Implicit Method for Incompressible Flow Calculations in Three-Dimensional Ducts and Cascades

A method is presented for the numerical solution of the incompressible Navier-Stokes equations in three-dimensional ducts and cascades. Both laminar and turbulent flows are resolved, the latter through the k-epsilon turbulence model. The method is based on an elliptic formulation, which consists of the sequential solution of the mean flow and the turbulence equations through an approximate factorization technique. The cost of factorization is minimized through the formation and inversion of a single matrix for all but the continuity equations. The continuity constraint is enforced by means of the pressure-correction technique for which a more efficient variant of the approximate factorization scheme is employed. The method exhibits good convergence characteristics, as depicted from the analyzed three-dimensional problems. The prediction capabilities of this method are demonstrated by analyzing the laminar flow in a three-dimensional bend and the turbulent flow in a linear compressor cascade, with zero and nonzero tip clearance. For cascade how problems with nonzero tip clearances, a variant of the present method accommodating multiple, patched subdomains is devised.