Compressible jets impinging on a perpendicular surface can produce high-intensity, discrete-frequency tones. The character of these tones is a function of nozzle shape, jet Mach number, impingement-plate geometry, and the distance between nozzle and plate. Though it has long been recognised that these tones are associated with a resonance cycle, the exact mechanism by which they are generated has remained a topic of some debate. In this work, we present evidence for a number of distinct tone-generation mechanisms, reconciling some of the different findings of prior authors. We demonstrate that the upstream-propagating waves that close resonance can be confined within the jet, or external to it. These waves can be either weak and relatively linear, or strong and nonlinear from their inception. The waves can undergo coalescence or merging, and in some configurations, pairs of waves rather than singletons appear. We discuss both historical and new evidence for multiple distinct processes by which upstream-propagating waves are produced: direct vortex sound, shock leakage, wall-jet-boundary fluctuations, and wall-jet shocklets. We link these various mechanisms to the disparate collection of upstream-propagating waves observed in the data. We also demonstrate that multiple mechanisms can be provoked by a single vortex, providing an explanation as to why sometimes pairs of waves or merging waves are observed. Through this body of work, we demonstrate that rather than being in opposition, the various pieces of past research on this topic were simply identifying different mechanisms that can support resonance.

This study identifies two previously unrecognised screech modes in non-axisymmetric jets. Spectral proper orthogonal decomposition (SPOD) of ultra-high-speed schlieren images reveals a bi-axial flapping mode in a rectangular jet and a quasi-helical mode in an elliptical jet. To educe the complex three-dimensional structure of these new modes, SPOD is performed on datasets from different viewing perspectives, produced by rotating the nozzle with respect to the schlieren path to an azimuthal angle $\theta$. The bi-axial flapping mode is strongly antisymmetric from any perspective. However, the SPOD eigenvalue at the screech frequency ($\lambda _s$) varies with $\theta$ and the axial distance of the SPOD domain from the nozzle lip. This mode most closely resembles a flapping mode in the minor-axis plane close to the nozzle lip and a wagging mode in the major-axis plane further downstream. This transition from flapping to wagging at the same frequency correlates with the axis switching defined by the shock-cell structure in the mean flow. The quasi-helical mode in the elliptical jet is characterised by an antisymmetric structure present in the SPOD spatial modes whose eigenvalue $\lambda _s$ is insensitive to both $\theta$ and the axial domain. These findings indicate that the spatial evolution of the mean flow in non-axisymmetric jets may allow them to support a range of additional screech modes that differ significantly from those supported by the original three-dimensional shape of the jet.

In this work, the screech resonance loop in a military-style, converging–diverging nozzle is explored using a range of experimental and modeling techniques. Schlieren measurements of both major and minor axes were performed at a range of nozzle pressure ratios (NPRs), with the images decomposed via spectral-proper orthogonal decomposition. The decomposed data allow for the identification of modal staging and also provide information about the symmetry of the waves involved in the resonance loop. Further analysis was performed using particle image velocimetry (PIV) data, with the velocity fields associated with the different screech modes obtained by modal decomposition. The PIV data was also used to provide mean flows for linear stability analysis, which is used to predict the wavenumbers of the different waves involved in the resonance loop. These predictions are used in conjunction with a weakest-link model to predict the screech frequency of the flapping modes at a range of NPRs and are found to be in good agreement with the experimentally observed tones.

In this work, the characteristics of the screech resonance loop of a military-style, converging-diverging nozzle are explored using a range of experimental and modelling techniques. Schlieren measurements at both major and minor axes were performed at a range of nozzle pressure ratios (NPR), on which spectral-proper orthogonal decomposition was performed. This allowed for the identification of the staging behaviour in these nozzles, and also provided some information about the symmetry of the waves involved in the resonance loop. Further analysis was performed using particle-image velocimetry (PIV) data, where the velocity fields associated with the different screech modes were obtained by modal decomposition. The PIV data was also used to provide mean flows for linear-stability analysis (LSA), which was used to predict the wavenumbers of the different waves involved in the resonance loop. These were used in conjunction with a weakest-link model to predict the screech frequency at a range of NPR, which were found to be in good agreement with the experimentally observed tones.

Upstream-travelling guided jet waves have been shown to be one of the key elements in many resonance processes underpinned in high-speed jets. Despite its importance, many of its characteristics, including how these waves are generated and how it can travel subsonically, have not been detailed in the literature. In this work, we aim to provide a clarification about the dynamics of this mode. With the aid of an acoustic scattering formulation, we are able to show that the guided-jet mode results from total-internal-reflection and transmission to decaying waves, arising from the shear layer behaving like a hard duct. After total reflection, only discrete streamwise wavenumbers may be supported by the flow, with these wavenumbers dictated by the fact that the standing wave formed inside of the jet must fit between the two shear layers. Close to the sonic line, the transmission of this mode to the outside is maximum, leading to a net-energy flux directed upstream, which dictates the direction of propagation of this mode in the eigenspectrum, providing a clear connection to the better understood soft-duct mode.

The rotating-detonation engine is perhaps the most promising means to realize pressure-gain combustion in modern engines. The physical processes underpinning the dynamics of the combustion wave are complex, and a lack of understanding of these processes represents a significant barrier to practical implementation of the technology. While the propagation of the detonation wave in the azimuth is pseudo-steady in time when the observer is fixed to the motion of the wave, the interaction of the wave with the fuel and reactant injectors is highly unsteady. This interaction directly relates to the performance of the engine, as the pressure rise behind the detonation wave alters the pressure differential across the injector, and thus the flow of reactant into the detonation annulus. This variation in flowrate can result in instability of the detonation waves in the annulus, and consequently in the power output and efficiency of the engine. Between the complexity of the geometry, the unsteadiness of the flow, and the intrinsic challenge of studying shock-driven combustion, the details of this interaction remain relatively obscure. As a first step towards understanding the injector-wave interaction, a significant simplification of the problem is considered through an abstracted experimental setup. The detonation wave is replaced with a non-reacting shock generated by a shock tube, and the annulus is unwrapped into a single linear channel. Both simplifications make direct visualization of the problem via schlieren imaging tractable. The experimental work is then used primarily as a validation for computational fluid dynamics simulations of the simplified problem; simulations that permit the extraction of quantitative data that can be used to characterize the time-varying performance of the injector.

Despite decades of research, many of the mechanisms underpinning jet screech remain poorly understood. Though there have been significant recent advances in understanding, one as-yet unexplained phenomenon is the tendency of some jet configurations to produce multiple screech tones at a single operating condition. In this work, we investigate multimodal behaviour in screeching elliptical and rectangular jets with an aspect ratio AR = 2.0 using high-speed schlieren. Spectral proper orthogonal decomposition (SPOD) is used to isolate energetic structures in both minor-axis and major-axis planes. The data reveal that jet screech may manifest in one of three modes within the pressure range considered, with each of these modes characterized by particular symmetries about the major and minor axes. Time-frequency analysis of the results show that multiple screech modes are mutually exclusive. In addition, comparison of axial wavenumber spectra of the spatial modes demonstrates that, in the absence of multimodal behaviour, the guided jet mode (G-JM) is energized by triadic interactions between the Kelvin-Helmholtz (KH) wavepacket and the primary peak in the shock-cell wavenumber spectra. When multiple screech modes are present, the secondary peak in the shock-cell spectra is responsible for closing all screech resonance loops. These findings pave the way for a better understanding of screech.

The dynamics of wavepackets in an elliptical jets are studied using direct numerical simulation (DNS) data of an AR = 2 incompressible elliptical jet at Reynolds number Re = 400. Analysis of the numerical data displays several complex features, the most striking being axis switching, a phenomenon that strongly affects the development of coherent structures in the flow. By applying spectral proper orthogonal decomposition (SPOD), it was found that modes in the SA symmetry were dominated by the se(1) flapping geometry in the upstream region. After the axis-switching point, the mode structure becomes more complex and multi-modal at mid-frequencies, while the mode structure remains largely unchanged for very low frequencies. Linear parabolised stability equations (PSE) are also used to evaluate the development of the different Kelvin-Helmholtz wavepackets in this elliptical jet showing excellent agreement with the SPOD modes.

In this study, the Kelvin-Helmholtz (KH) instability in co-axial jets with non-uniform mean velocity and temperature profiles is analysed. Linear stability analysis and spectral proper orthogonal decomposition were used to investigate existing particle-image velocimetry (PIV) and time-resolved Doppler global velocimetry (TR-DGV) data. Comparisons between predicted mode shapes and decomposed experimental data reveal several similarities. Parameters such as azimuthal wave number m, Mach number M, velocity ratio h, and temperature ratio S-2 are investigated through a parametric analysis, isolating their influence on the growth rate, axial wave-number, and phase velocity of KH instability waves. An analysis of an isothermal co-axial jet with an inverted velocity profile confirms the existence of two KH modes (inner and outer) arising from the two shear layers, with the outer mode generally exhibiting a much larger growth rate than the inner mode. Varying the Mach number minimally affects the inner mode, while significantly increasing the growth rate of the outer mode. Increasing the velocity ratio drastically decreases the frequency range in which the outer mode is active but increases the frequency range of the inner mode. Finally, introducing thermal non-uniformity in the form of heating the bypass increases the growth rate of the outer mode while also decreasing the frequency range in which it is growing.

Abstract Streaks in rectangular-jet flows are modeled using resolvent analysis, providing insight into the underlying physics of coherent structures. Two-dimensional, cross-plane resolvent analysis is used to evaluate the most-amplified coherent structures at very low frequencies. The highest-gain mode exhibits a large dipole-like structure, featuring a high-speed streak on one major-axis edge of the jet and a low-speed streak on the other, while the second-highest gain mode is the minor-axis-aligned counterpart. Higher-order modes exhibit finer streak spacing, resembling boundary layer modes. Varying the curvature of the jet corners has minimal impact on the gains and mode shapes, suggesting corner vortices in real rectangular-jet flows may not be primarily caused by free-shear streak formation, at least under the modeling hypothesis. Increasing shear thickness typically decreases gains and disperses mode shapes but sensitivity to the forcing weighting method is evident. Increasing the aspect ratio increases the gains for all modes except for the leading dipole-type modes which exhibit a monotonic decrease. The position of streaks relative to the corners changes with aspect ratio causing some complicated gain dependence.

This work presents models for the behaviour of both upstream- and downstream-travelling waves in screeching elliptical jets. Proper orthogonal decomposition is performed on experimental velocity data in both the major and minor axis planes, for an aspect ratio AR = 2 converging elliptical jet operating at nozzle pressure ratios of 2.6 and 3.4. From this decomposition, the radial and axial structure of the guided-jet mode (GJM) and the Kelvin-Helmholtz instability are educed. Linear-stability analysis (LSA) is performed using both the experimentally obtained mean flow, and one obtained using Reynolds-averaged Navier-Stokes (RANS) at matched conditions. It is shown that the wavenumber predicted by LSA for both waves are within the range of experimentally observed wavenumbers. Furthermore, the model accurately predicts the structure of these waves at multiple axial locations, using either the experimental or RANS mean flow. Most critically, it is demonstrated that the GJM is only predicted to be neutrally stable at the screech frequency for a relatively limited streamwise domain, the size and location of which is dependent on the nozzle pressure ratio. A comparison with the amplitude envelope for the GJM extracted from the experimental measurements indicates that the maximum fluctuations associated with the GJM are collocated with this region of the flow that is predicted to support the GJM. While there have been extensive discussions about the frequency dependence of the GJM, this is the first demonstration that its existence is highly dependent on streamwise position within the flow.

This work focuses on the experimental characterisation of the acoustic field of an aspect-ratio-two elliptical jet, with comparison to the baseline axisymmetric jet. Measurements are taken at various azimuthal and polar observer angles across both the subsonic and supersonic regimes and are supplemented by particle-image-velocimetry measurements to link the hydrodynamic field to the acoustics. The subsonic elliptical jet almost exactly matches the acoustic field of the axisymmetric jet, while the supersonic elliptical jet displays signs of non-axisymmetric azimuthal directivity in both the screech tone and broadband spectrum. The hydrodynamics suggest that structures involved in driving the screech tone affects its azimuthal directivity across all measured polar angles considered, whereas axis-switching may be associated with the reversed azimuthal directivity of the broadband spectrum downstream of the jet exit.

There is currently considerable interest in the guided-jet mode, as a result of recent works demonstrating it being the upstream component of various resonant systems in high-speed flows. For given jet operating conditions, the mode is known to exist over only a finite-frequency range that, for a twin-jet system, has been observed to vary with both jet separation and solution symmetry. Vortex-sheet and finite-thickness linear stability models are here employed to consider the behaviour of the guided-jet mode as the two jets are brought together, for both a planar and round twin-jet system. It is demonstrated that in both cases as the twin-jet system merges it forms a higher-order mode of an equivalent single-jet geometry. This then imposes a constraint on the guided-jet mode as the finite-frequency range must change to meet that of the equivalent geometry the system merges to, explaining the previously observed dependence on jet separation.

The rotating detonation engine is perhaps the most promising means to realize pressure-gain combustion in modern engines. The physical processes underpinning the dynamics of the combustion wave are complex, and a lack of understanding of these processes represents a significant barrier to practical implementation of the technology. A significant simplification of the RDE is considered through an abstracted experimental setup. The detonation wave is replaced with a nonreacting shock generated by a shock tube, and the annulus is unwrapped into a single linear channel. Both simplifications make direct visualization of the problem via schlieren imaging tractable. Several performance metrics are used to relate the fluid-dynamic behavior of the shock-injector interaction to the performance of a theoretical rotating detonation engine. The first such metric is "recovery time," based on the time taken for the injector to return to a fully flowing state after the passage of a detonation wave. The second such metric not only considers the mass flow through the injector exit but also accounts for potential backflow into the injector nozzle that may occur for sufficiently strong waves. Finally, a reactant mass-deficit metric is used to characterize the reduction in mass injection due to the interaction with the wave.

In this paper, the acoustic and hydrodynamic characteristics of streaks-modulated wavepackets in chevron nozzles are explored using linear models. Particle-image velocimetry data available in the literature for three nozzle types (SMC000, SMC001 and SMC006) was further post-processed and given as input to the linear models, and the resulting trends were compared to results from the literature, aiming to elucidate the noise benefits achieved in recent aircraft applications. The mean flow structure of chevron jets is explored and compared to that of an axisymmetric jet, focusing on identifying the main differences between the azimuthally averaged flows in both cases. The characteristics of the Kelvin-Helmholtz wavepackets are studied using locally parallel linear stability analysis (LSA) and the one-way Navier-Stokes equations (OWNS) using as input: i) the axisymmetric mean flow; ii) the azimuthally averaged chevron flow; and iii) different streak-containing mean flows in the chevron case. Analysis of the characteristics of the resulting acoustic radiation suggest that a shift in polar directivity is achieved by the modification of the axisymmetric mean flow, with chevron jets leading to acoustic beams more directed towards higher polar angles (towards the sideline direction), in line with previous experimentally obtained trends. Results from the 3D OWNS show similar trends for the SMC001 case, suggesting that the 2D analysis may still provide a good approximation of some of the jet behaviour for chevrons with low penetration levels.

Guided-jet waves have been shown to close resonance loops in a myriad of problems such as screech and impingement tones in jets. These discrete, upstream-travelling waves have long been identified in linear-stability models of jet flows, but in this work they are instead considered in the context of an acoustic-scattering problem. It is shown that the guided-jet mode results from total internal reflection and transmission of acoustic waves, arising from the shear layer behaving like a duct with some given wall impedance. After total reflection, only discrete streamwise wavenumbers may be supported by the flow, with these wavenumbers dictated by the fact that the standing wave formed inside of the jet must fit between the two shear layers. Close to the sonic line, the transmission of this mode to the outside is maximum, leading to a net-energy flux directed upstream, which dictates the direction of propagation of this mode, providing a clear connection to the better understood soft-duct mode (Towne et al., J. Fluid Mech., vol. 825, 2017, pp. 1113-1152). The model also indicates that these waves are generated in the core of the flow and can only be efficiently transmitted to the quiescent region under certain conditions, providing an explanation as to why screech is only observed at conditions where the discrete mode is supported by the flow. The present results explain, for the first time, the nature and characteristics of the guided-jet waves.

Supersonic jets impinging on a surface normal to the jet can produce high-intensity, discrete-frequency tones. The appearance and character of these tones is a function of both nozzle and plate geometry, as well as nozzle operating condition, and the distance between the nozzle and the plate. Though a resonance cycle has long been recognized as underpinning these tones, the exact mechanism by which they are generated has remained a topic of some debate. In this work we present evidence for a number of distinct mechanisms that occur at different jet Mach numbers, reconciling some of the different findings of prior authors. At a wide range of operating conditions, a shock-leakage mechanism similar to that previously demonstrated for jet screech is observed to be active at the standoff shock, producing waves that are highly non-linear from their moment of inception. As the velocity of the wall jet is increased, whether by changing the impingement geometry or increasing the primary jet velocity, the wall-jet shocklet mechanism gains strength. In some cases a synchronicity between these two mechanisms is observed to produce a merging of two already strong acoustic waves into a single highly non-linear wavefront. In select cases, rather than the production of an initially sharp non-linear wave, a diffuse family of acoustic waves are produced, which appear to undergo a non-linear steepening during propagation. A novel wave-tracking methodology is applied to select cases to quantify changes in source location with operating condition.

This paper aims to identify if a screech-like resonance loop is responsible for the side-load generation in rocket nozzles as hypothesized in recent studies. Reynolds-averaged Navier-Stokes (RANS) simulations are conducted for the flow inside a subscale thrust-optimised parabolic (TOP) nozzle for different nozzle pressure ratios (NPRs). Linear stability analysis (LSA) is performed on the resultant mean flow fields to characterise the waves involved in the resonance loop. Finally, the weakest-link model is implemented across several streamwise positions to provide a prediction for the peak frequency at which resonance may occur. The LSA suggests the presence of both upstream and downstream-propagating waves associated with the helical m = +/- 1 azimuthal mode. Moreover, the predicted peak frequencies from the weakest-link model show a strong agreement with past literature hence strengthening the proposed hypothesis.

Jet noise in turbulent round jets has been linked to coherent structures with low-rank azimuthal wavenumbers. This work proposes a novel, non-intrusive method for optically measuring and reconstructing the density fields of axisymmetric and helical coherent structures within fluid flows using a single-camera perspective. By performing the proper orthogonal decomposition (POD) on 2D vector-displacement fields generated from background-oriented schlieren (BOS) we can extract structures associated with azimuthal-Fourier wavenumbers m = 0 and m = 1. Tomographic reconstruction can then be performed using various Abel-inversion techniques. We present a modified-Abel-inversion algorithm that allows for reconstruction of m = 1 structures from a single camera perspective. This work shows that the POD accurately extracts the modes of interest, and several reconstruction algorithms including three-point Abel, modified Fourier-Hankel and a bi-directional method produce accurate results.

The interaction of high-speed jets with a perpendicular surface produces not only broadband sound, but “impingement tones,” that can be more than 30 dB above the broadband noise. It is well recognized that these tones are the result of an aeroacoustic resonance, driven by a feedback loop between the jet nozzle and the plate. However, the exact mechanism by which the tones are produced remains a topic of some dispute; some researchers locate the source within the core of the impinging jet, others in the wall jet generated after impingement with the plate. In this work, we demonstrate that both camps have correctly identified sources; there are two distinct mechanisms, with two distinct locations. The relative strength of these sources depends on the geometry of the problem, but we show that they can actually coexist at a single condition. Decomposition of high-speed schlieren data directly visualizes the location of these sources as a function of jet operating condition.