| A method for a comprehensive approach to analysis of the dynamics of an actively controlled combustion chamber, with detailed analysis of the combustion models for the case of a solid rocket propellant, is presented here. The objective is to model the system as interconnected blocks describing the dynamics of the chamber, combustion and control.; The analytical framework for the analysis of the dynamics of a combustion chamber is based on spatial averaging, as introduced by Culick.; Combustion dynamics are analyzed for the case of a solid propellant. Quasi-steady theory is extended to include the dynamics of the gas-phase and also of a surface layer. The models are constructed so that they produce a combustion response function for the solid propellant that can be immediately introduced in the our analytical framework. The principal objective mechanisms responsible for the large sensitivity, observed experimentally, of propellant response to small variations. We show that velocity coupling, and not pressure coupling, has the potential to be the mechanism responsible for that high sensitivity. We also discuss the effect of particulate modeling on the global dynamics of the chamber and revisit the interpretation of the intrinsic stability limit for burning of solid propellants.; Active control is also considered. Particular attention is devoted to the effect of time delay (between sensing and actuation); several methods to compensate for it are discussed, with numerical examples based on the approximate analysis produced by our framework.; Experimental results are presented for the case of a Dump Combustor. The combustor exhibits an unstable burning mode, defined through the measurement of the pressure trace and shadowgraph imaging. The transition between stable and unstable modes of operation is characterized by the presence of hysteresis, also observed in other experimental works, and hence not a special characteristic of this combustor. Control is introduced in the form of pulsed secondary fuel. We show the capability of forcing the transition from unstable to stable burning, hence extending the stable operating regime of the combustor. The transition, characterized by the use of a shadowgraph movie sequence, is attributed to a combined fluid-mechanic and combustion mechanism. |
