H∞ loop-shaping control of azimuthal combustion instabilities in annular combustors

Sheng Feng,Jingxuan Li

doi:10.1177/1461348419873455

Sheng Feng, Jingxuan Li

Open Access

https://doi.org/10.1177/1461348419873455

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Abstract

Lean combustion technique and annular geometries are preferred in aero-engines and gas turbines, which however may lead to azimuthal combustion instabilities. Active control can be used to stabilize combustion instabilities. Due to its easy use, linear feedback controllers embedded with linear flame response models under weak perturbation amplitude are typically preferred. However, flame responses to oncoming disturbances are typically nonlinear; such controllers are not guaranteed to stabilize. Model-based control strategies generally focus on axisymmetric cases, even though symmetry breaking of azimuthal thermoacoustic modes often occurs in annular combustors. This work uses an improved thermoacoustic model to simulate combustion instabilities within annular combustors, providing a platform on which control strategies development can be performed. The improved model takes into account the nonlinear flame response and the symmetry breaking of azimuthal modes. Single-input single-output control strategies targeting on these nonlinear instabilities are developed in this work. Such controllers can achieve stability for linear and nonlinear fluctuations as well as in symmetric and non-axisymmetric cases. The controllers adopt the [Formula: see text] loop-shaping control strategy and a satisfactory robust performance is obtained.

Highlights

In order to reduce NOx emissions, modern gas turbines and aero-engines are desirable to operate under lean premixed combustion conditions
Lean premixed systems are highly susceptible to undesirable combustion instabilities caused by a coupling between unsteady heat release and acoustic waves within the combustion chamber
The modified model takes into account the effects of flame nonlinearity, bulk fluid flow, and viscothermal damping inside the burners which are ignored in the original model for the sake of simplicity

Summary

Introduction

In order to reduce NOx emissions, modern gas turbines and aero-engines are desirable to operate under lean premixed combustion conditions. This work improves the annular combustor model developed by Bauerheim et al.[13] The modified model takes into account the effects of flame nonlinearity, bulk fluid flow, and viscothermal damping inside the burners which are ignored in the original model for the sake of simplicity. The “Feedback control of azimuthal combustion instabilities” section presents the design processes of H1 loop-shaping controllers which are guaranteed to be stabilizing from within limit cycle oscillations for the axisymmetric and the non-axisymmetric cases. This work improves the previous model by taking into account the flame nonlinear response, bulk fluid flow, and thermal viscosity inside the burners. For each individual sector, the acoustic problem is separated into three parts: 1. Propagation in the annular cavities (plenum and chamber) can be described by a 4 Â 4 rotation matrix RA, similar as equation (23) in Bauerheim et al.[13]

Propagation in the kth burner without passing through the flame

Coupling between the plenum and the chamber via the burners

Conclusions