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Research Papers

Synchronization of Thermoacoustic Modes in Sequential Combustors

[+] Author and Article Information
Giacomo Bonciolini

CAPS Laboratory,
Mechanical and Process
Engineering Department,
ETH Zürich,
Zurich 8092, Switzerland
e-mail: giacomob@ethz.ch

Nicolas Noiray

CAPS Laboratory,
Mechanical and Process
Engineering Department,
ETH Zürich,
Zurich 8092, Switzerland
e-mail: noirayn@ethz.ch

Manuscript received July 10, 2018; final manuscript received July 11, 2018; published online October 4, 2018. Editor: Jerzy T. Sawicki.

J. Eng. Gas Turbines Power 141(3), 031010 (Oct 04, 2018) (9 pages) Paper No: GTP-18-1477; doi: 10.1115/1.4041027 History: Received July 10, 2018; Revised July 11, 2018

Sequential combustion constitutes a major technological step-change for gas turbines applications. This design provides higher operational flexibility, lower emissions, and higher efficiency compared to today's conventional architectures. Like any constant pressure combustion system, sequential combustors can undergo thermoacoustic instabilities. These instabilities potentially lead to high-amplitude acoustic limit cycles, which shorten the engine components' lifetime, and therefore, reduce their reliability and availability. In the case of a sequential system, the two flames are mutually coupled via acoustic and entropy waves. This additional interstages interaction markedly complicates the already challenging problem of thermoacoustic instabilities. As a result, new and unexplored system dynamics are possible. In this work, experimental data from our generic sequential combustor are presented. The system exhibits many different distinctive dynamics, as a function of the operation parameters and of the combustor arrangement. This paper investigates a particular bifurcation, where two thermoacoustic modes synchronize their self-sustained oscillations over a range of operating conditions. A low-order model of this thermoacoustic bifurcation is proposed. This consists of two coupled stochastically driven nonlinear oscillators and is able to reproduce the peculiar dynamics associated with this synchronization phenomenon. The model aids in understanding what the physical mechanisms that play a key role in the unsteady combustor physics are. In particular, it highlights the role of entropy waves, which are a significant driver of thermoacoustic instabilities in this sequential setup. This research helps to lay the foundations for understanding the thermoacoustic instabilities in sequential combustion systems.

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Figures

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Fig. 1

Side view of the laboratory sequential combustor used in this study with key dimensions in (mm). All the main components are indicated with arrows. All acoustic measurements presented in this work are recorded by means of the piezoelectric sensor located in the first stage. An additional sensor is placed close to the outlet. Two series of four instantaneous snapshots of the two flames are shown. These four images correspond to an acoustic cycle, later displayed in Fig. 3, recorded at thermal power of first and second stages equal to Q˙1=30 kW and Q˙2=27 kW.

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Fig. 2

(a) P(p; Q˙2), PDF of the acoustic pressure oscillations p as a function of the second stage thermal power Q˙2. In the insets, the PDFs at three example points (Q˙2=15, 27, 35 kW) of the acoustic pressure signal band-pass filtered in the bands 40–100 Hz (pI) and 110–170 Hz (pII). (b) Power spectral density of the acoustic pressure at the three example operative points. The shaded areas represent the bands used to filter the signal and obtain pI and pII. The labels indicate the peaks associated with the eigenfrequency of the two main thermoacoustic modes of the chamber. (c) pI and pII time traces. (d) The two main acoustic modes shapes, obtained with the Helmholtz solver AVSP.

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Fig. 3

Modal dynamics in the thermoacoustic bifurcation. Bottom row: joint PDF P(pI, pII) of the modal components of the acoustic signal, at six different powers of the second stage. This joint PDF highlights the creation of regular oscillation patterns, which is further explained via the joint PDF of the oscillation phases P(ϕI, ϕII), presented for the usual three operating conditions. For the Q˙2=27 kW case, the acoustic filtered time traces are also shown, together with the original signal p. The labels A–D indicate the four steps of the synchronized two-modes oscillation, and they are reported for reference also on the two corresponding joint PDFs. The images of the flames at these four steps were shown in Fig. 1.

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Fig. 4

(a) Heat release rate spectra of the two flames, compared with the acoustic one, at the three operating conditions. (b) Cross-correlation χ(τ) between the two heat release rate signals of the two flames, filtered in a band (indicated in the left panels) around the dominant frequency in the specific operating condition. The maximum χ is highlighted with a cross.

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Fig. 5

(a) Spectra of the total heat release rate q and acoustic pressure p. All and only the peaks of the source q are featured in p. This justifies the adoption of a transfer function to model the chamber acoustics. (b) Comparison between two possible cubic models for the flame describing function. While the VDP oscillator has been already adopted and validated in the context of thermoacoustic low-order modeling, a cubic function featuring the quadratic term is necessary to reproduce the observed system dynamics.

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Fig. 6

Block diagram representing the proposed model. In the middle, the acoustic transfer functions, outputting the two modal amplitudes ηm. The flames responses bf,m are on top and on the bottom, and they take as input the acoustic modal pressure at the flame location, pf,m=Ψmxfηm, with Ψmxf=Ψm(xf) being the mode m shape at the flame position xf. The outputs are weighted with the factor Γmxf=(γ−1)/VfΛf. The flame 2 FRFs are followed by a delay block, reproducing the time lag between the two heat release rate sources.

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Fig. 7

Block diagram representing the low-order model adopted for the simulations. This model results absorbing of the gains of the model shown in Fig. 6 into the functions in the blocks. On the top, the two transfer functions Hm (one for each eigenfrequency), reproducing the conversion of heat release rate fluctuations into acoustic pressure oscillation. On the bottom, the two flame response functions, each with the two frequency components Bf,m, representing the coherent and nonlinear response of the two flame to acoustic perturbations. The flame 2 FRF is followed by a delay block, reproducing the time lag between the two heat release rate sources. The output of the FRF is weighted with the mode shapes at the flames locations Ψmxf before feeding back to the acoustic block.

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Fig. 8

Results of the simulink simulations of the low-order model (7), for three different sets of system parameters. In the panels, the joint PDFs for the two filtered output signals and phases. Cases (a), (b), and (c) reproduce qualitatively the dynamics observed at the three operating points Q˙2=15, 27, and 35 kW, respectively.

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Fig. 9

Joint PDF of the oscillation pattern at condition Q˙2=27 kW (see also Fig. 3), for the acoustic pressure measured in the sequential chamber (see again Fig. 1 for the position of the second piezoelectric sensor)

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