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The objective of the current study is development of a coupled orthogonal curvilinear/Cartesian grid solver. The solver requires a thin orthogonal boundary layer grid and a non-uniform Cartesian grid to resolve the boundary layer on a solid surface and the flow region away from the surface, respectively. Flows inside the orthogonal boundary layer and Cartesian background grids are solved by different CFD solvers which are coupled by an overset grid method. SUGGAR code writes the grid domain connectivity information into a file that identifies grid points necessary for the overset grid interpolation. In order to satisfy mass conservation across the overlapping region, the pressure Poisson equations and the overset interpolation equations are encompassed from both of the solvers and solved simultaneously by an iterative method.
Accuracy of the coupled orthogonal curvilinear/Cartesian grid solver was evaluated in terms of flows past circular cylinders because the orthogonal boundary layer grids can be generated easily due to its simple cylindrical shape. In this study, additional numerical simulations were also performed by the original orthogonal curvilinear and Cartesian grid solvers in order to obtain the benchmark data to compare with the results of the coupled orthogonal curvilinear/Cartesian grid solver.
The coupled orthogonal curvilinear/Cartesian grid solver was applied to steady and unsteady laminar flows at Re = 40 and 200, single-phase turbulent flows at subcritical Re = 3900 and supercritical Re = 5×105 and 1×106, and two-phase flows at (Re, Fr) = (2.7×104, 0.20), (2.7×104, 0.80), and (4.58×105, 1.64). Those numerical results are in good agreement with the experimental and numerical results in the literature.
Effects of the grid resolution on the numerical results were analyzed in this study. The analysis showed the more accurate resolution of near-wall regions by the boundary layer grids for the coupled orthogonal curvilinear/Cartesian grid solver. It also presented the similar trends of the flow at the subcritical Re with the vertical resolution to those observed in the literature.
The coupled orthogonal curvilinear/Cartesian grid solver predicted much delayed separations of the boundary layers at both the supercritical Re, which caused the narrower wakes and the shorter recirculation regions than those at the subcritical Re. The features of surface pressure corresponded to the postponed separations.
The solver developed in this study showed the similar trends in the two-phase flows at Fr = 0.20 and 0.80 to those observed by the past numerical studies. The trends of the vortex shedding, deviating shear layers, and the expanded wake on the free surface are more prominent in the flow at Fr = 0.80 than that at Fr = 0.20.
At Re = 4.58×105 and Fr = 1.64, the flow near the free surface includes the small recirculation region behind the cylinder, which corresponds to the cavity structure on the free surface in the same region, and two large symmetric recirculation regions. The shear layers separating from the cylinder surface move along the outer edges of the recirculation regions. Another pair of the shear layers is separated from the smaller recirculation region.