Numerical investigation of laminar flows through 90-degree diversions of rectangular cross-section

Numerical solutions of the incompressible Navier-Stokes equations are obtained for steady, laminar flows through 90-degree diversions of rectangular cross-section. Calculations are carried out for various Reynolds numbers, discharge ratios and duct aspect ratios. The computed solutions are compared with available experimental measurements and analysed to elucidate the complex three-dimensional separation and flow topology patterns. It is shown that, even for large aspect ratio ducts, the flow at the symmetry plane is significantly affected by the distant top and bottom solid boundaries. These boundaries induce a complex three-dimensional flow which includes: a depth-varying dividing stream-surface in the main channel; depth-varying recirculation zones in both main and branch channels within which low velocity flow spirals upward; and secondary circulation currents which sweep near-bottom boundary flow into the two recirculation zones. These same flow patterns have been observed experimentally in diversions of circular as well as rectangular cross-sections for both turbulent and laminar flow regimes, but their details were not accessible to previous calculations.