrypted to precisely depict the flame flow
characteristics and particle in-flight behaviors. The de-
fined types of boundary conditions are mass flow inlet,
axis, wall, and pressure outlet. The mass flow rates of the
A, B, and C inlets are respectively 0.012047 kg/s,
0.011034 kg/s, and 0.00054 kg/s. The temperatures of
the three mass flow inlets are all 300 K. The pressure
value in the free jet region is assumed to be 1 atm. It is
usually supposed that the wall is non-slip and the tem-
perature is 350 K. The material characteristics of the
Al
86
Ni
6.75
Co
2.25
Y
3.25
La
1.75
amorphous alloy powders used
in this paper are as follows:
2
T
S
= 899 K, T
L
= 1200 K,
 p
= 3300 kg/m
3
, and c
p
= 834.03 J/(kg·K).
2.2 Model description
The conservation equations of mass, momentum, and
energy constitute the compressible reactive
Navier-Stokes equations for the gas-phase model. The
control equations in the Cartesian coordinate system are
given below:
32
Mass conservation:
∂
∂
∂
∂
  t
u
x
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 conservation:
[]
∂
∂
∂
∂
∂
∂
∂
∂
t
E
x
uEp
x
k
T
x
u
i
i
j
eff
j
ii j
() ( )
()

 ++ =
=+
⎛ ⎝ ⎜ ⎜ eff
⎞ ⎠ ⎟ ⎟ + S
h
(3)
where T is the temperature,  is the density, p is the
pressure, k
eff
is the effective thermal conductivity, t is
the turbulent environment, u is the velocity, x is the co-
ordinate,  ij
is the deviatoric stress tensor, E is the
enthalpy, S
h
is reaction source energy, and ( ij
)
eff
is the
sum of effective values for the viscosity turbulence and
non-turbulence.
Compared to other k-# models, the renormalization
group (RNG) k-# model has a powerful ability to simu-
late complex shear flows. The RNG k-# model and the
non-equilibrium wall functions are employed to predict
the flow characteristics of the turbulent center in the
warm-spray system. The model expressions are shown
below:
33
Turbulent kinetic energy:
∂
∂
∂
∂
∂
∂ x
ku
x
k
x
PY
j
j
jj
() ()    # =+
⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟+−−
k t kM
(4)
Rate of turbulent kinetic energy dissipation:
∂
∂
∂
∂
∂
∂
x
u
xx k
cP c
j
j
jj
()
()(
#

##
#
#
=
=+
⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟+−
t k12
) −R
#
(5)
P
u
x
u
x
u
x
k
u
x
i
j
j
i
i
j
l
l
ktt
=+
⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ −+
⎛ ⎝ ⎜ ⎜  
∂
∂
∂
∂
∂
∂
∂
∂
2
3
⎞ ⎠ ⎟ ⎟ ∂
∂
u
x
k
k
(6)
where k is the turbulent kinetic energy, μ is the molecu-
lar viscosity,  is the inverse effective Prandtl number,
P
k
is the turbulent kinetic energy production rate, μ
t
is
the turbulent viscosity, # is the turbulence dissipation
rate, and R
#
is an additional term for the # equation;
c
1
= 1.42 and c
2
= 1.68.
The reaction process inside the combustion chamber
was simulated using the eddy-dissipation model (EDM)
32
in the warm-spray system. The model hypothesizes that
the combustion reaction rate is affected by the turbulent
mixing motions of propylene and oxygen, and not deter-
mined by the chemical reaction rate.
R
k
Am
m
S
B
m
S
FF
P
P
=
⎡ ⎣ ⎢ ⎤ ⎦ ⎥ #
min , ,
0
0
(7)
where
S
nM
nM
0
00
≡
FF
(8)
D. WANG et al.: OPTIMIZATION OF Al-BASED AMORPHOUS COATINGS BY WARM SPRAYING BASED ON ...
Materiali in tehnologije / Materials and technology 58 (2024) 6, 819–832 821
Figure 2: Computational grids and boundary conditions for: a) com-
bustion chamber and convergent nozzle, b) mixing chamber and C-D
nozzle, c) barrel and free jet region

S
nM
nM
P
PP
FF
≡ (9)
A and B are empirical constants; A = 4 and B = 0.5.
The burning of hydrocarbons is an unknown and
complex process. The combustion process involves nu-
merous elementary reactions and strong thermal atomic
vibrations, which lead to the main reactants decompos-
ing into many low molecular weight species, including
CO, O, H, H
2
,H
2
O, CO
2
, OH, and O
2
. The chemical
equilibrium equation is described as:
36
C
3
H
6
+ 4.307O
2
 2.004H
2
O + 1.903CO + 0.432H
2
+
+ 0.692O
2
+ 0.382H + 0.745OH + 1.097CO
2
+
+ 0.388O (10)
The discrete phase model (DPM)
34
can consider both
one-way and two-way coupling between the gas and the
particle phases. The model uses the gas-phase momen-
tum and heat-transfer equations to solve the temperature
and velocity of the particles based on the Euler-Lagrange
method. Compared with the gas flow field, the volume
flow of particles is less than 12 %,
41
so the effect of par-
ticles on the gas phase can be ignored. Thus, this study
uses the one-way coupling approach to simulate the in-
teraction between the gas and the particle phases. When
other external forces are ignored, the particles are mainly
affected by drag forces during flight. The following mo-
tion equations for spherical particles are given in:
32
m
U
t
A CUUUUF
x p
p
gp D gpgp
d
d
=−− +
1
2
 () (11)
where m
p
is the particle mass, U
p
is the particle velocity,
 g
is the gas density, A
p
is the surface area of the parti-
cle, C
D
is the drag coefficient, U
g
is the gas velocity, and
F
x
is the particle force source term.
The thermal equilibrium equation of particles is de-
scribed as:
34
mC
T
t
Ah T T
pp
p
pcg p
d
d
=− () (12)
where T
g
is the gas temperature, T
p
is the particle tem-
perature, C
p
is the particle specific heat, and h
c
is the
heat-transfer coefficient.
2.3 Experimental method
The coating materials used in the study were
Al
86
Ni
6.75
Co
2.25
Y
3.25
La
1.75
amorphous alloy with the best
glass-forming ability.
2
The powders were produced by
the gas-aerosolization method in a high-purity nitrogen
environment. The powders with sizes of 10–50 μm were
sieved using the conventional sieve-analysis methods for
the production of Al-based AMCs. The sprayed substrate
used was AA 2024 plates with dimensions of 100 mm ×
30 mm × 2 mm. Before conducting the spraying experi-
ment, the substrate is sanded, degreased, dried, and sand-
blasted, which helps the deposition of the spray particles.
The operating parameters for the warm-spraying experi-
ment are as follows: 22.1 m
3
/h for the oxygen flow rate,
22.8 L/h for the propylene flow rate, 31.8 m
3
/h for the
cooling flow rate, 30 g/min for the particle feeding rate,
and 142 mm for the spraying distance.
The microstructures of the powders and coatings
were characterized using scanning electron microscopy
(SEM, Quanta 600). An X-ray diffractometer (XRD, To-
kyo, Japan) was utilized to determine the phase structure
constituents of powders and coatings under mono-
chromated Cu-K
 radiation. Image Pro Plus 6.0 software
was used to analyze the SEM micrographs of the
Al-based AMCs and evaluate their porosity.
D. WANG et al.: OPTIMIZATION OF Al-BASED AMORPHOUS COATINGS BY WARM SPRAYING BASED ON ...
822 Materiali in tehnologije / Materials and technology 58 (2024) 6, 819–832
Figure 3: Effects of reactant flow rate on the particle: a) temperature and b) velocity

3 RESULTS AND DISCUSSION
3.1 Numerical simulation
3.1.1 Effects of the reactant flow rate on particle
in-flight behaviors
Figure 3 shows the temperature and velocity of a
30 μm particle for different reactant flow rates
(0.004370–0.013110 kg/s). The particle temperature
rises with increasing reactant flow rate (Figure 3a). At a
low reactant flow rate (0.004370 kg/s), the 30-μm parti-
cles always remain in a solid state during flight. With an
increasing reactant flow rate, the particle temperature
gradually rises. When the reactant flow rate is between
0.006555 and 0.013110 kg/s, the 30 μm particles hit the
substrate in a semi-molten state because their tempera-
ture is between T
S
and T
L
. There is a similar influence of
the reactant flow rate on particle velocity as there is on
particle temperature (Figure 3b). The particle velocity
rises as the reactant flow rate increases as well. When the
reactant flow rate is increased from 0.004370 kg/s to
0.013110 kg/s, the velocity of the 30 μm particles when
they impact the substrate increases from 387.57 m/s to
604.39 m/s. This is due to the favorable environment for
particle acceleration provided by the gas flow field corre-
sponding to the reactant flow rate.
3.1.2 Effects of the O/F ratio on particle in-flight
behaviors
Figure 4 shows the temperature and velocity of a
30 μm particle for different O/F ratios (2.0–3.4). The
30 μm particle has the highest temperature at an O/F ra-
tio of 2.7 (Figure 4a). The 30 μm particles can reach a
semi-molten state before impacting the substrate when
the O/F ratio is between 2.0 and 3.4. As the O/F ratio
rises from 2.0 to 3.4, the particle temperature first in-
creases (2.0–2.7) and then decreases (2.7–3.4). The O/F
ratio has a smaller effect on particle velocity compared
with the particle temperature (Figure 4b). The 30 μm
particle has the highest velocity at an O/F ratio of 2.7. In-
side the barrel, the influence of the O/F ratio on particle
velocity can be ignored. Outside the barrel, the particle
velocity also first rises (2.0–2.7) and then drops
(2.7–3.4) as the O/F ratio increases (2.0–3.4).
D. WANG et al.: OPTIMIZATION OF Al-BASED AMORPHOUS COATINGS BY WARM SPRAYING BASED ON ...
Materiali in tehnologije / Materials and technology 58 (2024) 6, 819–832 823
Figure 4: Effects of the O/F ratio on the particle: a) temperature and b) velocity
Figure 5: Effect of coolant flow rate on the particle: a) temperature and b) velocity

3.1.3 Effects of the coolant flow rate on particle in-flight
behaviors
Figure 5 shows the temperature and velocity of a
30 μm particle for different coolant flow rates
(0.001471–0.013241 kg/s). The particle temperature
drops with increasing coolant flow rates (Figure 5a).
When the coolant flow rate is between 0.001471 and
0.011034 kg/s, the 30 μm particles hit the substrate in a
semi-molten state. At higher coolant flow rates
(0.013241 kg/s), the 30 μm particles always remain in a
solid state during flight. The coolant flow rate has the
opposite influence on particle velocity as it does on parti-
cle temperature (Figure 5b). The particle velocity is pos-
itively correlated with the coolant flow rate and this ef-
fect is noticeable outside the barrel.
3.1.4 Effects of the spraying distance on particle
in-flight behaviors
Figure 6 shows the axial temperature and axial ve-
locity of the particles when they impact the substrate for
10–50 μm particles. Compared with the large-size parti-
cles, the axial temperature and velocity of the small-size
particles (less than 25 μm) are more easily affected by
the spraying distance. The axial temperature of the parti-
cles drops as the spraying distance lengthens (Fig-
ure 6a). The particle axial temperature falls with increas-
ing particle size when the spraying distance is fixed.
When the spraying distance is short (less than 122 mm),
the 10 μm and 15 μm particles can completely melt be-
fore impacting the substrate. The 10–35 μm particles hit
the substrate in a semi-molten state at a spraying dis-
tance of 142 mm. When the spraying distance is more
than 162 mm, particles larger than 35 μm remain in a
solid state when they impact the substrate. Due to the
limited glass-forming ability of Al-based amorphous al-
loys, particles of small to medium size are more easily
able to form Al-based fully AMCs.
2
The axial velocity of
the particles decreases as the spraying distance increases
(Figure 6b). The small-size particles have higher axial
velocities than the large-size particles when the spraying
distance is fixed. In summary, the 10–35 μm particles hit
the substrate at a high velocity and in a semi-molten state
for a spraying distance of 142 mm.
3.2 Optimization and analysis of RSM
3.2.1 Modeling of response surface equations and
reasonability analysis
In this study, the RSM was used to optimize the pro-
cess of preparing Al-based AMCs by warm spraying and
predict the OSP. The RSM is an approach to expressing
relationships between nonlinear functions by using com-
plex multinomials.
36
The method expresses the nonlinear
effects of the various factor interactions on the response
variable by using images to predict the OSP. The sec-
ond-order polynomial equation is as follows:
29
Yxxx x
ii
i
k
ii i
i
k
ij i
ij
k
j
=+ + + +
==≤ ≤
∑∑∑
#
0
111
(13)
where k is the number of design factors, x is the design
factor, Y is the response variable,  0
is the response av-
erage, and # is the error;  i
,  ii
, and  ij
represent the lin-
ear, quadratic, and interaction coefficients, respectively.
The RSM is constructing and optimizing multi-re-
sponse surfaces simultaneously based on the desirability
function method.
36
Due to the different optimization
goals, the conversion formulas of the response function
also differ. The minimum, target, and maximum of the
response function are shown in Equations (14)–(16)
33
,
respectively. To obtain optimization solutions for differ-
ent response functions, the overall desirability is calcu-
lated by the geometric average, as shown in Equation
(17).
33
D. WANG et al.: OPTIMIZATION OF Al-BASED AMORPHOUS COATINGS BY WARM SPRAYING BASED ON ...
824 Materiali in tehnologije / Materials and technology 58 (2024) 6, 819–832
Figure 6: Effect of spraying distance on: a) axial temperature and b) axial velocity of particles when they impact the substrate

d
fX B
fXB
AB
AfXB
s
r
r
r
r
,
min
()
()
,( )
,
=
>
−
−
⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ≤≤
0
1 fX A
r
() >
⎧ ⎨ ⎪ ⎪ ⎩ ⎪ ⎪ (14)
d
fXA
tA
fXt
fXB
r
target
r
s
r
r
1
,A
=
−
−
⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ≤≤
−
()
()
()
0
0
tB
tfXB
s
0
2
0
−
⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ≤≤
⎧ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩ ⎪ ⎪ ⎪ ,( )
,o t h e r w i s e
0 r
⎪ (15)
d
fX A
fXA
BA
AfXB
s
r
r
r
r
,
max
()
()
,( )
,
=
<
−
−
⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ≤≤
0
1 fX B
r
() >
⎧ ⎨ ⎪ ⎪ ⎩ ⎪ ⎪ (16)
Dd
r
r
R
R
=
⎛ ⎝ ⎜ ⎞ ⎠ ⎟ =
∏
1
1/
(17)
where A is the minimum value, t
0
is the target value, B is
the maximum value, and f
r
(X) is the response equation
fitted by RSM.
Table 1: Design factor coding and level
Factor Variable
Level
–1 0 +1
Reactant flow
rate (kg/s)
F 0.004370 0.008740 0.013110
O/F ratio R 2.0 2.7 3.4
Coolant flow
rate (kg/s)
C 0.003678 0.007356 0.011034
Spraying dis-
tance (mm)
L 102 142 182
The RSM includes the Central Composite Design
(CCD) method and the BBD method.
36
The CCD method
is usually applied to experiments with multi-factor and
multi-level. The BBD method is usually applied to trials
with few factors and levels (below 5 factors and 3 lev-
els). In this paper, the design factors include reactant
flow rate (F), O/F ratio (R), coolant flow rate (C), and
spraying distance (L). The deposition temperature (Pt)
and deposition velocity (Pv) of the particles are selected
as the response variables. Therefore, this study applies
the BBD method to devise the random test scheme. The
codes and levels of the design factors are presented in
Table 1. The random test scheme and response results
are summarised in Table 2.
Based on the summative analysis of the stochastic
test program and response results (Table 2), the relation-
ships between design factors and response values were
D. WANG et al.: OPTIMIZATION OF Al-BASED AMORPHOUS COATINGS BY WARM SPRAYING BASED ON ...
Materiali in tehnologije / Materials and technology 58 (2024) 6, 819–832 825
Table 2: RSM random scheme and results
Order number F (kg/s) RC (kg/s) L (mm) Pt (K) Pv (m/s)
1 0.004370 3.4 0.007356 142 732.88 365.16
2 0.008740 2.7 0.007356 142 953.85 518.62
3 0.013110 2.7 0.011034 142 996.59 608.56
4 0.013110 2.7 0.007356 182 1045.63 596.64
5 0.008740 2.7 0.011034 102 910.88 537.59
6 0.004370 2.7 0.003678 142 900.99 345.36
7 0.008740 2.7 0.003678 102 1067.08 513.97
8 0.013110 3.4 0.007356 142 979.38 579.21
9 0.008740 2.7 0.003678 182 1018.35 489.34
10 0.004370 2.7 0.011034 142 737.24 396.12
11 0.004370 2.0 0.007356 142 777.64 368.40
12 0.008740 3.4 0.011034 142 831.13 501.66
13 0.013110 2.7 0.003678 142 1143.20 593.15
14 0.008740 2.0 0.007356 182 909.86 480.11
15 0.004370 2.7 0.007356 182 750.55 349.27
16 0.013110 2.7 0.007356 102 1063.88 608.90
17 0.008740 2.0 0.007356 102 939.12 506.63
18 0.008740 3.4 0.003678 142 962.16 472.06
19 0.008740 2.7 0.007356 142 953.85 518.62
20 0.008740 3.4 0.007356 102 900.72 504.52
21 0.008740 2.7 0.011034 182 884.08 514.44
22 0.008740 2.0 0.003678 142 1005.31 472.44
23 0.013110 2.0 0.007356 142 1018.61 582.27
24 0.008740 2.7 0.007356 142 953.85 518.62
25 0.008740 3.4 0.007356 182 864.20 480.82
26 0.008740 2.0 0.011034 142 873.01 510.68
27 0.004370 2.7 0.007356 102 816.09 400.25

expressed by using multiple-regression equations. The
response-surface equations for particle temperature (Pt)
and particle velocity (Pv) were eventually derived as
shown below:
Pt = 307.6 + 44993F + 507.8R – 39356C – 1.06L –
– 1452214F × F – 99.62R × R + 1344260C × C +
+ 67.6F × L (18)
Pv = –88.3 + 44822F + 232.7R + 14249C – 0.820L –
– 1316248F × F – 43.47R × R – 360465C × C –
– 549840F × C + 55.4F × L (19)
where F is the reactant flow rate, R is the O/F ratio, C is
the coolant flow rate, and L is the spraying distance; Pt
and Pv represent the response surface equations for par-
ticle temperature and particle velocity, respectively.
The analysis of the variance test results for parti-
cle-deposition temperature is shown in Table 3. The
F value indicates the effect level of the design factor on
the response variable. The larger the F value, the higher
the effect level. The P value indicates the significant
level of the design factor. The design factor is significant
when P < 0.05 and more significant when P < 0.001. For
the F value, the effect level of the design factor on parti-
cle-deposition temperature is L (66.77) < R (84.40) <
C (984.03) < F (3092.30). For the P value, the linear
terms (F, R, C, and L), square terms (F×F, R×R, and
C×C), and interaction terms (F×L) all have a conspicu-
ous effect on Pt. R-Squared is 99.61 %, which shows
that the response surface model of particle-deposition
temperature has a relatively accurate predictive preci-
sion. The margin between Adj R-Squared (99.44%) and
D. WANG et al.: OPTIMIZATION OF Al-BASED AMORPHOUS COATINGS BY WARM SPRAYING BASED ON ...
826 Materiali in tehnologije / Materials and technology 58 (2024) 6, 819–832
Table 3: Analysis of variance test results for particle-deposition temperature
Source Freedom Seq SS Distribution Adj SS Adj MS F value P value
Model 8 291230 99.61 % 291230 36404 575.64 <0.0001
Linear 4 267351 91.44 % 267351 66838 1056.87 <0.0001
F 1 195560 66.89 % 195560 195560 3092.30 <0.0001
R 1 5337 1.83 % 5337 5337 84.40 <0.0001
C 1 62231 21.29 % 62231 62231 984.03 <0.0001
L 1 4223 1.44 % 4223 4223 66.77 <0.0001
Square 3 23320 7.98 % 23320 7773 122.92 <0.0001
F×F 1 3112 1.06 % 4615 4615 72.97 <0.0001
R×R 1 18224 6.23 % 14298 14298 226.08 <0.0001
C×C 1 1984 0.68 % 1984 1984 31.37 <0.0001
Interaction 1 559 0.19 % 559 559 8.84 0.008
F×L 1 559 0.19 % 559 559 8.84 0.008
Error 18 1138 0.39 % 1138 63
Lack of fit 16 1138 0.39 % 1138 71
Pure error 2 0 0.00 % 0 0
Total 26 292368 100.00 %
R-Squared = 99.61 %, Adj R-Squared = 99.44 %, Pred R-Squared = 98.82 %.
Table 4: Analysis of variance test results for particle deposition velocity
Source Freedom Seq SS Distribution Adj SS Adj MS F value P value
Model 9 161591 99.74 % 161591 17955 736.71 <0.0001
Linear 4 155539 96.01 % 155539 38885 1595.52 <0.0001
F 1 144752 89.19 % 144752 144752 6178.03 <0.0001
R 1 2783 1.72 % 2783 2783 114.17 <0.0001
C 1 5837 3.76 % 5837 5837 381.59 <0.0001
L 1 2167 1.34 % 2167 2167 88.90 <0.0001
Square 3 5364 3.31 % 5364 1788 73.37 <0.0001
F×F 1 2640 1.63 % 3791 3791 155.55 <0.0001
R×R 1 2581 1.59 % 2723 2723 111.72 <0.0001
C×C 1 143 0.09 % 143 143 5.85 0.027
Interaction 2 687 0.42 % 687 344 14.10 <0.0001
toF×C 1 312 0.19 % 312 312 12.82 0.002
F×L 1 375 0.23 % 375 375 15.38 0.001
Error 17 414 0.26 % 414 24
Lack of fit 15 414 0.26 % 414 28
Pure error 2 0 0.00 % 0 0
Total 26 162005 100.00 %
R-Squared = 99.74 %, Adj R-Squared = 99.61 %, Pred R-Squared = 99.25 %.

Pred R-Squared (98.82 %) is below 0.1, showing that the
response-surface model of particle-deposition tempera-
ture has stronger predictive ability.
The analysis of the variance test results for parti-
cle-deposition velocity is shown in Table 4. For the
F value, the effect level of the design factor on particle
deposition velocity is L (88.90) < R (114.17) <
C (381.59) < F (6178.03). For the P value, the linear
terms (F, R, C, and L), square terms (F×F, R×R, and
C×C), and interaction terms (F×C and F×L) all have a
prominent effect on Pv. R-Squared is 99.74 %, which
shows that the response surface model of particle deposi-
tion velocity has a relatively accurate predictive preci-
sion. The margin between Adj R-Squared (99.61 %) and
Pred R-Squared (99.25 %) is below 0.1, showing that the
response surface model of particle deposition velocity
has stronger predictive ability. In summary, the response
surface models for both temperature and velocity of par-
ticle deposition have higher predictive precision.
Figure 7 illustrates the probability plots of the resid-
ual normal distributions for particle-deposition tempera-
ture and velocity. In Figure 7a, the residual data points
of particle-deposition temperatures are approximately
linearly distributed and fluctuate within a permissible
range, indicating that the residuals are normally distrib-
uted. In Figure 7b, the residual data of particle deposi-
tion velocity are essentially dispersed around a straight
line, indicating that the normal distribution of the resid-
ual terms is acceptable. The residual plots further dem-
onstrate the validity of the response surface model for
temperature and velocity of particle deposition, which is
in agreement with the variance analysis results.
3.2.2 The analysis of RSM results
Figure 8 presents the effects of factor interactions on
particle temperature. The influence of the interaction be-
tween F and R on Pt is displayed in Figure 8a. When F
and R increase at the same time, Pt first rises and then
falls slightly. Pt is always the maximum value when F is
fixed and R is 2.7. Figure 8b illustrates the influence of
the interaction between F and C on Pt. The effect of F on
Pt is opposite to the effect of C on Pt. Pt reaches a mini-
mum value when F decreases and C increases. Pt
reaches a maximum value when F increases and C de-
creases. Figure 8c demonstrates the effect of the interac-
tion between F and L on Pt. Compared with L, the effect
of F on Pt is obvious. When F is 0.004370 kg/s and L is
182 mm, Pt is the smallest. When F is 0.013110 kg/s and
D. WANG et al.: OPTIMIZATION OF Al-BASED AMORPHOUS COATINGS BY WARM SPRAYING BASED ON ...
Materiali in tehnologije / Materials and technology 58 (2024) 6, 819–832 827
Figure 8: Response surface graphs for particle temperature: a) effect of F and R, b) effect of F and C, c) effect of F and L, d) effect of R and C,
e) effect of R and L and f) effect of C and L
Figure 7: Graphs of the residual normal distributions for: a) parti-
cle-deposition temperature and b) particle deposition velocity

L is 102 mm, Pt is the largest. The effect of the interac-
tion between R and C on Pt is depicted in Figure 8d.
When R increases and C decreases, Pt first increases and
then decreases. Pt reaches a minimum value when R and
C increase simultaneously. The influence of the interac-
tion between R and L on Pt is presented in Figure 8e.
When R and L increase at the same time, Pt first in-
creases and then decreases. Pt is the smallest when R is
3.4 and L is 182 mm. The effect of the interaction be-
tween C and L on Pt is plotted in Figure 8f. The effect of
C on Pt is the same as the effect of L on Pt. Pt reaches a
minimum value when C and L increase simultaneously.
Pt is the largest when C is 0.001471 kg/s and L is 102
mm.
Figure 9 exhibits the effects of factor interactions on
particle velocity. The influence of the interaction be-
tween F and R on Pv is shown in Figure 9a. Compared
with F , the effect of R on Pv can be ignored. Pv is always
the maximum value when F is fixed and R is 2.7. The in-
fluence of the interaction between F and C on Pv is illus-
trated in Figure 9b. The effect of F on Pv is the same as
the effect of C on Pv. When F and C increase together,
Pt rises significantly. When F is 0.013110 kg/s and C is
0.013241 kg/s, Pv is the largest. Figure 9c demonstrates
the effect of the interaction between F and L on Pv.
Compared to L, the effect of F on Pv is obvious. Pv
reaches a maximum value when F increases and L de-
creases. Pv is the smallest when F is 0.004370 kg/s and
L is 182 mm. The influence of the interaction between R
and C on Pv is shown in Figure 9d. When R and C in-
crease at the same time, Pv first rises and then drops. Pv
is the largest when R is 2.7 and C is 0.013241 kg/s. The
influence of the interaction between R and L on Pv is
presented in Figure 9e. When R and L increase concur-
rently, Pv first rises and then drops. Pv is the largest
when R is 2.7 and L is 102 mm. Figure 9f shows the ef-
fect of the interaction between C and L on Pv. The effect
of C on Pv is opposite to the effect of L on Pv. When C
increases and L decreases, Pv increases significantly. Pv
is the largest when C is 0.013241 kg/s and L is 102 mm.
3.2.3 Determination of OSP
To obtain Al-based fully AMCs with low porosity, it
is necessary to make more sizes of Al-based amorphous
alloy particles to reach a high velocity and semi-molten
state before impacting the substrate. Due to the limited
glass-forming ability of Al-based amorphous alloys, the
particles with small to medium sizes are more easily able
to form Al-based fully AMCs.
2
Therefore, the optimiza-
tion goals of RSM in this study are maximization of par-
ticle velocity and more particles with small-to-medium
sizes impacting the substrate in a semi-molten state.
According to the optimization strategy exhibited in
Equations (14)–(17), the response surface equations for
particle temperature (Pt) and particle velocity (Pv) were
combined with the optimization goals to obtain the cor-
responding optimization results (Figure 10). Among
them, the desirability of particle velocity and tempera-
ture is 0.93085 and 0.67486, respectively. The composite
desirability is 0.7926 and close to 1, which indicates that
the OSP predicted by RSM satisfies the optimization in-
D. WANG et al.: OPTIMIZATION OF Al-BASED AMORPHOUS COATINGS BY WARM SPRAYING BASED ON ...
828 Materiali in tehnologije / Materials and technology 58 (2024) 6, 819–832
Figure 10: Optimization analysis results for OSP
Figure 9: Response surface graphs for particle velocity: a) effect of F and R, b) effect of F and C, c) effect of F and L, d) effect of R and C, e) ef-
fect of R and L, and f) effect of C and L

tent. Based on the OSP predicted by RSM (Table 5), the
flame flow field (Figure 11) and the particle in-flight be-
havior (Figure 12) of the warm-spraying process were
simulated using numerical simulation methods. In Fig-
ure 11a, the flame flow pressure in the combustion
chamber has a maximum value and remains constant. It
falls rapidly at the inlet of the C-D nozzle and eventually
stabilizes at 0 kPa in the free jet region. In Figure 11b,
the flame flow temperature reaches a peak of 3083 K at
the end of the mixing chamber. When the flame flows
into the C-D nozzle, the flame flow temperature begins
to drop and eventually drops to 827 K. In Figure 11c,
the velocity of flame flow reaches a peak of 1687 m/s at
the barrel entrance. There are four complete Mach cones
formed in the free jet region, which play a crucial role in
the particle acceleration. In the corresponding flame flow
field conditions, the 10–35 μm particles reach a semi-
molten state before impacting the substrate (Figure 12a).
The particles of almost all sizes maintain relatively sta-
ble and higher axial velocities before impacting the sub-
strate (Figure 12b). Moreover, the simulation results
show that the temperature and velocity of 30 μm parti-
cles when they hit the substrate are 977.069 K and
589.788 m/s, respectively. Compared with the tempera-
ture (978.3999 K) and velocity (590.676 m/s) of particles
predicted by the RSM (Figure 10), the relative errors are
respectively 0.15 % and 0.14 %, which further proves the
validity of the optimal results predicted by RSM.
3.3 Experimental validation
Figure 13a shows the SEM images of Al-based
amorphous alloy powders. The powders produced by gas
atomization were mainly spherical or near-spherical par-
ticles. According to the OSP (Table 5), the Al-based
AMCs were prepared using warm-spraying experiments.
Figure 13b shows the XRD patterns of the
Al
86
Ni
6.75
Co
2.25
Y
3.25
La
1.75
amorphous alloy powders and
as-sprayed Al-based AMCs. The diffuse pattern and the
D. WANG et al.: OPTIMIZATION OF Al-BASED AMORPHOUS COATINGS BY WARM SPRAYING BASED ON ...
Materiali in tehnologije / Materials and technology 58 (2024) 6, 819–832 829
Figure 12: The a) temperature and b) velocity of particles based on OSP
Figure 11: The a) pressure, b) temperature, and c) velocity of the
flame flow based on OSP. (I), (II), (III), (IV), (V), and (VI) represent
combustion chamber, convergent nozzle, mixing chamber, C-D noz-
zle, barrel, and free jet region, respectively

absence of any peaks associated with crystalline phases
indicate that they are fully amorphous. Figure 13c and
13d illustrate the surface morphology and cross-sectional
structure of the as-sprayed Al-based AMCs. Al-based
amorphous alloy powders are deposited on the substrate
in a semi-molten state and the coating exhibits a uniform
and dense structure with 0.08 % porosity. In summary,
the Al-based fully AMCs with a porosity of 0.08 % were
prepared using warm-spraying experiments based on the
OSP predicted by RSM.
Table 5: OSP predicted by RSM for specific optimization intent
Spraying parameters Value
Reactant flow rate (kg/s) 0.012047
O/F ratio 2.70
Coolant flow rate (kg/s) 0.011034
Spraying distance (mm) 142
4 CONCLUSIONS
In this paper, numerical simulations and RSM were
combined to study the effect of the warm-spraying pro-
cess parameters on the particle temperature and velocity
and to predict the OSP. According to the OSP, the
Al-based, fully AMCs with low porosity were prepared
using warm-spraying experiments. The main conclusions
were as follows:
(1) The influences of spraying parameters (reactant
flow rate, O/F ratio, coolant flow rate, and spraying dis-
tance) on particle temperature and velocity were investi-
gated by numerical simulation methods. The particle
temperature and velocity increase with the reactant flow
rate. The particles have the highest temperature and ve-
locity at an O/F ratio of 2.7. Compared with the particle
velocity, the particle temperature is significantly affected
by the coolant flow rate and drops as the coolant flow
rate rises. With the increase in spraying distance, the
temperature and velocity of the particle gradually de-
crease. The 10–35 μm particles hit the substrate in a
semi-molten state when the spraying distance is 142 mm.
(2) The RSM was used to investigate the influence of
interactions between spraying parameters on particle
temperature and velocity and to analyze their sensitivity.
The reactant flow rate has the maximum effect on the
particle temperature and velocity, followed by the cool-
ant flow rate, O/F ratio, and spraying distance.
(3) The OSP predicted by the RSM were:
0.012047 kg/s for the reactant flow rate, 0.011034 kg/s
for the coolant flow rate, 2.7 for the O/F ratio, and
142 mm for the spraying distance. According to the OSP,
the warm-spraying process was simulated using numeri-
D. WANG et al.: OPTIMIZATION OF Al-BASED AMORPHOUS COATINGS BY WARM SPRAYING BASED ON ...
830 Materiali in tehnologije / Materials and technology 58 (2024) 6, 819–832
Figure 13: a) SEM image of the Al
86
Ni
6.75
Co
2.25
Y
3.25
La
1.75
amorphous alloy powders, b) XRD patterns of the Al
86
Ni
6.75
Co
2.25
Y
3.25
La
1.75
amor-
phous alloy powders and the as-sprayed Al-based AMCs, c) Surface morphology and d) cross-section structure of the as-sprayed Al-based AMCs

cal simulation methods to verify the viability of the RSM
optimization process and to obtain the 10–35 μm size
range of the sprayed particles. Finally, the Al-based fully
AMCs with a porosity of 0.08% were prepared by
warm-spraying experiments.
Acknowledgements
This work was supported by Natural Science Founda-
tion of Liaoning Province under Grant No. 2022-
MS-364; Fushun Revitalization Talents Program under
Grant No. FSYC202107011. The financial support pro-
vided by the China Scholarship Council (CSC) is greatly
acknowledged.
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