Modeling and Control of Combustion Instability Using Fuel Injection

Active control using periodic fuel injection has the potential of suppressing combustion instability without radically changing the engine design or sacrificing performance. In this paper, we carry out a study of optimal model-based control of combustion instability using fuel injection. The model developed is physically based and includes the acoustics, the heat-release dynamics, their coupling, and the injection dynamics. A heat-release model with fluctuations in the flame surface area as well as in the equivalence ratio is derived. We show that area fluctuations coupled with the velocity fluctuations drive longitudinal modes to resonance caused by phase-lag dynamics, while equivalence ratio fluctuations can destabilize both longitudinal and bulk modes caused by time-delay dynamics, similar to experimental observations. The dynamics of proportional and two-position (on-off) fuel injectors are included in the model. Using the overall model, two different control designs are proposed. The first is an LQG/LTR controller where the time-delay effect is ignored, and the second is a Posi-Cast controller which explicitly accounts for the delay. Injection at (i) the burning zone and (ii) further upstream is considered. The characteristics of fuel injectors including bandwidth, authority (pulsed-fuel flow rate), and whether it applies a proportional or a two-position (on-off) injection are discussed. We show that increasing authority and bandwidth result in improved performance. Injection at (ii) compared to (i) results in a trade-off between improved mixing and increased time-delay. We also note that proportional injection is more successful than on-off injection since the former can modulate both amplitude and phase of the control fuel.