zbMATH — the first resource for mathematics

Sound generated by instability wave/shock-cell interaction in supersonic jets. (English) Zbl 1141.76451
Summary: 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 RANS equations with a \(k-\epsilon \) 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 \(M_{j}\) = 1.22 jet, a hot under-expanded \(M_{j}\) = 1.22 jet, and a cold over-expanded \(M_{j}\) = 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 C.K.W. Tam and H.K. Tanna [J. Sound Vib. 81, 337–358 (1982; Zbl 0488.76071)]. 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 addition to streamwise growth. The effect of heating on the \(M_{j} = 1.22\) jet is shown to enhance the sound radiated due to the axisymmetric instability waves while the other modes are relatively unaffected. Solutions to a Lilley-Goldstein equation show that sound generated 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 momentum and thermodynamic sources. However, higher modes show destructive interference between these two sources and are relatively unaffected by heating.

76Q05 Hydro- and aero-acoustics
76J20 Supersonic flows
76L05 Shock waves and blast waves in fluid mechanics
76E99 Hydrodynamic stability
Full Text: DOI
[1] DOI: 10.1017/S0022112098001852 · Zbl 0929.76122
[2] DOI: 10.1016/0022-460X(82)90244-9 · Zbl 0488.76071
[3] DOI: 10.1016/0022-460X(91)90656-5
[4] DOI: 10.1016/0022-460X(90)90906-G · Zbl 1235.76054
[5] Tam, J. Sound Vib. 116 pp 265– (1987)
[6] DOI: 10.1017/S0022112006001613 · Zbl 1104.76023
[7] DOI: 10.1006/jcph.1998.5986 · Zbl 0952.76063
[8] DOI: 10.1006/jcph.1993.1044 · Zbl 0781.65082
[9] DOI: 10.1006/jcph.1996.0052 · Zbl 0849.76046
[10] DOI: 10.1098/rsta.1978.0061 · Zbl 0385.76078
[11] DOI: 10.1006/jcph.1999.6333 · Zbl 0956.78020
[12] DOI: 10.1017/S002211200100547X · Zbl 1011.76074
[13] DOI: 10.1137/S1064827594276540 · Zbl 0882.76061
[14] DOI: 10.1146/annurev.fluid.29.1.245
[15] DOI: 10.1017/S0022112001004414 · Zbl 1013.76075
[16] Harper-Bourne, AGARD Conf. Proc. 131 pp 1– (1973)
[17] DOI: 10.1137/1008063 · Zbl 0168.14101
[18] DOI: 10.1063/1.868864 · Zbl 1025.76536
[19] DOI: 10.1016/j.paerosci.2004.09.001
[20] DOI: 10.1017/S0022112004000813 · Zbl 1060.76519
[21] DOI: 10.1016/S0377-0427(00)00510-0 · Zbl 0974.65093
[22] Thies, AIAA J. 34 pp 309– (1996)
[23] DOI: 10.1016/0021-9991(92)90012-N · Zbl 0757.65009
[24] Agarwal, AIAA J. 42 pp 80– (2004)
[25] DOI: 10.1006/jsvi.1999.2181
[26] DOI: 10.1088/0370-1301/66/12/306
[27] Norum, AIAA J. 20 pp 68– (1982)
[28] DOI: 10.1016/S0045-7930(99)00013-4 · Zbl 0978.76030
[29] DOI: 10.2307/2006332 · Zbl 0393.65039
[30] Lighthill, Proc. R. Soc. Lond. 222 pp 1– (1952) · Zbl 0055.19109
[31] Tanna, J. Sound Vib. 50 pp 426– (1977)
[32] DOI: 10.1017/S0022112085001173 · Zbl 0585.76077
[33] DOI: 10.1146/annurev.fl.27.010195.000313
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.