A model for the response of technically premixed flames to equivalence ratio perturbations is proposed. The formulation, which is an extension of an analytical flame tracking model based on the linearized G-equation, considers the flame impulse response to a local, impulsive, infinitesimal perturbation that is transported by convection from the flame base towards the flame surface. It is shown that the contributions of laminar flame speed and heat of reaction to the impulse response exhibit a local behavior, i.e. the flame responds at the moment when and at the location where the equivalence ratio perturbation reaches the flame surface. The time lag of this process is related to a convective time scale, which corresponds to the convective transport of fuel from the base of the flame to the flame surface. On the contrary, the flame surface area contribution exhibits a non-local behavior: albeit fluctuations of the flame shape are generated locally due to a distortion of the kinematic balance between flame speed and the flow velocity, the resulting wrinkles in flame shape are then transported by convection towards the flame tip with the restorative time scale. The impact of radial non-uniformity in equivalence ratio perturbations on the flame impulse response is demonstrated by comparing the impulse responses for uniform and parabolic radial profiles. Considerable deviation in the phase of the flame transfer function, which is important for thermo-acoustic stability, is observed.

中文翻译：

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基于G方程的技术模型，用于技术预混火焰对当量比的扰动的响应

提出了一种技术上预混火焰对当量比扰动响应的模型。该公式是基于线性G方程的分析火焰跟踪模型的扩展，它考虑了火焰对局部，脉冲，无穷微扰动的响应，该扰动是通过对流从火焰底部向火焰表面传递的。结果表明，层流火焰速度和反应热对脉冲响应的贡献表现出局部行为，即，当当量扰动到达火焰表面的时刻和位置，火焰响应。该过程的时滞与对流时间标度有关，其对应于燃料从火焰底部到火焰表面的对流传输。反之，火焰表面积的贡献表现出非局部行为：尽管由于火焰速度和流速之间的运动学平衡的畸变而局部产生了火焰形状的波动，但火焰形状的皱纹随后通过对流向火焰输送。火焰尖与恢复时间的比例。通过比较均匀和抛物线形径向分布的脉冲响应，可以证明当量比扰动径向不均匀性对火焰脉冲响应的影响。观察到火焰传递函数的相位有相当大的偏差，这对于热声稳定性很重要。然后，通过对流以恢复性的时间尺度将产生的火焰状皱纹通过对流向火焰尖端传输。通过比较均匀和抛物线形径向分布的脉冲响应，可以证明当量比扰动径向不均匀性对火焰脉冲响应的影响。观察到火焰传递函数的相位有相当大的偏差，这对于热声稳定性很重要。然后，通过对流以恢复性的时间尺度将产生的火焰状皱纹通过对流向火焰尖端传输。通过比较均匀和抛物线形径向分布的脉冲响应，可以证明当量比扰动径向不均匀性对火焰脉冲响应的影响。观察到火焰传递函数的相位有相当大的偏差，这对于热声稳定性很重要。