Title:
Nonlinear Dynamics of Coupled Thermoacoustic Modes in the Presence of Noise
Nonlinear Dynamics of Coupled Thermoacoustic Modes in the Presence of Noise
Author(s)
John, Tony
Advisor(s)
Lieuwen, Timothy C.
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Abstract
This thesis 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. Typically, practical combustion systems consist of multiple thermoacoustic modes that are linearly stable or unstable at a wide range of frequencies. These modes can express independently or can interact with each other. The interactions between different modes is a strong function of the frequency spacing between them amongst other parameters such as its linear growth/decay rate, mode shapes etc. Studies have shown that, in a configuration with two linearly unstable modes, these modal interactions could lead to the suppression of one of the modes, and under certain conditions the more unstable mode (higher growth rate) can be suppressed. Frequency spacing between the modes particularly influenced the stability and existence of potential limit cycle solutions.
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. Examples are presented that show the dynamics of the system in its ensemble averaged state space and numerically obtained probability density functions (PDFs) are used to support the observations in the ensemble averaged state space. For certain frequency spacing and low noise intensity, two fixed points can be observed in the phase 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. As the noise intensity is increased, changes in the qualitative features of the system are evident in the ensemble averaged state space and PDFs.
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Date Issued
2022-07-30
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Resource Type
Text
Resource Subtype
Dissertation