Heat transfer from a rarefied plasma flow to a metallic or nonmetallic particle

Heat transfer from a plasma flow to a metallic or nonmetallic spherical particle is studied in this paper for the extreme case of free-molecule flow regime. Analytical expressions are derived for the heat flux due to, respectively, atoms, ions, and electrons and for the floating potential on the sphere exposed to a two-temperature plasma flow. It has been shown that the local or average heat flux density over the whole sphere is independent of the sphere radius and approximately in direct proportion to the gas pressure. The presence of a macroscopic relative velocity between the plasma and the sphere causes substantially nonuniform distributions of the local heat flux and enhances the total heat flux to the sphere. The heat flux is also enhanced by the gas ionization. Appreciable difference between metallic and nonmetallic spheres is found in the distributions along the oncoming flow direction of the floating potential and of the local heat flux densities due to ions and electrons. The total heat flux to the whole sphere is, however, almost the same for these different spheres. For a fixed value of the electron temperature, the heat flux decreases with increasing temperature ratio T_e/T_h.     

Effect of particle charging on momentum and heat transfer from rarefied plasma flow

The features of interaction of a spherical metallic particle with a rarefied thermal plasma flow due to the presence o charges-electrons and ions in the gaseous phase-are considered. Analytical expressions describing charge, momentum, and energy exchange between the plasma and the particle für the cases of strong and weak Debye screening are obtained. It is illustrated that the efficiency of particle heating in the plasma considerably grows as compared with a hot molecular gas due to participation of electrons and ions in file transfer processes.     

Thermophoretic Force on a Small Particle Suspended in a Plasma with a Combined Specular and Diffuse Reflection at the Particle Surface

Additional kinetic-theory analytical results are presented concerning the thermophoretic force acting on a spherical nonmetallic or metallic, nonevaporating or evaporating particle suspended in a plasma for the extreme case of free-molecule regime and thin plasma sheath. A combined specular and diffuse reflection of the atoms incident on or formed in the ion–electron recombination process at the particle surface has been taken into account in this analysis as an extension of the previous paper (Xi Chen, J. Phys. D: Appl. Phys. 30, 826–841, 1997). It has been shown that the specular reflection fraction of gas particles at the surface does not affect the thermophoretic force acting on a nonevaporating, metallic or nonmetallic, spherical particle, but they affect significantly the evaporation-added thermophoretic force. The evaporation-added thermophoretic force decreases linearly with the increase of the specular reflection fraction, and the decreasing rate for a nonmetallic evaporating particle is much greater than that for a metallic one at high plasma temperatures.     

Drag force acting on an evaporating particle immersed in a rarefied plasma flow

Analytical expressions are presented for the drag force acting on an evaporating or nonevaporating particle immersed in a plasma flow for the extreme case of free-molecule flow regime and thin plasma .sheath. It is shown that the drag force on a spherical particle is proportional to the square of the particle radius and to the relative velocity between the particle and the bulk plasma at low speed ratios. The existence of a relative velocity between the particle and the plasma results in a nonuniform heat flux distribution with its rnaximum value at the frontal stagnation point of tire sphere. This nonuniform distribution of the local heat fux density causes a nonuniforrn distribution of the local evaporated-mass flux and vapor reaction force around the surface of an evaporating particle, and thus induces an additional force on the particle. Consequently, the drag force acting on art evaporating particle is always greater than that on a nonevaporating one. This additional drag force due to particle evaporation is more significant for nonmetallic particles and for particle materials with lower latent heat of evaporation and lower vapor molecular mass. It increases with increasing plasma temperature and with decreasing gas pressure at the high plasma temperatures associated with appreciable gas ionization. The drag ratio increases with increasing electron/heavy-particle temperature ratio at high electron temperatures for a two-temperature plasma.     

Thermophoretic force on a metallic or nonmetallic particle immersed into a rarefied Plasma

Analytical results of the thermophoretic force on a metallic or nonmetallic spherical particle immersed into a rarefied plasma with a heat flux within the plasma are presented for the extreme case of free-molecule regime and thin plasma sheath. It has been shown that the thermophoresis is predominantly caused by atoms at low plasma temperatures with negligible gas ionization, while it is mainly due to ions and electrons at high plasma temperatures with great degree of ionization. The ion flux incident to a particle is constant on the whole sphere surface, while the electron flux to the metallic sphere is dependent on the -position with slightly greater value at the fore stagnation point. Consequently, there is a small difference between the metallic and nonmetallic spheres in their -distributions of the floating potential on the surface, which causes the thermophoretic force on a nonmetallic sphere to be appreciably greater than that on a metallic sphere at high plasma temperatures. Expressions for the total thermophoretic force on a metallic sphere and its components due to, respectively, atoms, ions, and electrons have been given in a closed form. Calculated results are also presented on the effects of pressure and of electron/heavy-particle temperature ratio. These results can be understood based on the variation of atom, ion, and electron thermal conductivities with the gas pressure, the temperature, and the temperature ratio.     

Experimental study of effective particle heating by a thermal plasma flow confined in a porous ceramic tube

The heating of a single alumina particle (1 mm diameter) was experimentally investigated using a thermal argon plasma flow confined in a tube. Two kinds of tube were used; a porous ceramic tube (PCT) with a transpiration gas and a water-cooled copper tube (WCT). The temperature and velocity of the particle heated in a thermal plasma flow were measured at the exit of the tube by the calorimetric and optical method, respectively. The plasma temperature and velocity at the exit of the tube were also measured. The heating rate of a particle was estimated from these experimental results. According to the results, the heating rate of a particle is higher for PCT with a small flow rate of transpiration gas than for WCT. Therefore, PCT is effective for the particle heating.Notation A cross-sectional area - Bi Biot number - C constant - c _p specific heat - D diameter - h heat transfer coefficient - k thermal conductivity - L length of tube - l distance for heat conduction loss - M mass - m flow rate of plasma jet gas - Nu Nusselt number - P pressure - Pr Prandtl number - Q heat transfer rate - Q _p total heat delivered to the particle - r radial distance - T plasma temperature - T _p particle temperature - T temperature rise - t time - U plasma velocity - U _p particle velocity - x axial distance - density - viscosity - residence time of the particle - a atmospheric (static) - Ar argon - b bulk - c centerline - cond conduction - cu probe - f film - i entrance of the tube - free stream - loss heat transferred to the wall of the tube - p particle - r room - rad radiation - t total - W wall, sphere surface - wa water - 0 exit of the tube     

Plasma-particle momentum transfer under conditions of great knudsen numbers and thin plasma sheath

Particle drag force and thermophoresis results previous obtained are revised by including modified expressions for ion and electron components of the surface pressure. The present analysis shows that there is almost no difference between non-evaporating metallic and nonmetallic particles in their drags and there is only a little difference between those particles in their thermophoretic forces. The effect of evaporation on thermophoretic and drag forces is still marked, but the drag or thermophoretic force ratio with to without accounting for evaporation assumes somewhat different values from those obtained previously and depends notably on whether the particle is metallic or nonmetallic at high plasma temperatures.     

Thermophoretic force acting on an evaporating particle suspended in a rarefied plasma

Analytical results of the thermophoretic force on an evaporating spherical particle immersed in a rarefied plasma with a large temperature gradient are presented for the extreme case of free-molecule regime and thin plasma sheath. It has been shown that the existence of a temperature gradient in the plasma causes a nonuniform distribution of the local heat flux density on the sphere surface with its maximum value at the fore-stagnation point of the sphere, although the total heal flux to the whole particle is independent of the temperature gradient existing in the plasma. This nonuniform-distribution of the local heat flux density causes a nonuniform distribution of the. local evaporated-mass flux and related reaction force around the surface of an evaporating particle, and thus causes an additional force on the particle. Calculated results show that the thermophoretic force on an evaporating particle may substantially exceed that on a nonevaporating one, especially for the case of a metallic particle (with infinite electric conductivity). The effect of evaporation on the thermophoretic force is more pronounced as the evaporation latent heat of the particle material is comparatively low and as high plasma temperatures are involved.     

Particle dynamics and particle heat and mass transfer in thermal plasmas. Part II. Particle heat and mass transfer in thermal plasmas

This paper is concerned with a review of heat and mass transfer between thermal plasmas and particulate matter. In this situation various effects which are not present in ordinary heat and mass transfer have to be considered, including unsteady conditions, modified convective heat transfer due to strongly varying plasma properties, radiation, internal conduction, particle shape, vaporization and evaporation, noncontinuum conditions, and particle charging. The results indicate that (i) convective heat transfer coefficients have to be modified due to strongly varying plasma properties; (ii) vaporization, defined as a mass transfer process corresponding to particle surface temperatures below the boiling point, describes a different particle heating history than that of the evaporation process which, however, is not a critical control mechanism for interphase mass transfer of particles injected into thermal plasmas; (iii) particle heat transfer under noncontinuum conditions is governed by individual contributions from the species in the plasma (electrons, ions, neutral species) and by particle charging effects.     

Unsteady heating of metallic particles in a rarefied plasma

Analytical results are presented concerning the unsteady heating of a metallic spherical particle innnersed in a rarefied plasma. The results show that the tinte periods required for the solid-phase heating, melting, liquid-phase heating, and evaporation are all proportional to the particle radius. For estimating the time needed for the solid-phase heating and that for the melting, the additional heat transfer rmechanism due to the thermionic emission front the particle surface is usually negligible since the surface temperatures of the particle heated in the plasma are, in general, compartively low during those heating steps. Thermionic emission assumes its effect only as the higher surface temperatures of the heated particle are involved (e.g., higher than 4000 K), while radiation loss shows its effects at much lower wall temperatures. As the plasma temperature is comparatively low, radiation heat loss may restrict the surface temperature of a particle to such a low value that the effect of thermionic emission on the overall heating time can he neglected and complete evaporation of refractor y metallic particles becomes impossible. The uncertainty in the calculation of the effect of thermionic emission is associated with the choice of the value of the effective work function for the particle material.     

Heat Generation and Particle Injection in a Thermal Plasma Torch

The operation of plasma guns used for plasma spraying involves a continuous movement of the anode arc root. The resulting fluctuations of voltage and thermal energy input introduce an undesirable element in the spray process. This paper deals with the effects of these arc instabilities on the plasma jet, and the behavior of particles injected in the flow. The first part refers to the formation of the plasma jet. Measurements show that the static behavior of the arc depends strongly upon the plasma-forming gas mixture, especially the mass flow rate, of the heavy gas, injection mode, nozzle diameter, and arc current. These parameters control the electric field in the arc column, the arc length, its stability, and the gas velocity and temperature. The dynamic behavior of the arc is examined to determine how the tempeature and velocity of the plasma gas vary with voltage variations. Relationships between the gas velocity at the nozzle exit and the lifetime of the arc roots, and the independent operating parameters of the gun can be established from a dimensional analysis. The second part discusses the interaction between the plasma jet and the particles injected into the flow. The parameters controlling particle injection and trajectory are examined to determine how injection velocity must vary with particle size and density to achieve a given trajectory. The effect of the transverse injection of the powder carrier gas is investigated using a 3-D computational fluid dynamics code. Finally, the effect of the jet fluctuations on particle trajectory is studied under the assumption that the jet velocity follows the voltage variation. The result is a continuous variation of the particle spray jet position in the flow. Experimental observations confirm the model predictions.     

Study of deposition offset in plasma spray of zirconia

Numerical modeling and experimental measurements have been performed to study the effects of powder carrier gas flow rates and powder sizes on the deposition offset in a plasma spray of yttria-stablized zirconia. The mathematical model involved simultaneous solution of the continuity, momentum and energy equations of the plasma gas, the dynamics and heat transfer of powder particles in the plasma, and the coupling effects between the plasma and panicles. Experiments included measurement of particle velocities by laser strobe technique and measurement of deposition offset. Calculated plasma temperatures and velocities are greater than 13,000 K and 2,000 m/s, respectively, in the vicinity of nozzle exit. For the plasma-particle momentum transfer, the drag coefficient was computed in two ways- with corrections accounting for the strongly varying plasma properties, and without these corrections. Calculated and experimental results, in respect to deposition offset, are in agreement to within 25% when calculated without varying properties corrections, and within about 40% with corrections; agreement in respect to average particle velocities is within 20% when calculated without varying properties corrections, and within the range 30–50% with corrections.     

Modeling of the Subsonic–Supersonic Flow and Heat Transfer in a DC Arc Plasma Torch

Two-dimensional modeling results are presented concerning the subsonic–supersonic flow and heat transfer within a DC plasma torch used for low-pressure (or soft vacuum) plasma spraying. The so-called fictitious anode method is used in the modeling in order to avoid inclusion of the complex three-dimensional effects near the anode arc root and also to avoid the forced heating of all the incoming cold gas stream by the arc. A nonorthogonal boundary-conforming grid, nonstaggered variable arrangement and the all-speed SIMPLE algorithm are employed for the solution of the governing equations, including gas viscous effects, temperature-dependent properties, and compressible effects. Good agreement of the predictions with available results for a few benchmarked compressible flow problems shows that the new version of the FAST-2D program can be employed for the present plasma flow modeling. Temperature, axial velocity, Mach number, and static pressure contours, and streamlines within the DC arc plasma torch are presented to show the flow and heat transfer characteristics. The flow transits gradually from upstream subsonic regime into downstream supersonic regime with the subsonic–supersonic transition within the cylindrical segment of the torch nozzle. Additional numerical tests show that gas viscosity and Lorentz force have only a slight effect on the plasma flow.     

Molecular kinetic aspects of vaporization of volatile coordination compounds with organic ligands

We present results of the experimental study and numerical simulation of radiation-convective heat and mass transfer during the sublimation of spherical particles of metal β-diketonates in a high-temperature inert gas flow (argon or helium). The sublimation process is visualized, and experimental data on the temperature variation dynamics and particle size are obtained. It is shown that at stable transfer of the compound from the particle surface the sublimation proceeds with the formation of large pores in its structure. The effect of inert gas properties on the kinetics of the vaporization process of precursor particles with various initial diameters is analyzed in the temperature range from 200 °C to 330 °C. Due to a higher thermal conductivity and heat capacity of helium as compared with argon, the choice of helium as carrier gas causes an increase in the sublimation intensity.     

Thickness dependent sensing mechanism in sorted semi-conducting single walled nanotube based sensors

Single walled carbon nanotube (SWCNT) networks present outstanding potential for the development of SWCNT-based gas sensors. Due to the complexity of the transport properties of this material, the physical mechanisms at stake during exposure to gas are still under debate. Previously suggested mechanisms are charge transfer between gas molecules and SWCNT and Schottky barrier modulation. By comparing electrical measurements with an analytical model based on Schottky barrier modulation, we demonstrate that one mechanism or the other is predominant depending on the percolation of metallic carbon nanotubes. Below the metallic SWCNT percolation threshold, sensing is dominated by the modulation of the Schottky barrier, while above this threshold, it is only attributed to a charge transfer between SWCNT and gas molecules. Both mechanisms are discussed in terms of sensitivity and resolution leading to routes for the optimization of a gas sensor architecture based on highly enriched semiconducting carbon nanotube films.     

Behavior of particulates in thermal plasma flows

Injection of particulate matter into a thermal plasma represents one of the approaches used in thermal plasma processing. The injected particles are usually treated as a dispersed phase, governed by the equation of motion and the rate equations for heat and mass transfer in Lagrangian coordinates. A stochastic approach is introduced to take particle dispersion into account due to turbulent fluctuations by randomly sampling instantaneous flow fields. Three-dimensional effects are also considered which are mainly due to particle injection and the presence of a swirl component. A modified approach for investigating noncontinuum effects on plasma-particle heat transfer is proposed, incorporating both electric and aerodynamic effects on the boundary layer around a particle immersed into a thermal plasma. Comparisons of theoretical predictions based on the present model with available experimental data are, in general, in reasonable agreement.     

System for <Emphasis Type="Italic">In Situ</Emphasis> Characterization of Nanoparticles Synthesized in a Thermal Plasma Process

We have designed a particle diagnostic system that is able to measure particle size and charge distributions from low stagnation pressure (≥746 Pa) and high temperature (2000–4000 K) environments in near real time. This system utilizes a sampling probe interfaced to an ejector to draw aerosol from the low pressure chamber. Particle size and charge distributions are measured with a scanning mobility particle sizer. A hypersonic impactor is mounted in parallel with the scanning mobility particle sizer to collect particles for off-line microscopic analysis. This diagnostic system has been used to measure size and charge distributions of nanoparticles (Si, Ti, Si–Ti–N, etc.) synthesized with our thermal plasma reactor. We found that the mean particle size increases with operating pressure and reactant flow rates. We also found that most particles from our reactor are neutral for particles smaller than 20 nm, and that the numbers of positively and negatively charged particles are approximately equal.