Kinetic modelling of the transport of dust praticles in a rarefied atmosphere


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Abstract: We propose kinetic models to describe dust particles in a rarefied atmosphere in order to model the beginning of a Loss Of Vacuum Accident (LOVA) in the framework of safety studies in the International Thermonuclear Experimental Reactor (ITER). After having studied characteristic time and length scales at the beginning of a LOVA in ITER and underlined that these characteristic scales justify a kinetic approach, we firstly propose a kinetic model by supposing that the collisions between dust particles and gas molecules are inelastic and are given by a diffuse reflexion mechanism on the surface of dust particles. This collision mechanism allows us to take into account the macroscopic character of dust particles compared to gas molecules. This leads to establish new Boltzmann type kinetic operators that are non classical. Then, by noting that the mass of a dust particle is huge compared to the mass of a gas molecule, we perform an asymptotic expansion to one of the dust-molecule kinetic operators with respect to the ratio of mass between a gas molecule and a dust particle. This allows us to obtain a dust-molecule kinetic operator of Vlasov type whose any numerical discretization is less expensive than any numerical discretization of the original Boltzmann type operator. At last, we perform numerical simulations with Monte-Carlo and Particle-In-Cell (PIC) methods which validate and justify the derivation of the Vlasov operator. Moreover, examples of 3D numerical simulations of a LOVA in ITER using these kinetic models are presented.

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Date: 2012-03-19