Acoustic oscillations in solid propellant rocket chambers

Acoustic Oscillations in Solid Propellant Rocket Chambers. Among the various kinds of periodic motions observed in rocket combustion chambers, the most common and simplest to analyze are those related to classical acoustic modes. If the amplitudes are small, the main perturbations of the familiar standing or travelling waves in a closed chamber are proportional to the Mach number of the mean flow. The correct equations describing the problem are here obtained from the general equations of motion by a limit process which will also provide equations for studying waves of finite amplitude. Subsequently, a single non-homogeneous wave equation is deduced, and solved by an iteration· perturbation procedure. The principal result is a simple formula for the complex frequency showing explicitly the effects of burning, suspended particles in the gases, the exhaust nozzle, and viscous wall forces as well as the mean flow itself. The last is particularly interesting since, owing primarily to the flow inward from the burning surface, the mean flow, if it is irrotational, never acts to damp modes which do not involve axial oscillations. As a particular application, the extensive data taken by BROWNLEE and MARBLE are interpreted to the extent that the linear analysis permits. A stability boundary was obtained from 250 firings of small cylindrical rockets, the principal variables being initial port diameter and length. The propellant did not contain metal particles, and it appears that the observations cannot be explained by the supposition that viscous damping associated with particles in the product gases was the main source of energy loss. Apparently dissipation at the head end, such as that associated with tangential wall shear forces, was an important loss. On the other hand, there is little doubt that if the combustion produces particles, the consequent dissipation is adequate to damp small amplitude waves.