A direct numerical method for the solution of unsteady Navier-Stokes equations in generalized orthogonal coordinates

An implicit numerical analysis is developed for the unsteady, incompressible, two-dimensional Navier-Stokes equations in generalized orthogonal coordinates. Two internal separated, viscous fluid flows, characterized by multiple length scales, are studied in detail. Comparisons with available laser-Doppler measurements are made for several backstep channel geometries. Tabulated separation and reattachment lengths, recirculation intensities, and vortex-center locations are given for the backstep channel and for channels with an asymmetric constriction over a wide range of Reynolds numbers. Predicated stream-function contours, vorticity contours, and horizontal velocity profiles are also provided. The velocity profiles are compared with experiment whenever possible. Three-dimensionality in the experimental data is revealed and a Taylor-Gortler vortex instability mechanism is discussed as a probable cause for this observed three-dimensionality.