Mach Wave Radiation Research Articles

Acoustic resolvent analysis of turbulent jets

Abstract We perform a resolvent analysis of a compressible turbulent jet, where the optimisation domain of the response modes is located in the acoustic field, excluding the hydrodynamic region, in order to promote acoustically efficient modes. We examine the properties of the acoustic resolvent and assess its potential for jet-noise modelling, focusing on the subsonic regime. Resolvent forcing modes, consistent with previous studies, are found to contain supersonic waves associated with Mach wave radiation in the response modes. This differs from the standard resolvent in which hydrodynamic instabilities dominate. We compare resolvent modes with SPOD modes educed from LES data. Acoustic resolvent response modes generally have better alignment with acoustic SPOD modes than standard resolvent response modes. For the optimal mode, the angle of the acoustic beam is close to that found in SPOD modes for moderate frequencies. However, there is no significant separation between the singular values of the leading and sub-optimal modes. Some suboptimal modes are furthermore shown to contain irrelevant structure for jet noise. Thus, even though it contains essential acoustic features absent from the standard resolvent approach, the SVD of the acoustic resolvent alone is insufficient to educe a low-rank model for jet noise. But because it identifies the prevailing mechanisms of jet noise, it provides valuable guidelines in the search of a forcing model (Karban et al. in J Fluid Mech 965:18, 2023). Graphical abstract

Acoustical Holography and Coherence-Based Noise Source Characterization of an Installed F404 Engine

Understanding the acoustic source characteristics of supersonic jets is vital to accurate noise field modeling and jet noise reduction strategies. This paper uses advanced, coherence-based partial field decomposition methods to characterize the acoustic sources in an installed, supersonic GE F404 engine. Partial field decomposition is accomplished using an equivalent source reconstruction via acoustical holography. Bandwidth is extended through the application of an array phase-unwrapping and interpolation scheme. The optimized-location virtual reference method is used. Apparent source distributions and source-related partial fields are shown as a function of frequency. Local maxima are observed in holography reconstructions at the nozzle lipline, distinct in frequency and space. The lowest-frequency local maximum may relate to noise generated by large-scale turbulence structures in the convectively subsonic region of the flow. Other local maxima are correlated primarily with Mach wave radiation originating from throughout the shear layer and into the fully mixed region downstream of the potential core tip. Source-elucidating decompositions show that the order and behavior of the decomposition lend to the local maxima being related to distinct subsources. Between the local maxima, however, there may be a combination of sources active, which is likely the cause of the spatiospectral lobes observed in other full-scale, supersonic jets.

A photographic analysis of Mach wave radiation from a rocket plume

At 7:30 AM on October 6, 2020 Space-X launched a Falcon-9 rocket from pad 39A at Kennedy Space Center. Photographer Trevor Mahlmann had positioned his camera in the location where the rocket would pass in front of the rising sun and took a series of images of that encounter. These images are visually stunning, but they are also scientifically useful. The high-intensity sound and shock waves originating in the plume are imaged by passing in front of the sun, particularly near the edge of the sun. This can be considered a background-oriented schlieren system. The sound from a supersonic rocket plume is thought to be due to Mach wave radiation, but the details are not yet well understood. We are analyzing these images to determine the position and radiation characteristics of the sound source in the plume. The results of this analysis will be presented.

A study of rocket launch directivity and the potential correlation of various parameters

A rocket launch produces sound that is highly directional. This radiation is presumed to be due to Mach wave radiation, but the production mechanism is poorly understood. Previous research has shown that launch vehicle sound directivity peaks at an angle near 65° relative to the plume for most large rockets during early stages of the launch, yet limited attention has been given to the physical parameters involved in this sound production. This study explores the influence of some additional parameters that are not usually considered, such as ambient atmospheric pressure effects and the launch vehicle's Mach number on a rocket's directivity. Drawing parallels with similar studies on military jets, we aim to compare results and further our understanding of rocket acoustics, contributing to improved modeling precision.

Vector acoustic properties of underwater noise from impact pile driving measured within the water column

Vector acoustic properties of the underwater noise originating from impact pile driving on steel piles has been studied, including the identification of features of Mach wave radiation associated with the radial expansion of the pile upon hammer impact. The data originate from a 2005 study conducted in Puget Sound in the U.S. state of Washington, and were recorded on a four-channel hydrophone system mounted on a tetrahedral frame. The frame system measured the gradient of acoustic pressure in three dimensions (hydrophone separation 0.5 m) from which estimates of kinematic quantities, such as acoustic velocity and acceleration exposure spectral density, were derived. With frame at a depth of 5 m in waters 10 m deep, the data provide an important look at vector acoustic properties from impact pile driving within the water column. Basic features of the Mach wave are observed in both dynamic (pressure) and kinematic measurements, most notably the delay time T leading to spectral peaks separated in frequency by 1/T∼ 106 Hz, where T equals the travel time of the pile radial deformation over twice the length of the pile. For the two piles studied at range 10 and 16 m, the strike-averaged sound exposure level (SEL) was ∼ 177 dB re 1μPa2-s and the acceleration exposure level (AEL) was 122-123 dB re μm2/s4 s. The study demonstrates an approximate equivalence of observations based on dynamic and kinematic components of the underwater acoustic field from impact pile driving measured within the water column.

Near-field coherence analysis of noise from an installed F404 engine

Because phenomena observed in noise radiated from high-performance military aircraft are not fully understood, different analysis techniques can yield complementary insights into their characteristics. Here, a coherence analysis from a 120-microphone near-field array is used to identify and characterize the noise radiation and source-related properties of a T-7A-installed F-404-GE-103 engine over a broad range of frequencies. Some of the noteworthy findings include: a) coherence trends for mixing noise and spatiospectral lobes generally match those observed for previously studied aircraft; and b) bands of coherence between upstream and downstream locations are observed at higher engine powers, suggesting a coherent interaction between upstream broadband shock-associated noise radiation and downstream Mach wave radiation. [Work supported by ONR Grant No. N00014-21-1-2069.]

A robust physics-based method to filter coherent wavepackets from high-speed schlieren images

A complete understanding of jet dynamics is greatly enabled by the accurate separation of acoustically efficient wavepackets from their higher-energy convecting turbulent counterparts. Momentum potential theory (MPT) has proven highly effective in filtering the desired acoustic component irrespective of operating conditions or nozzle complexity. However, MPT is a data-intensive method predicated on the knowledge of fluctuation quantities in the entire flow field; as such, it has to date been applied only to numerically obtained data. This work develops an approach to extend its application to extract coherent wavepacket data from high-speed schlieren images. Pixel intensities from the schlieren image are mapped to a scaled surrogate for the line-of-sight integrated density gradient. The linear relation between the irrotational scalar MPT potential and time derivatives of density fluctuations is then exploited to perform the filtering. The effectiveness of the procedure is demonstrated using experimental as well as numerical schlieren images representing a wide range of imperfectly expanded free and impinging jet configurations. When combined with spectral proper orthogonal decomposition (SPOD), the method yields modes that accurately capture (i) the Mach wave radiation from a military-style jet, (ii) the mode shapes of the feedback tones in an impinging jet and (iii) the screech signature in twin rectangular jets, without recourse to user adjusted parameters. This technique can greatly enhance the use of high-speed diagnostics for real-time monitoring of the near-field acoustic content for potential feedback control. Additionally, the general nature of the approach allows a straightforward application to other flows, such as cavity and airfoil flow-acoustic interactions.

On the generation of entropy noise in a shock containing nozzle of high-performance aircraft at afterburner

High performance aircraft operate at high jet temperature and velocity. Measured noise data indicate that at afterburner condition their noise contain components not found in high temperature supersonic laboratory model jets. The combustion process inside an afterburner is highly unsteady and incomplete. Residual combustion takes place in the jet plume. This suggests that the flow from the afterburner into the jet nozzle would contain significant amount of hot and cold temperature blobs, generally referred to as entropy waves. It is known that when entropy waves move through a non-uniform mean flow, indirect combustion noise (also called entropy noise) would be generated. Military styled nozzles have a rather abrupt area change at and near the throat. This induces the formation of internal shocks inside the nozzle. This paper investigates the generation of entropy noise when strong entropy blobs or waves are convected through the internal shocks. It is found that the result of entropy blobs-shock interaction could lead to the radiation of intense entropy noise out of the nozzle exit into the jet plume as fast waves with a speed equal to sound speed plus jet flow speed. These fast waves create highly supersonic flow disturbances in the jet flow leading to strong Mach wave radiation. It is proposed that this Mach wave radiation is the source of a new noise component observed in the spectra of the F-22A aircraft. Detailed analysis of the F-22A noise data provides support for the proposal.

Flow and aeroacoustic attributes of highly-heated transitional rectangular supersonic jets

Heated transitional supersonic jets exhausting from a rectangular nozzle at over-expanded conditions are investigated by Large Eddy Simulations and Ffowcs-Williams and Hawkings acoustic analogy. Four cases with a fixed nozzle pressure ratio but different temperature ratios (TR) of 1.0, 2.0, 4.0, and 7.0 are analyzed. Numerical results show that with the increasing temperature the jet velocity significantly increases, whereas its Reynolds number decreases by about one order of magnitude, which leads to a 30% decrease in the jet potential core length and reduction in the number of shock cells. The increasing temperatures also result in supersonic shear layer convection Mach numbers and consequently Mach wave radiations in the acoustic fields. Pressure skewness and kurtosis factors indicate crackle noise and non-linear propagation effects in high temperatures. For the most heated jet TR 7.0, the Mach wave radiation is identified radiating noise at about 120 degrees, while the large turbulence structure noise at about 150 degrees. Furthermore, the vortex sheet model analysis and the LES data detect the existence of upstream-propagating neutral waves inside jet TR 7.0. The observed screech frequency falls within the range of antisymmetric mode indicating that the highly-heated jet is characterized by an antisymmetric oscillation mode at the screech frequency.

Source Localization of Crackle-Related Events in Military Aircraft Jet Noise

Crackle is a perceptual feature of supersonic jet noise that is related to the presence of acoustic shocks. This study investigates the apparent source locations of the steepest shocklike events in the noise field of a high-performance military jet aircraft using an event-based time-domain beamforming method. This method uses the cross correlation between adjacent microphones to determine the angle of propagation of an ensemble of shock-related events within the time waveform. This angle of propagation is then traced back toward the source to find the apparent source location. Based on the propagation angle, derivative skewness, and overall sound pressure level, the microphone positions along the array are sorted into six groups. Shock events from groups related to crackle perception in the near field originate anywhere from 2 to 14.5 m downstream along the nozzle lip line, with distributions that shift downstream and broaden with increasing engine power. The crackle-related events appear to be generated by Mach wave radiation and large-scale turbulence structure noise.

A study of noise reduction mechanisms of jets with fluid inserts

The fluid insert technology is an active noise reduction technique that has been shown to successfully reduce supersonic jet noise in model scale nozzles. The goal of this paper is to better understand the noise reduction mechanisms of fluid insert jets using Doak's Momentum Potential Theory and Spectral Proper Orthogonal Decomposition applied to an LES database. It is found that the use of fluid inserts results in a lower convection speed of the wavepacket-like coherent structures in the jet shear layer resulting in a shallower Mach wave radiation angle. It is also shown that the use of fluid inserts results in a reduction of length scales of the turbulent fluctuations in the shear layer, which correlates correctly with the observed noise reductions.

Resolvent-based study of compressibility effects on supersonic turbulent boundary layers

The resolvent formulation of McKeon & Sharma (2010) is applied to supersonic turbulent boundary layers to study the validity of Morkovin's hypothesis, which postulates that high-speed turbulence structures in zero pressure-gradient turbulent boundary layers remain largely the same as its incompressible counterpart. Supersonic zero-pressure-gradient turbulent boundary layers with adiabatic wall boundary conditions at Mach numbers ranging from 2 to 4 are considered. Resolvent analysis highlights two distinct regions of the supersonic turbulent boundary layer in the wave parameter space: the relatively supersonic region and the relatively subsonic region. In the relatively supersonic region, where the flow is supersonic relative to the freestream, resolvent modes display structures consistent with Mach wave radiation that are absent in the incompressible regime. In the relatively subsonic region, we show that the low-rank approximation of the resolvent operator is an effective approximation of the full system and that the response modes predicted by the model exhibit universal and geometrically self-similar behaviour via a transformation given by the semi-local scaling. Moreover, with the semi-local scaling, we show that the resolvent modes follow the same scaling law as their incompressible counterparts in this region, which has implications for modelling and the prediction of turbulent high-speed wall-bounded flows. We also show that the thermodynamic variables exhibit similar mode shapes to the streamwise velocity modes, supporting the strong Reynolds analogy. Finally, we demonstrate that the principal resolvent modes can be used to capture the energy distribution between momentum and thermodynamic fluctuations.

Steepened Mach waves near supersonic jets: study of azimuthal structure and generation process using conditional averages

The azimuthal structure and the generation process of steepened acoustic waves are investigated in the near field of temporal round jets at Mach numbers of 2 and 3. Initially, the shear layers of the jets are in a laminar state and display instability waves whose main properties are close to those predicted from linear temporal analysis. Then, they transition to a turbulent state and generate high-intensity Mach waves displaying sharp compressions typical of those recorded for jets producing crackle noise. These waves are first shown to be poorly reproduced when only the axisymmetric mode is considered, but to be well captured with the first five azimuthal modes. Their generation process is investigated by performing conditional averages of the flow and acoustic fields triggered by the detection of intense positive pressure peak close to the jets. No steepened waves are visible in the conditionally averaged pressure profiles when the procedure involves only one azimuthal mode at a time. However, sharp compressions are obtained based on the first five modes taken together. In that case, the steep compressions are correlated over a limited portion of the jet circumference and are steeper as more azimuthal modes are considered. Moreover, a direct link is established between the steepened waves and the supersonic convection of large-scale coherent flow structures located in the supersonic core of the jets. This indicates that these waves constitute an extreme, nonlinear case of Mach wave radiation by these structures. In addition, the capacity of flow structures to generate sharp, steepened waves is related to their shapes. More particularly, flow structures with a large extent in the radial direction are shown to produce stronger and steeper Mach waves than those that are elongated in the flow direction.

Visualization and acoustic-triggered conditional sampling analysis of acoustic phenomena with screech-tone of an over-expanded supersonic jet

In the liftoff of launch vehicles and supersonic aircrafts, jet noise is required to be reduced because it causes various problems. To reduce the influence of jet noise, it is significant to clarify the source location and the direction of propagation as well as the spectrum of each acoustic phenomenon. For this purpose, the authors have proposed the acoustic-triggered conditional sampling analysis to obtain acoustic information from high-speed schlieren movies. In the authors’ previous studies, this method was applied to correctly and under expanded jets, and the broadband phenomena were clarified, such as Mach wave radiation and shock associated noise. In this study, this method was applied to an over-expanded jet, in which screech tone is observed in addition to the broadband acoustic phenomena. First, it was found that the broadband phenomena and screech tone could be observed separately by this method with choosing the microphone location for trigger detection. Then, two screech tone noises of different frequencies are observed, and it was clarified that they are propagating to different directions from different source locations. Also, the acoustic phenomenon generated by impingement of the same over-expanded jet on an inclined flat plate will be discussed.In the liftoff of launch vehicles and supersonic aircrafts, jet noise is required to be reduced because it causes various problems. To reduce the influence of jet noise, it is significant to clarify the source location and the direction of propagation as well as the spectrum of each acoustic phenomenon. For this purpose, the authors have proposed the acoustic-triggered conditional sampling analysis to obtain acoustic information from high-speed schlieren movies. In the authors’ previous studies, this method was applied to correctly and under expanded jets, and the broadband phenomena were clarified, such as Mach wave radiation and shock associated noise. In this study, this method was applied to an over-expanded jet, in which screech tone is observed in addition to the broadband acoustic phenomena. First, it was found that the broadband phenomena and screech tone could be observed separately by this method with choosing the microphone location for trigger detection. Then, two screech tone noises of differ...

Reducing noise from twin supersonic jets using very-low-frequency control

The intense jet noise radiated by closely spaced, twin supersonic hot jets leads to sound-induced structural vibration, fatigue and personnel related operational difficulties. Experimental, theoretical, and computational investigations into the physics and control of jet noise have identified several important sound sources, including wavepackets, screech, Mach wave radiation, and broadband shock associated noise (BBSAN). Reducing the loudest sources of jet noise, without sacrificing propulsive performance, has relied on intuition, parametric survey, or optimal control techniques. With the aim of developing a more general and robust method of jet noise reduction (JNR), we present a physics-based approach that leverages very-low-frequency jet dynamics in order to achieve JNR whilst preserving propulsive performance. Our approach formulates the control problem using the very-low-frequency global modes of the compressible Navier-Stokes operator linearized about the jet mean flow to disrupt the nonmodal transient growth processes. The presentation will showcase uncontrolled and controlled single and twin supersonic hot jets issuing from biconical nozzles, with conditions and geometries motivated by tactical Naval aircraft. The predictions utilize fully resolved numerical simulations whose data inform the control development and which evaluate its performance on the jet exhaust and on its radiated noise.

Antisymmetric Oscillation Modes in Rectangular Screeching Jets

In this paper, the origin and the properties of the oscillation modes in screeching non-ideally expanded rectangular jets are investigated using compressible implicit LES of rectangular supersonic jets. At the exit of a converging diverging rectangular nozzle of aspect ratio 2 and of design Mach number 1.5, the jets are under- and over-expanded. Seven simulations with four different temperature ratios ranging from 1 to 3 and two different nozzle pressure ratios are performed. The geometry of the nozzle and the exit conditions are chosen such that to match the experimental study conducted at the University of Cincinnati. First, the over-expanded jets are studied. It is shown that the total number of shock cells decreases with increased temperature ratio. However, the temperature does not influence the size of the first shock cell and the linear decrease of the shock cell size in the downstream direction. The spreading of the jet is observed to be higher along the minor axis plane than along the major axis plane. The intensity of the screech noise increases with the temperature ratio in the present study although the opposite is observed in the experiments. Moreover, for jet temperature ratios of 2.5 and 3, the strong flapping motion of the jet along the minor axis plane due to the screech feedback mechanism yields to an antisymmetric organization of the Mach wave radiation. Thereafter, the near- and far-field acoustic are studied. In the near-field, screech tones are captured, whose frequencies are consistent with both experimental data and theoretical models. In the far-field, four acoustic components typical of non-ideally expanded supersonic jets are observed, namely the screech noise, the broadband shock-associated noise, the mixing noise and the Mach wave noise. Their directivities and frequencies are in agreement with experimental results and models. The mechanism of the screech noise generation is studied by using a Fourier decomposition of the pressure field. For the four over-expanded jets, a flapping motion along the diagonal or along the minor axis plane of the jet is noted. Finally, the hypothesis that the acoustic waves completing the feedback loop in these jets are linked to the upstream-propagating acoustic wave modes of the equivalent ideally expanded jets is tested. Using a jet vortex sheet model to describe the dispersion relations of these modes, it is found that this hypothesis allows us to explain the antisymmetric jet oscillation observed at the screech frequencies. Based on frequency-wavenumber decomposition of the pressure fluctuations in the jets, it is shown that at the screech frequencies, acoustic waves propagating in the upstream direction at the ambient speed of sound exist also in the jet flow, additionally to the acoustic waves propagating outside of the jet. These acoustic waves belong to the neutral acoustic wave modes of the equivalent ideally expanded jet. These results support the idea that a vortex sheet model of the corresponding 2-D planar ideally expanded jet is capable of predicting the wave modes of a non-ideally expanded rectangular supersonic jet. They also suggest that these waves are involved in the feedback part of the screech mechanism; explaining why, for the simulated screeching rectangular jets, the associated oscillation mode is antisymmetric.

Conditional sampling analysis of high-speed schlieren movies of Mach wave radiation in a supersonic jet.

Acoustic-triggered conditional sampling analysis can extract the broadband-noise-related intermittent fluctuations from complicated schlieren visualization movies around the source region, which is difficult when using conventional methods. In this study, an analysis of the Mach wave radiation from a supersonic jet was performed. The extracted results properly captured the known features of the Mach waves and their sources (i.e., wavepacket at the jet boundary) and clearly showed the correlation between these near-field fluctuations and the far-field intermittent acoustic events. This analysis can potentially be applied to other broadband, intermittent turbulent noise and will provide a better understanding of their generation mechanisms.

Results of scale model acoustic tests using supersonic cold jets for H3 launch vehicle

Acoustic test using Mach 2 cold jet was conducted for the H3 launch vehicle currently being developed in Japan. Effect of the clustered engines and the newly built movable launcher on the lift-off acoustics was investigated. The overall acoustic level taken by the farfield microphones did not show proportional increase in the number of engines, especially for the angles corresponding to the Mach wave radiation from the free jets. The observation here disagrees with the empirical prediction model. The computational fluid dynamics was also employed to analyze the acoustic mechanism of clustered engines.

第三ヘリカルモードペアによりマッハ波が抑制された超音速ジェットの音波放射特性

The three-dimensional compressible Navier-Stokes equations are numerically solved to study suppress Mach wave emission in a supersonic round jet at high Mach number using high-order compact upwind schemes. Two cases of inlet disturbance for Mach number Mj=2.0 are presented. The first case is the jet flow forced randomly. The second case is the jet forced by random disturbances and a pair of unstable 3rd helical modes (m=±3) with a subsonic phase speed. The numerical results show that the jet potential core region is reduced in the jet forced by a pair of 3rd helical modes. Therefore, the intense Mach wave radiation observed in the randomly forced jet can be reduced by forcing with a pair of 3rd helical modes.

Acoustic field of a shielded rectangular supersonic jet

The impact of a flat surface installed parallel to a supersonic rectangular jet of AR = 2 on the far field noise is studied. Far-field cold jet results at design, over-expanded and under-expanded conditions are compared between the free-field jet, the nozzle with the surface matching with the exit lip (h = 0De), and the surface at different stand-off positions away from the jet axis, h = 1, 2, 3 De. Results are shown for all jet azimuthal angles. When the surface is installed at h = 0De, broadband shock-associated noise intensity was decreased and its peak frequency shifted. At NPR = 2.5, shock noise appears to be entirely mitigated. Also, a low frequency noise component is observe below St = 0.15, and assumed to be related to the trailing edge/jet plume interaction. At NPR = 3.0, strong screech tones are mitigated with the surface installed at h = 0De. In the shielded region, noise levels are significantly lower for all plate positions. Mixing noise and Mach wave radiation are affected by the plat stand-off location at the ϕ = 90o. Heated jet measurements up TR = 3.0, near-field and high-speed shadowgraph visualization are performed and reported.