Developing laminar flow in elliptical ducts via the F.E.M.

A finite element based numerical method is presented for the prediction of three-dimensional flow in the entrance region of noncircular passages with incompressible Newtonian laminar flow. The governing equations are parabolized and developed into a two-level integration method employing bi-quadratic isoparametric elements. The procedure is here applied to elliptical ducts to provide the first available solutions of all three velocity components directly from the Navier-Stokes equations. Good agreement with all relevant limiting cases is demonstrated including the circular duct where developing flow experimental data is available. Developing elliptical duct flow predictions are then presented and the main features discussed in comparison with existing simplified analytical solutions as no experimental data is available. Significant effects of the secondary, cross-plane velocities can be seen in the mean flow prediction and interesting asymmetric flow developments on the major and minor axes of the duct are also revealed.