Study of laminar and turbulent flow in ducts of polar cross-section

The viscous incompressible flow in curved ducts of some regular cross sections was analyzed for laminar as well as turbulent flow configurations. Rectangular, circular as well as polar cross sections were considered. The mathematical model is formulated using the time averaged three dimensional parabolized Navier-Stokes equations in a surface oriented toroidal coordinate system. An appropriate discretized representation is derived for the Poisson operator in analytically transformed coordinates in order to obtain efficient solutions of the Neumann boundary value problems encountered in the analysis. For turbulent flow configurations, turbulence closure is achieved by a two equation turbulence model employing the turbulent kinetic energy and its dissipation rate, which in turn yield the turbulent eddy viscosity. The Neumann boundary value problems encountered for the cross plane pressure distribution and for a velocity potential, introduced in order to satisfy local mass conservation, are solved by the successive over-relaxation method.