Mathematical modeling of film chemical reactions of condensed-phase metal oxides with thermal protective materials

Abstract

The aim of the present work is to mathematically model the film chemical reaction of particles of c-phase oxide metals that have been inertially precipitated from a high-temperature two-phase flow with carbon-graphite TPM. The interaction of high-temperature two-phase flows with carbon-graphite TPM of multilayer walls in the vicinity of the frontal point of spreading of flat or blunt bodies at low collision velocities and substantial mass flows of inertially precipitated polydispersed liquid particles of the c-phase is examined. Under conditions of intense combined heating, a liquid c-phase film appears on the surface of carbon-graphite TPM. It is chemically active and enters into the reduction reaction with carbon, accompanied by the formation of condensed gaseous products. During the direct chemical reaction, the condensed components ensure wettability of the surface, while the gaseous products cool the melt layer by transpiration through it. The liquid c-phase film is an additional thermal resistance to the incident total heat flow, thus ensuring relatively low and moderate contact temperatures, and also has a damping effect through the impact of liquid particles. The liquid film thickness is determined by the competition of mass-transport processes: inertial precipitation of the c-phase particles, spreading and spraying of the melt, its dispersion (mechanical destruction during the transpiration of gaseous products), and suction due to the chemical reduction reaction. A physical diagram of the direct chemical reaction of the melted c-phase metal oxides with carbongraphite TPM of multilayer walls is shown in Fig. 1. We introduce the following main assumptions concerning the mathematical modeling of the interaction of high-temperature two-phase flows with carbon-graphite TPM of multilayer walls by the mechanism of a direct film chemical reaction under conditions of inertial precipitation of polydispersed particles of the c-phase metal oxides in the vicinity of the frontal point of spreading. 1. The hydrodynamics and heat and mass transport in a relatively thin reacting film of the c-phase are described by a model of a laminar incompressible boundary layer of a two-phase, one-temperature, twocomponent "frozen" gas-liquid medium. The inertia and convective terms in the momentum equation are neglected. The dynamic viscosity coefficient of the liquid phase is assumed to be constant. 2. The ablation of the carbon-graphite TPM proceeds by an overall heterogeneous reduction reaction at the contact between the carbon and melted metal oxides, which is described by efficient kinetics and the