A simple momentum integral model for estimating the minimum or “critical” swirl intensity required to produce central recirculation in a swirling sudden expansion flow is presented. An explicit equation is given for the critical swirl as a function of expansion ratio and inlet velocity profile shape, the latter expressed by the radius of the solid body vortex core and a parameter describing an axial velocity maximum or minimum on the axis. The model is tested against experimental data for expansion diameter ratios from 1.25 to 3.0 and a variety of inlet conditions, and found to give good predictions.

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