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Transient energy growth analysis of a thermoacoustic system with distributed mean heat input

机译：具有平均输入热量分布的热声系统的瞬态能量增长分析

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摘要

Transient growth of flow disturbances has great potential to trigger unwanted thermoacoustic instability. So far transient growth analysis has tended to focus on thermoacoustic systems with acoustically compact heat sources, even though many systems are associated with distributed mean heat input, such as a premixed flame. In this work, transient growth analysis of both choked and open-ended thermoacoustic systems in the presence of a mean flow and a spatially distributed mean heat input is conducted. Unsteady heat release is modeled within the classical time-lag N-τ formulation. Both uniform and triangular distributions for the rate of mean heat input are considered. The generation of entropy disturbances with such distributed heat input is studied first. It is shown that the entropy waves generated by the uniform and triangular distributed heat input are increased first and then decreased with increased frequency. This is different from the conventional concentrated heat input, of which the entropy waves produced is frequency-independent. In addition, the entropy eigenmodes are shown to be non-orthogonal. To quantify transient growth of flow disturbances, two energy measures are defined, calculated and compared. One is associated with the conventional acoustical energy. The other is associated with both acoustic and entropy disturbances. It is shown that the maximum transient growth G_(ac)~(max) of acoustical energy is in the range of 10~2-10~3 in the choked system, while 10° ≤ G_(ac)~(max) ≤ 10~1 in the open-ended system. Furthermore, the longer of the uniform distributed heat input, the larger G_(ac)~(max). However, such finding is not observed for the triangular heat input. Further insights are obtained by examining the contribution of eigenmodes in different frequency ranges. It is found that the lower frequency eigenmodes play a dominant role. Finally, the effect of the interaction index N on transient growth is examined. It is found that the maximum transient growth of acoustical energy G_(ac)~(max) and total energy G_(tot)~(max) are decreased with increased N. It is also found that the longer of the uniform distributed heat input, the lower G_(tot)~(max). These findings are consistent with those obtained in our non-orthogonality and entropy generation analyses.
机译：流动扰动的瞬态增长具有引发不希望的热声不稳定性的巨大潜力。到目前为止，尽管许多系统与分布式平均热量输入（例如预混火焰）相关联，但瞬态增长分析已趋向于集中在具有声学紧凑热源的热声系统上。在这项工作中，在存在平均流量和空间分布平均热量输入的情况下，对节流和开放式热声系统的瞬态生长进行了分析。在经典时滞N-τ公式中模拟了不稳定的热释放。考虑平均热量输入速率的均匀分布和三角形分布。首先研究了这种分布的热量输入产生的熵扰动。结果表明，均匀和三角形分布的热输入产生的熵波首先增加，然后随着频率增加而减小。这不同于常规的集中热输入，传统的集中热输入产生的熵波与频率无关。此外，熵本征模显示为非正交的。为了量化流动扰动的瞬态增长，定义，计算和比较了两种能量度量。一种与常规声能有关。另一个与声学和熵扰动有关。结果表明，在ked系统中，声能的最大瞬态增长G_（ac）〜（max）在10〜2-10〜3的范围内，而10°≤G_（ac）〜（max）≤10在开放式系统中为〜1。此外，均匀分布的热量输入越长，G_（ac）〜（max）越大。然而，对于三角形热输入没有观察到这种发现。通过检查本征模在不同频率范围内的贡献，可以获得更多的见解。发现低频本征模式起主要作用。最后，考察了相互作用指数N对瞬时生长的影响。发现随着N的增加，声能G_（ac）〜（max）和总能量G_（tot）〜（max）的最大瞬时增长减小。此外，还发现均匀分布的热量输入越长，较低的G_（tot）〜（max）。这些发现与我们在非正交性和熵生成分析中获得的结果一致。

著录项

  • 来源
    《International Journal of Heat and Mass Transfer》 |2016年第11期|287-301|共15页
  • 作者

    Lei Li; Dan Zhao; L.P.H. de Goey;

  • 作者单位

    School of Mechanical & Aerospace Engineering, College of Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore,Key Laboratory for Power Machinery and Engineering of Ministry of Education, Shanghai Jiao Tong University, Shanghai 200240, China;

    School of Mechanical & Aerospace Engineering, College of Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore;

    Department of Mechanical Engineering, Technische Universiteit Eindhoven, P.O. Box 513, 5600 MB Eindhoven, Netherlands;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Thermoacoustic instability; Transient growth; Entropy disturbances; Non-normality; Combustion instability; Non-orthogonality;

    机译：热声不稳定性;暂时增长;熵扰动;非正常燃烧不稳定;非正交;

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