Self-sustained azimuthal aeroacoustic modes. Part 2. Effect of a swirling mean flow on the modal dynamics

The whistling induced by a low-Mach turbulent flow through a deep axisymmetric cavity in a duct is investigated theoretically and experimentally. The experiments include acoustic measurements and stereoscopic particle image velocimetry (PIV). The paper focuses on the effect of a mean swirl on the dynamics of the azimuthal aeroacoustic modes. The mean swirl in the cavity has two origins: one component is imposed by a controlled tangential air injection upstream of the cavity, and the other component spontaneously arises under the action of the self-sustained azimuthal aeroacoustic mode, as explained in the companion paper, Part 1 (Faure-Beaulieu, Xiong, Pedergnana & Noiray, J. Fluid Mech. , vol. 971, 2023, A21). Experiments show that the dynamics of the aeroacoustic wave is influenced by the imposed swirl. In particular, the spinning wave propagating against the swirl is promoted. To explain this, a linear perturbation analysis is performed around an incompressible mean swirling flow obtained from RANS simulations. It reveals that the dominant shear layer modes of azimuthal order 1 and −1 involved in the whistling phenomenon are helical modes winding respectively with and against the swirl, and spinning respectively in counterswirl and co-swirl directions. The counterswirl hydrodynamic mode is the least damped of the two, which is in agreement with the experimental observations. Finally, a low-order model based on the wave equation is derived. With only a few parameters, it fully reproduces the experimental observations for a wide range of imposed swirl intensity in the duct flow, and it allows us to disentangle the mechanisms responsible for this complex aeroacoustic instability.