JTTEE5 18:965–974
DOI: 10.1007/s11666-009-9366-6
1059-9630/$19.00 ! The Author(s). This article is published with open access at Springerlink.com

H. Fukanuma, R. Huang, Y. Tanaka, and Y. Uesugi(Submitted January 29, 2009; in revised form July 6, 2009)
Particle deformation and cooling significantly affect the characteristics of thermally sprayed coatings,
such as the adhesion and cohesion strength between a splat and a substrate and between splats, as well as
the internal stresses of deposits. It is essential to understand these processes for the successful industrial
application of thermal spray technology. However, to date, the microstructure of the boundary of a splat
and the substrate has not been clarified, although much research has been conducted on splat formationand the cooling process. We have developed a microstructure model of the boundary between the splat
and the substrate, based on splat morphology obtained from experiments. In the model, it is assumed that
gaps, or voids, and contact areas are arranged on the splat boundary with the substrate in an orderly
fashion. The model includes phase changes and heat resistance simulating the function of the microstructure during splat cooling. Assumptions in the model are that ambient gas trapped in the gaps, or
voids, transfers heat only by conduction and not by convection or radiation. The results of the simulation
indicated that the extent of gaps, or voids, significantly affects the rate of decrease of the averagetemperature of the splat surface, as well as the temperature distribution inside the splat.

Keywords

microstructure of splat/substrate boundary, modeling, splat morphology, splats cooling

1. Introduction
The deformation of a splat and its cooling affectadhesion, cohesion, porosity, and residual stress of plasma
sprayed deposits. It has been shown that adhesion andcohesion are influenced by the characteristics of theimpinging particles such as velocity and molten state, as
well as by the substrate characteristics, such as temperature and oxidative state (Ref 1). Bahbou et al. (Ref 2)
have shown that substrate conditions influence the coolingrate of particles, as well as the flattening speed. Arataet al. (Ref 3) have reported that plasma sprayed deposits
contain gaps (nonbonded interfaces) between splats. By
measuring the curvature of a substrate in situ during
plasma spraying, Kuroda et al. (Ref 4) have shown thatthe tensile stress depended on substrate temperature, as
well as spray materials and characteristics.
Research on splat morphology and flattening ratios aswell as particle splash has been conducted (Ref 5-10).
Fukumoto et al. (Ref 5, 6) have suggested that above acertain temperature, molten particles do not splash when
they impinge on a smooth flat surface. Li (Ref 7) has
H. Fukanuma and R. Huang, R&D, Plasma Giken Co., Ltd.,Tokyo, Japan; and Y. Tanaka and Y. Uesugi, Department ofElectrical and Electronic System, Kanazawa University,
Kanazawa, Japan. Contact e-mail: fukanuma@plasma.co.jp.

Journal of Thermal Spray Technology

indicated that substances adsorbed on a substrate cause
splat splashing because of evaporation resulting fromheating by the molten droplet during its spreading.
Splat cooling rates during thermal spray coating processes depend significantly on the microstructure of theinterface between the splat and the substrate, and on the
splat and substrate materials (Ref 1, 2, 11, 12). Trapped
ambient gas in pores, or gaps, causes heat resistance that
affects the splat cooling rates. Although many studies havebeen conducted on splat forming and cooling, few studies
Nomenclature

T
T0
Tp
Lm
Tm
k
c
r,h,z
t
Rp
R0
Rs
Hp
h
Hs
u
w
Tav
S

temperature
initial temperature
splat surface temperaturelatent heat of solidification
melting temperaturethermal conductivity
specific heatcoordinates
time
splat radius
radius of center contacting area of splat
substrate radiussplat thickness
gap depth
substrate thickness
central angle of trenchangle of distributing trenches
average temperature on splat top facesplat top area

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Mathematical Modeling and Numerical
Simulation of Splat Cooling in Plasma
Spray Coatings

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have focused on the microstructure of the boundary
between a splat and the substrate. Moreover, to date, actual
contact ratios of splat/substrate boundary and defects suchas gaps, or pores, on the boundary have not been clarified.
Amara et al. (Ref 13) have presented a three-dimensional(3D) computational model of heat transfer between asplat and a substrate based on a splat/substrate interface
model, in which contact spots were randomly distributed.
The model indicated that when the contact was perfect,
the thermal conductivity was equal to that of the substratematerials, whereas when it was imperfect, the thermal
conductivity was equal to that of the gas trapped in thenoncontact areas. McDonald et al. (Ref 11) have studied aone-dimensional heat conduction model with uniform
thermal contact resistance between the splat and substrate. The thermal resistance of the splat/substrateinterface was determined based on the model by experiments that measured Mo and ZrO2 splat cooling rates on
glass and Inconel substrates.
In this study, we first sprayed metal particles onto glass
substrates and photographed the splat patterns. Then, asplat/substrate boundary model was developed by simplifying the complicated morphology of the splat bottom
faces we observed. The splat bottom face was divided into
two parts consisting of perfect contact and noncontact
areas that were placed on the face in an orderly way. It
was assumed that the noncontact regions were filled with
ambient gas. In order to clarify how different the temperature, or cooling rate, is between the portion above theperfect and that above the imperfect contact boundary, amathematical model was developed. This model was
based on the interface model that included phase changes.
A 3D simulation was conducted to see how the model
functioned.

2. Modeling of Splat Cooling
2.1 Splat/Substrate Interface Model
Nickel (Ni), aluminum (Al), and molybdenum (Mo)particles were sprayed onto smooth flat glass substrates
with a SG-100 plasma torch (Praxair, Inc., Danbury, CT,
USA), and the top and bottom views of captured splats
were photographed. Both top and bottom views of typicalsplat examples obtained from our plasma spray experiments are shown in Fig. 1. The photographs in Fig. 1 show
the top and bottom faces of Ni, Al, and Mo splats: (a) and(b) show the top and bottom views of a Ni splat, respectively. Figure 1(c) and (d) show top and bottom views of
Al, and Fig. 1(e) and (f) top and bottom views of Mo splat.
Many trenches or ditches are clearly seen extending fromthe centers of the Ni and Al splats to their peripheries inthe bottom views in (b) and (d) of Fig. 1. No such trenches
are seen in the photographs of the top views. It appears
that in these trenches the bottom of the splat does notcontact the glass substrates. The trenches may be generated by ambient gas that was trapped under the particle
because the flattening speed was too fast to blow the gas
out from under the particle. Fine lines or trenches,

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however, are seen in both top and bottom views of the Mo
splat. The lines on the top face might be generated in adifferent way from the ones on the bottom face. We do notunderstand how the fine lines on the top were formed. The
fine lines on the bottom face could have formed as a resultof the long time taken for the molten molybdenum particle
to solidify; therefore, the lines became finer because mostof the initially trapped gas gradually escaped from beneaththe particle by the time the solidification was completed. In
any event, there are radial trenches, or lines, running on
the bottom view of every splat. On the other hand, none of
the center areas of the bottom views had trenches, andthose central areas made contact with the substrates, albeit
some small defects that could be seen.
We developed a splat morphological model on the basisof the results of the above experiments. In this model,
radial trenches stretch on the bottom face of the splat asshown in Fig. 2, under the assumption that at the moment
when the flattening process of the particle finished (nofurther expansion), the splat morphology was completed,or fixed, even if the material was in a molten state.
In the model, the outer radius and thickness of the splat
were Rp and Hp, respectively. We created a trench by
aggregating some finer trenches shown in the bottom viewof the splat. The dimensions of the trench were defined:
the central angle of the sector, the depth, and the length
were u, h, and Rp ! R0, respectively, where R0 was theradius of the inner contact area. Each trench was distributed at every angle of w over the splat. The substrateradius and thickness were Rs and Hs in the coordinate
system as is shown in Fig. 3.

2.2 Mathematical Modeling and Solution Method
The splat and substrate temperature T a function oftime t is written in cylindrical coordinates:! 2"@T@ T 1 @T 1 @ 2 T @ 2 T
@fL
¼k
þ
! qLm
þ
þ
qc
@t
@r2 r @r r2 @h2@z2@tðEq 1Þ

where q, c, k, Lm, and fL are density, specific heat, thermal
conductivity, latent heat, and local liquid fraction,
respectively. The last term in Eq 1 shows that phasechanges are taken into consideration in the splat solidification process using the enthalpy method (Ref 13, 14). In
the numerical calculation, the solidification temperature
range was taken as 10 "C between (Tm + 9) and (Tm ! 1)
in order to save calculation time. It was assumed that theradiative and convective heat transfer from plasma jet tothe splat/substrate system was negligible; therefore theboundary condition of the top face of the system and thesplat side face was adiabatic. The heat transfer throughthe interfaces between the gas trapped in the trenches andthe splat or the substrate was assumed to be conductivewith neither convection nor radiation in the trenches. It wasalso assumed that the boundary conditions of the cylindrical and bottom walls of the substrate were at a constanttemperature. Figure 4 illustrates the boundary conditions
so the reader can quickly comprehend the complicated

Journal of Thermal Spray Technology

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Fig. 1 Splat morphology of Ni, Al, and Mo on glass, top face view in (a), (c), and (e), and bottom face view in (b), (d) and (f),respectively

Fig. 2 Bottom view of a splat model developed based on Ni
splat on glass substrate

Journal of Thermal Spray Technology

Fig. 3 Coordinates and the dimensions of splat, gap, andsubstrate

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Conductive

Adiabtic

Conductive

Splat

Adiabtic

Trench filled with environmental gas
Adiabticϕ

Conductive

ψ

=

°

20

conditions mentioned previously. The calculation domain
is shown in Fig. 5. The number of cells was 347,072 in thedomain. The time step for computation was 10!9 s.
The simulations were conducted with commerciallyavailable software, Fluent 6.3 (ANSYS, Inc., Canonsburg,
PA, USA), which uses finite volume schemes. Thermophysical properties of materials and the dimensions of the
splat/substrate system are shown in Table 1 and 2,
respectively. We selected four central angles ‘‘u’’ of 0, 2, 6,
and 10" for the computation. At these angles, the ratios ofthe splat making contact with the substrate were 100, 90.4,
71.2, and 52.0%, respectively. The contact ratios wereobtained by the formula:#$#$p R2p ! R20 u 360
R2p ! R20 u¼
Contact ratio ¼
360 w
w
pR2p
R2p
ðEq 2Þ

Substrate
Constant temperature
Constant temperature

Fig. 4 Illustration of the boundary conditions of the splat, theambient gas trapped in the trench and substrate

Gz

Gy

(a)

Splat

Gz

3. 3D Computational Simulation Resultsand Discussion
Images of the computational results for the temperature distributions in cross section of the splat and substrate
systems including the trench with an angle ‘‘u’’ of 0, 2, 6,
and 10" are shown in Fig. 6. At 10!8 s after splat coolingbegan, the splat with 100% contact with substrate uniformly decreased in temperature. However, in the otherthree splats with imperfect contact with the substrates, thetemperature fell around the center portions. At 10!7 s, thetemperatures in splats with 100 and 90.4% contact fell
uniformly faster than those with 71.2 and 52.0% contact.
The temperatures in the peripheries were much higher
than those in the centers for u = 6 and 10", because theTable 1 Thermophysical properties of the materials
for computationk,c,Material W/(m Æ K) J/(kg Æ K)(b)

TrenchSubstrate

Fig. 5 Calculation domain. (a) Entire splat, trench, and substrate system. (b) Enlarged part to show the detail of the splat
and the trench

Splat
Mo
Solid
LiquidSubstrateFe
Solid
Trench
Air
Gas

q,
kg/m3

Tm, !CLm,
J/kg

T0, !C

84
84

339
570

9340
9340

2630 2.90 9 105 …
…
…
3500

29.7

791

7015

1536 2.47 9 105

100

0.02421006.4

…

3500

1.225

…

Table 2 Dimensions of model splat and substrate

Splat
Substrate

Radius,lm

Thickness,lm

Trench depth(h), lm

Central angle(u), degrees

Pitch angle(w), degrees

Trench length(Rp 2 R0), lm

Rp = 50
Rs = 500

Hp = 2
Hs = 1000.2…

0, 2, 6, 10
…

20
…

40
…

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Fig. 6 Temperature distributions on the splat/substrate cross section of the splat for contact ratios of 100, 90.4, 71.2, and 52.0% at 10!8,
10!7, 10!6, and 10!5 s

trenches resisted heat transfer. The peripheral temperatures of the splats were higher on the order of 52.0, 71.2,
90.4, and 100% contact ratio. At 10!6 s, the temperatureof the splat with 100% contact fell almost uniformly to1500 "C from the original temperature of 3500 "C; theperipheral temperature of the 52.0% contact splat, however, was still higher than 2500 "C. There was a differenceof 1000 "C between the splats. It is clear that the heat
resistance of air trapped in the trenches was significant.

Journal of Thermal Spray Technology

At 10!5 s, all the temperature distributions become nearly
identical. It appears that when contact ratios are less thanapproximately 70%, the temperature distribution in the
splat becomes uneven. The simulations indicated that
noncontact interfaces between splats and substrates significantly affected cooling rates.
Images of the temperature distribution on the upperside of the splats are shown at 10!7, 10!6, and 10!5 s in
Fig. 7. The temperature distribution of the splat making

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Fig. 6 Continued

perfect contact with the substrate shows that the temperature differences on the top were less than 200 "C at eachtime period. Moreover, in these splats, the temperature of
the periphery was lower than that of the center. On theother hand, for the splat with 52.0% contact, the temperature differences on the top were more than 500 "C at
10!7 s and about 1000 "C at 10!6 s. The temperature
above a trench was much higher than that above a contact
point. It can be seen that at 10!7 and 10!6 s the temperature distribution images for the top were identical to the970—Volume 18(5-6) Mid-December 2009

configuration of trenches. Moreover, the temperature of
the periphery, above the trench, was much higher thanthat of the center. At 10!5 s, the temperature of theperiphery became lower than that of the center for allcontact ratios.
In Fig. 8, the average temperatures on the top faces
with 100, 90.4, 71.2, and 52.0% contact with the substrate
are shown against the passage of time. It is clear that thecooling rates for the splats with 100 and 90.4% contact
were identical. The cooling rates for the splats with 71.2

Journal of Thermal Spray Technology

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Fig. 7 Temperature distributions on the top face of the splat for contact ratios of 100, 90.4, 71.2, and 52.0% at 10!7, 10!6, and 10!5 s

and 52.0% contact were slower than those for the splatswith 100 and 90.2% contact. The average surface temperature of the splat with 52.0% contact decreased more
slowly. The temperature on the splat with 52.0% contact
was nearly 500 "C higher than that on the splat with 100%
contact after about 0.5 ls. The gradient for the curves was
gradual at 0.1 to 0.5 ls because of the effect of latent heat.
The influence of latent heat on cooling time was relatively
small, because the time to needed to solidify was only 0.1

Journal of Thermal Spray Technology

to 0.2 ls. The definition of the average temperature Tav iswritten:RTp ds
ðEq 3Þ
Tav ¼ S
S
where Tp is the top surface temperature of the splat and S
is the area of the top surface.
The splat temperature cooling curves at the centerand at the periphery above the contact and theVolume 18(5-6) Mid-December 2009—971

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Fig. 7 Continued

noncontact points are shown for the splat with 52.0%
contact in Fig. 9. It can be seen that the temperature on
the periphery above the noncontact point fell slowly
compared with that at other points until 3 ls, then, it
became similar to that of other points, and finallythe temperature became lower than that of the center.
The temperature was significantly higher than that of

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the other points until nearly 2 ls and the temperaturedeference was more than 1000 "C around 1 ls. This
indicates that the trenches or gaps filled with ambient gas
play a critical role in the splat cooling process. Figure 10
shows that from the start, the temperature at the rim of
the splat that made perfect contact cooled faster than thetemperature at the center.

Journal of Thermal Spray Technology

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Fig. 8 Average temperature on top face of splat for contact
ratios of 100, 90.4, 71.2, and 52.0% with the passage of time

Fig. 10 Variation with respect to time of the top face temperature at the center and periphery for the splat having a contact
ratio of 100%

Both cooling curves were similar, although these coolingrates were different. More experimental results on splat
cooling are necessary to appreciate precisely the model
since cooling rates depend on many factors such as the
microstructure of the boundary between a splat and asubstrate, splat thickness and diameter, substrate materials, and temperature.

4. Summary and Conclusions

Fig. 9 Variation with respect to time of the top face temperature at the center and periphery above contact and noncontact
point for the splat having 52.0% contact

As for the validity of our splat morphology and coolingmodel, the authors compared their calculated results withexperimental results conducted by McDonald et al., whohave reported that the cooling rate of Mo splat on a preheated Inconel substrate was 22 9 107 K/s at the splat
temperature of 2300 "C (Ref 12). In the model, the coolingrates of Mo splat on Fe substrate were 354 9 107 and 158 9
107 K/s at 2250 "C of splat temperature when the contact
ratios were 100 and 52.0%, respectively. The cooling rateeven in the case of 52.0% contact was one digit larger thanthat of Mo splat on Inconel in McDonald!s experiments.

Journal of Thermal Spray Technology

A splat/substrate interface model was created by analyzing the morphology of Ni, Al, and Mo splats sprayedonto glass using a plasma torch. The splats contained
many fine lines, or microscopic trenches, on the boundaries between the glass substrate and the splats. The
model was characterized by grouping many radial lines
into a number of fine trenches, or ditches, on the splat
bottom for mathematical modeling and computation. The
assumptions of the model were (1) that the trenches werefilled with ambient gas that acted as heat resistance during
the splat cooling, and (2) that the boundary conditions
on the interfaces between the gas trapped in the trenches
and the splat, or the substrate, were only conductive, suchthat radiative and convective heat transfers inside thetrenches were not taken into consideration in the computational simulations of the splat cooling process.
The splat cooling rates depended significantly on theratios of noncontact areas occupied by the trenches filledwith ambient gas. The average temperature on the top faceof the splat that had more noncontact areas fell more slowly
than that of the splat with fewer noncontact areas. The
temperature on the top face above a trench cooled muchslower than that above a contact position. The temperature

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gap between the positions above the trench and the contact
point was more than 1000 "C in the case of the splat in which
the trench had 10" of central angle. The images of temperature patterns on the top faces were the same as the distribution of trenches in the splats. The simulation results
showed that the trapped ambient gas on the boundary
between the splat and the substrate plays a critical role inthe splat cooling process. Further research on the morphology of the splat/substrate interfaces is needed to clarify
how the microstructure of the boundary is formed in orderto further understand the cooling processes.

Open AccessThis article is distributed under the terms of the Creative Commons Attribution Noncommercial License
which permits any noncommercial use, distribution, andreproduction in any medium, provided the original
author(s) and source are credited.

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974—Volume 18(5-6) Mid-December 2009

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