Numerical simulation of a supersonic gas–solid flow over a blunt body: The role of inter-particle collisions and two-way coupling effects

A supersonic dusty gas flow over a blunt body is considered. The mathematical model of the two-phase gas–particle flow takes into account the inter-particle collisions and the two-way coupling effects. The carrier gas is treated as a continuum, the averaged flow field of which is described by the complete Navier–Stokes equations with additional source terms modeling the reverse action of the dispersed phase. The dispersed phase is treated as a discrete set of solid particles, and its behavior is described by a kinetic Boltzmann-type equation. Particles impinging on the body surface are assumed to bounce from it. Numerical analysis is carried out for the cross-wise flow over a cylinder. The method of computational simulation represents a combination of a CFD-method for the carrier gas and a Monte Carlo method for the “gas” of particles. The dependence of the fine flow structure of the continuous and dispersed phases upon the free stream particle volume fraction αp∞ and the particle radius rp is investigated, particularly in the shock layer and in the boundary layer at the body surface. The particle volume fraction αp∞ is varied from a negligibly low value to the value αp∞ = 3 × 105 at which inter-particle collisions and two-way coupling effects are simultaneously essential. Particular attention has been given to the particles of radii close to the critical value rp∗, because in this range of particle size the behavior of the particles and their effect on the carrier gas flow are not yet completely understood. An estimate of the turbulent kinetic energy produced by the particles in the shock layer is obtained.