Integral transformation of the Navier-Stokes equations in cylindrical geometry

Abstract

The Generalized Integral Transform Technique (G.I.T.T.) is extended to handle the incompressible Navier-Stokes equations for two-dimensional steady laminar flow in cylindrical geometries. Hybrid numerical-analytical solutions with controlled accuracy are obtained, as a result of an appropriate choice of the associated eigenfunction expansion basis, extracted from the diffusion operator of the stream function-only formulation for this class of problems. The approach is illustrated for developing laminar flow within an annular channel and numerical results are obtained to demonstrate the excellent convergence characteristics of this hybrid method. Critical comparisons against the boundary layer formulation are provided, and a set of benchmark results is produced, for different values of Reynolds number and aspect ratio.