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Research Papers

Analytical and Experimental Study on Passive Stabilization of Thermoacoustic Dynamics in a Rijke Tube

[+] Author and Article Information
Umut Zalluhoglu

Department of Mechanical Engineering,
University of Connecticut,
Storrs, CT 06269-3139
e-mail: umut.zalluhoglu@uconn.edu

Nejat Olgac

Department of Mechanical Engineering,
University of Connecticut,
Storrs, CT 06269-3139
e-mail: olgac@engr.uconn.edu

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received February 19, 2017; final manuscript received July 19, 2017; published online September 20, 2017. Assoc. Editor: Ming Xin.

J. Dyn. Sys., Meas., Control 140(2), 021007 (Sep 20, 2017) (11 pages) Paper No: DS-17-1109; doi: 10.1115/1.4037388 History: Received February 19, 2017; Revised July 19, 2017

This paper deals with passive stabilization of thermoacoustic dynamics in a Rijke tube using a Helmholtz resonator. Thermoacoustic instabilities result from the dynamic coupling between the heat release and pressure in a chamber. Helmholtz resonators are used akin to vibration absorbers to suppress unwanted pressure oscillations in such structures and prevent instabilities. The first contribution of the paper is a state-space representation of the thermoacoustic dynamics for the resonator-mounted Rijke tube. This relationship happens to be in the class of linear time invariant, neutral multiple time delay systems (LTI-NMTDS). Then, benefiting from the cluster treatment of characteristic roots (CTCR) paradigm, we investigate the effect of resonator location on suppression of thermoacoustic instability. CTCR is a mathematical tool that determines the stability of LTI-NMTDS exhaustively and nonconservatively in the parameter space of the system. This capability provides a novel tool for the futuristic design concepts of combustors. These analytically obtained findings are also supported with experimental results from a laboratory-scale Rijke tube. In addition, a conceptual case study is presented where the stabilizing contributions of the resonator to the dynamics are investigated under strong thermoacoustic coupling.

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Figures

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Fig. 1

The Helmholtz resonator and the mechanical vibration absorber

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Fig. 2

(a) Functional sketch of a Rijke tube with Helmholtz resonator, (b) its block diagram, and (c) the experimental Rijke tube setup

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Fig. 3

(a) Stability map of the Rijke tube with no Helmholtz resonator and (b) L versus ω variations. The thick black the selected line in (a) represents tube length. The “ο” markers (stable) and “×” markers (unstable) denote the experimental test results. Analytically assessed stable regions are shaded.

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Fig. 4

(a) Stability map of Rijke tube with a Helmholtz resonator in (xu,xr) domain, (b) xr versus ω variations, (c) ω versus xu variations, and (d) a schematic of xu and xr definitions on the Rijke tube. The “ο” markers (stable) and “×” markers (unstable) in pane (a) denote the experimental test results. Analytically assessed stable regions are shaded. The thick black line corresponds to the case when no resonator is mounted on the tube.

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Fig. 5

(a) Unstable pressure oscillations during experimental tests and (b) fast Fourier transform (FFT) information deducted from the oval windows in pane (a), representing the onset of instabilities

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Fig. 6

(a) White noise test at a stable operating point and (b) the corresponding FFT result. The frequency splitting (from A to split C's) phenomenon appears with the attachment of resonatorto the Rijke tube.

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Fig. 7

Characteristic roots of the system at the operating points (a) A, B, D and (b) A, C in Figs. 3(a) and 4(a)

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Fig. 8

Stability maps in (xu,xr) domain for (a) a=200, (b) a=400, and (c) a=600. Stable regions are shaded and the NU information is provided at most regions.

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