• Accepted Paper

Phase dynamics in the flow-induced vibration of an inclined D-section cylinder at low Reynolds numbers

Bin Liu, J. Geoffrey Chase, Ye Chen, and Xiaoqi Chen

Phys. Rev. Fluids - Accepted 29 September, 2026

DOI: https://doi.org/10.1103/n8mg-cjvs

Abstract

Non-circular and asymmetric bluff bodies are widely encountered in engineering applications, such as micro air vehicle wings and small-scale underwater sensor supports, where vibration induced by flow is often more complex than that of canonical circular cylinders. In particular, inclined bluff bodies may exhibit transitional responses that cannot be fully classified within the conventional frameworks of vortex induced vibration and galloping. This study investigates such an anomalous response for an inclined D-section cylinder undergoing transverse vibration in two dimensions at Re = 100. The angle of incidence is fixed at α = 60◦, and three mass ratios, m∗ = 5, 10, and 20, are examined over a range of reduced velocities. The analysis combines numerical simulations with ERA-based linear stability analysis, structural energy share analysis, instantaneous phase statistics, and dynamic mode decomposition. A finite phase wandering regime is identified between the locked response at low values of U∗ and the low amplitude response at high values of U∗. Within this regime, the vibration frequency departs from the conventional lock-in relation, whereas the displacement amplitude does not develop into sustained galloping type growth. Instead, the response exhibits amplitude reduction, local recovery, persistent phase slipping, and the coexistence of two separated time scales in the wake. The stability and structural energy share analyses show the offset between the lift and displacement peaks at low reduced velocities is associated with modal redistribution, whereas the anomalous response at higher reduced velocities is not caused by a second switching of modal participation. The phase and DMD results further indicate the phase wandering regime corresponds to a finite reorganization of the phase relation between the fluid force and the structural motion, together with a reorganization of the wake dynamics. These results provide a mechanistic interpretation of the anomalous transitional response of inclined D-section cylinders and clarify why frequency separation does not necessarily lead to sustained galloping type growth.

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