Response of a subsonic nozzle to acoustic and entropy disturbances

The one-dimensional response of a subsonic nozzle flow to small pressure and entropy disturbances is calculated. The response is expressed in terms of transmitted acoustic waves (which propagate from the nozzle in the same direction as the disturbance wave) and reflected acoustic waves (which propagate from the nozzle in the direction opposite to that of the disturbance wave) for three independent disturbances: a downstreampropagating acoustic wave impinging upon the nozzle inlet, an upstream-propagating wave impinging upon the nozzle exit, and an entropy wave convecting through the nozzle. The solution for high frequency disturbances is discussed and used with the compact (long wavelength disturbance) solution to normalize several numerical calculations. The normalization shows that the transmitted waves created by the two acoustic disturbances may be represented by the same function offrequency for a given inlet and exit nozzle Mach number. The same is seen to be true for the reflected waves created by the two acoustic disturbances. The normalization allows results for a wide range of nozzle Mach number distributions and disturbance frequencies to be presented concisely