Forces on Bodies Moving in a Weak Density Gradient without Buoyancy Effects

Abstract

Particle laden flows and variable density gas streams passing through cool environments or near cool boundaries, are just two examples of environments where density gradients occur and solid particles or lumps of fluid with different densities move relative to their surrounding flow. In these situations the effect on the flow of density gradients and the flow induced by pressure gradients may be greater than buoyancy effects, and can materially alter the nature of the flow, such as the eddy structure and entrainment into plumes (e.g. Rooney & Linden 1996). Previous studies of particles and lumps have focussed on how the flow and force depend on external factors such as the gradient of local velocity field (Auton et al. 1987) and on differences between the local fluid and body density. Current models of turbulence and two phase flows tend to consider the effect of the movement of control volumes having different densities from their surroundings (Hunt, Perkins & Fung 1995), but do not generally represent the effect of the local gradients of density on the forces acting on the particles or eddies, although Chassaing et al. (1994) have proposed a model that includes these effects. In this paper we examine the flow generated by a body moving with constant velocity U in constant density gradient, ∇ρ0, and provide an insight into the forces and movement of eddies or particulate in flows with variable density. We focus on flows where inertia force dominates viscous and buoyancy forces, so that they are characterised by high Reynolds and Froude numbers.