The shock-cell structures and screech tone frequencies of rectangular and non-axisymmetric supersonic jets

The source locations of axisymmetric modes of screech tones are numerically investigated. Fourth-order optimized compact scheme and fourth-order Runge–Kutta method are used to solve the 2-D axisymmetric Euler equations. The screech tone is successfully reproduced, and the change in wavelength with respect to jet Mach number shows good agreement with the experimental data. At various low supersonic jet Mach numbers, the time-averaged contours of Mach number and root-mean-square pressure are investigated to identify the location of maximum interaction between shock cell structures and vortices. The source locations of two axisymmetric modes, A1 and A2 modes, are distinctly visualized and identified; the screech tones of A1 mode are generated at the apex of fifth shock cell, and the screech tones of A2 mode are generated at the apex of fourth shock cell. Based on the observation, a simple formula for the prediction of axisymmetric modes of screech tones is proposed. The formula is derived based on a form of Rossiter equation, with the assumption of different convection speeds along the jet mixing layer. The proposed formula successfully estimates the frequency of two axisymmetric modes of screech tones, which verifies that the identified source locations of the axisymmetric screech tones are reasonable.

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Impact of coherence decay on wavepacket models for broadband shock-associated noise in supersonic jets

Journal of Fluid Mechanics ◽

10.1017/jfm.2018.984 ◽

2019 ◽

Vol 863 ◽

pp. 969-993 ◽

Cited By ~ 5

Author(s):

Marcus H. Wong ◽

Peter Jordan ◽

Damon R. Honnery ◽

Daniel Edgington-Mitchell

Keyword(s):

Dynamic Models ◽

Critical Role ◽

Coherence Function ◽

Supersonic Jets ◽

Far Field ◽

Shock Cell ◽

Acoustic Spectrum ◽

Flow Mechanisms ◽

The Relationship ◽

Field Sound

Motivated by the success of wavepackets in modelling the noise from subsonic and perfectly expanded supersonic jets, we apply the wavepacket model to imperfectly expanded supersonic jets. Recent studies with subsonic jets have demonstrated the importance of capturing the ‘jitter’ of wavepackets in order to correctly predict the intensity of far-field sound. Wavepacket jitter may be statistically represented using a two-point coherence function; accurate prediction of noise requires identification of this coherence function. Following the analysis of Cavalieri & Agarwal (J. Fluid Mech., vol. 748, 2014. pp. 399–415), we extend their methodology to model the acoustic sources of broadband shock-associated noise in imperfectly expanded supersonic jets using cross-spectral densities of the turbulent and shock-cell quantities. The aim is to determine the relationship between wavepacket coherence-decay and far-field broadband shock-associated noise, using the model as a vehicle to explore the flow mechanisms at work. Unlike the subsonic case where inclusion of coherence decay amplifies the sound pressure level over the whole acoustic spectrum, we find that it does not play such a critical role in determining the peak sound amplitude for shock-cell noise. When higher-order shock-cell modes are used to reconstruct the acoustic spectrum at higher frequencies, however, the inclusion of a jittering wavepacket is necessary. These results suggest that the requirement for coherence decay identified in prior broadband shock-associated noise (BBSAN) models is in reality the statistical signature of jittering wavepackets. The results from this modelling approach suggest that nonlinear jittering effects of wavepackets need to be included in dynamic models for broadband shock-associated noise.

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Flow Characterization of Supersonic Jets Issuing From Double-Beveled Nozzles

Journal of Fluids Engineering ◽

10.1115/1.4040447 ◽

2018 ◽

Vol 141 (1) ◽

Cited By ~ 6

Author(s):

Jie Wu ◽

H. D. Lim ◽

Xiaofeng Wei ◽

T. H. New ◽

Y. D. Cui

Keyword(s):

Supersonic Jets ◽

Navier Stokes ◽

Shock Cell ◽

Potential Core ◽

Schlieren System ◽

Flow Characterization ◽

Mixing Behavior ◽

Nozzle Pressure ◽

Significant Mass

Supersonic jets at design Mach number of 1.45 issuing from circular 30 deg and 60 deg double-beveled nozzles have been investigated experimentally and numerically in the present study, with a view to potentially improve mixing behavior. Reynolds-averaged Navier–Stokes (RANS) simulations of the double-beveled nozzles and a benchmark nonbeveled nozzle were performed at nozzle-pressure-ratios (NPR) between 2.8 and 5.0, and the results are observed to agree well with Schlieren visualizations obtained from a modified Z-type Schlieren system. Double-beveled nozzles are observed to produce shorter potential core lengths, modifications to the first shock cell lengths that are sensitive toward the NPR and jet half-widths that are typically wider and narrower along the trough-to-trough (TT) and peak-to-peak (PP) planes, respectively. Lastly, using double-beveled nozzles leads to significant mass flux ratios at NPR of 5.0, with a larger bevel-angle demonstrating higher entrainment levels.

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Reflection coefficients and screech-tone prediction in supersonic jets

25th AIAA/CEAS Aeroacoustics Conference ◽

10.2514/6.2019-2522 ◽

2019 ◽

Cited By ~ 1

Author(s):

Matteo Mancinelli ◽

Vincent Jaunet ◽

Peter Jordan ◽

Aaron Towne ◽

Stève Girard

Keyword(s):

Supersonic Jets ◽

Reflection Coefficients ◽

Screech Tone

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Schlieren 3D-CT Measuremsnt of Instantaneous Density Distributions of the Shock-cell Structure of Under-Expanded Supersonic Jets

The Proceedings of Mechanical Engineering Congress Japan ◽

10.1299/jsmemecj.2016.j0510203 ◽

2016 ◽

Vol 2016 (0) ◽

pp. J0510203

Author(s):

Ahmad Z. NAZARI ◽

Naoki HAYASHI ◽

Yuta ISHIKO ◽

Kimihiro NAGASE ◽

Kazuma KAKIMOTO ◽

...

Keyword(s):

Cell Structure ◽

Supersonic Jets ◽

3D Ct ◽

Shock Cell ◽

Density Distributions

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Experimental study of shock-cell noise in underexpanded supersonic jets

19th AIAA/CEAS Aeroacoustics Conference ◽

10.2514/6.2013-2080 ◽

2013 ◽

Cited By ~ 7

Author(s):

Alessandro Savarese ◽

Peter Jordan ◽

Steve Girard ◽

Erwan Collin ◽

Mauro Porta ◽

...

Keyword(s):

Experimental Study ◽

Supersonic Jets ◽

Shock Cell

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On Sound Generated by Instability Wave-Shock Cell Interaction in Supersonic Jets

10th AIAA/CEAS Aeroacoustics Conference ◽

10.2514/6.2004-2950 ◽

2004 ◽

Author(s):

Prasun Ray ◽

Lawrence Cheung ◽

Sanjiva Lele

Keyword(s):

Cell Interaction ◽

Supersonic Jets ◽

Instability Wave ◽

Shock Cell

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Sound generated by instability wave/shock-cell interaction in supersonic jets

Journal of Fluid Mechanics ◽

10.1017/s0022112007007306 ◽

2007 ◽

Vol 587 ◽

pp. 173-215 ◽

Cited By ~ 21

Author(s):

PRASUN K. RAY ◽

SANJIVA K. LELE

Keyword(s):

Cell Structure ◽

Cell Interaction ◽

Linear Instability ◽

Supersonic Jets ◽

Instability Wave ◽

Destructive Interference ◽

Source Terms ◽

Mean Flow ◽

Shock Cell ◽

Instability Waves

Broadband shock-associated noise is an important component of the overall noise generated by modern airplanes. In this study, sound generated by the weakly nonlinear interaction between linear instability waves and the shock-cell structure in supersonic jets is investigated numerically in order to gain insight into the broadband shock-noise problem. The model formulation decomposes the overall flow into a mean flow, linear instability waves, the shock-cell structure and shock-noise. The mean flow is obtained by solving RANSequations with a k-ε model. Locally parallel stability equations are solved for the shock structure, and linear parabolized stability equations are solved for the instability waves. Then, source terms representing the instability wave/shock-cell interaction are assembled and the inhomogeneous linearized Euler equations are solved for the shock-noise.Three cases are considered, a cold under-expanded Mj = 1.22 jet, a hot under-expanded Mj = 1.22 jet, and a cold over-expanded Mj = 1.36 jet.Shock-noise computations are used to identify and understand significant trends in peak sound amplitudes and radiation angles. The peak sound radiation angles are explained well with the Mach wave model of Tam & Tanna J. Sound Vib. Vol. 81, 1982, p. 337). The observed reduction of peak sound amplitudes with frequency correlates well with the corresponding reduction of instability wave growth with frequency. However, in order to account for variation of sound amplitude for different azimuthal modes, the radial structure of the instability waves must be considered in additionto streamwise growth. The effect of heating on the Mj = 1.22 jet is shown to enhance the sound radiated due to the axisymmetric instability waves while the other modesare relatively unaffected. Solutions to a Lilley–Goldstein equation show that soundgenerated by ‘thermodynamic’ source terms is small relative to sound from ‘momentum’ sources though heating does increase the relative importance of the thermodynamic source. Furthermore, heating preferentially amplifies sound associated with the axisymmetric modes owing to constructive interference between sound from the momentumand thermodynamic sources. However, higher modes show destructive interference between these two sources and are relatively unaffected by heating.

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