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EFFECT OF COLLISIONS AND FEEDBACK IN AN IDEALIZED ANNULAR FLOWS

Thomas J. Hanratty
Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign Urbana, Illinois 61801, USA

Yoichi Mito
Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign Urbana, Illinois 61801, USA

Resumo

Droplet behavior in a vertical annular flow is represented as the result of an array of point sources of spheres at the walls. The spheres mix in the turbulent flow and eventually deposit. A fully-developed condition can be reached when the rate of injection equals the rate of deposition. The deposition constant is found to be approximately equal to the root-mean-square of the wall-normal particle velocity fluctuations at a location just outside the viscous wall layer. It decreases dramatically with increasing concentrations at solid fractions as low as 4 × 10−4. The main cause of this appears to be a damping of fluid turbulence rather than particle collisions. By representing the feedback effect of particles with a point force method, the deposition constant is found to decrease at solid volume fractions as low as α > 10−4. In agreement with annular flow measurements, it is calculated to vary as α−1 at large α. An interesting consequence of this, demonstrated in the calculations, is that a stationary state cannot be reached above a critical rate of injection from the wall sources.