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.
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Acknowledgements-This paper is based upon work supported through both the Electric Power Research Institute (EPRI) and the Institute’s Electric Power and Research in Iowa program, which is funded by Iowa’s Investor-Owned Utilities, under the general guidance ‘of Professor A. J. Odgaard. The authors are grateful to Mr Timothy Johnson for his contribution in analysing the flow topology, as well as Professors A. J. Odgaard and V. C. Pate1 for their helpful comments and suggestions. The calculations in this study were carried out at the San Diego Supercomputing Center (SDSC).