Dynamics of hydrodynamically unstable premixed flames in a gravitational field ? local and global bifurcation structures
Dynamics of hydrodynamically unstable premixed flames in a gravitational field ? local and global bifurcation structures
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重力场中流体动力学不稳定预混火焰的动力学？
DOI：
10.1080/13647830.2023.2165968
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发表时间：
2023
影响因子：
1.3
通讯作者：
Matalon Moshe
中科院分区：
文献类型：
--
作者：
Matsue Kaname;Matalon Moshe
采用非线性michael - sivashinsky （MS）方程对流体动力不稳定预混火焰的动力学进行了研究，并对其进行了适当的修正以纳入重力效应。这个问题取决于两个参数：表征可燃混合物及其扩散特性的马克斯坦数，以及表示浮力与惯性力之比的重力参数。利用分岔理论中的延拓方法，得到了大范围参数下所有可能的平衡解的全貌。结果强调了向上和向下传播之间的区别。在没有重力的情况下，非线性发展总是导致固定解，即细胞火焰以恒定速度传播而不改变形状。当减小马克斯坦数时，观察到振幅的适度增长，传播速度达到上限。对于向上传播，平衡态也是固定解，但其空间结构取决于导致其发展的初始条件。达里厄斯-朗道不稳定性和瑞利-泰勒不稳定性结合在一起，产生了恒定的较大振幅和更尖锐的波峰，当马克斯坦数减少时，波峰以越来越快的速度传播。对于向下传播，平衡状态除了稳定结构外还包括时间周期解，即以恒定平均速度传播的脉动火焰。重力的稳定作用抑制了非线性生长，导致火焰形态的时空变化，如多波峰平稳剖面或脉动细胞分裂和合并模式的形成，以及传播速度的总体降低。这些状态之间的过渡发生在稳定性点的分岔和交换处，当减小Markstein数和/或增加重力的影响时，这种转变变得更加突出。除了局部分岔特征外，通过追踪分岔点本身的延拓获得的方程的全局分岔结构揭示了定性特征，如双稳定性和滞后的表现，和/或时间周期解的开始和持续。总的来说，这些结果显示出，当引力无论多么微小，在物理上变得有意义时，所发生的丰富而复杂的动力学。
The dynamics of hydrodynamically unstable premixed flames are studied using the nonlinear Michelson–Sivashinsky (MS) equation, modified appropriately to incorporate effects due to gravity. The problem depends on two parameters: the Markstein number that characterises the combustible mixture and its diffusion properties, and the gravitational parameter that represents the ratio of buoyancy to inertial forces. A comprehensive portrait of all possible equilibrium solutions are obtained for a wide range of parameters, using a continuation methodology adopted from bifurcation theory. The results heighten the distinction between upward and downward propagation. In the absence of gravity, the nonlinear development always leads to stationary solutions, namely, cellular flames propagating at a constant speed without change in shape. When decreasing the Markstein number, a modest growth in amplitude is observed with the propagation speed reaching an upper bound. For upward propagation, the equilibrium states are also stationary solutions, but their spatial structure depends on the initial conditions leading to their development. The combined Darrieus–Landau and Rayleigh–Taylor instabilities create profiles of invariably larger amplitudes and sharper crests that propagate at an increasingly faster speed when reducing the Markstein number. For downward propagation, the equilibrium states consist in addition to stationary structures time-periodic solutions, namely, pulsating flames propagating at a constant average speed. The stabilising influence of gravity dampens the nonlinear growth and leads to spatiotemporal changes in flame morphology, such as the formation of multi-crest stationary profiles or pulsating cell splitting and merging patterns, and an overall reduction in propagation speed. The transition between these states occurs at bifurcation and exchange of stability points, which becomes more prominent when reducing the Markstein number and/or increasing the influence of gravity. In addition to the local bifurcation characterisation the global bifurcation structure of the equation, obtained by tracing the continuation of the bifurcation points themselves unravels qualitative features such as the manifestation of bi-stability and hysteresis, and/or the onset and sustenance of time-periodic solutions. Overall, the results exhibit the rich and complex dynamics that occur when gravity, however small, becomes physically meaningful.