On the shock cell structure and noise of supersonic jets

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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A multiple-scales model of the shock-cell structure of imperfectly expanded supersonic jets

Journal of Fluid Mechanics ◽

10.1017/s0022112085001173 ◽

1985 ◽

Vol 153 (-1) ◽

pp. 123 ◽

Cited By ~ 120

Author(s):

Christopher K. W. Tam ◽

Jay A. Jackson ◽

J. M. Seiner

Keyword(s):

Multiple Scales ◽

Cell Structure ◽

Supersonic Jets ◽

Shock Cell

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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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Studies on high speed jets from nozzles with internal grooves

The Aeronautical Journal ◽

10.1017/s000192400000498x ◽

2004 ◽

Vol 108 (1079) ◽

pp. 43-50 ◽

Cited By ~ 7

Author(s):

S. Elangovan ◽

E. Rathakrishnan

Keyword(s):

High Speed ◽

Cell Structure ◽

Pressure Profile ◽

Equivalent Diameter ◽

Streamwise Vortices ◽

Shock Cell ◽

Underexpanded Jets ◽

Pitot Pressure ◽

Mean Pressure ◽

The Mean

Experiments were carried out on jets issuing from circular nozzles with grooved exits and the results compared with those of the plain nozzle. The plain nozzle had an exit diameter of 10mm. Because of the introduction of semi-circular grooves at the exit, the effective or equivalent diameter of the grooved nozzles was 10·44mm. The groove lengths were varied as 3, 5 and 8mm. The nozzles were operated at fully expanded sonic and underexpanded exit conditions. The corresponding fully expanded Mach numbers were 1·0 and 1·41. The shock cell structure of the underexpanded jets from grooved nozzles appeared to be weaker than that of the plain nozzle, as indicated by lesser amplitudes of the cyclic variation of the Pitot pressure. The iso-Mach contours indicate that the jet spread along the grooved plane is significantly higher than that along the ungrooved plane. Off-centre peaks were observed in the mean pressure profile of underexpanded jets from grooved nozzles. They were probably due to the streamwise vortices shed from the grooves.

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