NUMERICAL-METHOD FOR THE COMPUTATION OF FLOW IN IRREGULAR DOMAINS THAT EXHIBIT GEOMETRIC PERIODICITY USING NONSTAGGERED GRIDS

Flows in many engineering applications occur in devices that exhibit g eometric periodicity, giving rise to flow characteristics that are spa tially periodic. This periodicity can be of two types, translational a nd rotational. Since the geometries encountered in practice are often complex, periodic boundary-fitted grids are used over a typical module to predict such flows. Nonstaggered grids are frequently used for dis cretizing the equations governing the flow. These methods employ Carte sian velocities as the primary unknowns. In rotationally periodic geom etries, these components themselves are not periodic, necessitating sp ecial considerations in incorporating the periodicity conditions over the periodic modules. The aim of the present study is to propose modif ications to the conventional nonstaggered grid methods for computation s of spatially periodic flows, so that geometric periodicities can be treated in a unified manner. The proposed formulation represents a gen eralization of the existing formulations for nonstaggered grids and ca n be applied for the discretization of the governing equations in doma ins with or without periodicity. The proposed formulation is first val idated by comparing the computed solutions with the exact solutions fo r Couette flows in a parallel-plate channel and a cylindrical annulus. The method is then applied to three physical situations to illustrate its utility.