Study and numerical resolution of an aero-thermochemistry problem

This paper is related to the chemical deposition in vapour phase. Due to the diversity of possible situations, we have restricted the problem to the case of 'frozen' incompressible laminar flows with wall-catalyzed chemical reactions. The concrete problem to be solved is the following: we seek to cover the lateral wall of a cylindrical carbon substrate with molybdenum. The depot is carried out according to the reaction heterogeneous: MoF₆ + 3H₂ → Mo + 6 HF. This reaction is kinetically governed. It is total on the substrate wall and in its immediate vicinity. The substrate is placed in a vertical concentric quartz tube. It is supported by an alumina cylinder of the same diameter. The substrate is heated by electromagnetic induction. The tube is cooled by a stream of water, in order to avoid the deposit on its wall. A mixture of hydrogen and molybdenum hexafluoride is introduced into the bottom of the tube, possibly diluted in argon in order to reduce partial pressures. A pump is used to vary the flow rates in the laminar area. The question is to provide answers to the following two questions 1/What happens when conditions given for speed, temperature and concentrations are fixed? 2/How to set these conditions to obtain a deposit of good quality, thick and regular? In chapter I, the necessary theoretical data are set, first of all the equations of balance, then the laws of variation of the coefficients of transport, the parameters dimensionless, and then the influence of the chemical reactions on the flows are examined. By doing some simplifying hypotheses, it is then possible to formulate the equations of the problem and the boundary conditions. In chapter II, the methods of solving the problem are described. After exposing the particular problem of asymptotic solutions, which does not present numerical difficulties, the general theoretical elements on the finite differences are developed. The actual resolution of the problem can be done by two types of complementary methods: on the one hand the method based on the parabolic formulation which results from the hypothesis of the boundary layer; on the other hand the most general method, which is also the heaviest. Chapter III presents results, and first of all those corresponding to flows of pure gases, in order to highlight the aero-thermal aspect of the problem; then the mass transfer is taken into account