SESSION 2
TRANSPORT AND RADIATIVE PROPERTIES FLOW MODELING
Chairman:  T. Murphy
J. Van der Mullen

MODELING OF FLOW AND TEMPERATURE FIELDS IN THERMAL PLASMA JET REACTORS:
RECENT AND FUTURE DEVELOPMENTS
Pierre Proulx^{1} and Stéphane Cyr^{2}
^{1}Plasma Technology Research Centre (CRTP) , Département de génie chimique, Faculté
de génie, Université de Sherbrooke, Sherbrooke (Québec) J1K 2R1 CANADA
^{2}Département de génie mécanique, Faculté de génie, Université de Sherbrooke,
Sherbrooke (Québec) J1K 2R1 CANADA
INTRODUCTION
The problems involved in the modeling of plasma spraying equipment are numerous. At
the basis of this modeling we have to evaluate overall transfer coefficients for drag, heat
and mass transfer for small particles surrounded by the plasma. This is already a
significant hurdle. Furthermore, since we inject a significant amount of particles in the
plasma, we have to take into account the twophase interactions. These interactions are
numerous. There are direct interphase exchange terms, and there are also indirect effects
due to the modifications of the plasma properties due to the presence of the particles.
Evaporation of the particle material, per example, can cause drastic changes in the plasma
properties. In the case of turbulent flows, it is also known that the presence of the
particles have a complex influence on the turbulence properties. The objectives of the
present paper is to underline the progresses made in the modeling of this plasma
technology , and to introduce some new results obtained using a different approach to
fluid dynamics the latticeBoltzmann method, that could have a great influence on the
modeling of plasma flows in the next years. This method could represent an alternative to
DNS or LES methods for turbulence modeling, accurate but costly techniques.
PLASMAPARTICLE INTERACTIONS IN PLASMA JET MODELING
In this paper we deal with some aspects of the plasma jet used for plasma spraying,
dealing mostly with the importance of plasmaparticle interactions and the use of a model
to optimize the conditions of injection. Since plasma jets and torches are used extensively
in the treatment of powders, the plasmaparticle interactions under the dense loading
conditions generally encountered has attracted a lot of attention since the early 80's (1,2).
One of the greatest advances that the increase in computational power has brought in the
last decade is the possibility of better geometric approximations using full three
dimensional geometry instead of approximated two dimensional. In the case of the
plasma spray torch, this is a great advantage.
Per example, in Figure 1 we present the
comparison obtained from a 2D model (annular) and a 3D model (radial) of a plasma
spray torch. The models involve the solution of NavierStokes equations using a control
volume technique, coupled to a Lagrangian description of the particulate phase, as
described in ref. 1 and 2. The ordinate of this graph is the dimensionless energy absorbed
by the powders injected in the plasma torch (Q_{p}/Q_{p0}). Q_{p0} represents the value of the energy that is absorbed by the particles when the twophase interaction is not taken into account (dilute conditions). In this figure we can see that the annular approximation of
the plasma spray torch overestimates the amount of heat transferred to the particles. At a
particle flow rate of 1 g/min, the 2D approximation predicts a heat transfer that represents
70% of the dilute conditions, while the full 3D model predicts 50%. These results show
clearly also that the twophase coupling begins to be significant at a particle flow rate that
is roughly an order of magnitude lower.
Figure 2 shows the local temperature asymmetry caused by the radial injection of
particles in the plasma jet, at a constant radial position (r=5.8 mm). These curves show
the importance of the carrier gas and the particles on the plasma jet. The position 0 in the
graph represents the position of the particle injector. It is seen that the particles have an
overall cooling effect on the jet, increasing the cooling effect of the carrier gas at the
point of injection but also we can see the particles crossing the plasma jet and cooling
the side opposite to the injection point.
PERSPECTIVES IN THE MODELING OF PLASMA JET TURBULENCE
Over the last decade, turbulence modeling using DNS or LES techniques, based on
transient NavierStokes equations, which reduce the degree of empirism associated with
the popular turbulence models, has grown steadily due to the availability of low cost high
power computing. Parallel to these developments, a family of techniques based on the
ideas of Von Newman(3), has also found its niche in fluid dynamics. Recent progress in
the lattice gas theory has given rise to exciting results that now clearly compete with the
DNS methods. A very efficient use of modern parallel computers is one of the advantages
of these methods, that are very rapidly being applied to more and more complex fluid
dynamic problems. In the present paper we will present preliminary results obtained for
the two perpendicular interacting jets, a problem that is essentially similar to the plasma
spray torch. Although these calculations are still restricted to isothermal and low Mach
number conditions, the quality of the predictions are very encouraging and further work
on plasma jets will ensue.
ACKNOWLEDGMENTS
The authors gratefully acknowledge the contribution of the National Sciences and
Engineering Research Council of Canada (NSERC) and the Canadian Foundation for
Innovation (CFI) for their financial support.
REFERENCES
 Lee Y.C., Hsu K.C., Pfender E., "Modelling of particles in a plasma jet", ISPC5, p. 795,
Edinburgh (Scotland), (1981)
 Proulx P, Mostaghimi J., Boulos M.I., "Plasmaparticle interaction effects in induction
plasma modelling under dense loading conditions", ISPC6 , Montréal,(Canada), p. 59,
(1983).
 Von Newman, John, "Theory of selfreproducing automata", edited by A. Burks,
University of Illinois press (1966).
HEAT EXCHANGE OF MODELBODY IN EQUILIBRIUM AND NONEQUILIBRIUM PLASMA JETS
S. Dresvin, J. Amouroux
St. Petersburg State Technical University. Russia
LGPP, University Pierre et Marie Curie, Paris
This article is devoted to the investigation of heat exchange of model bodies in plasma jets for equilibrium and non equîlibrium conditions.
There exist a 1ot af results of heat flow megements are obtained in plasma jets for equilibrium condition, but there are plasma torch. When plasma is not in the equilibrium conditions.
Radiofrequency capacity plasma torch is an example of the non equilibrium condition  the electron temperature is 14000°K but the temperature atom and ion is ~2000°K.
We investigated the heat exchange of non equilibrium plasma of Radiofrequency Capacity plasma torch with spherical models.
Non oquilibrium plsma jet was produced from Radiofrequency generator at the frequency 13.56 MHz in Plasma torch at the diameter 40 mm at the atmospheric pressure (p=1 at.), Power 15 kWt. Plasmagas air and argon G=34 g/s.
The temperature af atom and ion T_{al} was measured by means of enthalpy probe, it was equal to 18002700°K. The temperature of elecron gas T_{e}, was measured by means of spectrline emission method, it was equal to 14000°K. The velocity of plasma jet was means of Pitottube (watercooling) it was 2030 m/s.
The heat flow was measured for stationary and non stationary method by means of heatîng the spherical model.
Tha measurement and control of temperature surface of model bodies T_{s} , were done by phirometric method.
The results of measurement are: temperature of electron T_{e}, temperature of atom and ion T_{al}. Velocity of plasma V heat flow to spherical model q and temperature surface modelbodies T_{s}.
The analysis of the results show that heat flow from non equilibrium plasma to model bodies is bigger then the heat flow for equilibrium conditions.
LASER PRODUCED PLASMAS FOR THE GENERATION OF EXTREME UV
Jeroen Jonkers, Raluca Constantinescu, Michiel van den Donker and Joop Vrakking
Philips Research Laboratories Eindhoven, Prof. Holstlaan 4 (WB 21), 5656 AA Eindhoven, the Netherlands
email: jonkersj@natlab.research.philips.com
Extreme Ultra Violet (EUV) refers to radiation with wavelengths around 10 nm. It can be
produced in hot plasmas, like pinch or laser produced plasmas. In the near future there may be
two important applications for EUV: lithography and microscopy.
In lithography radiation with a wavelength between 10 and 15 nm will be used, since for this
interval multilayer mirrors with a high reflectivity are available. At this moment EUV is one
of the most promising techniques to be applied in lithography below 100 nm.
For microscopy the socalled water window, between 2.4 and 4.4 nm, is of interest. Water is
transparent for this region while carbon containing structures absorb these wavelengths
strongly. This makes EUV microscopy suitable for the study of biological samples with high
contrast and high resolution.
Laser produced plasmas (LPP) are relatively efficient sources for the generation of EUV.
Using a focused, pulsed laser a solid, liquid or gaseous target is brought into the plasma state.
The atoms are multiply ionised due to the high temperature (typically 30 to 300 eV), so that
their resonant lines are in the EUV range. In the past very high conversion efficiency were
obtained using metal targets. Since these plasmas also emit small clusters of atoms (debris)
which can damage or decrease the reflectivity of the EUV optics, liquids and gases are the
most promising targets nowadays. A review on these new sources will be given.
The research at Philips is focused on liquid targets. A small water droplet (around 10 ?m) is
used as target to create an oxygen plasma. With a frequency doubled Nd:YAG laser (10 Hz
and 0.5 J in every 0.8 ns pulse). The spectral line of interest is the
4d®2p transition in O^{5+} at
13 nm. Conversion efficiencies up to 0.5% are claimed.
A simple model has been developed which considers the plasma as a homogeneous sphere.
Deviations from equilibrium due to the expansion of the plasma and transient effects are taken
into account. The measured spectra will be compared with those predicted by the model.
Electron temperatures around 30 eV and electron densities of the order 10^{27} m^{3} are found.
NUMERICAL SIMULATION OF GAS MOTION IN THE RADIOFREQUENCY INDUCTIVE PLASMA TORCH
Alexander Gutsol^{*} andRolf Hernberg^{**}
^{*}Institute of Chemistry and Technology of Rare Elements and Mineral Raw Materials Kola Science Centre of the Russian Academy of Sciences
Fersman St., 14, Apatity, Murmansk Reg., 184200, Russia (temporary in **)
^{**}Tampere University of Technology, Plasma Technology Laboratory P.O. Box 692, FIN33101 Tampere, Finland
The flow of publications about modelling of radiofrequency inductive plasma torches is very
intensive. Authors tried to include in their models all possible physical effects. Nevertheless until now
nobody have used modern turbulence models even for the flows with rotation. But it is well known
from the broad experience of Computational Fluid Dynamics of rotating flows that standard ke
model of turbulence is not appropriate for this case.
For numerical simulations of the RF inductive argon plasma torch we used the fluid flow and heat
transfer simulation program FLUENT. In the 2D axisymmetric geometry the conservation equations
for mass, energy and radial, axial and azimutal momentum were solved simultaneously. To account
for turbulence under the experimental1 conditions, different opportunities presented by FLUENT
such as the ke model, the Renormalization Group (RNG) ke
turbulence model and the Reynolds
Stress Model (RSM), were used. More over, we try to use this models combining with different wall
functions: standard, nonequilibrium and twolayer based nonequilibrium wall function.
The heating of the plasma was assumed to take place in circular uniform or nonuniform heat
generation zone in the rotating flow. This heating zone length was 120 mm (a little more than
inductive coil length) . Its outer diameter was 52 mm which is equal to the diameter of shining region
and to the diameter of the region with significant electron concentration^{1}. The thickness of the
heating zone was 10 mm which corresponds to the thickness of the skinlayer under the experimental
conditions^{1}.
To account radiation heat transfer the Discrete Transfer Radiation Model was used. The
electromagnetic construction of the plasma region due to the Lorenz force was account buy applying
the radial momentum source in the same cells where heat was generated. The momentum of the
Lorenz force was estimated from the experimental conditions^{1} and the momentum distribution was
proportional to heat generation.
Using of the standard ke model gives very smooth and nice picture (Fig. 1a) of the flow patterns
with the reverse flow zone till the middle of the inductive coil, but very low level of maximal
temperature (about 8000K). The RSM is the most elaborated turbulence model that FLUENT
provides. For the case under discussion it was the most appropriate to use nonequilibrium wall
function and to account the directional diffusivity. In that case (Fig. 1b) we obtained a reasonable
temperature field with maximum equalled to 10400 K and the central reverse flow from the one to
another ends of the discharge tube. This result was not change considerably when grid was doubled,
and it was not changed significantly if the heat zone was uniform and if the Lorenz force was
neglected. The length of the experimental and simulated plasma torch shown on Fig. 1 is 440 mm,
the outer diameter of the quartz tube is 80 mm. Argon comes into the torch trough 4 tangential inlets
just near the bottom on the radius 38 mm (3.57 g/s) and through 12 axial openings in the bottom on
the radius 30 mm (0.75 g/s).
So, we may consider, that using of appropriate turbulence model for numerical simulations of RF
inductive plasma torches is much more important than accounting of twodimentionality of
electromagnetic field or accounting of electromagnetic mass forces.
Figure 1. Temperature distribution, stream lines, heating zone and profiles of axial velocity for five
different crosssections of the RF inductive plasma torch obtained by numerical simulation with using
ke turbulence model (a) and the Reynolds Stress Model with nonequilibrium wall function and the
directional diffusivity account (b).
REFERENCES
 Hernberg R. G., Jaffe S. M., Larjo J., Saari J., Vattulainen J. Kinetic Gas and Electron
Temperature Measurement in RF Induction Plasma. ISPC10, Bochum, Aug. 1991, 1.26, p.16.
