Acoustic oscillations in solid propellant rocket chambers

Abstract

Acoustic Oscillations in Solid Propellant Rocket
\nChambers. Among the various kinds of periodic motions
\nobserved in rocket combustion chambers, the most
\ncommon and simplest to analyze are those related to
\nclassical acoustic modes. If the amplitudes are small,
\nthe main perturbations of the familiar standing or
\ntravelling waves in a closed chamber are proportional
\nto the Mach number of the mean flow. The correct
\nequations describing the problem are here obtained from
\nthe general equations of motion by a limit process which
\nwill also provide equations for studying waves of finite
\namplitude. Subsequently, a single non-homogeneous
\nwave equation is deduced, and solved by an iteration·
\nperturbation procedure. The principal result is a simple
\nformula for the complex frequency showing explicitly
\nthe effects of burning, suspended particles in the gases,
\nthe exhaust nozzle, and viscous wall forces as well as
\nthe mean flow itself. The last is particularly interesting
\nsince, owing primarily to the flow inward from the
\nburning surface, the mean flow, if it is irrotational,
\nnever acts to damp modes which do not involve axial
\noscillations. As a particular application, the extensive
\ndata taken by BROWNLEE and MARBLE are interpreted
\nto the extent that the linear analysis permits. A stability
\nboundary was obtained from 250 firings of small cylindrical
\nrockets, the principal variables being initial port
\ndiameter and length. The propellant did not contain
\nmetal particles, and it appears that the observations
\ncannot be explained by the supposition that viscous
\ndamping associated with particles in the product gases
\nwas the main source of energy loss. Apparently dissipation
\nat the head end, such as that associated with tangential
\nwall shear forces, was an important loss. On the other
\nhand, there is little doubt that if the combustion produces
\nparticles, the consequent dissipation is adequate
\nto damp small amplitude waves.