Study of Fully Developed Incompressible Flow in Curved Ducts, Using a Multi-Grid Technique

Abstract

Fully developed flows inside curved ducts of rectangular as well as polar cross sections have been analyzed using the Navier-Stokes equations in terms of the axial velocity and vorticity and the cross-flow stream function. Numerical solutions of the three second-order coupled elliptic partial differential equations governing this flow have been obtained using efficient numerical schemes. For curved-duct flows, the similarity parameter of significance is the Dean number K, rather than the Reynolds number Re. Results have been obtained for curved ducts with square cross sections for K up to 900 which, in the present study, corresponds to Re = 9,000 for this internal flow configuration. The fine-grid calculations show that, for square cross-section ducts, Dean’s instability occurs at K ≈ 125 and, further, that this phenomenon does not disappear even for K = 900. In ducts of polar cross sections, which are geometrically more representative of turbomachinery cascade passages, the phenomenon of Dean’s instability is not seen to occur for K up to 600.