Influence of Resonant Acoustic Mode Shape on Source and Sink Patterns in the Wake of a Single Cylinder Based on Howe’s Energy Corollary

Abstract

Abstract The interaction between the acoustic field and periodic flow structures in the wake of a cylinder can self-excite resonance and lead to undesirable noise and vibrations in heat exchangers. The underlying energy exchange mechanism responsible for the emergence of a resonant acoustic field depends on the coupling between flow and acoustic parameters in time and space. Previous investigations have demonstrated that a net positive acoustic energy rate over a complete coupled cycle is essential to sustain resonant conditions. However, existing models have primarily focused on the excitation of the fundamental acoustic mode, considering only one-way coupling, resulting in predominantly qualitative findings. This study utilizes Howe’s energy corollary to determine the amount of acoustic energy produced and absorbed by the flow moving downstream of a single cylinder in a rectangular duct. By considering full coupling, resonant mode shapes are self-excited, enabling the computation of the acoustic and flow fields, acoustic energy generation, and the phase delay between the acoustic field and the lift force. Results provide detailed insights into the coupling mechanism governing the first three transverse acoustic modes, which can be excited by the unsteady vorticity shedding from the cylinder within the relevant velocity range of interest.