| This study deals with the development of simplified models for simulation of combustion instabilities and their active control. Modulation of a part of the fuel supply is used to damp instabilities by generating heat release oscillations that are out of phase with the existing pressure oscillations.; A model that accounts for mixing using a heuristic source term has been developed, and used for simulation of combustion instabilities and their control in a premixed gaseous rocket motor. For validation with experimental data, the model is used to investigate the combustor's response to open loop excitation by pulsation of the secondary fuel injection rate. The numerical model's prediction that (a) the pressure oscillation amplitude decreases, and (b) the phase shift between the fuel injection rate and heat-release oscillations increases linearly, as the frequency of fuel injection rate increases, are in good agreement with experimental data from a gas rocket. Subsequently, the heuristic model is used to study the performances of an observer based control system and an adaptive control system.; A modular model that is oriented towards application in a lean premixed gas turbine combustor has been developed. A dump combustor geometry has been used to demonstrate cases of stable and unstable combustion. The two modules of the model are the recirculation zone, which is modeled as either a quasi steady or unsteady well stirred reactor, and the separation-free core flow region which is modeled as a quasi one dimensional flow with source terms. The observed cases of unstable combustion involve fluctuations in local equivalence ratio, and in the mass and energy exchange between the recirculation zone and the core flow.; Roe scheme, the numerical scheme used for the solution of the heuristic and the modular models, has been extended to appropriately account for various source terms that occur in a generalized quasi one dimensional flow. The effect of the source terms is accounted by the use of relevant compatibility relations from the theory of characteristics. This approach is demonstrated with examples for not only Roe scheme but also for characteristics-based boundary conditions. |
