Ph.D. Defense: Tony John

Tue Jul 12 2022 10:00 AM
Montgomery Knight Building 317
"Nonlinear Dynamics of Coupled Thermoacoustic Modes in the Presence of Noise"

Ph.D. Defense

Tony John

(Advisor: Prof. Tim Lieuwen)

"Nonlinear Dynamics of Coupled Thermoacoustic Modes in the Presence of Noise"


Tuesday, July 12
10:00 a.m.
Montgomery Knight Building 317

This work investigates the dynamics of nonlinearly coupled thermoacoustic modes in the presence of noise. 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 this work, the earlier studies are extended to include the effects of noise in the system, studying how deterministic dynamics change with the addition of noise and the impact of frequency spacing (i.e., closely or widely spaced) on the results. Noise can broaden the distribution of amplitudes ("diffusion"), change both the average limit cycle amplitudes ("drift"), and alter the bifurcation characteristics of the limit cycle solutions. In order to identify these noise-induced features, a local asymptotic analysis is performed to characterize the diffusive effects in the limit of low noise intensity. The width of the distribution is observed to be sensitive to frequency spacing and the variation in width along the limit cycle can be significant for widely spaced modes. Drift effects of noise are characterized by quantifying the shift in the averaged solutions from the deterministic values and the sensitivity of this shift to frequency spacing is explored. Further, bifurcation scenarios that exist due to symmetric/asymmetric coupling as well as those introduced by noise are identified in the ensemble averaged state space. The system is visualized using ensemble averaged phase portraits and numerically obtained probability density functions (PDFs) are used to support the observations made in these phase portraits. For certain frequency spacing and low noise intensity, two fixed points can be observed in the state space and the most probable solution can be identified from the PDFs as well as by visually observing the domain of attraction for the fixed points from the phase portraits. As the noise intensity is increased, changes in the qualitative features of the system are evident in the ensemble averaged state space and PDFs.



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