解析熱聲動力與控制

Analytic Thermoacoustic Dynamics and Control

林祖佑(Tsu-Yu Lin)

指導教授 ： 洪博雄

國立中正大學/工學院/機械工程學系/博士(2014年)

摘要

本論文探討不均勻溫度壓力分佈的熱聲運動，和儲存在熱聲運動的機械能。其核心是熱聲運動的斯特姆-劉維爾標準式，讓熱聲運動配備有雷利儲量、特徵函數系統、時間空間投影轉換。研究方法整理如下：
(1).藉由不均勻溫度壓力分佈熱聲運動的斯特姆-劉維爾標準式，熱聲運動可表示成一簡諧運動。根據慣性運算子和剛性運算子的正定性和自伴性，證明熱聲運動的極點座落在虛軸上。不管平均溫度和壓力在空間分佈是多麼不均勻，熱聲振盪將一直持續，不會放大也不會衰減。
(2).熱聲運動的慣性運算子和剛性運算子定義雷利儲量。搭配環境壓力和邊界條件，雷利儲量將熱聲運動的機械能，從均勻溫度壓力分佈擴展到不均勻溫度壓力分佈。同時，雷利準則也擴展到不均勻溫度壓力分佈的熱聲運動。
最後，應用解析熱聲動力於燃燒不穩定和熱聲引擎控制。數值模擬展示解析熱聲動力在建模、分析和控制的優勢。

關鍵字

分佈參數系統 ； 轉移函數 ； 熱聲引擎 ； 熱聲動態 ； 雷利準則

並列摘要

This thesis investigates thermoacoustic dynamics with mean temperature and pressure variations. The kernel is formulating thermoacoustic dynamics to Sturm-Liouville form, which equips thermoacoustic dynamics with eigenfunctions/ eigenvalues, and thermoacoustic storages. The research method includes two modules.
(1).Formulating thermoacoustic dynamics with mean temperature and pressure variations to Sturm-Liouville form. Thermoacoustic dynamics is represented by a canonical form of linear vibration systems. Since mass operator and stiffness operator of thermoacoustics is self-adjoint and positive, the poles of the vibration system are always on the imaginary axis for arbitrary mean temperature/ pressure distributions.
(2).The mass operator and stiffness operator defines the Rayleigh storage, the Lyapunov function of thermoacoustics. Cooperated with environment pressure and the boundary condition, Rayleigh storage extends mechanical energy of thermoacoustics from uniform mean temperature/ pressure to mean temperature/ pressure variations. Meanwhile, Rayleigh criterion is extended to mean temperature/ pressure variations.
Finally, Rayleigh storage is applied to combustion instability and thermoacoustic engine control. A series of simulations demonstrate the advantages of the proposed method.

並列關鍵字

Transfer function ； Thermoacoustic engine ； Thermoacoustic dynamics ； Rayleigh criterion

參考文獻

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