To describe the acoustic instabilities in the combustion chambers of laterally burning
solid propellant rockets the interaction of the mean flow with the acoustic waves is
analysed, using multiple scale techniques, for realistic cases in which the combustion
chamber is slender and the nozzle area is small compared with the cross-sectional
area of the chamber. Associated with the longitudinal acoustic oscillations we find
vorticity and entropy waves, with a wavelength typically small compared with the
radius of the chamber, penetrating deeply into the chamber. We obtain a set of
differential equations to calculate the radial and axial dependence of the amplitude
of these waves. The boundary conditions are provided by the acoustic admittance of
the propellant surface, given by an existing analysis of the thin gas-phase reaction
layer adjacent to the solid–gas interface, and of the nozzle, accounting here for the
possible effect of the vorticity and entropy waves. The equations are integrated in
closed form and the results provide the growth rate of the disturbances, which we use
to determine the conditions for instability of the longitudinal oscillations.