Stability analysis and control of nonlinear thermoacoustic systems with multiple deterministic and stochastic sources by a Green’s function approach

Arabi, Sadaf

Abstract

Thermoacoustic instabilities result from the interaction between heat and sound in a confined space, and they pose challenges due to self-sustained high amplitude oscillations. This study advances an analytical approach based on a tailored Green’s function to predict and control thermoacoustic instabilities.
The Green’s function approach is a robust and flexible method with clear physical meaning, building upon the acoustic analogy equation by incorporating source terms and converting the partial differential equation into an integral governing equation.
The nonlinear heat release rate is modelled by a generalized nτ-law for a 1-D Rijke tube with a temperature jump. The extension of the tailored Green’s function approach to include mean flow, is achieved through an adjoint-Green’s function. This provides insights into the effects of a non-zero Mach number on limit cycle amplitude, frequencies, and stability margins.
Moreover, this work explores the stochastic nature of thermoacoustic systems, building upon the foundations laid in the previous chapter. External noise can affect transient time, noise-induced triggering, and bistable region.
In order to control unstable behavior in a thermoacoustic system, a hybrid control technique is investigated using a Green’s function approach. This technique is based on the coupling of two Rijke tubes or one Rijke tube to itself through a connecting tube. The Amplitude Death regions, where oscillations are fully suppressed, are characterized by varying coupling parameters, specifically, time delay and strength of coupling, linked to the length and diameter of the connecting tube. The self coupling scheme is shown to be more effective in suppressing the amplitude of the limit cycle. Experimental measurements validate specific aspects of the results, focusing on the effects of external noise on the growth rate. The findings indicate that noise does not significantly alter the growth rate and this is in line with theoretical predictions.

Citation

Arabi, S. Stability analysis and control of nonlinear thermoacoustic systems with multiple deterministic and stochastic sources by a Green’s function approach. (Thesis). Keele University. https://keele-repository.worktribe.com/output/1109590

• Thesis Type: Thesis
• Deposit Date: Mar 21, 2025
• Keywords: Thermoacoustic instability; tailored Green’s function; bistable region; coupling Rijke tubes
• Public URL: https://keele-repository.worktribe.com/output/1109590
• Additional Information: Embargo on access until 2 February 2026 - The thesis is due for publication, or the author is actively seeking to publish this material.
• Award Date: 2025-03