Newtonian flow theory for slender bodies in a dusty gas

Abstract

Hypersonic small-disturbance theory is extended to consider the problem of dusty-gas flow past thin two-dimensional bodies. The mass fraction of suspended particles is assumed to be sufficiently large that the two-way interaction between particle phase and gas phase must be considered. The system of eight governing equations is further reduced by considering the Newtonian approximation γ → 1 andM∞→ ∞. The Newtonian theory up to second order is studied and the equations are solved for the case of a thin wedge at zero angle of attack. Expressions for the streamlines, dust-particle paths, shock-wave location and all flow variables are obtained. It is seen that the presence of the dust increases the pressure along the wedge surface and tends to bend the shock wave towards the body surface. Other effects of the interaction of the two phases are also discussed.