Spherical flame initiation and propagation in particle-laden mixtures are investigated theoretically in this work. Within the framework of constant density, large activation energy and quasi-steady assumptions, a correlation describing spherical flame propagation speed as a function of flame radius is derived. This correlation is used to assess the influence of gas and particle properties on initiation and propagation of premixed spherical flames. Spherical flame initiation and propagation are shown to be influenced noticeably by the appearance of inert solid particles. It is found that the flame propagation speed and temperature both decrease with increased particle heat capacity and thermal relaxation time. A non-monotonic change of the flame propagation speed with flame radius is observed when there are particles with large heat capacity. Furthermore, the bifurcation of flame propagation speed is observed for particles with large heat capacity and thermal relaxation time. Within a certain flame radius range, there are both strong and weak flame solutions. The abrupt jump from the strong flame to weak flame results from the excessive heat loss caused by the solid particles and the energy balance is re-established along the weak flame branch. The Lewis number strongly affects the flame propagation speed, particularly for small thermal response time and high particle heat capacity. Additionally, the minimum ignition energy of the particle-laden spherical flames is found to increase with the Lewis number. At higher Lewis number, the difference of minimum ignition energy between gaseous and particle-laden situations becomes larger. To validate the theoretical results, one-dimensional transient simulations of particle-laden spherical flames with detailed chemistry have been conducted. Qualitative agreement is achieved for results from numerical simulations and theoretical analysis.

中文翻译：

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具有惰性固体颗粒的球形预混火焰的引发和传播

在这项工作中，从理论上研究了颗粒混合物中的球形火焰引发和传播。在恒定密度、大活化能和准稳态假设的框架内，导出了描述球形火焰传播速度与火焰半径函数的相关性。这种相关性用于评估气体和颗粒特性对预混球形火焰的引发和传播的影响。惰性固体颗粒的出现显着影响了球形火焰的引发和传播。发现火焰传播速度和温度都随着颗粒热容和热弛豫时间的增加而降低。当存在具有大热容量的颗粒时，观察到火焰传播速度随火焰半径的非单调变化。此外，对于具有大热容和热弛豫时间的粒子，观察到火焰传播速度的分叉。在一定的火焰半径范围内，有强火焰和弱火焰两种解决方案。从强火焰突然跃迁到弱火焰是由于固体颗粒造成的热量损失过多，能量平衡沿着弱火焰分支重新建立。路易斯数强烈影响火焰传播速度，特别是对于小热响应时间和高粒子热容量。此外，发现载有颗粒的球形火焰的最小点火能量随着路易斯数的增加而增加。在较高的刘易斯数下，气体和颗粒负载情况之间的最小点火能量的差异变得更大。为了验证理论结果，已经进行了带有详细化学成分的颗粒状球形火焰的一维瞬态模拟。数值模拟和理论分析的结果达到定性一致。