Characterization and Modeling of a Spinning Thermoacoustic Instability in an Annular Combustor Equipped With Multiple Matrix Injectors

Abstract

Oscillations in fully annular systems coupled by azimuthal modes are often observed in gas turbine combustors but not well documented. One objective of the present study is to characterize this type of oscillation in a laboratory scale system, allowing detailed pressure measurements and high speed visualization of the flame motion. The experiment is designed to allow detailed investigations of this process at a stable limit cycle and for an extended period of time. Experiments reported in the present article are carried out in the MICCA facility which was used in our previous work to analyze instabilities arising when the chamber backplane was equipped with multiple swirling injectors (Bourgouin et al., 2013, “Self-Sustained Instabilities in an Annular Combustor Coupled by Azimuthal Acoustic Modes,” ASME Paper No. GT2013-95010). In the present study, these units are replaced by a set of matrix injectors. The annular plenum feeds 16 such devices confined by two cylindrical quartz tubes open to the atmosphere. The multiple flames formed by the matrix injectors are laminar and have a well documented describing function. This constitutes an ideal configuration allowing systematic investigations of thermo-acoustic oscillations coupled by longitudinal or azimuthal modes while avoiding complexities inherent to swirling turbulent flames studied previously. Optical access to the chamber allows high speed imaging of light emission from the flames providing instantaneous flame patterns and indications on the heat release rate fluctuations. Eight waveguide microphones record the pressure signal at the combustor injection plane and in the plenum. Among the unstable modes observed in this setup, this analysis focuses on situations where the system features a spinning azimuthal mode. This mode is observed at a frequency which is close to that associated with the 1A mode of the plenum. A theoretical analysis is then carried out to interpret the angular shift between the nodal lines in the plenum and chamber, and the measured flame describing function (FDF) is used to quantify this shift and determine the linear growth rate.

Weakly nonlinear analysis of thermoacoustic instabilities in annular combustors

“…The example is the first analytical study of an annular combustor capable of exhibiting thermoacoustic triggering, and shows that flames responding with a weak gain at small amplitudes and with a strong gain at large amplitudes can lead to self-excited stable standing and spinning solutions in annular configurations. Finally we validate in § 5 this theory for the experiment of Bourgouin et al (2015) and draw the conclusions in § 6.…”

“…As exemplified in § 4, the model captures the effect of the nonlinear saturation of the flame response on the amplitudes and stability of the solutions. We predict in this section the stability of standing and spinning solutions for the experimental work of Bourgouin et al (2015). This is the only published experimental paper on azimuthal instabilities in rotationally symmetric combustors that makes available the nonlinear saturation of the flame.…”

“…We assume good transferability of the measurements in the single burner test rig to the annular configuration, as discussed by Bourgouin et al (2015). Five values of the root mean square amplitude A u =û rms /u of this velocity were tested, respectively 0.1, 0.2, 0.3, 0.4, 0.5.…”

“…We first model the whole experiment as a network of acoustic elements (Evesque & Polifke 2002;Schuermans et al 2003;Hirschberg & Rienstra 2015) and calculate the eigenvalues of the system. The model consists of the plenum and the combustion chamber and of the transition ducts and burners between plenum and combustion chamber, based on the detailed description of the modelling that also Bourgouin et al (2015) carry out. We do not discuss the details of the linear acoustic modelling because it does not introduce any element of novelty, but report that when the unsteady flame response is switched off we find three modes that are first-order azimuthal with frequencies at 501, 1171, 2457 Hz, which are within 4% of the values calculated by Bourgouin et al (2015), giving confidence in the validity of the model.…”

“…The model consists of the plenum and the combustion chamber and of the transition ducts and burners between plenum and combustion chamber, based on the detailed description of the modelling that also Bourgouin et al (2015) carry out. We do not discuss the details of the linear acoustic modelling because it does not introduce any element of novelty, but report that when the unsteady flame response is switched off we find three modes that are first-order azimuthal with frequencies at 501, 1171, 2457 Hz, which are within 4% of the values calculated by Bourgouin et al (2015), giving confidence in the validity of the model. We then evaluate (5.1) at ω s , where Z(ω s ) = 0.035e 1.879i was extracted from the model, and the values ofQ come partly from Figure 11 of Bourgouin et al (2015) at 500 Hz and from values reported in the same paper.…”