Uniformly valid asymptotic flow analysis in curved channels

• Published in: Physics of fluids (1994) 2012-01, Vol.24 (1), p.013601-013601-25
• Main Authors: Zagzoule, M., Cathalifaud, P., Cousteix, J., Mauss, J.
• Format: Article
• Language: English
• Subjects: Exact sciences and technology; Flows in ducts, channels, nozzles, and conduits; Fluid Dynamics; Fluid mechanics; Fundamental areas of phenomenology (including applications); Laminar boundary layers; Laminar flows; Mechanics; Physics
• ISSN: 1070-6631; 1089-7666
• DOI: 10.1063/1.3673568

The laminar incompressible flow in a two-dimensional curved channel having at its upstream and downstream extremities two tangent straight channels is considered. A global interactive boundary layer (GIBL) model is developed using the approach of the successive complementary expansions method (SCEM) which is based on generalized asymptotic expansions leading to a uniformly valid approximation. The GIBL model is valid when the non dimensional number μ = δ R e 1 3 is O( 1 ) and gives predictions in agreement with numerical Navier-Stokes solutions for Reynolds numbers R e ranging from 1 to 10 4 and for constant curvatures δ = H R c ranging from 0.1 to 1, where H is the channel width and R c the curvature radius. The asymptotic analysis shows that μ, which is the ratio between the curvature and the thickness of the boundary layer of any perturbation to the Poiseuille flow, is a key parameter upon which depends the accuracy of the GIBL model. The upstream influence length is found asymptotically and numerically to be O ( R e 1 7 ) .