1993 Fiscal Year Final Research Report Summary
Stability limit for a self-excited oscillation due to thermoacoustic effect.
| Project/Area Number |
04452056
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| Research Category |
Grant-in-Aid for General Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
物理学一般
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| Research Institution | Aichi University of Education |
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Principal Investigator |
YAZAKI Taichi Aichi Univ of Education, Education, Associate Professor, 教育学部, 助教授 (20144181)
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| Co-Investigator(Kenkyū-buntansha) |
TOMINAGA Akira Tsukuba University, Physics, Lecturer, 物理学系, 講師 (10015563)
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| Project Period (FY) |
1992 – 1993
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| Keywords | Thermoacoustic Effect / Taconis Oscillation / Self-excited Oscillation / Nonlinear Phenomenon / Turbulence / Chaos / Nonequilibrium Open System / Quasiperiodic Motion |
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| Research Abstract |
In the first half of this work we discuss about energy flows and conversions associated with oscillating fluid using the Lagrange frame. Discussion of entropy oscillations is corrected including that of heat exchange between oscillating fluid and solid wall. Stability limit for a self-excited oscillation is qualitatively given by this theory. In the latter half we report experimental results of strongly nonlinear phenomena observed in a thermoacoustic system. The hydrodynamic system attracting our interest, called "T aconis oscillation" in cryogenics, is a spontaneous acoustic oscillation of a gas column induced by large temperature gradients. Stability curves for two or three diferent oscillatory modes intersect with each other for proper conditions. Near the overlapped region and the intersection of the stability curves we find that three or two different modes with incommensurate frequencies can be excited simultaneously, and that competition between them leads to chaotic oscillations through two routes, two-frequency and three-frequency quasiperiodicities. Taconis oscillation with a limit cycle is periodically perturbed by a mechanical force with the amplitude and frequency externally controlled. We find that nonlinear coupling between two oscillating modes leads to quasiperiodicities, frequency-lockings and the onset of chaos for suitable conditions. The global and local universal properties for the quasiperiodic transition to chaos are determined and compared with the circle map universality. We present some experimental evidence for universal scaling properties in favor of the applicability of the map to thermoacoustic systems. The experiment demonstrates that the thermoacoustic system belongs to the same universality class as the simple circle map, at least up to the onset of chaos, in spite of the complexity of the system.
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