Dynamics, wakes, and regime transitions of a fixed angular particle in an unbounded inertial flow. II. From tetrahedron to sphere

In this study, we investigate an unbounded Newtonian fluid flow past a stationary Platonic polyhedron. To reveal the effects of the particle angularity and angular position on the flow regime transitions, we select the three following different angular positions of the Platonic polyhedrons: a face facing the flow (F), an edge facing the flow (E), and a vertex facing the flow (V). We consider all five Platonic polyhedrons whose sphericity increases with the number of faces and a sphere as an asymptotic polyhedron of sphericity 1 featuring an infinite number of faces. Two well-known regime transitions are studied as a function of the particle sphericity, the particle angular position and the particle Reynolds number Re: the loss of symmetry in the particle wake region and the loss of stationarity of the flow. In the multiplanar symmetry regime, the flow symmetry in the particle wake region is highly related to the particle front surface. The number and orientation of particle front surface edges determine the wake vorticity pattern. With increasing Re, the steady flow past an angular particle transitions to a planar symmetry regime for all particle shapes and all particle angular positions. The plane of symmetry in the planar symmetry regime selects one of the axis in the multiplanar symmetry regime, and its direction may change in time and/or with Re. In the unsteady regime, we notice a wide variety of periodic hairpin vortex shedding modes. These vortex shedding modes are determined by the shape of the flow recirculation region, which itself is a reflection of the angularity and the angular position of the particle. Furthermore, we present an in-depth analysis of the hydrodynamic forces exerted on the Platonic polyhedrons at the vertex angular position (V) for a wide range of Reynolds numbers 100 Re 500. We attempt to understand and explain the significant variations in the flow regime transitions brought by the particle angularity and the particle angular position.