Steady three-dimensional unbounded flow past an obstacle continuously deviating from a sphere to a cube

Abstract

We perform three-dimensional particle resolved direct numerical simulations of the flow past a non-spherical obstacle by a Finite Volume cut-cell method, a sub-class of non-body-conforming methods that provides a sharp description of the boundary, which is strictly mass and momentum conservative and can be easily extended to adaptive grids. The present research work discusses the effect of corner rounding and the incidence angle for a range of Reynolds numbers for which the flow exhibits a steady-state behavior. The obstacle is placed in a large cubic domain that properly models an unbounded domain. Hierarchically refined Cartesian meshes are used where the obstacle resides at the finest level of the mesh hierarchy, thus ensuring that the resolution of the boundary layer and the wake of the obstacle is highly accurate, along with significantly reducing the number of grid cells and the computing time. Specifically, we characterize the drag force and the main features of the flow past a bluff obstacle transitioning in shape from spherical to cuboidal through a superquadric geometrical representation. A superquadric representation is suitable for our study since it preserves geometric isometry, and our analysis, thus, focusses on non-sphericity caused by the level of curvature. We investigate a range of Re from 10 to 150, which spans the flow from attached to symmetric and separated past five different obstacle shapes, with the corner radius of the curvature of r/a=2/ζi=1,2/2.5,2/4,2/8 and 0 placed at incidence angles of α=0°, 15°, 30°, and 45° with respect to the streamwise direction. In general, our results show that the obstacle bluffness increases with α and ζi and this increase is more prominent at higher Re. Higher drag forces are a consequence of either higher viscous forces for more streamlined bodies and in less inertial regimes or higher pressure forces for more bluff bodies and in highly inertial regimes, depending on how the corners are contributing to the frontal and lateral surface areas.