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.     

Heat transfer to nonspherical particles in a rarefied plasma flow

The interaction of a nonspherical metallic or nonmetallic particle with a rarefied thermal plasma flow is considered. Heat transfer to a particle of arbitrary shape with an extremely thin plasma sheath due to, respectively, gas molecules, electrons, and ions is described. Analytical expressions are derived for charge and heat fluxes in the particular case of a spheroidal metallic or nonmetallic particle in a subsonic plasma flow. It has been shown that the intensity of heat exchange is greatly influenced by gas ionization, charge transfer processes, and particle shape, velocity, and orientation in the plasma flow.     

Heat transfer to a single particle exposed to a thermal plasma

This paper is concerned with an analytical study of the heat and mass transfer process of a single particle exposed to a thermal plasma, with emphasis on the effects which evaporation imposes on heat transfer from the plasma to the particle. The results refer mainly to an atmospheric-pressure argon plasma and, for comparison purposes, an argon-hydrogen mixture and a nitrogen plasma are also considered in a temperature range from 3000 to 16,000 K. Interactions with water droplets, alumina, tungsten, and graphite particles are considered in a range of small Reynolds numbers typical for plasma processing of fine powders. Comparisons between exact solutions of the governing equations and approximate solutions indicate the parameter range for which approximate solutions are valid. The time required for complete evaporation of a given particle can be determined from calculated values of the vaporization constant. This constant is mainly determined by the boiling (or sublimation) temperature of the particles and the density of the condensed phase. Evaporation severely reduces heat transfer to a particle and, in general, this effect is more pronounced for materials with low latent heat of evaporation.     

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.     

Particle behavior in thermal plasmas

In this overview, effects exerted on the motion and on heat and mass transfer of particulates injected into a thermal plasma are discussed, including an assessment of their relative importance in the context of thermal plasma processing of materials. Results of computer experiments are shown for particle sizes ranging from 5–50 μm, and for alumina and tungsten as sample materials. The results indicate that (i) the correction terms required for the viscous drag and the convective heat transfer due to strongly varying properties are the most important factors; (ii) noncontinuum effects are important for particle sizes <10 μm at atmospheric pressure, and these effects will be enhanced for smaller particles and/or reduced pressures; (iii) the Basset history term is negligible, unless relatively large and light particles are considered over long processing distances; (iv) thermophoresis is not crucial for the injection of particles into thermal plasmas; (v) turbulent dispersion becomes important for particle <10 μm in diameter; and (vi) vaporization 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.     

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.     

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.     

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.     

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.     

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     

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.     

Heat transfer in RF plasma sintering: Modeling and experiments

The mechanisms of heat transfer from an argon RF plasma, generated in a water-cooled quartz tube, to a sintering sample immersed into the plasma and to the walls of the plasma torch have been studied both analytically and experimentally for pressures from 1 to 50 torr. The model, based on the assumption of chemical equilibrium in a two-temperature plasma with rotational symmetry, includes the influence of the magnetic field and of the Knudsen number on the thermal conductivity of the plasma. At pressures below 20 torr heat transfer to the sintering sample is enhanced compared to heat transfer to the wall of the plasma torch. This nonsymmetry is attributed to the Hall parameter and Knudsen number effect. The relative importance of the two effects is a function of the pressure. A comparison with experiments, based on calorimetric and indirect heat transfer measurements for a range of pressures and power levels, indicates satisfactory agreement with analytical predictions, with the exception of larger discrepancies at higher power levels and relatively low pressures. For pressures below 5 torr, the chemical equilibrium assumption becomes questionable, i.e., the sintering model underestimates the heat transfer to the sintering sample.     

Atmospheric Plasma Spraying Evolution Since the Sixties Through Modeling,Measurements and Sensors

This paper presents, through examples, the evolutions of atmospheric plasma spraying since the sixties. The drastic improvement of the spray conditions and coatings reproducibility during more than 50 years was linked both to researches in laboratories and developments of spray equipment’s (plasma torches, computerized control panels, robots to spray coatings on complex parts, sensors working in the harsh environment of spray booths…). This evolution is illustrated through the following topics: (1) plasma forming gas thermodynamic and transport properties either at local thermodynamic equilibrium or more recently at two temperatures; (2) evolution of plasma spray torches since the nineties; (3) plasma jet and in-flight particle measurements with laboratory equipment’s and then sensors in spray booths; (4) plasma jets and torches modeling as well as heat and momentum transfer to particles; (5) splats formation and layering.     

The effect of multi-component aerosol particles on quantitative laser-induced breakdown spectroscopy: Consideration of localized matrix effects

Spectral measurements were performed in a laser-induced plasma to assess the changes in sodium or magnesium analyte emission response from particle-derived sources with the addition of concomitant mass to the aerosol particles. Temporally resolved measurements revealed up to a 50% enhancement in analyte emission with the addition of the elements copper, zinc or tungsten at mass ratios from 1:9 to 1:19, although the enhancement generally diminished by delay times of 60 μs. Additional measurements in magnesium–cadmium aerosol particles were performed to assess the temporal profile of plasma temperature in the spatial vicinity of the aerosol particles using the ion-to-neutral emission ratios. These measurements revealed a general increase in localized plasma temperature with increasing delay time, which is attributed with an initial suppression of plasma temperature about the aerosol particles as plasma energy is required to vaporize and ionize the aerosol particle mass. These measurements provide direct evidence of a matrix effect for aerosol particles, which is attributed primarily to perturbations in the localized plasma properties. These perturbations are minimized at longer plasma delay times; hence quantitative LIBS analysis of aerosol particles should be performed with careful attention given to the temporal plasma evolution. The data further elucidate the complex interactions between the plasma gas and the aerosol particles, during which the finite time-scales of particle dissociation, and heat and mass transfer are equally important.     

Knudsen effect on plasma-particle mass transfer. I. Formulation and application to self-diffusion

The Knudsen effect on mass transfer between a plasma gas and a small particle is investigated. A predictive model is developed by incorporating the Z-potential approach into the jump theory. The predictions of the model are explored through a case study. The results indicate that the Knudsen effect is significant and depends strongly on the particle size and the surface conditions. The plasma and the particle surface temperatures are also found to be determining factors. Under certain conditions, it is observed that the Knudsen effect can enhance the plasma-particle mass transfer, contrary to the predictions of the previous near-isothermal models.     

Diffusion mechanism of water vapour in a zeolitic tuff rich in clinoptilolite

The adsorption kinetics of H₂O in a clinoptilolite rich zeolitic tuff was experimentally investigated at 18°C. In the identification of the diffusion mechanism the isothermal adsorption model equation was used. It was found out that the intraparticle mass transfer becomes more dominant over the heat transfer with increase in particle size and the adsorptive dose pressure. Although initially intraparticle mass transfer was the controlling resistance later external heat transfer also contributes to the transfer mechanism.     

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.