The mechanisms for nonlinear saturation of a bluff-body stabilised turbulent premixed flame are investigated using LES with the transported flame surface density (TFSD) approach to combustion modelling. The numerical simulation is based on a previous detailed experimental investigation. Results for both the unforced non-reacting and reacting flows are validated against experiment, demonstrating that the fundamental flow features and predicted flame structure are well captured. Key terms in the FSD transport equation are then used to describe the generation and destruction of flame surface area for the unforced reacting flow. In order to investigate the non-linear response of the unsteady heat release rate to acoustic forcing, four harmonically forced flames are considered having the same forcing frequency (160 Hz) but different amplitudes of 10 %, 25 %, 50 % and 64 % of the mean inlet velocity. The flame response is characterised using the Flame Describing Function (FDF). Accurate prediction of the FDF is obtained using the current approach. The computed forced flame structure matches well with the experiment, where effects of shear layer rollup and growth of the vortices on the flame can be clearly observed. Transition to nonlinearity is also observed in the computed FDF. The mechanisms leading to the saturation of the flame response in the higher amplitude case are characterised by inspecting the terms in the FSD transport equation at conditions when the integrated heat release is at its maximum and minimum, respectively. Pinch-off and flame rollup can be seen in snapshots taken at the phase angle of maximum integrated heat release. Conversely, intense vortex shedding and flame-sheet collapse around the shear-layer, as well as small-scale destruction of flame elements in the wake, can be seen in snapshots taken at the phase angle of minimum integrated heat release. The pivotal role of FSD destruction on nonlinear saturation of the flame response is confirmed through the analysis of phase-averaged terms in the FSD transport equation taken at different locations. The phase-averaged subgrid curvature term is found to concentrate in the cusps and downstream regions where flame annihilation is dominant.

中文翻译：

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强制湍流预混火焰中非线性饱和度的 LES

使用 LES 和传输火焰表面密度 (TFSD) 方法进行燃烧建模，研究了钝体稳定湍流预混火焰的非线性饱和机制。数值模拟基于先前的详细实验研究。非受迫非反应流和反应流的结果都经过实验验证，证明基本流动特征和预测的火焰结构被很好地捕获。然后使用 FSD 传输方程中的关键术语来描述非受迫反应流火焰表面积的产生和破坏。为了研究非定常热释放率对声强迫的非线性响应，考虑了具有相同强迫频率 (160 Hz) 但幅度不同 10% 的四个谐波强迫火焰，平均入口速度的 25 %、50 % 和 64 %。火焰响应使用火焰描述函数 (FDF) 进行表征。使用当前方法获得 FDF 的准确预测。计算出的强制火焰结构与实验匹配得很好，可以清楚地观察到剪切层卷起和涡流对火焰的影响。在计算的 FDF 中也观察到向非线性的转变。在较高振幅情况下导致火焰响应饱和的机制的特征在于，在积分热释放分别处于最大值和最小值的条件下检查 FSD 传输方程中的项。夹断和火焰卷起可以在最大综合热释放的相位角拍摄的快照中看到。反过来，剪切层周围强烈的涡旋脱落和火焰片坍塌，以及尾流中火焰元素的小规模破坏，可以在最小综合热释放的相位角处拍摄的快照中看到。通过对不同位置的 FSD 输运方程中的相位平均项的分析，证实了 FSD 破坏对火焰响应非线性饱和的关键作用。发现相位平均子网格曲率项集中在火焰湮灭占主导地位的尖端和下游区域。通过对不同位置的 FSD 输运方程中的相位平均项的分析，证实了 FSD 破坏对火焰响应非线性饱和的关键作用。发现相位平均子网格曲率项集中在火焰湮灭占主导地位的尖端和下游区域。通过对不同位置的 FSD 输运方程中的相位平均项的分析，证实了 FSD 破坏对火焰响应非线性饱和的关键作用。发现相位平均子网格曲率项集中在火焰湮灭占主导地位的尖端和下游区域。