The interaction between various wavelike structures in screeching jets is considered via both experimental measurements and linear stability theory. Velocity snapshots of screeching jets are used to produce a reduced order model of the screech cycle via proper orthogonal decomposition. Streamwise Fourier filtering is then applied to isolate the negative and positive wavenumber components, which for the waves of interest in this jet correspond to upstream and downstream-travelling waves. A global stability analysis on an experimentally derived base flow is conducted, demonstrating a close match to the results obtained via experiment, indicating that the mechanisms considered here are well represented in a linear framework. In both analyses, three distinct wavelike structures are evident. These three waves are those first shown by Tam & Hu (1989) to be supported by a cylindrical vortex sheet. One is the Kelvin-Helmholtz mode. Another is the upstream-travelling guided jet mode that has been a topic of recent discussion. The third component, with positive phase velocity, has not previously been identified in screeching jets. We provide evidence that this downstream-travelling wave is a duct-like mode similar to that recently identified in high-subsonic jets by Towne et al. (2017). We further demonstrate that both of the latter two waves are generated by the interaction between the Kelvin-Helmholtz wavepacket and the shock cells in the flow, according to a theory first proposed in Tam & Tanna (1982). Finally, we consider the periodic spatial modulation of the coherent velocity fluctuation evident in screeching jets, and show that this modulation is the result of the superposition of the three wavelike structures, with no evidence that the shocks in the flow modulate the growth of the Kelvin-Helmholtz wavepacket.

Waves in screeching jets

The characteristics of acoustic tones near the nozzle of jets are investigated for Mach numbers between .

/pdf/acoustic-tones-in-the-near-nozzle-region-of-jets-1fol98fyx5.pdf

Acoustic tones in the near-nozzle region of jets: characteristics and variations between Mach numbers 0.5 and 2

The mechanism underpinning the generation of screech tones has remained an open question for many years. In this paper, direct experimental observations of the shock-leakage mechanism first proposed by Manning & Lele (AIAA Paper 1998, p. 282) are presented. Ultra-high-speed schlieren images are filtered to preserve only upstream-propagating components, with the upstream motion of the shock tip and subsequent emission of an acoustic wave visible for a number of operating conditions. The flow visualizations are supported by the ray-tracing model for shock leakage of Shariff & Manning (Phys. Fluids., vol. 25, issue 7, 2013, 076103), applied to velocity fields corresponding to a reconstructed screech cycle. The predictions of the model, when applied to real data, are in close agreement with the phenomena observed in the flow visualizations. It is demonstrated that shock leakage does not necessarily occur either at the point of maximum wave amplitude or maximum vorticity fluctuation. While the first point of shock leakage is shown to vary between cases, sound emission from multiple sources is observed for most cases considered. Finally, it is shown that variations in vortex strength captured in the velocity data are sufficient to explain variation in shock-leakage location observed in the flow visualization data.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/F53FC3CFCA79CEB23538325949B8F3D8/S0022112020009453a.pdf/div-class-title-the-generation-of-screech-tones-by-shock-leakage-div.pdf

The generation of screech tones by shock leakage

Abstract This paper describes the mechanism underpinning modal staging behaviour in screeching jets. An upstream-propagating subsonic guided-jet mode is shown to be active in all stages of screech. Axial variation of shock-cell spacing manifests in the spectral domain as a series of suboptimal peaks. It is demonstrated that the guided-jet mode may be energized by interactions of the Kelvin–Helmholtz wavepacket with not only the primary shock wavenumber peak, but also suboptimal peaks; interaction with suboptimals is shown to be responsible for closing the resonance loop in multiple stages of jet screech. A consideration of the full spectral representation of the shocks reconciles several of the classical models and results for jet screech that had heretofore been paradoxical. It is demonstrated that there are multiple standing waves present in the near field of screeching jets, corresponding to the superposition of the various waves active in these jets. Multimodal behaviour is explored for jets in a range of conditions, demonstrating that multiple peaks in the frequency spectra can be due to either changes in which peak of the shock spectra the Kelvin–Helmholtz wavepacket is interacting with, or a change in azimuthal mode, or both. The absence of modal staging in high-aspect-ratio non-axisymmetric jets is also explained in the context of the aforementioned mechanism. The paper closes with a new proposed theory for frequency selection in screeching jets, based on the observation that these triadic interactions appear to underpin selection of the guided-jet mode wavelength in all measured cases.

/pdf/a-unifying-theory-of-jet-screech-3eyvj7jo.pdf

A unifying theory of jet screech

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.

Absolute instability in shock-containing jets

The flow structures and the acoustic feedback loops of underexpanded round jets are investigated by numerical simulations. The jets have a Mach number of 1 at the nozzle exit and a diameter-based Reynolds number of . Three nozzle pressure ratios (NPRs) of 2.2, 2.4 and 2.6 are considered. The wavelengths of the screech tones are in good agreement with the experimental measurements on high-Reynolds-number jets in the literature. The screech tones are respectively at the A1 and B modes for the jets at NPRs of 2.2 and 2.6. Two screech tones at the A2 and B modes are identified in the jet at the NPR of 2.4 and the wavelet analyses conducted on the pressure fluctuations confirm that these two modes are contemporaneous. The amplitude and phase fields of fluctuating pressure at the screech frequencies are presented in the nozzle exit plane and azimuthal planes. The effective source locations of the screech tones are determined based on the distributions of the phase. The number of periods contained in the screech feedback loop is equal to the number of cells in the standing wave between the nozzle exit and the effective source. The screech frequencies estimated by the classical feedback model agree well with the numerical results at different modes. A modified model, in which the classical feedback model and the upstream-propagating acoustic wave mode of the jet are combined, shows that the screech feedback loops at the A1 and A2 modes are associated with the same acoustic wave mode. The modified model fails to estimate the screech frequencies at the B mode. Different feedback mechanisms lead to the coexistence of the A2 and B modes. The coherent structures corresponding to different screech modes are extracted by dynamic mode decomposition.

Acoustic feedback loops for screech tones of underexpanded free round jets at different modes

In many fluid experiments, we can only obtain low-spatial high-temporal resolution flow images and high-spatial low-temporal resolution flow images due to the limitation of high-speed imaging systems. To solve this problem, we proposed a degradation and super-resolution attention model (D-SRA) using unsupervised machine learning to super-resolution reconstruct high resolution (HR) time-resolved fluid images from coarse data. Unlike the prior research to increase the resolution of coarse data artificially generated by simple bilinear down-sampling, our model that consists of a degradation neural network and a super-resolution neural network aims to learn the mappings between experimental low-resolution data and corresponding HR data. What is more, channel and spatial attention modules are also adopted in D-SRA to facilitate the restoration of abundant and critical details of flow fields. The proposed model is validated by two high-speed schlieren experiments of under-expanded impinging supersonic jets. The comprehensive capability of D-SRA is statistically analyzed based on the synthetic unpaired schlieren images. The spatial-resolution of coarse images can be successfully augmented by [Formula: see text] times and [Formula: see text] times with most physical details recovered perfectly, which outperforms the existing method. The D-SRA also exhibits considerable generalization and robustness against unknown-degenerated schlieren images. Moreover, the practicability of the proposed method is also further explored on real unpaired jets schlieren images. It is convincingly demonstrated that the present study successfully surpasses the performance limitations of high-speed cameras and has significant applications in various fluid experiments to obtain flow images with high spatial and temporal resolution.

Deep-learning-based super-resolution reconstruction of high-speed imaging in fluids

A large-eddy simulation is performed to study the shock motions and flow structures of an underexpanded free jet. The jet is characterized by a nozzle pressure ratio of 3.4 and a fully expanded Mac...

Xiangru Li

Papers

Acoustic feedback loops for screech tones of underexpanded free round jets at different modes

A unifying theory of jet screech

Deep-learning-based super-resolution reconstruction of high-speed imaging in fluids

Shock Motion and Flow Structure of an Underexpanded Jet in the Helical Mode

Screech feedback loop and mode staging process of axisymmetric underexpanded jets