Musafir R.

A general representation scheme for solutions of Lilley’s equation [Musafir, 1993 (Proc. IOA), 2005 (12 ICSV)], along with a particular expression for the source terms obtained [Musafir 2004 (Acta Acustica, submitted)] as a simpler alternative of a formulation derived by Goldstein [2003 (JFM)], is used to establish a simple relationship between the far field spectra of hot and cold jets. For different situations (jet exit velocity and temperature) a measured cold jet spectrum at a given angle (usually 90, 140 or 150 degrees) is used as reference, in order to predict the corresponding hot jet spectra, which are compared with measured data. Narrow band jet noise data obtained by NASA is employed. The method is such that no precise knowledge of the actual Green’s function (G) is required, but only a ratio involving different space derivatives of G, which can be expressed in terms of simple coefficients, depending on Mach number, temperature ratio, jet diameter, polar angle and frequency. This feature makes the method suitable also for shallow angles, since refraction effects are expected to be fully eliminated. Both high- and low-frequency limiting expressions for the coefficients are used, along with an empirical formula that provides a smooth transition. For simplicity, plug flow coefficients are employed, since effects of mean velocity and temperature gradients are explicitly displayed in the model.