Resonance in axisymmetric jets with controlled helical-mode input

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Abstract
This work involves active control of fundamental two- and three-dimensional amplified modes in an axisymmetric jet by introducing localized acoustic disturbances produced by an azimuthal array of miniature speakers placed close to the jet lip on the exit face. The independent control of each speaker output allowed different azimuthal amplitude and phase distributions of periodic inputs. The types of inputs used in this study consisted of conditions to force helical mode pairs with the same frequency and equal but opposite azimuthal wavenumbers, m = ±1, separately, or with axisymmetric (m = 0) modes. Three forcing conditions were studied in detail. The first consisted of a weakly amplified helical mode pair which was essentially ‘superposed’ with the natural jet instability modes. This provided a reference to the second case which consisted of the same helical mode pairs along with an axisymmetric mode at the harmonic streamwise wavenumber. This combination led to the resonant growth of the otherwise weakly (linear) amplified subharmonic helical modes. A weakly nonlinear three-wave amplitude evolution equation with a coupling coefficient derived from the data was found to model the enhanced growth of the subharmonic helical modes well. The third case consisted of forcing only m = ±1 helical modes at a frequency which was close to the most amplified. This was compared to the results of Corke et al. (1991) who forced an axisymmetric mode at the same frequency and found it to lead to the enhanced growth of near-subharmonic modes, as well as numerous sum and difference modes. The helical modes had effects identical to the previous work and confirmed the resonant amplification of a near-subharmonic mode. The amplitude development was also well represented by the nonlinear amplitude equation, including the dependence of the streamwise amplification rate on the azimuthal change in the fundamental-mode initial amplitude. However, the coupling coefficient in this case was approximately one-third that with exact fundamental-subharmonic resonance. Finally we offer some explanation for the selection of the different mode frequencies in this case.