In this study, a thermal-diffusive model using a sinusoidal function for the oscillation term is presented. The model is employed to evaluate the pulsating behavior in a premixed counterflow flame fed with biomass particle cloud considering Lewis number and thermal radiation effects. In order to scrutinize the pulsating characteristics of a flame, time-related governing equations are written for the assumed multi-zone system and analytically solved utilizing Matlab and Mathematica software. To enforce continuity, suitable matching conditions for the temperature and heat flux at the interfaces are derived. Time-dependent characteristics of burning velocity, flame temperature, flame front position, reactants temperature, and mass distributions are presented, taking into account effective Lewis number, thermal radiation, and strain rate influences. An acceptable comparison with numerical simulations affirms the reliability of the mathematical procedure. The obtained results indicated that the pulsating instability of biomass-fueled premixed flames in counterflow arrangements significantly relevant not only to the effective Lewis number but also to thermal radiation transferred from the reaction zone to unburnt reactants. Furthermore, it is found that in counterflow premixed flames, strain rate, in addition to Lewis number and thermal radiation, can be the key to controlling the individual flame oscillation modes.

中文翻译：

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热辐射和路易斯数对湿生物质颗粒逆流预混火焰振荡热扩散不稳定性的影响评估

在这项研究中，提出了一个使用正弦函数作为振荡项的热扩散模型。该模型用于评估生物质颗粒云供给的预混合逆流火焰中的脉动行为，考虑路易斯数和热辐射效应。为了仔细研究火焰的脉动特性，为假设的多区域系统编写了与时间相关的控制方程，并利用 Matlab 和 Mathematica 软件进行分析求解。为了加强连续性，导出了界面处温度和热通量的合适匹配条件。考虑了有效路易斯数、热辐射和应变率的影响，给出了燃烧速度、火焰温度、火焰前锋位置、反应物温度和质量分布的时间相关特征。与数值模拟的可接受的比较证实了数学过程的可靠性。所得结果表明，逆流布置中生物质燃料预混火焰的脉动不稳定性不仅与有效路易斯数显着相关，而且与从反应区传递到未燃烧反应物的热辐射显着相关。此外，我们发现，在逆流预混火焰中，除了路易斯数和热辐射之外，应变率也是控制各个火焰振荡模式的关键。