Triggering axial instabilities in solid rockets - Numerical predictions

Kooker, Douglas E.; Zinn, B. T.

doi:10.2514/6.1973-1298

Cited by 13 publications

(11 citation statements)

References 8 publications

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“…But the third condition implies two possibilities. First a2 < 0 ; this case yields the same result (18) found for ~ = ' I1:a := 0 .…”

Section: Discussionsupporting

confidence: 53%

“…a2 > 0 ; this case yields the following stability condition (22) This conditicon shows clearly that it is possible to get a stable limit cycle when the first mode is stable and the second mode is unstable. In conclusion, the conditions (16)- (18) are sufficient here but not necessary.…”

Section: Discussionmentioning

confidence: 87%

“…This will be shown to be the reason for reducing the stability criteria. Equations (3)- (7) , in this case, become The criterion (21) is much less restrictive than the criteria (16)- (18). However, the initial conditions here are very restrictrive.…”

Section: Discussionmentioning

confidence: 99%

“…In the following part, it will be shown that the initial conditions, under very special circumstances, can change the stability criteria (16)- (18). Let us assume that t..1.e initial conditions are of the following form and that ~,~ both vanish.…”

Section: Discussionmentioning

confidence: 99%

“…Then. we app:!y the analysis to some numerical solutions reported in [18]. The purpose there is to show tha t we can replace 'Ielocity coupling by nonlinear particle losses and still predict triggering.…”

Section: Applicationmentioning

confidence: 99%

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Existence and stability of limit cycles for pressure oscillations incombustion chambers

Awad¹,

Culick²

1983

21st Aerospace Sciences Meeting

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In this paper, we discuss two problems. First, usiD8 a seco:ad order expansion in the pressure amplitude, some analytical results on the existence, stability and amplitude of limit cycles for pressure oscillations in combusticm chambers are presented. A stable limit cycle seems to be unique. The conditions for existence and stability are found to be dependent only on the linear parameters. The nonlinear parameter aff,ects only the wave amplitude. The imaginary parts of the linear responses, to pressure oscillations, of the different processes in the chamber play an import.ant role in the stability of the limit cycle. They also atIect the direction of flow of energy among modes. In the absence of the imaginary parts, in order for an infinitesimal perturbation in the flow to reach a finite amplitude, the lowest mode must be unstable while the highest must be stable; thus energy flows from the lowest mode to the highest one. The same case exists when the imaginary parts are non-zero, but in addition, the cOl1Ltrary situation is possible. There are conditions under which an infinitesimal perturbation may reach a finit.e amplitude if the lowest mode is stable while the highest is unstable. Thus energy can flow 'backward" from the highest mode to the lowest one. It is also shown that the imaginary parts increase the final wave amplitude.Second, the triggering of pressure oscillations in solid propellant rockets is discussed. In order to explain the triggering of the oscillations to a nontrivial stablE: limit cycle, the treatment of two modes and the inclusion in the combustion response of either a second order nonlinear velocity coupling or a third order nonlinear pressure coupling seem to be sufficient.

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“…But the third condition implies two possibilities. First a2 < 0 ; this case yields the same result (18) found for ~ = ' I1:a := 0 .…”

Section: Discussionsupporting

confidence: 53%

Section: Discussionmentioning

confidence: 87%

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Applicationmentioning

confidence: 99%

See 3 more Smart Citations

Existence and stability of limit cycles for pressure oscillations incombustion chambers

Awad¹,

Culick²

1983

21st Aerospace Sciences Meeting

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Multisized Inert Particle Loading for Solid Rocket Axial Combustion Instability Suppression

Greatrix

2012

International Journal of Aerospace Engineering

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In the present investigation, various factors and trends, related to the usage of two or more sets of inert particles comprised of the same material (nominally aluminum) but at different diameters for the suppression of axial shock wave development, are numerically predicted for a composite-propellant cylindrical-grain solid rocket motor. The limit pressure wave magnitudes at a later reference time in a given pulsed firing simulation run are collected for a series of runs at different particle sizes and loading distributions and mapped onto corresponding attenuation trend charts. The inert particles’ presence in the central core flow is demonstrated to be an effective means of instability symptom suppression, in correlating with past experimental successes in the usage of particles. However, the predicted results of this study suggest that one needs to be careful when selecting more than one size of particle for a given motor application.

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Simulation of Axial Combustion Instability Development and Suppression in Solid Rocket Motors

Greatrix

2009

International Journal of Spray and Combustion Dynamics

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In the design of solid-propellant rocket motors, the ability to understand and predict the expected behaviour of a given motor under unsteady conditions is important. Research towards predicting, quantifying, and ultimately suppressing undesirable strong transient axial combustion instability symptoms necessitates a comprehensive numerical model for internal ballistic simulation under dynamic flow and combustion conditions. An updated numerical model incorporating recent developments in predicting negative and positive erosive burning, and transient, frequency-dependent combustion response, in conjunction with pressuredependent and acceleration-dependent burning, is applied to the investigation of instabilityrelated behaviour in a small cylindrical-grain motor. Pertinent key factors, like the initial pressure disturbance magnitude and the propellant's net surface heat release, are evaluated with respect to their influence on the production of instability symptoms. Two traditional suppression techniques, axial transitions in grain geometry and inert particle loading, are in turn evaluated with respect to suppressing these axial instability symptoms. NOMENCLATURE INTRODUCTIONOver the last fifty years or so, there has been a number of research efforts directed towards understanding the physical mechanisms, or at least the surrounding factors, behind the appearance of symptoms associated with nonlinear axial combustion instability [1-2] in solid rocket motors (SRMs). Traditionally, these symptoms are a sustained axial pressure wave presence in the combustion chamber, sometimes accompanied by a substantial rise in the base chamber pressure [dc shift]. The motivation for these past and present studies was and is of course to bring this better understanding to bear in more precisely suppressing, if not eliminating, these symptoms. Studies of nonlinear axial combustion instability have ranged from numerous experimental test firing series on the one hand [3], and linear/nonlinear acoustic theory modelling on the other [2,[4][5][6]. Largely, the acoustic analysis produces frequency-based standing wave solutions for a given chamber geometry, but typically without some useful quantitative information. On occasion, researchers have employed a numerical modelling approach, to work towards a more comprehensive quantitative understanding of the physics involved [7][8]. The numerical model would typically produce a travelling wave solution to a limit pressure wave amplitude and a corresponding small or larger dc shift in chamber pressure, a time-based result evolving from an initial pulse disturbance introduced into the chamber flow. Available computational power and associated result turnaround times commonly forced some simplifications in the given numerical model. A comprehensive numerical model for simulation of nonlinear dynamic flow and combustion conditions is ultimately essential in the quest for the ability to predict and quantify axial combustion instability symptoms in SRMs. An effective model combines the ef...

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Triggering axial instabilities in solid rockets - Numerical predictions

Cited by 13 publications

References 8 publications

Existence and stability of limit cycles for pressure oscillations incombustion chambers

Existence and stability of limit cycles for pressure oscillations incombustion chambers

Multisized Inert Particle Loading for Solid Rocket Axial Combustion Instability Suppression

Simulation of Axial Combustion Instability Development and Suppression in Solid Rocket Motors

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