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Nonlinear development of hydrodynamically-unstable flames in three-dimensional laminar flows

机译：三维层流中流体动力不稳定火焰的非线性发展

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摘要

The hydrodynamic instability, which results from the large density variations between the fresh mixture and the hot combustion products, was discovered by Darrieus and Landau over seventy years ago, and has been named after its inventors. The instability, which prevents flames from being too flat, was thought to lead immediately to turbulent flames. Recent studies, initiated by weakly nonlinear analyses and extended by two-dimensional simulations suggest that this is not the case. It was established that the flame beyond the onset of instability, develops into a cusp-like structure pointing towards the burned gas region that propagates at a speed substantially larger than the laminar flame speed. In this work, we present for the first time a systematic study of the bifurcation phenomena in the more realisticthree-dimensional flow. The computations are carried out within the context of the hydrodynamic theory where the flame is treated as a surface of density discontinuity separating burned gas from the fresh mixture, and propagates at a speed that depends on the local curvature and hydrodynamic strain rate. A low Mach-number Navier–Stokes solver modified by an appropriate source term is used to determine the flow field that results from the gas expansion and the flame is tracked using a level-set methodology with a surface parameterization method employed to accurately capture the local velocity and stretch rate. The numerical scheme is shown to recover the known exact solutions predicted in the weak gas expansion limit and corroborates the bifurcation results from linear stability analysis. The new conformations that evolve beyond the instability threshold have sharp crest pointing towards the burned gas with ridges along the troughs, and propagate nearly 40% faster than planar flames. Indeed, the appearance of sharp folds and creases, which are some manifestations of the Darrieus–Landau instability, have been observed on the surface of premixed flames in various laminar and turbulent settings.
机译：由于新鲜混合物和热燃烧产物之间的巨大密度变化而引起的流体动力学不稳定性，是由Darrieus和Landau于20年前发现的，并以其发明者的名字命名。人们认为这种不稳定性会阻止火焰变得太平，从而立即导致湍流火焰。由弱非线性分析发起并由二维模拟扩展的最新研究表明，事实并非如此。可以确定的是，超出不稳定状态的火焰发展成尖头状的结构，指向燃烧的气体区域，该区域以比层流火焰速度大得多的速度传播。在这项工作中，我们第一次对更现实的三维流动中的分叉现象进行了系统的研究。这些计算是在流体力学理论的背景下进行的，在该理论中，火焰被视为密度不连续的表面，将燃烧的气体与新鲜混合物分开，并以取决于局部曲率和流体力学应变率的速度传播。通过适当的源项修改的低马赫数Navier-Stokes求解器用于确定由气体膨胀产生的流场，并使用水平设置方法和表面参数化方法跟踪火焰，以精确捕获局部速度和拉伸速率。数值方案显示出可以恢复在弱气体膨胀极限中预测的已知精确解，并证实了线性稳定性分析的分叉结果。演变超过不稳定性阈值的新构型具有尖锐的波峰，指向燃烧的气体，并带有沿着波谷的脊，其传播速度比平面火焰快40％。确实，在各种层流和湍流环境中，在预混火焰表面观察到了尖锐的褶皱和折痕的出现，这是Darrieus-Landau不稳定性的一些表现。

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