On the modal behaviour of trapped diametral modes in a ducted cavity

The excitation of trapped diametral acoustic modes within a square cavity attached to cylindrical pipes is investigated numerically and experimentally. Because the excited acoustic modes are highly three-dimensional, their interaction with the shear layer instability results in rather complex unsteady flow oscillations. These are investigated through three unique behaviours of the excited acoustic modes, including both stationary and spinning mode patterns. Flow visualization utilizing Phase-locked PIV, accompanied with numerical simulations of the resonant sound fields, indicate that the formation of disturbances is nonuniform and akin to the radial acoustic particle velocity distribution. In the case of two acoustic modes being excited simultaneously, separate circumferential segments of the cylindrical shear layer oscillate independently and at different frequencies, corresponding to the frequencies of the excited modes. Further, due to the symmetry inherent within the square geometry, two degenerate modes (i.e. orthogonal mode shapes with the same resonance frequency) generate a spinning mode when they are excited. The interaction of the spinning acoustic mode with the cavity shear layer leads to the formation of a three-dimensional helical vortex tube. These results indicate that a uniform synchronized excitation over the whole shear layer circumference is not necessary to maintain orderly and coherent vortical structures that produce and sustain strong acoustic resonances.