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Stability limit for a self-excited oscillation due to thermoacoustic effect.

Research Project

Project/Area Number 04452056
Research Category

Grant-in-Aid for General Scientific Research (B)

Allocation TypeSingle-year Grants
Research Field 物理学一般
Research InstitutionAichi University of Education

Principal Investigator

YAZAKI Taichi  Aichi Univ of Education, Education, Associate Professor, 教育学部, 助教授 (20144181)

Co-Investigator(Kenkyū-buntansha) TOMINAGA Akira  Tsukuba University, Physics, Lecturer, 物理学系, 講師 (10015563)
Project Period (FY) 1992 – 1993
Project Status Completed (Fiscal Year 1993)
Budget Amount *help
¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 1993: ¥700,000 (Direct Cost: ¥700,000)
KeywordsThermoacoustic Effect / Taconis Oscillation / Self-excited Oscillation / Nonlinear Phenomenon / Turbulence / Chaos / Nonequilibrium Open System / Quasiperiodic Motion / 非平衡開放系 / 散逸構造 / 複雑系 / フラクタル
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.

Report

(3 results)
  • 1993 Annual Research Report   Final Research Report Summary
  • 1992 Annual Research Report
  • Research Products

    (17 results)

All Other

All Publications (17 results)

  • [Publications] T.Yazaki: "Experimental observation of thermoacoustic turbulence and universal properties at the quasiperiodic transition to chaos." Physical Review E. 48. 1806-1818 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] 富永 昭: "粘性流体の熱音響理論 第一部 微小サイクルのエネルギー交換とエネルギー流束" 低温工学. 27. 543-548 (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] 富永 昭: "粘性流体の熱音響理論 第二部 流路断面内での平均" 低温工学. 27. 549-554 (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] 富永 昭: "粘性流体の熱音響理論 第三部 流路断面内での流速とエントロピーの分布" 低温工学. 28. 99-107 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] 富永 昭: "粘性流体の熱音響理論 第四部 軸方向の空間変化" 低温工学. 28. 108-113 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] T.Yazaki: "Experimental observation of thermoacoustic turbulence and universal properties at the quasiperiodic transition to chaos." Physical Review E. 48. 1806-1818 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] A.Tominaga: "Thermoacoustic theory of viscus fluid, Part 1 - Energy conversion and Energy flux of small cycles." Cryogenic Engineering. 27. 543-548 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] A.Tominaga: "Thermoacoustic theory of viscus fluid, Part 2 - average over the cross-sectional area of flow channel." Cryogenic Engineering. 27. 549-554 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] A.Tominaga: "Thermoacoustic theory of viscus fluid, Part 3 - radial distribution of velocity and entropy." Cryogenic Engineering. 28. 99-107 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] A.Tominaga: "Thermoacoustic theory of viscus fluid, Part 4 - axial variations." Cryogenic Engineering. 28. 108-113 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] T.Yazaki: "Experimental observation of thermoacoustic turbulence and universal properties at the quasiperiodic transition to chaos." Physical Review E. 48. 1806-1818 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] 富永 昭: "粘性流体の熱音響理論第3部.流路断面内での流束とエントロピーの分布" 低温工学. 28. 99-107 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] 富永 昭: "粘性流体の熱音響理論第4部.軸方向の空間変化" 低温工学. 28. 108-113 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] 富永 昭: "超伝導・低温工学ハンドブック" オーム社・低温工学協会, 5 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] K.Fukushima T.Yamada T.Yazaki: "A Self-Similar Structure of An Accumulated Expansion Rate in The Tacomis Osillation System" Patherm Formation in Complex Dissipative Systems.{in Proceedings edited by S.Kai (World Scientific)}. (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] 富永 昭: "流路断面内での流速とエントロピーの分布 -粘性流体の熱音響理論第3部-" 低温工学. 28. 35-43 (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] 富永 昭: "軸方向の空間変化 -粘性流体の熱音響理論第4部-" 低温工学. 28. 44-49 (1992)

    • Related Report
      1992 Annual Research Report

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Published: 1993-04-01   Modified: 2016-04-21  

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