| Two branches of research are conducted in this thesis. The first deals with nonlinear combustion response as a mechanism for triggering combustion instabilities in solid rocket motors. A nonlinear wave equation is developed to study a wide class of combustion response functions to second-order in fluctuation amplitude. Conditions for triggering are derived from analysis of limit cycles, and regions of triggering are found in parametric space. Introduction of linear cross-coupling and quadratic self-coupling among the acoustic modes appears to be how the nonlinear combustion response produces triggering to a stable limit cycle. Regions of initial conditions corresponding to stable pulses were found, suggesting that stability depends on initial phase angle and harmonic content, as well as the composite amplitude, of the pulse. Also, dependence of nonlinear stability upon system parameters is considered.; The second part of this thesis presents research for a controller to improve the emissions of an incinerator afterburner. The developed controller was experimentally tested at the Naval Air Warfare Center (NAWC), on a 50kW-scale model of an afterburner for Naval shipboard incinerator applications. Acoustic forcing of the combustor's reacting shear layer is used to control the formation of coherent vortical structures, within which favorable fuel-air mixing and efficient combustion can occur. Laser-based measurements of CO emissions are used as the performance indicator for the combustor. The controller algorithm is based on the downhill simplex method and adjusts the shear layer forcing parameters in order to minimize the CO emissions. The downhill simplex method was analyzed with respect to its behavior in the face of time-variation of the plant and noise in the sensor signal, and was modified to account for these difficulties. The control system has experimentally demonstrated the ability (1) to find optimal control action for single- and multi-variable control, (2) to maintain optimal control for time-varying operating states, and (3) to automatically adjust auxiliary fuel in response to changing stoichiometry of the incoming waste pyrolysis gas. Also presented but not tested in the experiments are an expert-type model-guidance feature to aid convergence of the controller to optimum control, and methodology for maintaining flammability. |
