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 decayingswirling flows have been derived for narrow- gap geometry. Expressions are derived for axial and swirl velocities, as well asfor the pressure. Generally, the swirl velocity exhibits a Hagen-Poiseuille flow profiles and these profiles decay graduallydownstream because of wall friction, which leads to damp the tangential velocity. For flows with small gap, the swirl velocitywill develop faster than a wider gap where the tangential velocity curves start flatter mid-gap and any further increases inaxial position, the decaying of swirl velocity will develop rapidly. When the Reynolds number increases the tangentialvelocity, profile flattens mid-gap. The dimensionless pressure is non-linear and it is very sensitive to inlet swirl and Reynoldsnumbers. It decreases downstream exponentially and steeper for small gap. The comparison between analytical and predictedresults shows good agreement in overall trends. A good correlation between the present analytical model and numericalresults is evident as the maximum difference between them is less than 5%