Determination of Acoustic Scattering Matrices from Linearized Compressible Flow Equations with Application to Thermoacoustic Stability Analysis

This study investigates the effect of partial acoustic reflection at inlet or outlet of a combustor on thermoacoustic stability. Parametric maps of the thermoacoustic spectrum are utilized for this purpose, which represent frequencies and growth rates of eigenmodes for a wide range of model parameters. It is found that a decrease of the acoustic reflection at the boundaries does not always imply an increase in the stability margin of the thermoacoustic system. As a matter of fact, a reduction in the acoustic reflection may sometimes destabilize a thermoacoustic mode. Additionally, we show that perturbed passive thermoacoustic modes may become intrinsic thermoacoustic (ITA) modes in the fully anechoic case. We briefly discuss the mode definitions “acoustic” and “intrinsic” commonly found in the literature. The computational analysis is based on a state-space formulation of the linearized Navier–Stokes equations (LNSEs) with discontinuous Galerkin discretization. This approach allows to describe the thermoacoustic system as a linear combination of internal acoustics, flame dynamics, and acoustic boundaries. Such a segregation grants a clear analysis of the respective effects of the individual subsystems on the general stability of the system, expressed in terms of adjoint-based eigenvalue sensitivity. The state-space formulation of the LNSE proposed in this paper offers a powerful and flexible framework to carry out thermoacoustic studies of combustors with arbitrary geometry and acoustic boundary conditions.

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Low-Frequency Acoustic Response of Gas Turbine Perforated Plate and Axial Swirler

Horn

Scarborough

2022

Journal of Engineering for Gas Turbines and Power

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The ability of acoustic network models to model combustion instabilities is dependent on the accuracy of acoustic two-port models. While several forms of two-ports are available, the most common for these types of analyses is the scattering matrix. To facilitate the modeling of industrial-type components in these models, two industrial components, a perforated plate and an axial swirler with vane-based fuel injection, are tested in an impedance tube. Both elements were tested from 100 Hz to 1000 Hz and with bias flow; the perforated plate was tested with a 1% to 4% differential pressure across the plate and the axial swirler was tested with a bias flow of 0 m/s to 50 m/s. The experimental results are then used to generate the scattering matrix, and the swirler experimental results are compared to previously published numerical and analytical results.

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Determination of Acoustic Scattering Matrices from Linearized Compressible Flow Equations with Application to Thermoacoustic Stability Analysis

Cited by 7 publications

References 49 publications

Oscillatory flow power cycles

Oscillatory flow power cycles

Thermoacoustic Spectrum of a Swirled Premixed Combustor With Partially Reflecting Boundaries

Low-Frequency Acoustic Response of Gas Turbine Perforated Plate and Axial Swirler

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