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Evaluation of precursor evaporation in Si nanoparticle synthesis by inductively coupled
thermal plasmas
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2013 Plasma Sources Sci. Technol. 22 035010
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IOP PUBLISHING
PLASMA SOURCES SCIENCE AND TECHNOLOGY
Plasma Sources Sci. Technol. 22 (2013) 035010 (11pp)
doi:10.1088/0963-0252/22/3/035010
Evaluation of precursor evaporation in
Si nanoparticle synthesis by inductively
coupled thermal plasmas
V Colombo1,2 , E Ghedini1,2 , M Gherardi1 and P Sanibondi1
1
Department of Industrial Engineering (D.I.N.) Alma Mater Studiorum-Università di Bologna,
Via Saragozza 8, 40123 Bologna, Italy
2
Industrial Research Centre for Advanced Mechanics and Materials (C.I.R.I.-M.A.M.) Alma Mater
Studiorum-Università di Bologna, Via Saragozza 8, 40123 Bologna, Italy
E-mail: [email protected]
Received 16 January 2013, in final form 21 March 2013
Published 20 May 2013
Online at stacks.iop.org/PSST/22/035010
Abstract
The evaporation of a micro-sized silicon solid precursor in a laboratory scale inductively
coupled thermal plasma system for nanoparticle synthesis is investigated numerically using a
customized version of the commercial CFD code ANSYS FLUENT©. Two turbulence
models—the standard k–ε and the Reynolds stress model—and two different models for the
computation of vapour production from the heated precursor—evaporation at boiling point and
vaporization driven by vapour concentration gradients—are compared. The choice of the
turbulence model can considerably influence the estimation of vapour production because
plasma temperature reduction by plasma–particle heat exchange is increased when the flow in
the torch region is predicted to be laminar, whereas the choice of the model for particle
evaporation may be critical when the plasma temperature is decreased by plasma–particle heat
exchange to values close to the boiling point of the material treated.
(Some figures may appear in colour only in the online journal)
of the precursor is strongly influenced by precursor dimensions
and feed rate. In fact, higher particle dimension results in
higher thermal inertia and thus longer particle travel before
the onset of evaporation, while high feed rate may locally cool
the plasma in the region where the material is injected as a
consequence of the plasma–particle heat exchange, resulting
in lower heat flux to the particles [4]. The reduction of
plasma temperature by plasma–precursor heat exchange is
called the loading effect and it can be considered one of
the main reasons that limit the spread of this technology to
industrial scale production of nanopowders. In fact, as the
feed rate is increased to reach industrial scale production rates,
the efficiency of precursor evaporation is reduced unless the
plasma power and torch dimensions are increased, resulting in
rising equipment and processing costs [5].
In order to characterize different systems and investigate
the performance of the process under different operating
conditions and process parameters, modelling has often been
used to support and complement experimental evidence. The
1. Introduction
In recent decades, the synthesis of nanopowders [1] has
become of prime importance among the industrial applications
of inductively coupled thermal plasmas, which include thermal
spray, powder densification and spheroidization, and waste
treatment [2]. Usually in these applications, the material
treatment is accomplished by introducing a precursor, which
can be either gas, liquid or solid, by means of an injection
probe in the middle of the plasma discharge, resulting in an
in-flight treatment. In nanopowder synthesis, the precursor
is evaporated and, after the vapour is transported to colder
regions of a reaction chamber where the gas temperature is
usually below 2000 K, nucleation of nanoparticles occurs; as
a consequence, complete evaporation is necessary for process
optimization [3]. When the precursor has an initial solid or
liquid state, the injected particles are heated and accelerated
by the plasma and they start to vaporize when the surface
temperature is higher than the melting point. The evaporation
0963-0252/13/035010+11$33.00
1
© 2013 IOP Publishing Ltd
Printed in the UK & the USA
Plasma Sources Sci. Technol. 22 (2013) 035010
V Colombo et al
trajectories and thermal histories of the material treated
in inductively coupled thermal plasma systems have been
modelled mainly for spheroidization applications, where the
process is optimized to melt completely the injected microsized powder without losing material through evaporation [6].
However, the same models can be used to investigate the
efficiency of precursor evaporation for nanopowder synthesis
applications.
The models for particle trajectory and thermal history
usually used for inductively coupled thermal plasmas were
originally developed for plasma conditions of dc nontransferred arc torches [7–16]. Later, models that take into
account plasma–particle heat exchange were developed [4].
In this work, the evaporation of a micro-sized silicon
solid precursor in a laboratory scale inductively coupled
thermal plasma system for nano-particles synthesis has been
investigated numerically using a customized version of the
commercial CFD code ANSYS FLUENT© with the aim
of comparing the predictions of different models developed
previously.
Since the plasma flow state inside the plasma torch plays
an important role in particle trajectory and thermal history
calculations, the choice of different flow and turbulent models
can lead to different results. Fluid dynamics inside the plasma
torch is still far from being fully understood and literature in
this field relies mainly on modelling results. For this reason a
comparison between two different turbulence models has been
performed: a standard isotopic turbulence k–ε model (KE)
that fits quite well enthalpy probe measurements [17–19] and
a more sophisticated Reynolds stress model (RSM) that can
take into account anisotropic turbulence. It will be shown
that the former model predicts a high turbulent flow inside the
torch while the latter predicts an almost laminar flow leading
to different results in terms of particle trajectory and thermal
history. Also, loading effects for the turbulent flow are less
pronounced with respect to the laminar one, resulting in higher
evaporation for the turbulent case.
Also, two different models for the computation of vapour
production from heated particles have been used. In fact,
Pfender [16] showed that two mechanisms for vapour mass
transfer from the particle surface to the plasma-free stream
can be applied: evaporation at boiling point (the boiling model)
and vaporization driven by vapour concentration gradients (the
vaporization model). Evaporation is a heat-driven mechanism
in which it is assumed that, once the particle has reached its
boiling point, all the heat delivered to the particle leads to
vapour production, whereas the mechanism driven by vapour
concentration gradient between the particle surface and the
plasma-free stream accounts also for vaporization below the
boiling point. Pfender showed that the choice between these
models is not critical because they predict the same timelapse for particles to completely evaporate. However, it will
be shown that different models for vapour production may
give different results as the feed rate is increased and the
evaporation of the precursor is not complete, especially when
the plasma temperature is decreased by plasma–particle heat
exchange to values close to the boiling point of the material
treated.
2. Modelling approach
A 2D model for the plasma torch and reaction chamber has
been implemented in the ANSYS FLUENT© environment in
an axisymmetric geometry. The model includes the following
hypothesis:
• the plasma is in local thermodynamic equilibrium (LTE);
• the combined diffusion approach of Murphy is used to
model the diffusion in a mixture of two non-reactive
gases [20];
• turbulent effects are taken in account through either the
standard k–ε model or the RSM;
• the plasma is optically thin and radiative losses are taken
into account considering only the presence of argon in the
mixture; resonance lines are neglected in the computation
of radiative losses;
• composition is computed taking into account six species:
Ar, Ar+ , H2 , H, H+ and electrons;
• the viscous dissipation term in the energy equation is
neglected;
• displacement currents are neglected.
2.1. Plasma model
The governing equations can be written as
∇ · (ρ v) = 0
1 ∇ · (ρ vv) = −∇p+∇ · τ + ρ g + Re J × B ∗
2
keff
1 ∇ · (ρ vh) = ∇ ·
∇h + Re J · E ∗
cp
2
k
,
hi Ji + ∇ Ȳi
−Qr + ∇ ·
cp
i
(1)
(2)
(3)
where ρ is the plasma density, v is the velocity, p is the
pressure, τ is the viscous stress tensor, h is the total enthalpy,
keff is the effective thermal conductivity that includes both
laminar and turbulent contributions; cp is the specific heat
at constant pressure, g is the gravitational force and Qr is
the volumetric radiative loss; Yi and Ji are the mass fraction
and the diffusion current of the ith gas; J is the complex
phasor for the current density induced in the plasma, B is the
magnetic induction complex phasor, and E is the electric field
complex phasor. The superscript ‘*’ indicates the complex
conjugate. Using the commercial software FLUENT to solve
the fluid equations, the Lorentz forces, ohmic heating, radiative
loss terms and energy sources due to diffusion must be taken
into account using suitable user-defined functions written in C
language.
Diffusion of gases can be described using the combined
approach of Murphy, assuming local chemical equilibrium.
This method allows one to treat diffusion of gases containing
a large number of species (six species in our case) solving
only (N − 1) equations, where N is the number of gases in
the mixture (N = 2 in our simulations), leading to a great
reduction in computational time.
2
Plasma Sources Sci. Technol. 22 (2013) 035010
V Colombo et al
The FLUENT software provides modules for the solution
of diffusion equations with the following form:
(4)
∇ · ρ vȲi + ∇ · Ji = 0,
where diffusion currents Ji can be written as
µ
t
+ ρDiY ∇ Ȳi − DiT ∇ lnT ,
Ji = −
Sc
2.2. Particle heating and vapour production models
The precursor particles are assumed to be spherical and with
a negligible internal resistance to heat transfer. The particle
trajectory is obtained by solving the following equation of
motion:
d
vp
3ρCD (11)
=
v − vp v − vp + g,
dt
4dp ρp
(5)
where Ȳi , DiY and DiT are the mass fraction, the mass fraction
diffusion coefficient and the temperature diffusion coefficient
for the ith gas, respectively [20, 21]; µt is the turbulent
viscosity and Sc is the Schmidt number, taken equal to 0.7.
Turbulent effects in the downstream region of the
discharge have been included in the flow calculations using two
different models: the KE model and the RSM. The equation
for the KE model can be written as
µt
(6)
∇k + Gk − ρε
∇ · (ρ vk) = ∇ ·
µ+
σk
∇ · (ρ vε) = ∇ ·
where vp , dp , ρp are the velocity, diameter and density of
the particle, respectively; g is the gravitational acceleration.
The first term on the right-hand side represents the fluid
drag force. The drag coefficient CD has been computed as
in [24]. Turbulent dispersion on the particles has been taken
into account as reported in [25].
The heating history of the precursor particle in the solid
phase is obtained by solving the following energy balance
equations:
dTp
q
,
(12)
=
dt
m p cp
µt
ε
ε2
µ+
∇ε + C1ε Gk − C2ε ρ + Sε ,
σε
k
k
(7)
where Tp is the particle temperature, q is the net heat to the
particle, mp and cp are the mass and the specific heat of the
particle, respectively. When the particle reaches the melting
point, the liquid fraction xp is changed accordingly to the
following particle heat balance equation:
where Gk represents the generation of turbulence kinetic
energy due to the mean velocity gradients; C1ε , C2ε , σk and
σε are constants with values 1.44, 1.92, 0.25, 1.0 and 1.3,
respectively.
A source term proposed by Bolot et al [22] to reduce
turbulent dissipation in the high temperature region of the
plasma tail has been added to the dissipation rate equation
of the KE model
G2
(8)
Sε = C3ε k ,
ρk
where C3ε has a constant value of 0.25.
In the RSM, the equations for the transport of the Reynolds
stresses are simultaneously solved [23]:
∇ · ρ vvi vj = ∇ · µ∇vi vj + DT,ij + Pij + Gij + φij + εij ,
(9)
dxp
6q
=
,
dt
ρp dp λ m
where λm is the melting latent heat for the particles.
When the particle is fully in the liquid phase, two
models have been used to predict precursor evaporation: the
vaporization model and the boiling model.
The vaporization model assumes that mass transfer
between the particle and the plasma starts as soon as the
concentration of vapour at particle surface is higher than the
partial pressure of vapour in the free stream plasma:
dmp
= −k c (Cs − Cf ) ,
dt
where DT,ij represents the turbulent diffusion, Pij is the stress
production, Gij is the production term due to buoyancy, φij
is the pressure strain term and, finally, εij is the dissipation
tensor. The last term is modelled with an additional equation
similar to equation (7) without the inclusion of the additional
source term Sε .
The electromagnetic field generated by the current flowing
in the coil (Jcoil ) and by the induced currents in the plasma (J )
can be described by means of Maxwell’s equations written in
their vector potential formulation:
∇ 2 A − iωµ0 σ A + µ0 Jcoil = 0,
(13)
(14)
where kc is the mass transfer coefficient, Cs is the vapour
concentration at particle surface, and Cf is the vapour
concentration in the free stream plasma. The mass transfer
coefficient kc can be computed as reported in [16, 26] starting
from the Sherwood Sh number and vapour diffusion coefficient
Dvap : kc = (ShDvap )/dp .
With this model, the temperature of the particle during
evaporation is computed according to the following equation
that takes into account particle cooling due to evaporation:
(10)
where µ0 is the magnetic permeability of the free space, σ
is the plasma electrical conductivity, and ω = 2πf , f being
the frequency of the electromagnetic field. The electric field
complex phasor E and the magnetic field complex phasor B
are obtained from the vector potential complex phasor A with
the following expressions: E = −iωA, B = ∇ · A. In this
work, we have used the simplified Ohm’s law J = σ E .
dTp
q
λv dmp
=
−
,
dt
m p cp
mp cp dt
(15)
where λv is the vaporization latent heat for the particle material.
In order to avoid the singularity as the particle mass is reduced
by evaporation, a lower limit for the particle diameter has been
set at 10−10 m.
3
Plasma Sources Sci. Technol. 22 (2013) 035010
V Colombo et al
Figure 2. Size distribution of the two Si precursors adopted for
calculation in this work.
walls, while a 300 K temperature is fixed at the external walls of
the torch and the internal walls of the chamber. The operating
pressure is fixed at 40 kPa.
The electromagnetic field equations are solved in an
enlarged domain extending 40 mm outside of the torch in the
y-direction, using the extended field approach [27].
Two conditions are analysed for the power coupled to
the torch and the precursor dimensions: the coupled power
is set to 10 kW or 15 kW, which corresponds to typical labscale generator plate power of 18 kW and 25 kW, respectively,
whereas the precursors are characterized by different particle
size distributions with mean diameter equal to 10 µm and
30 µm, respectively, as reported in figure 2.
For each condition, four simulations are carried out with
different precursor feed rates (1, 2, 3.5 and 5 g min−1 ).
Figure 1. Details of the computational domain (dimensions in mm).
The boiling model assumes that mass transfer starts when
the particle material reaches its boiling point. In this case, the
particle mass balance can be written as
ddp
2q
=−
dt
ρp λ v
(16)
and the temperature is fixed at the material boiling point.
The net heat to the particle q is given by
q = Ap hc T − Tp − Ap σ Tp4 − Ta4 ,
(17)
3. Results and discussion
where Ap is the surface area of the particle; ε is the emissivity
of the particle material; σ is the Stefan–Boltzmann constant;
Ta is the room temperature (300 K). The convective coefficient
hc has been calculated taking into account the local value of
the plasma properties [25] starting from Nusselt Nu number
and plasma thermal conductivity: hc = (N ukeff )/dp .
The evaporation rate and evaporation efficiency have been
calculated for different operating conditions (variation of
initial precursor particle size distribution, coupled power and
precursor feed rate) and for different physical models for
turbulence (KE and RSM) and precursor evaporation (boiling
and vaporization). The evaporation rate is defined as the
amount of vapour produced per unit time, while the evaporation
efficiency is defined as the ratio between evaporation rate
and the precursor feed rate. Since turbulent dispersion has
been adopted in the precursor particle tracking model, we
report selected particle histories that can be considered as
representative of the collective behaviour of powders released
from the whole probe tip [25].
2.3. Computational domain, boundary conditions and
plasma properties
The 2D domain analysed in this work included a PL-35
Tekna plasma source and an axisymmetric reaction chamber,
schematically shown in figure 1. The origin of the x-axis is
located at the top of the reaction chamber. Working gases are
supplied through three different inlet regions located in the
head of the torch: carrier gas from the probe tip (6 slpm pure
argon), primary gas from the gap between the probe and the
quartz tube (12 slpm pure argon) and sheath gas from the inlet
between the quartz and ceramic tubes (60 slpm Ar + 6 slpm
H2 ). A no-slip boundary condition is applied on all the internal
3.1. Standard k–ε model for turbulence and boiling model
for precursor evaporation (KE-boiling)
In figure 3, results for evaporation rate and efficiency obtained
with the KE-boiling model have been reported. For the
4
Plasma Sources Sci. Technol. 22 (2013) 035010
V Colombo et al
Figure 3. Evaporation rate (left) and efficiency (right) as a function of precursor feed rate for different precursor mean diameters (10 µm
and 30 µm) and different values of the coupled power (10 and 15 kW). Simulations are performed with boiling model for precursor
evaporation and KE model for turbulence.
Figure 4. Particle (continuous line) and plasma (dashed line) temperature along particle trajectory (left) and particle diameter (right) for
particles with different initial diameters. Simulations are performed with the boiling model for precursor evaporation and the KE model for
turbulence, case with precursor mean diameter = 10 µm, feed rate = 3.5 g min−1 , coupled power = 10 kW.
investigated operating conditions, this model predicts only
incomplete evaporation. As can be expected, the model
predicts higher precursor evaporation for higher coupled power
to the torch. For a precursor with higher mean diameter,
the evaporation efficiency predicted by this model is lower.
For increasing precursor feed rate, even if the evaporation
rate increases, the evaporation efficiency is reduced as a
consequence of a higher loading effect on the plasma that
induces lower plasma temperature and consequently lowers
heat flux to the particles.
Results of particle tracking with the KE-boiling model
under fixed operating conditions (coupled power = 10 kW,
precursor mean diameter = 10 µm and feed rate =
3.5 g min−1 ) are reported in figure 4.
Particles with different initial diameter have a different
thermal history and different evolution of particle diameter:
under these conditions, most of the particles reach the boiling
point at 3538 K but only some of them are completely
evaporated, mainly those with smaller initial diameter. As can
be seen from the plot of plasma temperature along particle
trajectory, this model predicts some loading effect, which
induces the maximum plasma temperature experienced by the
particles to be reduced to less than 7000 K, instead of typical
values of 9000–10 000 K estimated for the plasma core in the
absence of particles [17].
3.2. RSM for turbulence and boiling model for precursor
evaporation (RSM-boiling)
Results obtained with the RSM-boiling model for evaporation
rate and efficiency under different operating conditions are
reported in figure 5. As for the KE-boiling model, the predicted
evaporation is only partial. For increasing coupled power the
evaporation is higher in the whole range of precursor feed rate
investigated, whereas the evaporation behaviour is dependent
on the feed rate for increasing precursor mean diameter. In
particular, for feed rate equal to 1 g min−1 , the precursor with
higher mean diameter results in lower evaporation efficiency;
in contrast, for higher feed rate the evaporation efficiency is
higher for the precursor with higher mean diameter. The reason
behind this behaviour is the strong loading effect predicted
by this model: precursors with a lower mean diameter have
a lower thermal inertia and can be easily heated up to the
boiling point, but they induce the higher loading effect as a
5
Plasma Sources Sci. Technol. 22 (2013) 035010
V Colombo et al
Figure 5. Evaporation rate (left) and efficiency (right) as a function of precursor feed rate for different precursor mean diameters (10 and
30 µm) and different values of the coupled power (10 and 15 kW). Simulations are performed with the boiling model for precursor
evaporation and the RSM for turbulence.
Figure 6. Particle (continuous line) and plasma (dashed line) temperature along the particle trajectory (left) and particle diameter (right) for
particles with different initial diameters. Simulations are performed with the boiling model for precursor evaporation and the RSM for
turbulence, case with precursor mean diameter = 10 µm, feed rate = 3.5 g min−1 and coupled power = 10 kW.
particle diameter is unchanged along the whole trajectory.
Thus, the limited evaporation rate presented in figure 5 for these
operative conditions is related to the evaporation of particles
that are dispersed outside the cold plasma region affected by the
loading effect; as a consequence, these particles can evaporate
partially or completely.
In figure 7, particle temperature and diameter for the
case with precursor mean diameter = 30 µm (feed rate
at 3.5 g min−1 and coupled power = 10 kW) are reported
together with plasma temperature along the particle trajectory;
in this case, the plasma temperature along the particle trajectory
remains higher than for the case with mean precursor diameter
equal to 10 µm as a consequence of lower specific surface area,
resulting in particle partial evaporation.
consequence of their higher specific surface area (total particle
surface area per unit mass) as will be discussed later, referring
to the case with feed rate fixed at 3.5 g min−1 : for fixed mass
feed rate and heat flux from the plasma, the higher specific
surface area induces higher total power subtracted to the
plasma, resulting in a more pronounced cooling of the plasma.
For the precursor with lower mean diameter, for increasing
feed rate the evaporation rate is almost constant at 1 g min−1
and at 2 g min−1 when the coupled power is 10 kW and 15 kW,
respectively. This behaviour can be explained by the presence
of a cold axial channel along the particle trajectories due to
the high loading effect, in which the plasma temperature is
reduced below the boiling point of silicon (3538 K), resulting
in no particle evaporation; particles flowing in this channel
are not evaporated and the increase in feed rate cannot induce
higher evaporation of these particles.
Results for particle temperature and diameter for the case
with feed rate at 3.5 g min−1 (precursor mean diameter =
10 µm, coupled power = 10 kW) are reported in figure 6:
due to the loading effect, the plasma temperature seen by
the particles is lower than the silicon boiling point and the
3.3. Standard k–ε model for turbulence and vaporization
model for precursor evaporation (KE-vaporization)
With the vaporization model for precursor evaporation, some
operating conditions result in complete evaporation. Results
for the KE-vaporization model are reported in figures 8
6
Plasma Sources Sci. Technol. 22 (2013) 035010
V Colombo et al
Figure 7. Particle (continuous line) and plasma (dashed line) temperature along particle trajectory (left) and particle diameter (right) for
particles with different initial diameters. Simulations are performed with the boiling model for precursor evaporation and the RSM for
turbulence, case with precursor mean diameter = 30 µm, feed rate = 3.5 g min−1 and coupled power = 10 kW.
Figure 8. Evaporation rate (left) and efficiency (right) as a function of precursor feed rate for different precursor mean diameters (10 and
30 µm) and different values of the coupled power (10 and 15 kW). Simulations are performed with the vaporization model for precursor
evaporation and the KE model for turbulence.
Figure 9. Particle (continuous line) and plasma (dashed line) temperature along the particle trajectory (left) and particle diameter (right) for
particles with different initial diameters. Simulations are performed with the vaporization model for precursor evaporation and the KE
model for turbulence, case with precursor mean diameter = 10 µm, feed rate = 3.5 g min−1 and coupled power = 10 kW.
and 9. The estimated evaporation efficiency for the precursor
with lower mean diameter (d = 10 µm) is close to 100%
for the whole range of feed rate investigated. For higher
precursor mean diameter, the evaporation efficiency is lower
(around 80%) and decreasing with increasing feed rate, but
for all the conditions investigated the evaporation rate is
increasing for increasing feed rate. As can be seen from
the plasma temperature along the particle trajectory reported
7
Plasma Sources Sci. Technol. 22 (2013) 035010
V Colombo et al
Figure 10. Evaporation rate (left) and efficiency (right) as a function of precursor feed rate for different precursor mean diameters (10 µm
and 30 µm) and different values of the coupled power (10 and 15 kW). Simulations are performed with the vaporization model for precursor
evaporation and the RSM for turbulence.
Figure 11. Particle (continuous line) and plasma (dashed line) temperature along the particle trajectory (left) and particle diameter (right)
for particles with different initial diameters. Simulations are performed with the vaporization model for precursor evaporation and the RSM
for turbulence, case with precursor mean diameter = 10 µm, feed rate = 3.5 g min−1 and coupled power = 10 kW.
in figure 8, the loading effect is limited (plasma temperature
reduced to 7500 K) and particles are readily evaporated before
reaching the boiling point. In fact, particle temperature along
particle trajectory reaches a plateau at a temperature which
is determined by the equilibrium between heat flux from the
plasma and cooling due to particle evaporation, which is
related to vapour mass diffusion kinetics and heat transfer
mechanisms:
πdp2
p s Tp
ρp R
N ukeff
,
(18)
=
2
ShDvap
Mw
T − T p Tp
all the investigated operating conditions. The loading effect in
this case reduces the plasma temperature along the particle
trajectories to about 6000 K, but the plasma temperature
remains higher than the plateau temperature along the whole
particle trajectory with respect to the KE-vaporization case;
this results in the complete evaporation of all injected particles,
even those having the highest diameter in the considered
precursor size distribution.
3.5. Comparison of results from different models and
discussion
where R is the universal gas constant and Mw is the molecular
weight of the precursor. In our calculations, the plateau
temperature has been estimated at 3100 K, which is below the
boiling point of silicon (3538 K).
The models tested in this work result in very different
evaporation rates and efficiencies. On the one hand, the
turbulence models adopted predict a different flow regime
inside the torch, which is fully turbulent for the KE model
and almost laminar for the RSM, influencing the thermo-fluiddynamic behaviour of the plasma surrounding the evaporating
particle and thus influencing the evaporation process; on the
other hand, the models for precursor evaporation determine
directly the rate of mass reduction of the precursor particles
3.4. RSM for turbulence and vaporization model for
precursor evaporation (RSM-vaporization)
Results for the RSM-vaporization model are reported in
figures 10 and 11. A complete evaporation is predicted for
8
Plasma Sources Sci. Technol. 22 (2013) 035010
V Colombo et al
Figure 12. Evaporation rate (left) and efficiency (right) as a function of precursor feed rate for different models adopted. Simulations are
performed for the case with precursor mean diameter = 10 µm and coupled power = 10 kW.
Figure 13. Particle temperature (left) and diameter (right) obtained with different models adopted in this paper. Simulations are
performed for particles with initial diameter = 17 µm, case with precursor mean diameter = 10 µm, feed rate = 3.5 g min−1 and
coupled power = 10 kW.
in the torch region allows a higher heat transfer from the
hot plasma core to the region cooled by particle injection,
resulting in a lower loading effect; however, the evaporation
efficiency is around 80%, because particles with higher initial
diameter cannot be completely evaporated before leaving the
high temperature region of the plasma. Particle temperature in
this case can reach the silicon boiling point at 3538 K and at that
point the diameter starts decreasing, even if the evaporation is
not complete.
In contrast, when the vaporization model is adopted, the
evaporation efficiency is close to 100% for both KE and RSM
turbulence models; in this case, the models predict a lower
loading effect and a more efficient mass transfer for fixed
heat flux from the plasma: also particles with relatively high
initial diameter are completely evaporated. In this case, the
particles reach the plateau temperature around 3100 K, as
kinetically determined by the equilibrium between heating
from the plasma and cooling due to evaporation, and they are
completely evaporated.
Negligible differences between the vaporization model
and the boiling model have also been highlighted by Lee
et al [14], for plasma temperatures typically encountered in
and also have an indirect influence on the plasma, determining
the heat required by the particle to completely evaporate and,
consequently, the loading effect on the plasma.
For the sake of clarity, results obtained with different
models for fixed power coupled to the torch (10 kW) and
precursor type (mean diameter = 10 µm) are collected in
figure 12, while in figure 13 results for particle thermal history
and evolution of particle diameter are reported only for the
particles with initial diameter equal to 17 µm.
The RSM-boiling model predicts the lowest evaporation
efficiency and for feed rate higher than 1.5 g min−1 , the
onset of a cold channel along the particle trajectories blocks
further evaporation as the feed rate is increased, limiting the
evaporation rate to 1 g min−1 . In this case, particles flowing
inside the cold channel cannot be heated up to the boiling
point and the diameter is unchanged along the whole trajectory
(see for example particles with initial diameter = 17 µm in
figure 13), whereas particles with initial diameter of a few
micrometres are dispersed in the hot plasma region and are
evaporated.
Turning to the KE turbulence model, the evaporation
efficiency is increased since the higher turbulence predicted
9
Plasma Sources Sci. Technol. 22 (2013) 035010
V Colombo et al
thermal spray. For the system investigated in this work,
the plasma temperature is closer to the boiling point of the
treated material, especially under high loading conditions; this
induces a greater difference between the results of the two
models.
Since very different results can be obtained, the question
of which model is in better agreement with reality arises.
However, no validation of evaporation models has yet
been fully reported because of difficulties in experimentally
measuring the evaporation rate; even if some related
experimental works have been presented on measurement of
precursor vapour concentration [28] and of the size distribution
of treated and untreated precursors [6], a direct comparison
between modelling and experiments remains an unsolved
issue. A conclusion on the accuracy of these models will be
possible in the future by comparing results from modelling
and experimental measurements for test cases with simplified
and well controlled operating conditions (mainly torch coupled
power, precursor feed rate and gas composition).
Regarding the choice of the turbulence model, some
validation has been reported for the region downstream of
the plasma torch and to some extent also inside the torch,
demonstrating that the KE model is fitting enthalpy probe
measurements [17–19]. Further experimental work compared
with modelling results of the same experimental setup is
required to fully answer this question.
Acknowledgments
Partial funding from Seventh European Framework Programme, FP7-NMP-2008-SMALL-2, SIMBA project is acknowledged. The authors would like to express their gratitude
to Dr M Leparoux and Dr C Delval for providing the inductively coupled thermal plasma system configuration and operating conditions and for discussions concerning this work.
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The precursor evaporation process in an inductively coupled
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(Canonsburg, PA)
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