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論文題目「Numerical Analysis of Induction Thermal Plasma with Chemically Equilibrium Model for Nanoparticle Formation Investigation」

Liu Zishen

Introduction
Induction thermal plasma is considered to be usually used for the synthesis of nanoparticles. Indeed, its unique advantages include high enthalpy to enhance reaction kinetics, high chemical reactivity, and rapid quenching rate. However, the actual synthesis process is complicated which depends on some experimental conditions and geometrical equipment size. Therefore, the numerical analysis is essential for the measurement of induction thermal plasma and providing guidance for nanoparticle synthesis.
This study performs numerical simulation of argon induction thermal plasma and silicon nanoparticle formation. Meanwhile, the effects of different flow model, operation condition, quenching gas rate, and powder feed rate are discussed.

Modelling approach
The velocity and temperature field of the plasma gas were obtained by solving governing equations.
Standard k-e model and RNG k-e model are employed for the turbulence calculation. In the standard k-e model, the turbulence kinetic energy equation and the rate of dissipation of turbulence energy equation need to be solved.
The RNG k-e model has an additional term in its e equation that improves the accuracy for rapidly strained flows.
The governing equations were solved using SIMPLER algorithm. Thermodynamic and transport properties were calculated by Chapman-Enskog method.
The nodal model was applied to simulate the silicon nanoparticle formation. The governing equation for the particle concentration at the node is given by the general dynamic equation for aerosol.

Results and discussion
Three models have been applied for the simulation of argon induction thermal plasma including laminar flow model, standard k-e model, and RNG k-e model. These two turbulence flow models present much better temperature field which can fit the experiment observation.
The turbulent intensity is presented through the turbulence viscosity ratio. Due to the high flow rate and the confinement by electromagnetic field, the laminar flow dominates in the torch area in fact. Standard k-e model is a high-Reynolds-number model for fully turbulent flow which cannot provide the sufficiently reliable result in the torch area. RNG k-e model has an additional term in its e equation that improves the accuracy for rapidly strained flows and make it reliable for a wider class of flows. Thus, it can provide more accurate and reliable results in both torch and chamber region simultaneously.
The model of silicon nanoparticle formation has been developed. At the central axis, there are higher temperature and vapor concentration than the positions away from axis. The higher vapor concentration enhances nucleation, while the higher temperature decreases the supersaturation degree greatly on the contrary. The homogenous nucleation rate presents the smaller value, but the critical size increases. A smaller number of the larger nuclei are generated at the central axis. Thus, the nucleation consumption rates are maintained around the same level. At the outside position, the larger saturation degree results in the larger number of smaller nuclei. The growth of these nuclei consumes more silicon vapor.
In condensation process, less vapor can condense on smaller nanoparticles due to the larger Knudsen number. Therefore, the profile passes into the bimodal distribution with two peaks around 640 mm. The first peak of the smaller nanoparticles gradually disappears because the smaller nanoparticles are consumed by coagulation.
Conclusion
In this study, the validation of RNG k-e model has been verified. Several different operation conditions including oxygen gas concentration, input power and the quenching gas rate are applied for investigating their effect. A nodal model is conducted to clarify the nanoparticle formation and the effect of the powder feed rate.


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