Convective Gaseous Diffusion in Steady Axisymetric Cavity Flows

Abstract

Theoretical results on gaseous convective turbulent diffusion in steady axisymmetric flows are found to compare well with experimental results already in the literature. The investigation starts with the formulation of a highly idealized “slug-flow” model of the process for a quick estimate of the importance of turbulent boundary layer convection and for a comparison of previously published experimental and analytical results which had revealed order-of-magnitude discrepancies between calculated and measured air diffusion rates. Next, an existing two-dimensional convective diffusion model is adapted to axisymmetric cavity flow. Good agreement between experimental and calculated mass flow rates is found with a proper choice of turbulent diffusively from a Launder-Spaulding mixing-length model. The adapted “wrap around” model predicts a concentration boundary-layer thickness of the order of the cavity radius at the cavity terminus. Consequently, an axisymeetric analysis is also presented. From this it is found that the important part of the gaseous mass flow into the cavity occurs near the very front of the cavity where the concentration gradients are most severe. Downstream flow regions near the cavity are thereby depleted of dissolved air and the resulting concentration gradients are greatly reduced. Therefore the mass flow rate through downstream cavity surfaces are relatively unimportant and the simpler wrap around calculation can give useful engineering estimates of total mass flow rates.