SESSION 2

TRANSPORT AND RADIATIVE PROPERTIES FLOW MODELING

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 two-phase 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 lattice-Boltzmann 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.

PLASMA-PARTICLE 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 plasma-particle 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 plasma-particle 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 Navier-Stokes 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 two-phase 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 two-phase 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 Navier-Stokes 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", ISPC-5, p. 795, Edinburgh (Scotland), (1981)
• Proulx P, Mostaghimi J., Boulos M.I., "Plasma-particle interaction effects in induction plasma modelling under dense loading conditions", ISPC-6 , Montréal,(Canada), p. 59, (1983).
• Von Newman, John, "Theory of self-reproducing automata", edited by A. Burks, University of Illinois press (1966).

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.
Radio-frequency 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 Radio-frequency Capacity plasma torch with spherical models. Non oquilibrium plsma jet was produced from Radio-frequency 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. Plasma-gas air and argon G=3-4 g/s.
The temperature af atom and ion T_al was measured by means of enthalpy probe, it was equal to 1800-2700°K. The temperature of elecron gas T_e, was measured by means of spectr-line emission method, it was equal to 14000°K. The velocity of plasma jet was means of Pitot-tube (water-cooling) it was 20-30 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 model-bodies 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.

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 multi-layer 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 so-called 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 O⁵⁺ 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 10²⁷ m^-3 are found.

The flow of publications about modelling of radio-frequency 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 k-e 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 k-e model, the Renormalization Group (RNG) k-e turbulence model and the Reynolds Stress Model (RSM), were used. More over, we try to use this models combining with different wall functions: standard, non-equilibrium and two-layer based non-equilibrium wall function.

The heating of the plasma was assumed to take place in circular uniform or non-uniform 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 concentration¹. The thickness of the heating zone was 10 mm which corresponds to the thickness of the skin-layer under the experimental conditions¹.

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 conditions¹ and the momentum distribution was proportional to heat generation.

Using of the standard k-e 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 non-equilibrium 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 two-dimentionality 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 cross-sections of the RF inductive plasma torch obtained by numerical simulation with using k-e turbulence model (a) and the Reynolds Stress Model with non-equilibrium 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. ISPC-10, Bochum, Aug. 1991, 1.2-6, p.1-6.