On the Existence and Stability of Limit Cycles.for Longitudinal Acoustic Modes in a Combustion Chamber

Awad, E.; Culick, F. E. C.

doi:10.1080/00102208608959800

Cited by 60 publications

(22 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[11][12][13][14][15] An important conclusion of these studies is that systems that have linear heat release rate and nonlinear gas dynamics from first to third order do not exhibit subcritical bifurcations. 16 As well as in the above references, nonlinear heat release has been examined by Refs.…”

Section: Sources Of Nonlinearitymentioning

confidence: 99%

“…[73][74][75][76] Starting with an initial guess, we solve the direct equation (11) over the prescribed interval ½0, : The final solution is then propagated backwards in time from t ¼ to t ¼ 0 using the adjoint equation (12). The solution of the adjoint equation is then used in equation (13) to update the initial condition q 0 for the next iteration. The direct-adjoint cycle is repeated until convergence is reached.…”

Section: à2mentioning

confidence: 99%

See 1 more Smart Citation

Non-normality and nonlinearity in thermoacoustic instabilities

Sujith

Juniper

Schmid

2016

International Journal of Spray and Combustion Dynamics

View full text Add to dashboard Cite

Analysis of thermoacoustic instabilities were dominated by modal (eigenvalue) analysis for many decades. Recent progress in nonmodal stability analysis allows us to study the problem from a different perspective, by quantitatively describing the short-term behavior of disturbances. The short-term evolution has a bearing on subcritical transition to instability, known popularly as triggering instability in thermoacoustic parlance. We provide a review of the recent developments in the context of triggering instability. A tutorial for nonmodal stability analysis is provided. The applicability of the tools from nonmodal stability analysis are demonstrated with the help of a simple model of a Rjike tube. The article closes with a brief description of how to characterize bifurcations in thermoacoustic systems.

show abstract

Section: Sources Of Nonlinearitymentioning

confidence: 99%

Section: à2mentioning

confidence: 99%

Non-normality and nonlinearity in thermoacoustic instabilities

Sujith

Juniper

Schmid

2016

International Journal of Spray and Combustion Dynamics

View full text Add to dashboard Cite

show abstract

“…Instead, it is forced to reverse transfer part of this energy to the first mode, due to which the parametric excitations are larger than they ought to be, and the resulting dynamics may show large-amplitude limit cycles that are spurious. Such spurious limit cycles were observed, but could not be explained, in the two-mode continuation results of Jahnke and Culick [18], and, previously, in the two-mode analytical results reported by Awad and Culick [12], and by Paparizos and Culick [13]. Hence, the modal truncation should be such that all significant energy transfers up the modes are accommodated.…”

Section: Modal Truncationmentioning

confidence: 86%

“…Culick and Yang [11] reported a numerically computed solution for the acoustic oscillations with a five-mode truncation of the approximate equations that was found to compare reasonably with a more exact numerical solution [11]. Conditions for the existence and stability of the limit cycle oscillations, and the qualitative dependence of the limit cycles on the system parameters, for the case of two longitudinal acoustic modes, were reported by Awad and Culick [12], and by Paparizos and Culick [13]. However, none of these studies were able to demonstrate triggered instability.…”

Section: Introductionmentioning

confidence: 99%

Modeling and Dynamics of Nonlinear Acoustic Waves in a Combustion Chamber

Ananthkrishnan¹,

Deo²,

Culick³

2002

38th AIAA/ASME/SAE/ASEE Joint Propulsion Conference &Amp;amp; Exhibit

View full text Add to dashboard Cite

Future combustors designed for better efficiency and lower pollutant emission are expected to operate closer to their stability boundary, thereby increasing the risk of encountering combustion instability. Onset of combustion instability leads to limit cycle oscillations in the acoustical fluctuations that can often reach amplitudes large enough to cause severe damage. Active control strategies are, therefore, being considered to prevent combustion instabilities, but their development requires nonlinear models that can faithfully capture the combustor system dynamics. A framework for the approximate analysis of the nonlinear acoustics in a combustion chamber exists, which includes all relevant linear contributions and also second order gasdynamic nonlinearities. Nonlinear combustion effects in the form of pressure and velocity coupling models have also been incorporated into the analysis with the aim of capturing the phenomenon of triggered instability, where the acoustical fluctuations are linearly stable to small perturbations, but show a limit cycle behavior for larger perturbations. However, several questions such as those relating to 1) modal truncation of the equations for the acoustic dynamics, 2) absence of triggered limit cycles in the formulation with only second order gasdynamic nonlinearities, and 3) the form of the velocity coupling function, including the need for a threshold character, have not been satisfactorily resolved. In this paper, we address some of these questions on modeling and dynamics of acoustic waves in combustion chambers, using the approximate analysis, that have remained unanswered over the years.

show abstract

“…With the assumed form (32) for TIn' and the constraint (33) and add the results in pairs to form the equations for r;…”

Section: B Energy Transfer In Nonlinear Oscillationsmentioning

confidence: 99%