Nonlinear analysis of thermoacoustic instabilities

Andrew C Noble, Purdue University

Abstract

Thermoacoustic instabilities are prevalent in many practical combustion systems. They occur when fluctuations in pressure and heat release are in phase and can lead to catastrophic combustor damage. These instabilities have been studied for over two centuries, but only recently has nonlinear analysis been used to understand better the underlying dynamics. In the current study, a dynamic pressure sensor and picosecond time-resolved laser-induced fluorescence are employed to provide acoustic pressure and point-wise hydroxyl number density measurements in a Rijke-type tube combustor. These time series are used to show the need for a nonlinear and data-driven analysis. The limitations of linear and kernel-based techniques are shown. Through the use of a nonlinear, data-driven approach, cumulative results show that chaotic behavior exists even in this simple thermoacoustic system. Time series from both Rijke and Schmidt tube combustor configurations are analyzed using data-driven spatiotemporal analyses capable of detecting nonlinear trends. Mutualinformation- based proper orthogonal decomposition is used to investigate the modal behavior of two-point hydroxyl measurements. This decomposition separates instability growth from behavior associated with the resonant frequency and higher harmonics. The ability to use proper orthogonal decomposition as a predictive tool is shown. Singular spectrum analysis is applied to both the acoustic pressure and hydroxyl time series. This method permits detection of underlying oscillations even in noisy and nonstationary data, allowing for mitigation strategies to be implemented at an earlier stage than conventional linear methods. The noise reduction capabilities of singular spectrum analysis are also demonstrated. Recommendations for future work include the formulation of a nonlinear, or possibly chaotic, model that best matches the system dynamics of experimentally-obtained data sets. Through the appropriate determination of a model, novel control strategies can be developed for the manipulation of thermoacoustic instabilities.

Degree

Ph.D.

Advisors

Laurendeau, Purdue University.

Subject Area

Mechanical engineering

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