Minimizing transient energy growth of nonlinear thermoacoustic oscillations

Thermoacoustic oscillations triggered by transient energy growth of flow disturbances are wanted in thermoacoustic prime movers or cooling systems. However, they are undesirable in many combustion systems, such as aero-engines, gas turbines, boilers and furnaces. In this work, minimizing transient energy growth of flow disturbances in a thermoacoustic system with Dirichlet boundary conditions is considered. For this, a simplified thermoacoustic model of a premixed laminar flame with an actuator is developed. It is formulated in state-space by expanding acoustic disturbances via Galerkin series and linearizing flame model and recasting it into the classical time-lag N-τN-τ for controllers implementation. As a linear-quadratic-regulator (LQR) is implemented, the thermoacoustic oscillations exponentially decay. However, it is associated with transient energy growth of flow disturbances. To minimize the transient energy growth, a strict dissipativity controller designed basing on LQR is then implemented. Comparison is then made between the performances of these controllers. It is found that the strict dissipativity controller achieves both exponential decay of the thermoacoustic oscillations and unity maximum transient energy growth.