Waves in screeching jets

Edgington-Mitchell, Daniel; Wang, Tianye; Nogueira, Petrônio A. S.; Schmidt, Oliver T.; Jaunet, Vincent; Duke, Daniel J.; Jordan, Peter; Towne, Aaron

doi:10.1017/jfm.2020.1175

Cited by 66 publications

(56 citation statements)

References 74 publications

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“…Figure 1( b ) exhibits some of the leading characteristics of a shock-cell structure in an under-expanded jet, though with some differences in shape when compared with experiments (see, for example, Edgington-Mitchell et al. 2021 a ). As noted by Tam & Tanna (1982), the addition of other shock-cell wavenumbers may lead to a closer agreement in the shape of this structure with experiments; here, we consider the leading wavenumber to be sufficient to analyse the effect of such a structure on the different waves in the flow.…”

Section: Resultsmentioning

confidence: 95%

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Absolute instability in shock-containing jets

et al. 2021

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We present an analysis of the linear stability characteristics of shock-containing jets. The flow is linearised around a spatially periodic mean, which acts as a surrogate for a mean flow with a shock-cell structure, leading to a set of partial differential equations with periodic coefficients in space. Disturbances are written using the Floquet ansatz and Fourier modes in the streamwise direction, leading to an eigenvalue problem for the Floquet exponent. The characteristics of the solution are directly compared with the locally parallel case, and some of the features are similar. The inclusion of periodicity induces minor changes in the growth rate and phase velocity of the relevant modes for small shock amplitudes. On the other hand, the eigenfunctions are now subject to modulation related to the periodicity of the flow. Analysis of the spatio-temporal growth rates led to the identification of a saddle point between the Kelvin–Helmholtz mode and the guided jet mode, characterising an absolute instability mechanism. Frequencies and mode shapes related to the saddle points for two conditions (associated with axisymmetric and helical modes) are compared with screech frequencies and the most energetic coherent structures of screeching jets, resulting in a good agreement for both. The analysis shows that a periodic shock-cell structure has an impulse response that grows upstream, leading to oscillator behaviour. The results suggest that screech can occur in the absence of a nozzle, and that the upstream reflection condition is not essential for screech frequency selection. Connections to previous models are also discussed.

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Section: Resultsmentioning

confidence: 95%

“…Examples of analyses using such tools in shock-containing jets can be seen in Beneddine, Mettot & Sipp (2015) and Edgington-Mitchell et al. (2021 a ). In these previous works, screech can be seen as a global mode of the flow, when the shock-containing mean flow is considered as the base flow.…”

Section: Introductionmentioning

confidence: 99%

Absolute instability in shock-containing jets

et al. 2021

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“…These guided modes were first studied by Tam & Hu (1989) and have since been used to explain many resonance phenomena: in subsonic and supersonic impinging jets (Tam & Ahuja 1990;Bogey & Gojon 2017), in high-speed subsonic jets (Towne et al 2017) and in a jet-flap interaction configuration (Jordan et al 2018). Most importantly, they have been shown to be active in screeching supersonic jets (Edgington-Mitchell et al 2018;Gojon, Bogey & Mihaescu 2018;Edgington-Mitchell et al 2021a). Given this insight, we recently developed a screech-frequency prediction model based on a resonance between downstream-travelling Kelvin-Helmholtz (K-H) waves and upstream-travelling guided-jet modes (Mancinelli et al 2019a).…”

Section: Upstream-travelling Waves In the Resonance Loop And Implications For Frequencymentioning

confidence: 99%

“…Downstream-travelling Kelvin-Helmholtz waves, of wavenumber k + KH , interact nonlinearly with a stationary shock-cell structure characterised by wavenumber k s , and the interaction leads to a difference wavenumber k − p = k + KH − k s . Sound is then generated by the so-called Mach-wave mechanism, which radiates in the upstream direction because of the negative phase speed (more recent works by Towne et al (2017) and Edgington-Mitchell et al (2021a) have established that the group velocity of this wave is also negative). As shown by Lele (2005), the phased-array and wave-interaction models for sound radiation are equivalent, and there is a solid body of work suggesting that the sound-generation mechanisms of both broadband shock-associated noise (BBSAN) and screech are indeed underpinned by this distributed-source behaviour (see among many Tam & Tanna 1982;Tam et al 1986;Shen & Tam 2002;Wong et al 2021).…”

Section: Introductionmentioning

confidence: 99%

A complex-valued resonance model for axisymmetric screech tones in supersonic jets

et al. 2021

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We model the resonance mechanism underpinning generation of A1 and A2 screech tones in an under-expanded supersonic jet. Starting from the resonance model recently proposed by Mancinelli et al. (Exp. Fluids, vol. 60, 2019, p. 22), where the upstream-travelling wave is a neutrally stable guided-jet mode, we here present a more complete linear-stability-based model for screech prediction. We study temperature and shear-layer thickness effects and show that, in order to accurately describe the experimental data, the effect of the finite thickness of the shear layer must be incorporated in the jet-dynamics model. We then present an improved resonance model for screech-frequency predictions in which both downstream- and upstream-travelling waves may have a complex wavenumber and frequency. This resonance model requires knowledge of the reflection coefficients at the upstream and downstream locations of the resonance loop. We explore the effect of the reflection coefficients on the resonance model and propose an approach for their identification. The complex-mode model identifies limited regions of frequency–flow parameter space for which the resonance loop is amplified in time, a necessary condition for the resonance to be sustained. This model provides an improved description of the experimental measurements.

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“…For that reason, these waves, sometimes called neutral acoustic waves in the literature, will be referred to as guided jet waves in what follows, as in the recent paper of Edgington-Mitchell et al. (2021). They were shown in Tam & Ahuja (1990), Tam & Norum (1992), Gojon, Bogey & Marsden (2016), Bogey & Gojon (2017) and Jaunet et al.…”

Section: Introductionmentioning

confidence: 99%