Uniformly valid asymptotic flow analysis in curved channels

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 mu = delta 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 6 = H/R-c ranging from 0.1 to 1, where H is the channel width and R, the curvature radius. The asymptotic analysis shows that mu, 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)). (C) 2012 American Institute of Physics. [doi: 10.1063/1.3673568]