Aft Angles Research Articles

Thermochemical nonequilibrium effects on high-enthalpy double-wedge flows

A hypersonic laminar flow over double wedges with a fixed forward angle of 15° and varied aft angles is studied using computational fluid dynamics and global stability analysis (GSA) at a free-stream Mach number of 12.82 and a total enthalpy of 21.77 MJ/kg. The specific total enthalpy is high enough to trigger evident vibrational excitation and air chemistry. To assess the effects of thermal and chemical nonequilibrium, three different thermochemistry models of air are considered, including frozen, thermal nonequilibrium, and thermochemical nonequilibrium gases. Two-dimensional base-flow simulations indicate that the onset of incipient and secondary separation is insensitive to the inclusion of thermochemistry, although the size of the separation region is substantially reduced. GSA is then performed on the base flows and identifies a three-dimensional stationary global instability beyond a critical aft angle, which is also insensitive to thermochemical nonequilibrium. The criterion of the global stability boundary established for the supersonic flow over compression corners in a calorically perfect gas in terms of a scaled deflection angle [Hao et al., “Occurrence of global instability in hypersonic compression corner flow,” J. Fluid Mech. 919, A4 (2021)] is, thus, extended to high-enthalpy conditions.

Unsteady shock interaction mechanisms of high enthalpy reacting flows over double wedges at Mach 7

A recently developed and validated open-source nonequilibrium Navier–Stokes solver, hyperReactingFoam is used for analyses of Mach 7 flows of air with 8.0 megajoules per kilogram (MJ/kg) stagnation enthalpy over double wedges with four distinct aft angles of 45°, 50°, 55°, and 60°. The validation studies contain both qualitative and quantitative comparisons of the obtained results with experimental and two numerical results available in the literature for the 30°–55° double wedge model. Physics and characteristics of the flows are revealed by comparing the shock structures, chemical compositions, surface pressure, and wall heat flux distributions of each aft angle. It is seen that increased aft angle significantly enhances the magnitudes of wall heat flux and surface pressure. Fluctuations of wall heat flux and surface pressure distributions in time significantly increase along the second wedge surface in the case of higher aft angles. Faster chemical reaction rates take place also for larger aft angles, regardless of the assumption of the flow to be in thermal equilibrium or nonequilibrium. The flow is observed to be chemically frozen downstream of the expansion corner. Time-averaged wall heat flux magnitudes of the flow for the aft angle values of 55° and 60° are found to be three times larger than of the flow with 2.1 MJ/kg stagnation enthalpy.

Near to far field relationship of crackle-related events in military aircraft jet noise

Crackle perception in supersonic jet noise is attributed to the presence of acoustic shocks in the waveform. This study uses an event-based beamforming method to track shock events as they propagate from the near to the far field of a high-performance military aircraft operating at afterburner. Near-field events are propagated via a nonlinear model and compared with far-field measurements. Comparisons of overall sound pressure level and spectra validate the use of the nonlinear model. The skewness of the time-derivative pressure waveform, or derivative skewness, a metric indicative of jet crackle perception, is greatly overpredicted for nonlinearly propagated waveforms. Cross-correlation coefficients of waveform segments centered about the near-field beamformed events reveal that for farther aft angles, near-field events are more related to far-field measurements. Waveform observations show that shock-like events in the near field that are more spiked in nature tend not propagate into the far field. However, near-field, large-derivative events with broader, high-pressure peaks nonlinearly steepen and form shocks in the far field that are likely responsible for crackle perception.

Effects of Double-Wedge Aft Angle on Hypersonic Laminar Flows

The aim of this study is to reveal the physics of low-enthalpy Mach 7 flows over double wedges that have varied aft angles and a fixed fore angle of 30°. Comparisons of the obtained numerical schlieren images along with the contours of criterion and surface heat fluxes assert that the influence of the vortical structures on the flow becomes more significant in accordance with the value of the aft angle. For the aft angle of , the three-dimensionality effects are negligible. As the aft angle exceeds 50°, the vortical structures that align in the streamwise direction start to emerge and strengthen over the surfaces of the aft wedge. The characteristic signs of Görtler vortices, distinct striations, also become apparent in the contours of heat flux, density gradient, and pressure on the surfaces of the aft wedge for those cases. The presence of vortical structures enhances heat transfer from the surfaces and together with relieving effects breaks the symmetry down in the flowfield. In general, the vortical structures and relieving effects that take place in the computations diversify the shock structure from those obtained from the two-dimensional computations for the cases with .

Experimental investigation of jet noise from a high BPR dual-stream jet in a static model-scale test

The noise characteristics of a dual-stream jet of bypass ratios greater than 10 were investigated in response to area ratio, nozzle-operating conditions, installation effect, and chevron effect. The key conclusions were as follows. (1) The area ratio impacted the noise by up to 3 dB at aft angles and at mid-frequency for heated conditions. (2) The spectral variation due to the change of primary stream parameters was constant at low Strouhal numbers and diminished at high Strouhal numbers. (3) The impact of the secondary stream pressure was described by the scaling law of single-stream jets for unheated conditions. The flow parameters of other jets were required to describe the spectra of Strouhal numbers between 0.2 and 2.0, based on the secondary jet for heated conditions. (4) The installed jet noise was quantified for various wing configurations and was more pronounced at forward angles. (5) The chevron nozzle reduced overall noise by up to 4 dB, though it became less attractive when installed. The quantified information is expected to improve the estimation of noise from a dual-stream jet of high bypass ratios.

Time-periodic shock interaction mechanisms over double wedges at Mach 7

The present study focuses on the long-term behavior of low-enthalpy M = 7 flows over double wedges that have a fixed fore angle of 30° and aft angles ranging from 45° to 60°. Although there are numerical and experimental studies available in the literature, they mostly consider the short-term behavior of such flows. In one of those studies, Durna et al. (Phys. Fluids 28:096101, 2016) foresee the presence of an aft angle threshold for transition from steady flow to complex shock–boundary layer interactions. The present study investigates the presence of periodicity by performing computations up to 50 times the duration of the previous study. Our analyses show that beyond a threshold value of 47°, the flows become time-periodic. We are able to describe complex interaction mechanisms of the periodic flow by utilizing the density gradients, shock locations, separation angle, and distributions of the pressure and heat flux over the wedge surfaces. The computational results show that as the aft angle is increased, the period of the flow shortens, and the duration, when the transmitted shock impinges on the wedge surface, decreases.

Active Control of Noise from Hot Supersonic Jets

This paper presents diagnostic experiments aimed at understanding and mitigating supersonic jet noise from the coherent wave-packet structures that are the source of peak aft-angle mixing noise. Both isothermal and heated, nearly perfectly expanded, Mach 1.5 jets were forced in the near-nozzle region with air injection generated by a spinning-valve device designed to excite the jet at frequencies approaching those of the dominant turbulent structures. Substantial reductions in the peak aft-angle radiation were achieved with steady blowing at amplitudes corresponding to 2–6% of the mass flow rate of the primary jet. The noise benefit saturated at mass flow rates above 4%, with as much as a 6 dB reduction in overall sound pressure level at aft angles. Increasing the mass flow rates yielded a monotonically increasing high-frequency noise penalty at the sideline, where noise levels in the natural jet were already 15 dB lower than the aft-angle peak, so that the penalty due to actuation was minor. Although both steady and periodic unsteady mass injections were produced by the spinning valve when it rotated, it was calibrated to hold the steady mass flow rate constant as the frequency of unsteady blowing was changed. In this way, the effect of steady and unsteady blowings on the acoustic field could be decoupled. It is shown that the noise benefit was uniquely associated with the steady component of blowing, whereas the unsteady component resulted in additive tones in the spectra. This implied linearity is consistent with theory and experiments showing that the wave-packet structures, which give rise to the dominant aft-angle radiation, evolve in the turbulent mean flowfield in a nearly linear fashion from their origin in the near-nozzle region. The interpretation of noise reduction is that the steady component of blowing spreads the mean flow more rapidly, resulting in weaker wave packets. Periodic unsteady blowing forces coherent wave packets that are largely uncorrelated from the random natural ones, which then leads to the observed additive tones.

On the noise prediction for serrated leading edges

An analytical model is developed for the prediction of noise radiated by an aerofoil with leading-edge serration in a subsonic turbulent stream. The model makes use of Fourier expansion and Schwarzschild techniques in order to solve a set of coupled differential equations iteratively and express the far-field sound power spectral density in terms of the statistics of incoming turbulent upwash velocity. The model has shown that the primary noise-reduction mechanism is due to the destructive interference of the scattered pressure induced by the leading-edge serrations. It has also shown that in order to achieve significant sound reduction, the serration must satisfy two geometrical criteria related to the serration sharpness and hydrodynamic properties of the turbulence. A parametric study has been carried out and it is shown that serrations can reduce the overall sound pressure level at most radiation angles, particularly at small aft angles. The sound directivity results have also shown that the use of leading-edge serration does not significantly change the dipolar pattern of the far-field noise at low frequencies, but it changes the cardioid directivity pattern associated with radiation from straight-edge scattering at high frequencies to a tilted dipolar pattern.

Modeling the generation of supersonic turbulent jet noise by large-scale coherent structures

Large-scale coherent structures, or wavepackets, are a salient feature of turbulent jets, and the main source of jet mixing noise at aft angles. They are extracted from a high-fidelity Mach 1.5 LES database as spectral POD mode estimates. These most energetic wavepackets obtained via POD and their acoustic far-field radiation patterns are compared to solution to the one-way Euler (OWE) equations recently introduced by Towne & Colonius (AIAA Paper 2013-2171, 2013; AIAA Paper 2014-2903, 2014). Within the OWE framework, the linearized Euler equations are modified such that all upstream propagating acoustic wave components are removed from the solution. The resulting spatial initial value problem can be solved in a stable and computationally efficient manner by downstream marching the solution. Additionally, the scenario of stochastic forcing of wavepackets by the surrounding turbulence is considered in a resolvent analysis. The resolvent analysis allows for the computation of optimal forcing distributions an...

Shock interaction mechanisms on a double wedge at Mach 7

Present computational study investigates formation and interaction mechanisms of shocks and boundary layer for low enthalpy Mach 7 flows of nitrogen over double wedges, which have fixed fore and various aft angles of 30° and 45°–60°, respectively. We use a density based finite-volume Navier-Stokes solver to simulate low enthalpy Mach 7 flows of nitrogen over double wedges. The solver is first and second order accurate in time and space, respectively. The meshes used in simulations of two-dimensional laminar flows consist of multiple blocks of structured mesh. Depending on the intensity, impingement angle, and impingement location of transmitted shock wave, the resulting adverse pressure gradient related disturbances on the wedge surface can trigger complex flow physics both in subsonic and supersonic regions. We observe a strong interaction between the deformation of the boundary layer and the bow shock as well as the transmitted shock for high aft angles. Comparison of the obtained results in terms of general flow physics shows that there exists an aft angle threshold value for such interaction which is in the range of 45°–50°.

Near-Field and Acoustic Far-Field Response of a High-Speed Jet to Excitation

The near-field and acoustic far-field response of an unheated Mach 0.9 jet with Reynolds number was investigated. The study included both the baseline and controlled jets utilizing plasma actuators. Simultaneous acquisition of the near- and far-field signals with the actuation phase enabled the use of phase averaging to reconstruct the signature of the large-scale coherent structures generated by excitation of instabilities in the shear layer of the jet. Decomposition of the near-field pressure into its constitutive hydrodynamic and acoustic fields is accomplished via the application of a filter in the frequency/wave-number domain. The results showed that both the hydrodynamic and acoustic response to excitation for Strouhal numbers less than 0.50 could be well predicted by a simple linear superposition of the impulse response of the jet. The results appear to indicate that the dominant acoustic radiation reaching the far-field aft angles is being generated over an extended region of the jet mixing layer: the upstream portion of the jet, just before the end of the potential core, with highly temporally intermittent bursts occurring downstream of the potential core. Significantly lower temporal coherency of the acoustic response was found when compared to the hydrodynamic response. Finally, excitation for , which produces coherent interactions between the generated large-scale structures, was found to increase the temporal coherency of the acoustic response.

A model function for jet noise events at aft angles and what it says about the statistical relationships of the events

Previous works have shown that subsonic jet noise radiating to aft angles can be described as a succession of independent large fluctuations (i.e. events). Building on these previous works, a model function is found that can accurately reproduce the observed spectra for jets whose aft angle noise is well described the Large-scale Similarity Spectrum (LSS). The selection of the model function is informed by the LSS and autocorrelation analysis of experimental data. It is determined that the model function should be a bipolar pulse with zero mean in order to reproduce the LSS over low to midrange frequencies (i.e. frequencies much higher than the spectral peak frequency are not considered). It is also found that, without sacrificing much fidelity in terms of the resulting spectrum, the model function can be antisymmetric leading to a compact analytical expression with a minimal number of parameters. Along with the statistical parameters and distributions extracted from the data, it is shown that this model function for the events can reproduce the measured spectral characteristics quite well. The model function is then used to explore the link between the event distributions and parameters and the resulting spectrum.

A study on large coherent structures and noise emission in a turbulent round jet

A moderate Reynolds number, and high subsonic turbulent round jet is investigated by large eddy simulation. The detailed results (e.g. mean flow properties, turbulence intensities, etc.) are validated against the experimental data, and special attention is paid to study motions of coherent structures and their contributions to far-field noise. Eulerian methods (e.g. Q-criteria and λ2 criteria) are utilized for visualizing coherent structures directly for instantaneous flow fields, and Lagrangian coherent structures accounting for integral effect are shown via calculating fields of finite time Lyapunov exponents based on bidimensional velocity fields. All visualizations demonstrate that intrusion of three-dimensional vortical structures into jet core occurs intermittently at the end of the potential core, resulting from the breakdown of helical vortex rings in the shear layer. Intermittencies in the shear layer and on the centerline are studied quantitatively, and distinctively different distributions of probability density function are observed. Moreover, the physical sound sources are obtained through a filtering operation of defined sources in Lighthill’s analogy, and their distributions verify that intrusion of vortical structures into the core region serves as important sound sources, in particular for noise at aft angles. The facts that intermittent behaviors are caused by motions of coherent structures and correlated with noise generation imply that to establish reasonable sound sources in active noise production region based on intermittent coherent structures is one of the key issues for far-field noise prediction.

Spectral variations near a high-performance military aircraft

Spectral characteristics of jet noise depend upon location relative to the nozzle axis. Studies of the spectral variation in the far field led to a two-source model of jet noise, in which fine-scale turbulent structures are primarily responsible for noise radiation to the nozzle sideline and large-scale turbulent structures produce the broad, dominant radiation lobe farther aft. Detailed noise measurements near an F-22A Raptor shed additional insights into this variation. An initial study [Neilsen et al., J. Acoust. Soc. Am. 133, 2116–2125] was performed with ground-based microphones in the mid-field. The similarity spectra associated with the large and fine-scale turbulent structures [Tam et al., AIAA paper 96–1716 (1996)] provide a reasonable representation of measured spectra at many locations. However, there are additional features that need further investigation. This paper explores the presence of a double peak in the spectra in the maximum radiation direction and a significant change in spectral shape at the farthest aft angles using data from large measurement planes (2 m × 23 m) located 4–6 jet nozzle diameters from the shear layer. The spatial variation of the spectra provides additional insight into ties between the similarity spectra and full-scale jet noise. [Work supported by ONR.]

Investigations of Azimuthal and Flight Effects on Noise from Realistic Turbofan Exhaust Geometries

For airplane noise certification, noise measurements directly under the flight path, as well as at a lateral location, are required. Both azimuthal and flight effects are evaluated, with the aid of axisymmetric and realistic dual-stream nozzle geometries, in a controlled anechoic facility. The sound field is axisymmetric for dual-stream nozzles, both for simple and complicated internal geometries, as long as the exit plane is axisymmetric. In general, two effects are anticipated due to the presence of the pylon. The first effect pertains to the introduction of azimuthal variations in the spectra. Surprisingly, the sound field in the azimuthal angular range from to is axisymmetric except at very high engine power and low for which there is an increase in level at large aft angles. The second effect of the pylon pertains to modifications to the spectra, relative to those from an axisymmetric nozzle system. There is a noise reduction between and for the pylon nozzle at large aft angles and an increase of at the lower inlet angles. In general, the pylon effect is most pronounced at high engine power and gradually diminishes as engine power is lowered progressively. The following effects of forward flight have been established: 1) at the lower inlet angles, and up to 110 deg, the magnitude of the noise reduction due to forward flight is nearly uniform at all frequencies, at all velocity ratios and area ratios; 2) more complicated effects of forward flight are observed at large aft angles, which are a reduction at the lower frequencies and from to at the higher frequencies; 3) the area ratio plays no role at high but becomes important at lower .

Intermittent Nature of Subsonic Jet Noise

Following on previous works showing that far-field jet noise has significant intermittent aspects, the present work assumes that these intermittent events are the dominant feature of jet noise. A definition and method of detection for intermittent noise events is devised and implemented. Using a large experimental database of acoustically subsonic jets with different jet acoustic Mach numbers (), nozzle diameters (, 5.08, and 7.62 cm), and jet exit temperature ratios (0.84–2.70), these events are extracted from the far-field noise signals measured in the anechoic chamber of the NASA Glenn Aero-Acoustic Propulsion Laboratory. It is shown that a signal containing only these intermittent events retains all of the important aspects of the acoustic spectrum for jet noise radiating to aft angles, validating the assumption that intermittent events are the dominant feature of aft angle jet noise. Statistical analysis of the characteristics of these noise events reveals that these events can be described in terms of three parameters (the variance of the original signal, the mean width of the events, and the mean time between events) and two universal statistical-distribution curves. The variation of these parameters with noise-radiation direction, nozzle diameter, and jet velocity and temperature are discussed. There is a strong correlation between the mean width of the intermittent events and the mean time between the events () in all the cases investigated in this work, implying a strong link between dynamics governing the two quantities.

Towards Prediction of Dual-Stream Jet Noise: Database Generation

The accurate prediction of jet noise from dual-stream nozzle exhaust geometries typical of high bypass ratio turbofan engines has practical relevance for aircraft design studies and in aircraft noise certification. Existing empirical methods do not provide good predictions against measured data; in addition, they are restricted to lower area ratio (secondary to primary) nozzle geometries and lower bypass ratios (BPR). The area ratio and BPR of newer engines have increased substantially, well beyond the range of validity of existing prediction methods. Therefore, there is a dire need to develop an accurate empirical prediction method that is valid over a wider range of jet operating conditions and nozzle geometries that are representative of current engines. A wind tunnel test has been completed and a comprehensive database from realistic geometries and operating conditions has been generated. The data have been analyzed and investigated with an eye towards modeling that would lead to an empirical prediction method. The area ratio and BPR cover wide ranges that encompass all current engines and potential ultra-high BPR engines of the future. The spectral characteristics have been examined and the effects of the following parametric variations are reported in this paper: (1) impact of area ratio with fixed, but over a range of, power settings; (2) at a given As/Ap, fixed primary jet and systematically varying secondary conditions; (3) at a given As/Ap, fixed secondary jet and systematically varying primary conditions; and (4) the effects of forward flight for the above situations. It is established that the characteristics of dual-stream jets with velocity ratio less than 0.5 are similar to those for a single jet, with the velocity ratio being the main controlling parameter and the area ratio playing a lesser role. At higher velocity ratios, contributions from the secondary shear layer is dominant at higher frequencies and the contributions from the mixed jet component controls the peak spectral levels in the peak radiation sector at large aft angles. At low inlet angles, the spectral shape remains invariant for all jet and geometric conditions.

Understanding How Chevrons Modify Noise in Supersonic Jet with Flight Effects

Tests were conducted to determine the effect of chevrons on the sound radiated from the exhaust of a Mach 1.19 core flowwithsimulated flighteffects.Flighteffectswerestudiedbyusingasecondarycoaxial flowvariedfromstatic to Mach 0.50. Shadowgraphy, static pressure, and turbulence measurements were used to complement near-field pressure and far-field acoustic measurements. The presence of a secondary flow causes the shock-cell length to slightly lengthen and the shock cells to persist farther downstream; this was true for both the baseline and chevron nozzles. Compared with the baseline nozzle, the shadowgraphy and near-field static pressure showed that the chevronsreducedtheshock-cellspacingwithminimaleffectontheshock-cellstrength.Higherturbulencelevelsnear thenozzleexitandcomparableshock-cellstrengthledtohighershock-associatednoiseforthechevronconfiguration compared with the baseline. The decrease in shock-cell length caused the peak amplitude of the shock-associated noise to shift to higher frequencies. At the same time, the chevrons significantly reduced any screech tones that were initiallypresentforthebaselinecase.Finally,itwasshownthatthechevronsreducedturbulencelevelsneartheendof the potential core, which resulted in a reduction of the low-frequency mixing noise that dominates the aft angles.

Mechanisms of Jet Noise Generation: Classical Theories and Recent Developments

Lighthill's acoustic analogy and several variants of it have been used to interpret, analyze and explain measured data. In this paper, the validity of the main tenets of the classical theories is examined. This assessment is facilitated by a new comprehensive aeroacoustic database. The overall sound power level does not exactly follow the eighth power of velocity ( Vj/a), but has a weak dependence on jet temperature. It has been believed that an additional source of noise, with either sixth or fourth power variation with velocity, appears for heated jets; there is also a supposed change in spectral shape at 90°, even though effects associated with convection and flow/acoustic interaction are negligible at that angle. The new data indicate that the velocity exponent for overall power is close to eight even at a very high stagnation temperature ratio of 3.2. Moreover, the spectral shape is invariant with jet Mach number and jet temperature. A careful assessment of Tanna's database, which provided the rationale and justification for many of the theoretical models, reveals that this database is unreliable and exhibits incorrect spectral trends. A fundamental tenet of the classical theories, based on both the formalisms of Lighthill-Ffowcs Williams and Lilley, is the notion of moving sources. This idea immediately leads to a Doppler shift for frequency and a convective amplification factor for the noise radiated to the aft angles. It is demonstrated with the new database that there is no experimental evidence for these conjectured effects of moving sources. The jet temperature ratio (static or stagnation), in addition to jet velocity Vj/a, is an independent controlling parameter. New scaling laws that are valid for all angles have been developed with the current database. There are no multiplicative factors with adjustable constants for the spectrum functions; the spectrum function and the velocity exponent depend on the jet temperature ratio and the radiation angle. This relation represents the main difference between the current and the classical formulations. A single exponent collapses the entire spectrum from jets with different Vj/a, but at fixed jet temperature ratio. Therefore, there is no experimental evidence for the main classical ideas of jet noise, as consisting of multi-poles and moving sources, as they are inconsistent with the new data. The idea of two distinct sources that are related to the fine-scale and large-scale turbulence of the jet plume has been investigated. Experimental evidence for the importance of the noise from large coherent structures even at low velocities is offered. The observation at lower and large aft angles of distinct characteristics in, (1) the far field spectral shapes, (2) the directivities of the peak Strouhal number and the OASPL, (3) the directivity of the velocity exponent, and (4) the polar and azimuthal correlations of the farfield pressure, provides strong evidence to support the above view of two different sources of jet noise.

矩形ならびに軸対称プラグノズルから放出される超音速ジェット騒音の予測

Effects of nozzle geometry, and total temperature on supersonic jet noise radiated from rectangular and axi-symmetric plug nozzles are investigated, experimentally. In JAXA (Japan Aerospace Exploration Agency), a pre-cooled turbojet engine for an HST (Hypersonic transport) is under development. In the present study, three kinds of subscale nozzle models are employed, namely two kinds of rectangular plug nozzles (RPN1 and RPN2) and an axi-symmetric plug nozzle (APN), and the jet noise data are acquired at aft angles of the jets by use of 1/4 inch high frequency microphones. The total pressure is set at 0.3MPa(a), which corresponds to the take-off condition of the vehicle, and the total temperature is varied from 290K to 860K. The jet noise spectra obtained are reduced to normalized spectra by use of a scaling law of heated jets (AU n law). It is shown that the normalized spectra collapse onto two lines according to each nozzle geometry, regardless of the total temperature. For APN, the peak SPL is smaller by about 8 to 14 dB when compared with that for RPN1 and RPN2, which implies that the axi-symmetric plug nozzle could be much quieter than rectangular plug nozzle.