Wake transitions and scaling laws of a streamwise-rotating angular particle in an inertial flow

The wake dynamics and regime transitions of a streamwise-rotating angular particle in an inertial flow at moderate Reynolds numbers are investigated by particle-resolved direct numerical simulations, with particular focus on a rotating cube. We first identify the mechanisms of vortex generation on the front edges and the rear face, showing that rotation-induced vortex merging governs several key regime transitions. A previously unreported spearhead regime is uncovered, characterised by a helical near-wake and a steady filamentary far-wake structure. We demonstrate that it originates from the partial merging of edge vortices and the central rotation-induced vortex. Streamwise rotation is found to moderately stabilise the wake, and to induce a quadratic scaling of both the drag coefficient upper C Subscript d Baseline overbar C d ¯ $\overline {C_d}$ and the streamwise torque upper T Subscript x Baseline overbar T x ¯ $\overline {T_x}$ with the rotation rate upper Omega Ω $\varOmega$ . The evolution of the lift coefficient closely mirrors that of the recirculation length upper L Subscript r L r $L_r$ . For the rotating cube, the streamwise torque data collapse onto a single curve when expressed in terms of the rotation Reynolds number italic Re Subscript upper Omega Re Ω ${\textit{Re}}_{\varOmega }$ . Frequency analyses reveal that the fundamental transverse-force frequency is set by the number of rotational symmetry folds n Subscript upper Omega n Ω $n_{\varOmega }$ , while higher harmonics reflect the nonlinear nature of the flow–particle interaction. We further extend the analysis to general angular particles in their dual angular positions. Particles in dual configurations (sRCV, denoting a rotating cube with one vertex facing the incoming flow, and sROF, denoting a rotating octahedron with a front face facing the incoming flow) can display nearly identical regime transitions, as they share the same rotational symmetry folds and comparable vortex-pair strengths. Hydrodynamic responses remain strongly dependent on particle shape and orientation. Their frequency signatures likewise collapse when organised by n Subscript upper Omega