Fractal structures of hydrodynamically unstable and diffusive-thermally unstable flames
Fractal structures of hydrodynamically unstable and diffusive-thermally unstable flames
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DOI：
10.1016/j.combustflame.2013.05.017
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发表时间：
2013-11
影响因子：
4.4
通讯作者：
Kenjiro Mukaiyama;Shimon Shibayama;K. Kuwana
中科院分区：
文献类型：
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作者：
Kenjiro Mukaiyama;Shimon Shibayama;K. Kuwana
本文以爆炸危险性评价为背景，讨论了流体动力学不稳定火焰的分形结构。瓦斯爆炸事故通常发生在大规模的静止可燃混合物中。球形火焰从点火点向外传播，由于流体动力学不稳定性，火焰加速。从风险评估的角度来看，考虑火焰速度的增加是必要的，因为爆炸的损害受到火焰速度的显著影响。由于流体动力学不稳定火焰具有分形结构，并且火焰面积（从而火焰速度）可以使用分形维数来估计，因此了解潜在意外爆炸条件下火焰的分形维数是很重要的。三种方法（盒计数法，傅立叶分析，和基于火焰速度的尺度依赖性的方法）进行了测试，以计算一个纯粹的流体动力学不稳定的火焰，是中性的扩散热不稳定的分形维数。这些方法适用于Sivashinsky方程的数值解，但它们也可以用于普通CFD计算的结果。一个纯粹的扩散热不稳定火焰，这是中性的流体动力学不稳定的分形结构，也进行了研究比较。结果表明，对于流体动力学不稳定火焰，三种方法得到的分形维数一致，而扩散热不稳定火焰不具有分形特征。这是因为前者火焰具有层次结构，而特定波长的褶皱主要在后者火焰中生长。讨论了分形维数与热膨胀率的关系。
This paper discusses the fractal structure of a hydrodynamically unstable flame with the background of the risk assessment of an explosion hazard. An accidental gas explosion usually occurs in a large-scale quiescent combustible mixture. A spherical flame outwardly propagates from the ignition point, and the flame accelerates owing to hydrodynamic instability. From the viewpoint of risk assessment, it is essential to consider such an increase in flame speed because the damage of an explosion is significantly influenced by the flame speed. Because hydrodynamically unstable flames have fractal structures and the flame area (and hence the flame speed) can be estimated using the fractal dimension, it is important to know the fractal dimension of the flame under the condition of a potential accidental explosion. Three methods (a box-counting method, a Fourier analysis, and a method based on the scale dependence of the flame speed) are tested to calculate the fractal dimension of a purely hydrodynamically unstable flame that is neutral in terms of diffusive-thermal instability. These methods are applied to the numerical solution of the Sivashinsky equation, but they can be also used to the result of an ordinary CFD calculation. The fractal structure of a purely diffusive-thermally unstable flame, which is neutral in terms of hydrodynamic instability, is also studied for comparison. The results show that all the three methods yield consistent fractal dimensions for the hydrodynamically unstable flame, whereas the diffusive-thermally unstable flame does not exhibit fractal characters. This is because the former flame has a hierarchical structure, whereas wrinkles of a specific wavelength mainly grow in the latter flame. The dependence of the fractal dimension on the thermal expansion ratio is also discussed.