Abstract
This paper explores the screech closure mechanism for different axisymmetric modes in shock-containing jets. While many of the discontinuities in tonal frequency exhibited by screeching jets can be associated with a change in the azimuthal mode, there has to date been no satisfactory explanation for the existence of multiple axisymmetric modes at different frequencies. This paper provides just such an explanation. As shown in previous works, specific wavenumbers arise from the interaction of waves in the flow with the shocks. This provides new paths for driving upstream-travelling waves that can potentially close the resonance loop. Predictions using locally parallel and spatially periodic linear stability analyses and the wavenumber spectrum of the shock-cell structure suggest that the A1 mode resonance is closed by a wave generated when the Kelvin–Helmholtz mode interacts with the leading wavenumber of the shock-cell structure. The A2 mode is closed by a wave that arises owing to the interaction between the Kelvin–Helmholtz wave and a secondary wavenumber peak, which arises from the spatial variation of the shock-cell wavelength. The predictions are shown to closely match experimental data, and possible justifications for the dominance of each mode are provided based on the growth rates of the absolute instability.
Highlights
IntroductionDiscrete tones have been observed in shock-containing jets since the 1950s
Discrete tones have been observed in shock-containing jets since the 1950s. These are associated with the screech phenomenon, first studied by Powell (1953) using schlieren photographs, who suggested that this resonance loop was due to a mechanism involving large-scale structures and upstream-travelling acoustic waves
One should keep in mind that the models differ in the consideration of periodicity; while the first uses this assumption to obtain an expression for the resonance condition, the second (SPLSA) imposes periodicity directly in the formulation, and resonance is achieved by the presence of a saddle-point between upstream- and downstream-travelling waves with ω0i > 0
Summary
Discrete tones have been observed in shock-containing jets since the 1950s These are associated with the screech phenomenon, first studied by Powell (1953) using schlieren photographs, who suggested that this resonance loop was due to a mechanism involving large-scale structures and upstream-travelling acoustic waves. Recent studies have shown that, for both the axisymmetric A1 and A2 screech modes, the resonance phenomenon is underpinned by the downstream-travelling Kelvin-Helmholtz wavepacket and guided, upstream-travelling jet modes (Edgington-Mitchell et al 2018; Gojon et al 2018); the change in frequency cannot be explained by a change in the nature of the upstream-propagating wave The latter belongs to a branch of discrete modes of the stability eigenspectrum associated with a waveguide behaviour of the jet (Tam & Hu 1989), and only becomes discrete at specific (cut-on) frequencies, for which their phase velocity is below the sound speed. Prediction models using this upstream-travelling jet mode are in good agreement with experiments (Mancinelli et al 2019), prevailing over models that consider acoustic waves for resonance closure
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