Prediction of supersonic jet noise

Abstract

Noise radiated from a supersonic jet is computed using the Parabolized Stability Equations (PSE) method. The evolution of the instability waves inside the jet is computed using the PSE method and the noise radiated to the far field from these waves is calculated by solving the wave equation using the Fourier transform method. We performed the computations for a cold supersonic jet of Mach number 2.1 which is excited by disturbances with Strouhal numbers St=.2 and .4 and the azimuthal wavenumber m=l. Good agreement in the sound pressure level are observed between the computed and the measured (Troutt and McLaughlin 1980) results. In this work we computed the noise radiated from supersonic turbulent jets using the PSE (Parabolized Stability Equations) method. Jet noise can be divided into three categories: (1) shock-induced screech tone noise; (2) shock-induced broad band noise; and (3) turbulent mixing noise. The screech tone appears in an imperfectly expanded jet as discrete band in the front part of the jet. The screech tone phenomena is very complex and it is believed that the toroidal and helical vortices which shed at the lip of the nozzle interact with the shocks when they propagate downstream and makes the shock to oscillate and this radiates sound in the upstream direction at discrete frequency. In an imperfectly expanded jet, the shockcells formed by the oblique shocks or the expansion fans generated at nozzle lip interact with the large scale turbulence and generate broad band noise. The dominant part of the broad band shock-associated noise is comprised of a spectral peak with a relatively narrow half-width. Turbulent mixing noise is the noise component which is contributed from the largescale and small scale turbulence in the jet. For a perfectly expanded supersonic jet, the noise is completely generated by the turbulence in the jet and the predominant part of the noise is radiated in the downstream direction in the range between 25^5°. It is observed that at low Reynolds numbers the noise is radiated at a discrete frequency which is closer to the most unstable instability wave for that jet. At moderate and high Reynolds numbers there is discernible peak but they become broad band. These similarities between the noise generated from the high and low Reynolds number jets imply that the noise generation mechanisms in supersonic jets are same at different Reynolds numbers. Several experiments were performed to identify these mechanisms ( McLaughlin et al. 1975, 1977, Morrision and McLaughlin 1979, 1980, Troutt and McLaughlin 1982, Seiner et al. 1993) and it is concluded that the dominant part of the turbulent mixing noise of high Reynolds number supersonic jets is generated by the large-scale coherent structures. It is also concluded that these