Nonlinear Self-Excited Combustion Oscillations of a Premixed Laminar Flame

2011 ◽  
Vol 110-116 ◽  
pp. 1150-1154 ◽  
Author(s):  
Dan Zhao
Keyword(s):  
Heat Release ◽  
Acoustic Waves ◽  
Laminar Flame ◽  
Mode Selection ◽  
Kinematic Model ◽  
Classical Equation ◽  
Flow Disturbances ◽  
Flame Response ◽  
Premixed Laminar ◽  
Premixed Laminar Flame

Self-excited combustion oscillations are caused by a coupling between acoustic waves and unsteady heat release. A premixed laminar flame in a Rijke tube, anchored to a metal gauze, is considered in this work. The flame response to flow disturbances is investigated by developing a nonlinear kinematic model based on the classical-equation, with the assumption of a time-invariant laminar flame speed. Unsteady heat release from the flame is assumed to be caused by its surface variations, which results from the fluctuations of the oncoming flow velocity. The flame is acoustically compact, and its presence causes the mean temperature undergoing a jump, whose effect on the dynamics of the thermo-acoustic system is discussed. Coupling the flame model with a Galerkin series expansion of the acoustic waves present enables the time evolution of the flow disturbances to be calculated. It was found that the model can predict the mode shape and the frequencies of the excited combustion oscillations very well. Moreover, the fundamental mode is found to be the easiest one to be triggered among all acoustic modes. To gain insight about the mode selection and triggering, further numerical investigation is conducted by linearizing the flame model and recasting into the popular formulation.

Significance of the Direct Excitation Mechanism for High-Frequency Response of Premixed Flames to Flow Oscillations

2020 ◽  
Author(s):  
Vishal Acharya ◽  
Tim Lieuwen
Keyword(s):  
Heat Release ◽  
Acoustic Waves ◽  
Premixed Flames ◽  
Axial Flow ◽  
Flame Length ◽  
Excitation Mechanism ◽  
Direct Mechanism ◽  
Direct Excitation ◽  
Flow Disturbances ◽  
Flame Response

Abstract Premixed flames are sensitive to flow disturbances, which can arise from acoustic or vortical fluctuations. For transverse instabilities, it is known that a dominant mechanism for flame response is “injector coupling”, whereby pressure oscillations associated with transverse waves excite axial flow disturbances. These axial flow disturbances then excite heat release oscillations. The objective of this paper is to consider another mechanism — the direct sensitivity of the unsteady heat release to transverse acoustic waves, and to compare its significance relative to the induced axial disturbances, in a linear framework. The rate at which the flame adds energy to the disturbance field is quantified using the Rayleigh criterion and evaluated over a range of control parameters, such as flame length and swirl number. The results show that radial modes induce heat release fluctuations that always add energy to the acoustic field, whereas heat release fluctuations induced by mixed radial-azimuthal modes can add or remove energy. These amplification rates are then compared to the flame response from induced axial fluctuations. For combustor centered flames, these results show that the direct excitation mechanism has negligible amplification rates relative to the induced axial mechanism for radial modes. For transverse modes, the fact that the nozzle is located at a pressure node indicates that negligible induced axial velocity disturbances are excited; as such, the direct mechanism dominates. For flames that are not centered on pressure nodes, the direct mechanism for mixed-modes, dominates for certain nozzle locations and flame angles.

Significance of the Direct Excitation Mechanism for High-Frequency Response of Premixed Flames to Flow Oscillations

2020 ◽  
Vol 143 (1) ◽  
Author(s):  
Vishal S. Acharya ◽  
Timothy C. Lieuwen
Keyword(s):  
Heat Release ◽  
Acoustic Waves ◽  
Premixed Flames ◽  
Axial Flow ◽  
Flame Length ◽  
Excitation Mechanism ◽  
Direct Mechanism ◽  
Direct Excitation ◽  
Flow Disturbances ◽  
Flame Response

Abstract Premixed flames are sensitive to flow disturbances, which can arise from acoustic or vortical fluctuations. For transverse instabilities, it is known that a dominant mechanism for flame response is “injector coupling,” whereby pressure oscillations associated with transverse waves excite axial flow disturbances. These axial flow disturbances then excite heat release oscillations. The objective of this paper is to consider another mechanism—the direct sensitivity of the unsteady heat release to transverse acoustic waves—and to compare its significance relative to the induced axial disturbances, in a linear framework. The rate at which the flame adds energy to the disturbance field is quantified using the Rayleigh criterion and evaluated over a range of control parameters, such as flame length and swirl number. The results show that radial modes induce heat release fluctuations that always add energy to the acoustic field, whereas heat release fluctuations induced by mixed radial-azimuthal modes can add or remove energy. These amplification rates are then compared to the flame response from induced axial fluctuations. For combustor-centered flames, these results show that the direct excitation mechanism has negligible amplification rates relative to the induced axial mechanism for radial modes. For transverse modes, the fact that the nozzle is located at a pressure node indicates that negligible induced axial velocity disturbances are excited; as such, the direct mechanism dominates. For flames that are not centered on pressure nodes, the direct mechanism for mixed modes dominates for certain nozzle locations and flame angles.

Response of Non-Axisymmetric Premixed, Swirl Flames to Helical Disturbances

2014 ◽  
Author(s):  
Vishal Acharya ◽  
Timothy Lieuwen
Keyword(s):  
Heat Release ◽  
Surface Area ◽  
Local Area ◽  
Flame Surface ◽  
Flow Disturbances ◽  
Flame Response ◽  
Flow Oscillations ◽  
Phase Variations ◽  
The Mean ◽  
Flame Shape

Flow oscillations associated with hydrodynamic instabilities comprise a key element of the feedback loop during self-excited combustion driven oscillations. This work is motivated in particular by the question of how to scale thermoacoustic stability results from single nozzle or sector combustors to full scale systems. Specifically, this paper considers the response of non-axisymmetric flames to helical flow disturbances of the form u^i′∝expimθ where m denotes the helical mode number. This work closely follows prior studies of the response of axisymmetric flames to helical disturbances. In that case, helical modes induce strong flame wrinkling, but only the axisymmetric, m = 0 mode, leads to fluctuations in overall flame surface area and, therefore, heat release. All other helical modes induce local area/heat release fluctuations with azimuthal phase variations that cancel each other out when integrated over all azimuthal angles. However, in the case of mean flame non-axisymmetries, the azimuthal deviations on the mean flame surface inhibit such cancellations and the asymmetric helical modes (m ≠ 0) cause a finite global flame response. In this paper, a theoretical framework for non-axisymmetric flames is developed and used to illustrate how the flame shape influences which helical modes lead to net flame surface area fluctuations. Example results are presented which illustrate the contributions made by these asymmetric helical modes to the global flame response and how this varies with different control parameters such as degree of asymmetry in the mean flame shape or Strouhal number. Thus, significantly different sensitivities may be observed in single and multi-nozzle flames in otherwise identical hardware in flows with strong helical disturbances, if there are significant deviations in time averaged flame shape between the two, particularly if one of the cases is nearly axisymmetric.

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