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

Broadband shock-associated noise is an important component of the overall noise generated by airplanes. In this study, sound generated by the interaction between linear instability waves and the shock-cell structure in supersonic jets is investigated numerically to gain insight into the shock-noise problem. The 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 - &egr; model. Locally-parallel stability equations are solved for the shock structure, and parabolized stability equations are solved for the instability waves. Then, source terms representing the instability wave/shock-cell interaction are assembled and the linearized Euler equations are solved for the shock-noise. Three cases are considered, a cold underexpanded Mj = 1.22 jet, a hot underexpanded Mj = 1.22 jet, and a cold overexpanded M j = 1.36 jet.; The linear stability of the cold Mj = 1.22 jet is broadly characterized. The helical m = 1 instabilities are the most amplified. The axisymmetric modes tend to penetrate into the jet core whereas higher modes remain localized in the shear layer. The heated Mj = 1.22 and cold Mj = 1.36 cases show similar behavior.; Shock-noise computations are used to identify significant trends in peak sound amplitudes and radiation angles. The peak radiation angles are well-explained with the Mach wave model of Tam & Tanna (1982). The observed reduction of peak sound amplitudes with frequency correlates well with the corresponding reduction of instability wave growth with frequency. In order to account for variation of sound amplitude for different azimuthal modes, the radial structure of the instability waves must also be considered. 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 modes are relatively unaffected. We find 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 due to constructive interference between sound from momentum and thermodynamic sources. However, higher modes show destructive interference between these two sources and are relatively unaffected by heating.