Internal swirling flows by the Dorodnitsyn finite element formulation

The Dorodnitsyn boundary layer formulation is combined with a modified Galerkin finite element method to obtain the solution for swirling turbulent boundary layer flow inside a conical diffuser. The Dorodnitsyn formulation introduces a nondimensional normal velocity gradient as the primary independent variable, consequently skin friction is computed particularly accurately. The group finite element approach is used to generate a very efficient algorithm when combined with an implicit second-order, three-level, non-iterative marching algorithm. The systems of implicit equations, at each downstream location, are solved sequentially for the normal velocity gradient, circumferential velocity and pressure. An anisotropic eddy viscosity formulation is used to represent the Reynolds stresses. Results are presented for skin friction and displacement thickness for both a constant-area duct and a 10 deg included-angle conical diffuser with various initial swirl values. It is established that the addition of swirl helps to delay boundary layer separation.