Direct Numerical Simulations on the Flow Normal to a Plate With Transit Shape From Circular Disk to Triangle

Abstract This paper presents a numerical study of the flow normal to a triangular plate. A total of four plates with the same frontal area Ar and different curved edges are used. The curvature of edges is determined by the compression ratio k (k = 0.3, 0.4, 0.5, 0.8; the large value of k corresponds to the large curvature of the edges). A disk of χ = 50 (χ is the diameter-thickness aspect ratio) is used as the reference disk. The Reynolds number Re based on the characteristic length is up to 250. Four states are observed and denoted as: (I) steady and geometric symmetry state (SG); (II) steady and reflectional symmetry state (SR); (III) reflectional symmetry breaking with periodic flow (RSB); (IV) chaotic state (CS). The critical Reynolds numbers at the first two stages (Rec1, Rec2) decrease with the increasing k, indicating that flow of the plates with a larger curvature is more unstable. Therefore, we believe that the flow around a triangular plate is more stable than that around a circular disk.