Pulse triggered instability in solid rocket motors

Baum, Joseph D.; Levine, J.; Lovine, R.

doi:10.2514/6.1982-1219

Cited by 7 publications

(7 citation statements)

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“…When appropriate boundary conditions in x are set, the governing equations (19) and (20) reduce to an initial value problem in t. For the system examined in this article, @u=@x and p are both set to zero at the ends of the tube. These boundary conditions are enforced by choosing basis sets that match these boundary conditions uðx, tÞ ¼ X N j¼1 j ðtÞ cosð jxÞ, ð22Þ…”

Section: The Boundary Conditions and The Discretized Governing Equationsmentioning

confidence: 99%

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Non-normality and nonlinearity in thermoacoustic instabilities

Sujith

Juniper

Schmid

2016

International Journal of Spray and Combustion Dynamics

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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.

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Section: The Boundary Conditions and The Discretized Governing Equationsmentioning

confidence: 99%

“…16 As well as in the above references, nonlinear heat release has been examined by Refs. [17][18][19][20] Nonlinear heat release rate can cause subcritical bifurcations, whether the gas dynamics are linear or nonlinear. In general, the heat release rate is a function of the velocity and pressure fluctuations.…”

Section: Sources Of Nonlinearitymentioning

confidence: 99%

Non-normality and nonlinearity in thermoacoustic instabilities

Sujith

Juniper

Schmid

2016

International Journal of Spray and Combustion Dynamics

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“…There have been numerous papers on the subject covering both experimental observations and modeling. 4,30,31,32,33,40,41,45,46,49,50,51,52,53,59,60,61,66,68,71,72,73 The details of this work is well beyond the scope of this report. Some important conclusions and comments about non-linear combustion instability can be made.…”

Section: E Non-linear Effectsmentioning

confidence: 99%

Lessons Learned In Solid Rocket Combustion Instability

Blomshield¹

2007

43rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference &Amp;amp; Exhibit

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Over the last 60 years, a considerable amount of time and money has been spent improving our understanding of combustion instability in solid rocket propulsion systems. Over this period, significant knowledge has been accumulated that can influence the acoustic stability of solid propulsive systems. Unfortunately, many of these lessons learned about combustion instability remain the knowledge of a select few in government and industry who work with combustion instability on a daily basis. This paper attempts to organize many of these "rules of thumb" that propellant formulators and motor designers need to be aware of in order to minimize the chances of combustion instability. In addition, several mathematical relationships are presented which can be used to predict the frequency of potential acoustic modes and determine resultant thrust oscillations produced by acoustic oscillations. Also included are some key fundamental equations which can be used to gain insight into combustion instability in rocket motor systems and there is a short section on motor instrumentation. This paper is not an attempt to be an exhaustive study into combustion instability, but rather, will attempt to list in a clear fashion some of the more important lessons learned and empirical observations of solid propellant combustion instability. This paper emphasizes composite propellants, but many observations apply to double base and composite modified double base propellants, as well.

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“…The term '13' represents a reverse transfer of energy from the third mode to the second mode. It can be seen that terms with 6(1) and b(l) as coefficients appear in the second column of Table 2, while the third column consists of terms with 6(2) and b (2) as coefficients.…”

Section: Energy Transfermentioning

confidence: 99%

“…Solid propellant rocket motors have been known to exhibit two qualitatively different kinds of behavior at onset of combustion instability: 1) linear instability, where the acoustical fluctuations, in response to a small perturbation, build up to a limit cycle, and 2) nonlinear instability, where the acoustical fluctuations show a stable, damped response for small perturbations, but show a limit cycle response to larger perturbations. Nonlinear instability of this nature has been called pulsed or triggered instability [2,3]. Both linear and nonlinear (triggered) instability have been observed in recent experiments on a gas turbine combustor as well [4].…”

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

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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.

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Pulse triggered instability in solid rocket motors

Cited by 7 publications

References 0 publications

Non-normality and nonlinearity in thermoacoustic instabilities

Non-normality and nonlinearity in thermoacoustic instabilities

Lessons Learned In Solid Rocket Combustion Instability

Modeling and Dynamics of Nonlinear Acoustic Waves in a Combustion Chamber

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