Tony John
(Advisor: Prof. Tim Lieuwen]

will propose a doctoral thesis entitled,

Nonlinear Dynamics of Coupled Thermoacoustic Modes in the Presence of Noise

On

[date & time] Tuesday, October 26 at 1:00 p.m.
[building & room] Montgomery Knight Building 317
 

Abstract
The dynamics of a single linearly unstable thermoacoustic mode has been extensively studied in

literature. In the presence of a saturating type nonlinearity, a linearly unstable mode grows and in most cases saturate to a limit cycle. When there are multiple linearly unstable modes present, which is a situation often encountered in practical combustors, the interaction between the modes could lead to interesting dynamics due to the nonlinear coupling and frequency spacing between the modes. For example, the interactions between the modes could lead to the suppression of one of the modes even though both modes are linearly unstable. Further, the stability and existence of potential limit cycle solutions could be influenced by the frequency spacing.

In literature, the dynamics of coupled thermoacoustic modes is usually studied using a deterministic framework. Since there is always background noise in a practical system, a stochastic framework might be necessary to explain some of the observations from data. Therefore, the objective of this work is to include the effects of noise in the system to understand how the deterministic dynamics change in the presence of noise. Noise can alter the behavior of the system in two ways- by changing both the average limit cycle amplitudes, and by altering the stability of the limit cycle oscillations. The tasks that I will perform will be focused to identify and quantify these noise-induced features. The methods that I adopt involve analyzing the system behavior in state space. All the observations and results will be complemented with numerically obtained probability density functions of the state variables.

Committee

• Prof. Tim Lieuwen – School of Aerospace Engineering (advisor)
• Prof. Kyriakos Vamvoudakis – School of Aerospace Engineering
• Prof. Devesh Ranjan – School of Mechanical Engineering