Two-phase concave-type corner flows

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Abstract
The flow of a two-phase system past an arbitrary corner has been studied by Healy (1970a), using the method of small perturbations, and some results were presented for convex-type flows. This paper, which is an extension of the abovementioned one to concave-type flows, also compares the particle streamlines found from the perturbation with those obtained by numerically integrating the unperturbed equations. The agreement is found to be quite good for ξ0.2 and excellent when ξ = 0·1 or less, where ξ = ατ is the particle parameter, α is proportional to the speed of the fluid and τ is the particle relaxation time. The nature of concave corner flows abruptly changes when the angle β through which the flow is deflected is 90°. For β < 90°, all particles collide directly except those approaching on streamlines near the stagnation line. When β = 90° the critical value of ξ is ξc = 0·25 and, for 180° > β > 90°, only particles approaching on streamlines near the stagnation line all collide. No particle-free zones exist in concave-type flows and the particle density increases monotonically in the downstream direction along all particle streamlines. The approximate effects of viscosity are also discussed.

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