Dusty-gas flow in a laminar boundary layer over a blunt body

Abstract

Dusty-gas flow in laminar boundary layer over a body with a curved surface is considered. In addition to Stokes drag, particles experience a centrifugal force and lift which is due to fluid shear. The body size L is taken to be much greater than the relaxation length of the particle velocity due to the action of Stokes drag, & Lambda;st and is of the same order as or less than the relaxation length due to the action of lift. Λsa. Using an asymptotic approach, momentum equations for the particle phase are reduced to an algebraic equation accounting for the variation of lift coefficient with the shear and the slip velocity. Particle velocity and density are computed for the axisymmetric boundary layer in the neighbourhood of the front stagnation point of a blunt body of size much less than Λsa. It is shown that downstream of some point on the wall (the separation point) particle normal velocity becomes non-zero. As a result particle streamlines turn away from the wall, and a particle-free zone arises. The cause of separation is the lift effect; the centrifugal force cannot make the particle flow separate. This conclusion is extended to the case when L ∼ Λsa. The position of separation for the flow past a sphere is evaluated as a function of the ratio of its radius r′ and relaxation length. Dust flow ceases to separate when this value is greater than a critical value r′c /Λsa ≈ 29.2.