Jet Noise in the ‘Zone of Silence’

We analyze the far field acoustic power spectrum of a jet flow convecting a region of turbulent activity by formulating an acoustic analogy. The analogy is defined using Goldstein’s linearized Euler equation system (J. of Aero-Acoustics 2002, vol. 1, pp. 1) with the propagation based on a parallel mean flow, and the source statistics on a Reynolds averaged Navier Stokes (RANS) calculation. Our analysis confirms the jet noise spectrum can be thought of as being composed of two terms. The first is significant at high frequencies, while the second term is important at low frequencies and is especially dominant at small observation angles to the jet flow—in the so-called ‘zone of silence’. This additional term appears to account for the experimentally observed low frequency noise in the ‘zone of silence’ (Lush, JFM 1971, vol. 46, pp. 477) and has previously been discussed by Goldstein (JFM 1975, vol. 70, pp. 595). We show that the low frequency term does not occur if the fluctuating Reynolds stress source term in the momentum equation is assumed to be isotropic at all times, but that it is significant if that source is only supposed to be statistically isotropic—if the cross power spectral density of the fluctuating Reynolds stress source term is taken to be isotropic. The low frequency term depends on the gradient of the mean flow velocity. In this paper, we assess the relative magnitudes of the terms in noise spectrum, and show the behavior of the additional low frequency term. Our work contributes to showing that a unified treatment of the jet noise problem is possible using an acoustic analogy to predict both the high and low frequency noise within reasonable accuracy and a modicum of empirical tuning.