A Model of Liquid Metal Droplet Vaporization in Arc Heated Gas Streams
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T HE use of a thermal plasma as an energy source
seems feasible in a wide variety of high temperature metallurgical and chemical processes .1-3 Perhaps the most critical technical requirement in the application of thermal plasmas when condensed phases are involved is that the residence time of the solid or liquid be sufficient for the necessary heat and!or mass transfer. The importance of heat and mass transfer considerations in plasma process development has long been recognized 4 , 5 and failure to achieve the thermodynamically predicted yield is often a result of inadequate heat and mass transfer. A plasma reactor design that has been extensively used in the development of plasma processes is a dispersed phase reactor in which either solid particles or droplets are entrained in a plasma heated gas stream. In the case of liquid injection, the objective is normally to either partially or totally vaporize the droplets and, consequently, there are many similarities between plasma vaporization processes and other industrial processes such as fuel atomization in combustion systems, spray cooling, and gas absorption. Because of the importance of thermal and material transport in plasma processes as well as to other industrial processes as just noted, there have been a number of theoretical analysis of heat and mass transfer from spheres in flowing gas streams .6-9 The major emphasis in this theoretical work has been on modelling the transport processes between a single sphere and the fluid both in the presence and absence of other spheres. In the plasma medium, Bonet et aZlO,ll have considered in detail the multitude of processes that can occur during vaporization of a spherical particle in a thermal plasma. Although this work has been important in identifying the relative importance of various transport processes, the analysis is only valid for a single
sphere in an extensively flowing gas whose properties are unaffected by particle-gas interactions. On the other hand, reactor design requires a consideration of the multiparticle or droplet condition in which the effect of the droplets or particles on the gas velocity, temperature, and composition and on each other are taken into account. Thus a model of multidroplet vaporization in plasma heated gas streams would be desireable. In the present paper, a model of the simultaneous transfer of heat and mass between liquid metal droplets and a plasma heated gas stream is developed. This study is an extension of a model on heat transfer to particles in arc heated gas streams'" and is part of an overall study to develop a low cost, high capacity process for production of solar grade silicon based on arc heater technology .13 The proposed process will involve the reduction of silicon tetrachloride by a liquid metal such as sodium or magnesium, which will be injected into an arc heater gas stream in the form of droplets. A knowledge of the degree of vaporization of the droplets prior to mixing with the silicon tetrachloride is required for reactor design purposes. This predic
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