Linear control of thermoacoustic oscillations with flame dynamics modeled by a level-set method

This article focuses on co-simulation of the coupled nonlinear dynamics of flame heat release rate, acoustics, and feedback control in an active thermoacoustic oscillation control system. This work is motivated by an extensive existing body of literature showing the potential of closed-loop active control to suppress thermoacoustic oscillation. Linear algorithms such as linear quadratic Gaussian (LQG) control are often used for thermoacoustic oscillation control, with the important caveat that flame heat release rate oscillation is often highly nonlinear. This creates a need for a tool that can co-simulate the coupled nonlinear thermoacoustic dynamics with linear control. The main contribution of this article is the development of a tool capable of co-simulating nonlinear heat release dynamics using a level-set formulation, together with linear acoustics plus a linear feedback controller. The article demonstrates this framework on an LQG-controlled wedge flame in a unidimensional Rijke tube. The nonlinear thermoacoustic model is formed in a modified level-set solver by connecting the linear acoustics to the original nonlinear flame dynamics via a velocity convection equation. This framework succeeds in preserving the nonlinearity of the thermoacoustics in the Rijke tube without the LQG control. For the flame-driven Rijke tube in this article, LQG control is successful in suppressing the nonlinear thermoacoustic oscillation. In addition, the simulation based on the framework is useful in elucidating the impact of factors such as flame location, flame temperature rise, and the timing of the onset of LQG control on the instability suppression performance and energy needs.