Resonant mode interactions and the bifurcation of combustion-driven acoustic oscillations in resonance tubes
- Sandia National Labs., Livermore, CA (United States). Combustion Research Facility
Acoustic oscillations in practical combustion devices such as pulse combustors and rocket motors, whether desirable or not, are properly interpreted as combustion instabilities. A nonlinear stability analysis of the corresponding fluid motions than shows that the nonsteady behavior is governed by infinitely coupled systems of nonlinear evolution equations for the amplitudes of the classical acoustic modes. However, under certain conditions, it has been conjectured that relatively low-order truncations can give qualitatively correct physical results. In the present work, one particular model of a pulse combustor is considered, and a parameter regime in the neighborhood of a primary acoustic bifurcation where either one or a pair of purely longitudinal acoustic modes achieves a positive linear growth rate is focused upon. In the first case, it is formally shown that a decoupling occurs such that a two-mode approximation consisting of the linearly unstable mode and its first resonant harmonic completely determines the dynamics of the oscillation. In the later case, it is again demonstrated that a decoupling occurs, and although mode interactions require the retention of additional modes besides the two linearly unstable modes and their first resonant harmonics, a relatively low-order dynamical system still governs the bifurcation behavior. The presence of two linearly unstable modes is then shown to lead to more complicated dynamics, including the stable secondary bifurcation of a multiperiodic acoustic oscillation from one of the single-period primary branches.
- OSTI ID:
- 6796830
- Journal Information:
- SIAM Journal of Applied Mathematics (Society for Industrial and Applied Mathematics); (United States), Vol. 54:6; ISSN 0036-1399
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
PULSE COMBUSTORS
COMBUSTION INSTABILITY
MATHEMATICAL MODELS
COMBUSTION KINETICS
FLUID MECHANICS
MECHANICAL VIBRATIONS
NONLINEAR PROBLEMS
ROCKET ENGINES
SOUND WAVES
CHEMICAL REACTION KINETICS
COMBUSTORS
ENGINES
HEAT ENGINES
INSTABILITY
KINETICS
MECHANICS
REACTION KINETICS
421000* - Engineering- Combustion Systems