Analytical Approximate Solution for Decaying Laminar Swirling Flows within A Narrow Annulus

Analytical solutions of the Navier-Stokes equations for laminar fully developed flow in a cylindrical annulus for decaying swirling flows have been derived for narrow- gap geometry. Expressions are derived for axial and swirl velocities, as well as for the pressure. Generally, the swirl velocity exhibits a Hagen-Poiseuille flow profiles and these profiles decay gradually downstream because of wall friction, which leads to damp the tangential velocity. For flows with small gap, the swirl velocity will develop faster than a wider gap where the tangential velocity curves start flatter mid-gap and any further increases in axial position, the decaying of swirl velocity will develop rapidly. When the Reynolds number increases the tangential velocity, profile flattens mid-gap. The dimensionless pressure is non-linear and it is very sensitive to inlet swirl and Reynolds numbers. It decreases downstream exponentially and steeper for small gap. The comparison between analytical and predicted results shows good agreement in overall trends. A good correlation between the present analytical model and numerical results is evident as the maximum difference between them is less than 5%.