Three-dimensional laminar incompressible flow in straight polar ducts

The flow in the entrance region of long ducts of rectangular and polar cross sections is studied using the three-dimensional parabolized Navier-Stokes equations, together with the energy equation, for an incompressible viscous fluid. Numerical solutions are obtained using an alternating-direction implicit technique for the parabolized equations which are elliptic in the cross-plane of the duct, and the calculations march forward in the axial direction. Computations are also made for polar ducts with a rotating outer-radial wall so as to provide meaningful results for a model problem comprising the simplest form of a turbomachinery cascade. The study of this model problem serves to analyze some of the important features of three-dimensional internal viscous flows. Also of interest is the rapidly converging solution of the Neumann problem for the cross-plane variation of pressure for polar ducts.