Sources of acoustic resonance generated by flow around a long rectangular plate in a duct

This paper describes a numerical investigation of the acoustic resonance occurring at specific flow speeds when a long two-dimensional rectangular plate is placed on the centre-line of a duct. The flow Mach number is sufficiently small that the flow and acoustic fields can be modelled separately; however, the effect of the acoustic field in modifying the flow field is accounted for and, in turn, the flow field solution determines the time-dependent source distribution for the acoustic model. This allows the range of flow speeds, or equivalently the associated Strouhal numbers, where resonance is possible to be predicted. It is shown that the Strouhal number based on plate chord (or length) displays a stepping behaviour as the plate length is increased. The main source or sink region where energy is transferred between the acoustic and flow fields is shown to be immediately downstream of the trailing edge of the plate. Visualizations of the numerical solution show that the timing when the vortices enter this region relative to the phase of the acoustic cycle is crucial in determining if resonance can occur and is the cause of the observed stepwise increase. Comparison is made with previous physical experiments.