Resonant mode interactions and the bifurcation of combustion-driven acoustic oscillations in resonance tubes
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 then 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 we consider one particular model of a pulse combustor, and focus on 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. 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 latter 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 multi-periodic acoustic oscillation from one of the single-period primary branches.
- Research Organization:
- Sandia National Labs., Livermore, CA (United States)
- Sponsoring Organization:
- USDOE, Washington, DC (United States)
- DOE Contract Number:
- AC04-76DR00789
- OSTI ID:
- 10136162
- Report Number(s):
- SAND-93-8487; ON: DE93009448
- Resource Relation:
- Other Information: PBD: Jan 1993
- Country of Publication:
- United States
- Language:
- English
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Resonant mode interactions and the bifurcation of combustion-driven acoustic oscillations in resonance tubes
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Related Subjects
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
COMBUSTION
OSCILLATION MODES
TUBES
HARMONICS
ROCKETS
INSTABILITY
NONLINEAR PROBLEMS
ACOUSTICS
MECHANICAL VIBRATIONS
MATHEMATICAL MODELS
TWO-PHASE FLOW
EIGENVALUES
ITERATIVE METHODS
421000
420400
990200
COMBUSTION SYSTEMS
HEAT TRANSFER AND FLUID FLOW
MATHEMATICS AND COMPUTERS