Date of Completion


Embargo Period



Thermoacoustics, Stability, Time-delay, Passive control, Feedback control, CTCR

Major Advisor

Nejat Olgac

Associate Advisor

Jiong Tang

Associate Advisor

Chengyu Cao

Associate Advisor

Xu Chen

Field of Study

Mechanical Engineering


Doctor of Philosophy

Open Access

Open Access


Thermoacoustic instability arises from the interaction between unsteady heat release and pressure perturbations in an acoustic enclosure. The pressure oscillations grow and lead to excessive stress reversals in the structure, raising fatigue concerns and mechanical failures. This common phenomenon in the realistic combustors and rocket engines has been broadly studied over a simplistic laboratory abstraction called the Rijke tube. This simple set-up offers a convenient platform to elucidate the fundamental physics of thermoacoustic instabilities. As evident from the most recent literature, there are numerous aspects of this phenomenon even in the Rijke tube setting that are not fully understood and explored. The current work addresses some of them by forming a bridge between thermoacoustics research and time delay systems stability theory.

Under certain conditions, this phenomenon can be modeled as a linear time-invariant dynamics which is affected by multiple time delays. Moreover it falls into the “neutral” time delay systems sub-class, stability analysis of which is notoriously challenging. In order to assess its stability, a recent mathematical paradigm called the Cluster Treatment of Characteristic Roots (CTCR) is used throughout this work. This combination forms the key contributions of this doctoral study, which are summarized as:

(i) Analytical prediction of thermoacoustic instability in Rijke tube in the parametric space of the system.

(ii) Introduction of a time-delayed integral controller. This approach leads to novel frontiers for feedback stabilization of thermoacoustic oscillations via a holistic analysis.

(iii) Parametric assessment of passive control of thermoacoustic instability using Helmholtz resonator. Specifically geometric characteristics are investigated to stabilize an unstable operation.

(iv) Introduction of active-passive stabilization methods, combining a Helmholtz resonator and a feedback loop over a Rijke tube. A new capability is developed to predict control-induced instabilities over this setting.

All of these analytically-discovered features are verified with experiments performed in the Advanced Laboratory for Automation, Robotics and Manufacturing. This unique approach is expected to improve the initial design efforts of real-world combustors.