Extended Numerical simulation in a liquid spray
thermal plasma reactor assisted by a magnetic field.
Final version
J.Puerta, G. Torrente1 , J. Vollmann, L. Beiras
Departamento de Fisica, 1 Departamento de Mecánica, Universidad Simón Bolivar Apdo. 89000,
Caracas, Venezuela
E-mail: [email protected], [email protected], [email protected]
Abstract. This work is a 3 Temperatures - 2 Flows numerical simulation to describe the
behavior inside thermal plasma reactor assisted by magnetic mirror for nanostructured material
synthesis. This one is based on the energy transference between electrons and spray, meanwhile
the electrons follows shared to heavy particles, and then these last one drags the spray flow.
This simulation take into account the electron numbers and the ionization plasma to find then
Lorentz Force applied in the plasma by external magnetic fields, and then to get the drag force
applied by the plasma over the spray inside the cylindrical reactor. With this work is proposed
to novel initial conditions, where the initial temperature and velocity profile takes Maxwellian
form, based due on experimental observations to the plume profile . This numerical simulation
helps to clarify the heating in the system, as well, the interaction between the spray and the
plasma inside the reactor in presence of the magnetic field.
1. Introduction
reported the synthesis of carbon fibers aligned
Recently the interest on the works of investi- by the application of magnetic fields.
gation about the synthesis under the influence
of magnetic fields has increased. Possibly this 2. Theoretical Model
interest has been generated by the advances This numerical simulation is developed to claron investigations of nanostructural materials. ify the effect of gravity, external magnetic mirSince 2002 in Lomonosov Moscow State Uni- ror, ionization, temperature and velocity of
versity the professor Khomutov studied the ef- plasma, and as well the size, the type and the
fect of applies electric and magnetic fields in the quantity of precursor powder, in the transforgrowths of amorphous colloidal particles. He mation of the powder inside reactor. This simfound that the size and the forms of nanoparti- ulation is solved in cylindrical coordinates and
cles synthesized changes dramatically aligning their principal hypotheses are: (a) the pressure
itself when a external magnetic field parallel to of the plasma is uniform in radial direction, (b)
the plane is applied during the synthesis. He the powders are spherical and (c) Debye screenaccomplished that to control the morphology ing and joule heating is neglected. The external
of nonstructural materials by synthesis under magnetic field induced by the magnetic system,
magnetic fields will be a promising proposal for was measured and shows in fig.1 a minimum B
the engineering of nanofaces and nanotech. In fieldconfiguration in our machine.
2005 other authors notified the modification of
morphology growths and crystalline direction 3. Experimental data
by the applications of external magnetic fields, To perform good predictable capabilities of our
among them L. Bárdoš from Uppsala Univer- plasma torch experiments, 2D simulation has
sity in Sweden, he informed about the modifica- been carried out, but in order to make this job
tion of the morphology of growth of coating of in a better way 3D simulations must be made
TiN by the application of magnetic fields, and in order to understand the physics here inTakahashi from Yamagata University in Japan volved assuming thermodynamic equilibrium in
the stationary phase. In our experiment the gas
mixture is N2 with a nozzle of 4mm in diameters and the liquid injection is made transversally into the plasma via a peristaltic pump.
Good spray condition was obtained with the
parameters given by the table below.
The reactor parameters :
VEF ,IEF
ṁg
Rr
ṁp
220V olts, 54Amp
Nitrogen 13.2lpm, 40psi
0.7874inch
Aluminium 22µm, 0.3g/s
The experimental procedure was realized using an stainless steel cylindrical reactor. Inside this one was placed a magnetic coil(see fig.
1) and in backside of the reactor we find the
plasma torch, ” Plasjet 105/15” by Thermal
Dynamics of 15Kw total power. Connected to
the system we have a peristaltic pump in order
to introduce the neutralized Al-solution. In fig.
2 we show a schematic of the complete experiment. The magnetic field intensity inside of
the magnetic coil along the z - axis, was realized with a gauss meter and shown in fig.3.
The structure of the field present the minimum
B field configuration. This type of field was obtained due to the positive susceptibility of the
bobbin(made of steel 1050), in such a way that
a counter magnetic field is achieved near of the
center and quasi same sense at both sides(front
and back) of the coil. We speak also, about of a
mirror field configuration.In our point of view,
that is a nobel experiment considering the literature in this area of plasma spray. The solution of Al was prepared using HCl and after
this neutralized with NaOH in the appropriate Al concentration useful for our experiment.
We analyze the products and shown some of
the preliminary results .
Magnetic Field
350
Magnetic Field (Gauss)
300
4. Numerical Model
In our system the governing equation will be
written in axis symetric coordinates. We assume our torch used in steady state condition
and the plasma is considered as optical thin in
a local thermodynamic equilibrium. For simplicity we ignore the turbulence.
1.- Mass coservation
2.- Axial Momentum
{ (
)}
∂(ρvz vr ) 1 ∂(rρvr2 )
∂P ∂
∂vr
∂vz
+
=−
+
η
+
+
∂z
r ∂r
∂r ∂z
∂z
∂r
(
)
{ [
]}
2 ∂
∂vr
2 ∂
∂vz
1 ∂(rvr )
rη
−
η
+
−
r ∂r
∂r
3 ∂r
∂z
r ∂r
2vr
ω2
η
+ρ
+ Jθ Bz − Jz Bθ (1)
r2
r
3.- Radial Momentun
{ (
)}
∂(ρvz vr ) 1 ∂(rρvr2 )
∂P ∂
∂vr
∂vz
+
=−
+
η
+
+
∂z
r ∂r
∂r ∂z
∂z
∂r
(
)
{ [
]}
∂vr
2 ∂
∂vz
1 ∂(rvr )
2 ∂
rη
−
η
+
r ∂r
∂r
3 ∂r
∂z
r ∂r
2
2vr
ω
−η
+ρ
+ Jθ Bz − Jz Bθ (2)
r2
r
4.- Energy
∂
∂z
∂
∂r
(
)
(
)
5
1 ∂ 5
κB nh vzgas T +
κB nh vrgas T =
2
r ∂r 2
(
)
(
) (
)
∂Th
1 ∂
∂Th
g ∂Ph
g ∂Ph
Kh
+
Kh r
+ vz
+ vz
+
∂z
r ∂r
∂r
∂z
∂r
)
(
)
(
∂vr 2
∂vz 2
+η
+ Eeh − Ehgot (3)
η
∂r
∂z
250
With their respective boundary conditions .
200
150
100
50
-25
-20
-15
-10
-5
0
∂Te
∂Th
=
∂r (r=0)
∂r (r=0)
(4)
Te(r=R) = Tw
(5)
5
Z-Axis (cm)
Fig. 1 Magnetic field measurement inside the
reactor using a gauss-meter model YOKOGAWA
325i
Actualy, the pressure p is assumed to be
constant in the reactor. But, we believe that
the pressure profile like experiments realized by
Yoshiaki(Osaka University)and our fit given to
this one as it shows in fig.2, it is a more realistic
situation in a DC torch.
Fig. 3: Electron Temperature Profile without
Magnetic field
Fig. 2 : Presure distribution along the centeraxis.
Z- axis in mm., pressure in Torr, d = 4mm.,
Q = 250l/min.; Z-nozzle = 0.1 mm.
Experimental points and Fit
Fig. 4: Electron Temperature Profile with
Magnetic Field
5. Results and discusion
The electron temperature profile inside the reactor assisted by the nagnetic field shows that
the highest electron temperature are near the
plasma torch and better confined along the reactor in comparison with the case without magnetic field. In this case we obtain in the experimental procedure better results with magnetic
field than without it. Figure 5 shows the electron temperature in 2D each line represent the
axial temperature for several positions in radial
direction and our results are in good agreement
with those of Favalli et al. Figure 6 shows the
axial velocity distribution for diferent values of
r = 0.5mm; 1.0; 1.5.
Fig. 5 Electronic Temperature distribution along
the centeraxis. With r = 0.1mm curve with
maximum hight and decreasing up to 2.0mm,
curve with minimum hight. r = N ozzelradius.
356(2002)
4
12
x 10
10
[2] Cong, H., Ma, H., Sun, X., Phys. Rev.
B Phys. Rev. B 72, 045439 (2005).
Velocity (mm/s)
8
6
[3] G.Torrente, J.Puerta, N. Labrador,Phys.
Scr. Phys. Scr.T131(2008).
4
2
0
0
20
40
60
Z Axis
80
100
120
Fig. 6 Axial velocity distribution along the
centeraxis. Z- axis in mm.
[4] Davis, J. R., Handbook of thermal spray
technology, ASN International, Materials , OH
(2004)
[5] L. Bárdos, E. Gustavsson, H. Baránková,
”Effect of ferromagnetic substrates on the film
growth in magnetized plasma systems”, Surface
and Coatings Technology, Volume 200, Issues
5-6, (2005), pp. 1862-1866
[7] Alper Ozturk and Baki M. Cetgen, Material science and Engineering A 384, 331 - 351
(2004)
Fig. 7 TEM image. Precursor Al-OH4 solution.
Without Magnetic Field
[8] L. Beiras, G. Torrente and J. Puerta,
ICPP-LAWPP Conference, Chile(2010)
[9] R. C. Favalli and R. N. Szente, Brazilian
Journal of Physics, 28, 25 - 34 (1998)
[10]Arata, Y., Kobayashi, A. and Habara,
Y. Pressure distribution and basic properties
of gas tunnel type plasma jet torch. Transactions of JWRI, 235 239, (1985)
Fig. 8 TEM image. Precursor Al-OH4 solution.
With Magnetic Field.
7. Acknowledgments
Work supported by DID, Universidad
6. References
Simón Bolı́var,
[1] Tian, Y., Jia, Y., Bao, Y., Chen, Y., Physics We appreciate also very much to our coB: Condense Matter Vol. 323, 1-4,Issues 354- worker Ing. F. Blanco for the numeric.