High fidelity adaptive Cartesian octree grid computations of the flow past a Platonic polyhedron up to a Reynolds number of 200

Abstract

We use a high fidelity non-boundary fitted Distributed Lagrange Multiplier/Fictitious Domain method implemented on an adaptive Cartesian octree grid to investigate the unbounded flow of a Newtonian fluid past a stationary Platonic polyhedron. We consider five Platonic polyhedrons and a sphere as an asymptotic polyhedron featuring an infinite number of faces. We explore the impact of angularity on the drag and lift coefficients for a range of Reynolds numbers Re∈[1,200] over which the flow is steady or only mildly unsteady. In order to reduce the parameter space, we consider three specific angular positions of the polyhedron: face facing the flow, edge facing the flow and vertex facing the flow. The effects of these angular positions, notably on drag and lift coefficients, are discussed. For low Reynolds numbers, the particle crosswise cross-sectional surface area has a prominent influence on the drag coefficient while for higher Reynolds numbers the impact of the particle angular position becomes more significant. We also observe that the change in the symmetry of the wake region and the corresponding regime transitions are strongly related to the lift coefficient evolution with Re. Finally, we evaluate the accuracy of various non-spherical particle drag coefficient correlations available in the literature and provide new insights into the understanding of unbounded laminar flows past a non-spherical angular particle.