Compressible Model for Dilute Flows

International audienceIn this paper, a new model is built to treat two-phase flows with a carrier phase laden with compressible liquid droplets. In some applications, the pressure in the carrier phase varies so much that it obviously should impact the droplet's specific mass and temperature. This may be the case, for example, in solid rocket motors, where liquid droplets of aluminum at high temperature are ejected through a nozzle and endure pressure variations from 50 bar to atmospheric pressure or less. The same kind of problem may be observed in physics of explosive or in astrophysics. In these cases, a more precise description of the dispersed phase may be useful. Moreover, in extreme cases, it may become irrelevant to continue using a pressureless model for the dispersed phase, especially if a phase change or chemical reaction occurs. Therefore, a new thermodynamically consistent model is built for two-phase compressible dilute flows. Pressure in dispersed flow is reintroduced through the use of an equation of state. The mathematical nature of the obtain system for the dispersed phase remains unchanged compared to the pressureless Euler equation, but the compressibility of the dispersed phase is obtained by pressure relaxation terms for which the numerical resolution is simple and efficient. Numerical results are related to one-dimensional simulations of the propagation of a shock wave through a droplet's cloud and to a multidimensional nozzle flow of a solid rocket motor to show the impact of compressibility on an aluminum liquid droplet's temperature