Complex quasiperiodic and chaotic states observed in thermally induced oscillations of gas columns

Yazaki, Taichi; Takashima, Shiro; Mizutani, Fumikazu

doi:10.1103/physrevlett.58.1108

Cited by 37 publications

(15 citation statements)

References 14 publications

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“…4 Observations of such complex behaviors of self-excited oscillations in combustion-driven thermoacoustic systems such as those found in industrial gas turbines, furnaces, and other practical combustion applications, although reported by a few researchers, have not been investigated in detail. Hence, there is a need to further investigate the nonlinear aspects of combustion oscillations for the development of combustion systems.…”

Section: Introductionmentioning

confidence: 99%

Route to chaos for combustion instability in ducted laminar premixed flames

Kabiraj

Saurabh

Wahi

et al. 2012

Chaos: An Interdisciplinary Journal of Nonlinear Science

153

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Complex thermoacoustic oscillations are observed experimentally in a simple laboratory combustor that burns lean premixed fuel-air mixture, as a result of nonlinear interaction between the acoustic field and the combustion processes. The application of nonlinear time series analysis, particularly techniques based on phase space reconstruction from acquired pressure data, reveals rich dynamical behavior and the existence of several complex states. A route to chaos for thermoacoustic instability is established experimentally for the first time. We show that, as the location of the heat source is gradually varied, self-excited periodic thermoacoustic oscillations undergo transition to chaos via the Ruelle-Takens scenario.

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Section: Introductionmentioning

confidence: 99%

Route to chaos for combustion instability in ducted laminar premixed flames

Kabiraj

Saurabh

Wahi

et al. 2012

Chaos: An Interdisciplinary Journal of Nonlinear Science

153

View full text Add to dashboard Cite

show abstract

“…[4][5][6][7][8] Thermoacoustic oscillations are brought about by an active action of a thermoviscous layer on the tube wall in the presence of the temperature gradient together with an action of weak nonlinearity. [9][10][11] Since no flow is present in equilibrium, mechanisms in destabilization differ from the wellknown hydrodynamic ones for base laminar flows in which the instability is brought about by viscosity in the form of the second-order spatial derivative. They also differ from those in Bénard convection due to buoyancy in the absence of base flow where the gravity is of essential importance.…”

Section: Introductionmentioning

confidence: 99%

Marginal condition for the onset of thermoacoustic oscillations of a gas in a tube

Sugimoto¹,

Yoshida²

2007

Physics of Fluids

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This paper revisits a classical problem to derive a marginal condition for the onset of spontaneous thermoacoustic oscillations of a gas in a circular tube with one end open and the other closed by a flat wall, subjected to a temperature gradient along the side wall. Formulation is given in the framework of the linear theory and the first-order theory in the ratio of a boundary-layer thickness to the tube radius. An eigenvalue problem is posed on the second-order differential equation with variable coefficients of the axial coordinate for the excess pressure in the main-flow region outside of the boundary layer. A boundary layer on the end wall is taken into account in the form of an appropriate boundary condition. By using the idea of renormalization, the pressure is rescaled and a complex axial coordinate is introduced so that the pressure equation is transformed into a tractable form. It turns out that the equation includes a factor ͑frequency͒ determined by the product of the local sound speed and the logarithmic temperature gradient, though the boundary-layer effect is not completely eliminated. When this factor is constant everywhere, the temperature distribution is parabolic and solutions are obtained in a closed form. The frequency equation is then derived from the boundary conditions at both ends of the tube, from which the marginal condition is obtained for the ratio of temperature at the hot, closed end to the one at the cold, open end against the tube radius relative to the thickness of the boundary layer at the open end. The spatial modes of the oscillations are also analytically obtained and their profiles are displayed. Finally, some discussions on marginal oscillations are given from the viewpoint of energy balance.

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“…This produces a region where both modes are simultaneously excit- An extensive series of investigations on the behavior of a simple prime mover (although they didn't call it that) wa.i conducted by Yazaki, et al [Refs. [4][5][6] Their prime mover consisted of a symmetric stainless steel U-shaped tube (inner radius 1.2 -4.7 mm, length 1.5 m and greater) with two small pressure transducers affixed at both closed ends.…”

Section: Introductionmentioning

confidence: 99%

Stability curves for a thermoacoustic prime mover

Atchley

Kuo

1994

The Journal of the Acoustical Society of America

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The purpose of this paper is to investigate the stability curves of the fundamental and second modes in a helium filled prime mover. The predicted and measured stability limits are in reasonable agreement for both modes at most mean pressures. There is, however, evidence that the stability of one mode is affected by the presence of the other. It is also observed that one mode can suppress the other. Measurements are also reported on a prime mover modified to selectively inhibit the fundamental mode. Results indicate that the reduced fundamental amplitude allows the stability curve for the second mode to extend into the regions where the fundamental mode previously dominated. This produces a region where both modes are simultaneously excited. Analysis of the waveforms show that the resulting oscillations are quasiperiodic.

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Complex quasiperiodic and chaotic states observed in thermally induced oscillations of gas columns

Cited by 37 publications

References 14 publications

Route to chaos for combustion instability in ducted laminar premixed flames

Route to chaos for combustion instability in ducted laminar premixed flames

Marginal condition for the onset of thermoacoustic oscillations of a gas in a tube

Stability curves for a thermoacoustic prime mover

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