Reynolds number effects on the flow around a 4:1 rectangular cylinder

Two-dimensional (2D) laminar and three-dimensional (3D) large-eddy simulations (LES) are performed to comprehensively investigate the flow dynamics and aerodynamic characteristics of uniform flow around a 4:1 rectangular cylinder at Reynolds number Re = 1–1.2 × 10⁵. Four distinct flow regimes are found: steady flow (Regime Ⅰ, Re < 92), unsteady laminar flow (Regime Ⅱ, 92 ≤ Re < 4.5 × 10²), wake transition (Regime Ⅲ, 4.5 × 10² ≤ Re < 7.0 × 10²), and shear layer transition (Regime Ⅳ, 7.0 × 10² ≤ Re ≤ 1.2 × 10⁵). In Regime I, for Re < 3 (Regime I-a), flow fully attaches to surfaces, namely 'creeping' flow; for 3 ≤ Re < 92 (Regime Ⅰ-b), flow separates from trailing edges, forming a steady recirculation region in the wake, namely steady separated regime. In Regime Ⅱ, for 92 ≤ Re < 1.2 × 10² (Regime Ⅱ-a), flow separates from trailing-edge corners and forms laminar Kármán vortices; for 1.2 × 10² ≤ Re < 3.0 × 10² (Regime Ⅱ-b), flow separates from leading-edge corners, reattaches to lateral surfaces with symmetrical steady separation bubbles, and separates again from trailing-edge corners; for 3.0 × 10² ≤ Re < 4.5 × 10² (Regime Ⅱ-c), flow changes from Kármán vortices to impinging-leading-edge-vortex (ILEV) instability, causing Strouhal number (St) to suddenly drop from 0.162 (Re = 2.75 × 10²) to 0.130 (Re = 3.0 × 10²). In Regime Ⅲ, wake vortices transition from laminar to turbulence with ILEV instability. In Regime Ⅳ, separated shear layers transition to turbulence, and transition position moves upstream as Re increases.