Uniformly valid asymptotic flow analysis in curved channels

Abstract

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=δRe13 is O(1) and gives predictions in agreement with numerical Navier-Stokes solutions for Reynolds numbers Re ranging from 1 to 104 and for constant curvatures δ=HRc ranging from 0.1 to 1, where H is the channel width and Rc 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(Re17).