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Research Papers: Gas Turbines: Combustion, Fuels, and Emissions

Feedback Control of Self-Sustained Nonlinear Combustion Oscillations

[+] Author and Article Information
Xinyan Li

School of Mechanical and
Aerospace Engineering,
College of Engineering,
Nanyang Technological University,
50 Nanyang Avenue,
Singapore 639798, Singapore

Dan Zhao

School of Mechanical and
Aerospace Engineering,
College of Engineering,
Nanyang Technological University,
50 Nanyang Avenue,
Singapore 639798, Singapore;
School of Energy and Power Engineering,
Jiangsu University of Science and Technology,
Mengxi Road 2,
Zhenjiang 212003, Jiangsu, China
e-mail: zhaodan@ntu.edu.sg

1Corresponding author.

Contributed by the Combustion and Fuels Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received August 23, 2015; final manuscript received August 31, 2015; published online November 17, 2015. Editor: David Wisler.

J. Eng. Gas Turbines Power 138(6), 061505 (Nov 17, 2015) (9 pages) Paper No: GTP-15-1418; doi: 10.1115/1.4031605 History: Received August 23, 2015; Revised August 31, 2015

Detrimental combustion instability is unwanted in gas turbines, aeroengines, rocket motors, and many other combustion systems. In this work, we design and implement a sliding mode controller (SMC) to mitigate self-sustained combustion oscillations in an open-ended thermoacoustic system. An acoustically compact heat source is confined and modeled by using a modified form of King's Law. Coupling the heat source model with a Galerkin series expansion of flow disturbances provides a platform to conduct pseudospectra analysis to gain insight on the system stability behaviors, and to evaluate the performance of the SMC. Two thermoacoustic systems with monopole-like actuators implemented are considered. One is associated with 1 mode and the other is with four modes. Both systems are shown to be controllable. Furthermore, it is found that self-sustained limit cycle oscillations can be successfully generated in both systems, when the actuators are not actuated. In order to gain insight on the thermoacoustic mode selection and triggering, the acoustical energy exchange between neighboring eigenmodes are studied and discussed. As the controller-driven actuators are actuated, the nonlinear limit cycle oscillations are quickly dampened. And both thermoacoustic systems are stabilized by reducing the sound pressure level by approximately 40 dB. Comparison is then made between the performance of the SMC and that of the classical LQR (linear-quadratic-regulator) one. The successful demonstration indicates that the SMC can be applied to stabilize unstable thermoacoustic systems, even with multiple unstable modes.

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Figures

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Fig. 1

Schematic of closed-loop thermoacoustic system with multiple distributed actuators

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Fig. 2

Phase diagram of acoustic pressure p′(xf,t)/p¯ and velocity u′(xf,t)/u¯1 in the uncontrolled thermoacoustic system, as xf = 0.45 m, τ = 0.0014 s. (a) and (b) N = 1, (c) and (d) N = 4.

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Fig. 3

Pseudospectra of the uncontrolled thermoacoustic systems, as xf = 0.45 m, τ = 0.0014 s. The contour values are calculated by using  log10ξ = log10‖zI−A‖ and the maximum value corresponds to eigenvalues. (a) N = 1 and (b) N = 4.

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Fig. 4

Time evolution of acoustic pressure p′(xf,t)/p¯ and velocity u′(xf,t)/u¯1 in the closed-loop thermoacoustic system, as α = 1.5, Λ = I, xf = 0.45 m, τ = 0.0014 s. (a) and (b) N = 1, (c) and (d) N = 4.

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Fig. 5

Time evolution of control input for the first four mode oscillations, as α = 1.5, Λ = I, xf = 0.45 m, τ = 0.0014 s, N = 4

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Fig. 6

Time evolution of acoustical energy in (a)–(d) the uncontrolled system, (e)–(h) the controlled system t ≥ 0 s, as N = 4, α = 1.5, Λ = I, xf = 0.45 m, τ = 1.4 ms

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Fig. 7

Time evolution of pressure p′(xf,t)/p¯ and velocity u′(xf,t)/u¯1, as the controller is actuated at t = 0.65 s, α = 1.5, Λ = I, xf = 0.45 m, τ = 0.0014 s. (a) N = 1, (b) N = 1, (c) N = 4, and (d) N = 4.

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Fig. 8

Variation of sound pressure level before and after LQR and SMC controllers implemented, as xf = 0.45 m, τ = 0.0014 s. (a) N = 1 and (b) N = 4.

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