| An investigation of combustion instability in solid rocket motors was conducted using perturbation techniques, with particular emphasis placed upon understanding the fluid dynamics of the chamber environment. It was shown that although the phenomena generally manifests itself as oscillations of pressure, with the frequencies measured in tests well predicted by classical acoustic formulas, important aspects of the behavior cannot be explained without due recognition of the two basic processes of fluid dynamics---i.e., the compressing/expanding process and the shearing process.; Thus, a new framework for studying these instabilities that accommodated both linear and nonlinear behavior was developed. The approach differed from previous work in its use of linear stability eigenfunctions---that satisfy the no-slip boundary condition---as a basis for the expansion, with adjoints used to effect a spatial averaging. Among other things, this allowed for the self-consistent inclusion of vortical flow effects.; With respect to the linear behavior, two dominant vorticity-related pathways were shown to exist: one because of sound creating vorticity, and the other, because of that vorticity, in turn, creating more sound. These effects cancel however and thus to leading order no net contribution exists. Though this finding had been reported in an earlier study, restrictive assumptions were introduced. In contrast, we establish that the result is independent of grain geometry and holds for any fluid motion, turbulent or otherwise.; A nonlinear coupling to the flame zone owing to vorticity creation was also identified. The term was left unevaluated however, since no satisfactory model of the flame response presently exists. To help circumvent this difficulty, i.e., that much remains to be done on modeling nonlinear processes, the amplitude equations were studied in a general way using perturbation techniques based on ideas of resonance. The advantage of such an approach is that the nonlinear coefficients need not be specified a priori---only conditions on the linear behavior of the system need to be placed. Closed form results were derived for the limiting periodic behavior when the first mode is unstable and compared against results from numerical integration. Striking agreement was shown. |
