Control (management)

Engineering

Linear system

Statistics

Materials science

Applied mathematics

Stability (learning theory)

Transfer function

Range (aeronautics)

Computer science

Transfer matrix

Acoustics

Filter (signal processing)

Nyquist stability criterion

Physics

Mathematics

Mathematical analysis

Nyquist–Shannon sampling theorem

Artificial intelligence

Computational fluid dynamics

Composite material

Parametric statistics

Nyquist frequency

Control theory (sociology)

Mechanics

Machine learning

Computer vision

Electrical engineering

Journal of Computational Physics

A novel approach for the analysis of self-excited instabilities in thermo-acoustic systems is proposed. Combining computational fluid dynamics with low-order acoustic modeling, the open-loop transfer function of the system under investigation is computed. The system eigenmodes and the linear stability characteristics are then deduced from a Nyquist plot. The method is suitable for systems where – due to geometrical complexities or non-compact regions of heat release – a low-order formulation is not appropriate or not available. Explicit knowledge of the frequency response or the transfer matrix of the heat source is not required. Further advantages of the new approach are discussed in the paper. To establish proof of concept, the method is validated against a simple model of a Rijke tube. Over the frequency range considered, frequencies and growth rates of stable as well as unstable eigenmodes are predicted accurately. The new method, combining flow simulation, low-order acoustic modeling and control theory, makes possible a comprehensive analysis of acoustic stability behavior of complex thermo-acoustic systems at comparatively modest computational cost.

CFD-based application of the Nyquist criterion to thermo-acoustic instabilities