The Rijke tube — A thermo-acoustic device

Sarpotdar, Shekhar; Ananthkrishnan, N.; Sharma, S. D.

doi:10.1007/bf02834451

Cited by 18 publications

(32 citation statements)

References 4 publications

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“…Hence, for < , the steady state solution was stable for perturbations of any magnitude. For > , an infinitesimal perturbation would result in a large-amplitude It is well known that the generation of sound in a Rijke tube is a result of the standing acoustic wave being set up in the tube [40]. The heat source plays the role of exciting the duct mode acoustic waves as well as reinforcing and sustaining the excited waves.…”

Section: Resultsmentioning

confidence: 99%

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Thermoacoustic Instability in a Rijke Tube with a Distributed Heat Source

Yang

Turan

Lei³

2015

Journal of Thermodynamics

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A Rijke tube with a distributed heat source is investigated. Driven by the widely existing thermoacoustic instability in lean premixed gas turbine combustors, this work aims to explore the physicochemical underpinning and assist in the elucidation and analysis of this problem. The heat release model consists of a row of distributed heat sources with individual heat release rates. The integrated heat release rate is then coupled with the acoustic perturbation for thermoacoustic analysis. A continuation approach is employed to conduct the bifurcation analysis and capture the nonlinear behaviour inherent in the system. Unlike the conventional approach by the Galerkin method, the acoustic equations are originally discretized using the Method of Lines (MOL) to build up a dynamic system. The model is first validated and shown to yield good predictions with available experimental data. Influences of multiple heat sources, time delay, and heat release distribution are then studied to reveal the extensive nonlinear characteristics involved in the case of a distributed heat source. It is found that distributed heat source plays an important role in determining the stability of a thermoacoustic system.

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Section: Resultsmentioning

confidence: 99%

“…Moreover, the proportional increase or decrease of both time delays would make the system less or more stable, respectively (see = 0.01, 0.02 and = 0.015, 0.03). Time delay is the result of thermal inertia between the heat transfer and the velocity [40]. When the velocity varies, the corresponding heat release cannot change instantaneously.…”

Section: Resultsmentioning

confidence: 99%

Thermoacoustic Instability in a Rijke Tube with a Distributed Heat Source

Yang

Turan

Lei³

2015

Journal of Thermodynamics

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“…Since these initial investigations, many numerical, analytical, and experimental studies have been performed till date to understand the physical mechanisms responsible for driving of thermoacoustic oscillations and to devise methodologies that can mitigate these oscillations. For more details on such studies on Rijke tube systems, we recommend the readers to go through a number of review papers available on this topic [10,30,31,69,78,83,86].…”

Section: A Brief History Of Rijke-type Thermoacoustic Systemsmentioning

confidence: 99%

Bifurcation to Limit Cycle Oscillations in Laminar Thermoacoustic Systems

Sujith

Pawar

2021

Springer Series in Synergetics

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In this chapter, we study the bifurcation characteristics of a laminar thermoacoustic system through the application of dynamical system theory. We restrict our discussions to two simple prototypes of real thermoacoustic systems (known as Rijke-type thermoacoustic systems): a horizontal Rijke tube with an electrical heater and a ducted premixed flame combustor, both having a laminar flow field. We describe the transition of a thermoacoustic system from a state of stable operation (called stable fixed point) to unstable operation (called stable limit cycle) on variation of any control parameter. First, we will present the dynamical transitions and characteristics of the dynamical states observed in laminar thermoacoustic systems in the absence of any stochastic background fluctuations in the flow field. Subsequently, we will study the effect of external stochastic perturbations on the occurrence of different dynamical transitions in such systems. These investigations performed on simple laminar thermoacoustic systems can be considered as a baseline study before we attempt to understand the complex dynamics exhibited by turbulent thermoacoustic systems in Chap. 6.As mentioned in Chap. 1, the occurrence of thermoacoustic instability has been a concern for most practical combustion systems used in power generating units and propulsion engines. Traditionally, both linear and nonlinear methodologies have been used to explain the occurrence and the characteristics of thermoacoustic oscillations observed in such systems. In linear analysis, the equations describing flame-acoustic interactions are subjected to small amplitude perturbations for calculating the eigenvalues [12]. When all the eigenvalues are negative, the system is considered to be linearly stable, and when one of the eigenvalues is positive, the system is considered to be linearly unstable. For a linearly unstable system, an infinitesimally small perturbation introduced in the system grows in time and asymptotically approaches another stable state that is different from the initial state. As seen in Chap. 2, for the case of subcritical Hopf bifurcation, a finite amplitude perturbation (or initial condition) in the regime of bistability (hysteresis) can alter

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“…The frequency of the generated tonal sound corresponds to the first acoustic natural frequency of the tube. Depending on the heat-source position in the tube, the intensity of the tonal sound is amplified or the sound disappears [1].…”

Section: Rijke Tubementioning

confidence: 99%