High Reynolds Channel Flows: Variable Curvature

Abstract

Two-dimensional laminar flow, at high Reynolds number Re, of an incompressible Newtonian fluid in a curved channel connected to two fitting tangent straight channels at its upstream and downstream extremities is considered. The Successive Complementary Expansion Method (SCEM) is adopted. This method leads to an asymptotic reduced model called Global Interactive Boundary Layer (GIBL) which gives a uniformly valid approximate solution of the flow field in the whole domain. To explore the effect of the variable curvature on the flow field, the bend has an elliptical median line. The validity of the proposed GIBL model is confronted to the numerical solution of complete Navier–Stokes equations. This comparison includes the wall shear stress which is a very sensitive measure of the flow field. The GIBL results match very well the complete Navier–stokes results for curvatures K _max up to 0.4, curvature variations $\vert {K\prime}_{max}\vert$ up to 0.7 and eccentricities e up to $\simeq0.943$ in the whole geometrical domain. The upstream and downstream effects as well as the impact of the curvature discontinuities and the behaviour in the entire bend are well captured by the GIBL model.