Acoustic waves passing through a swirler generate inertial waves in rotating flow. In the present study, the response of a premixed flame to an inertial wave is scrutinized, with emphasis on the fundamental fluid-dynamic and flame-kinematic interaction mechanism. The analysis relies on linearized reactive flow equations, with a two-part solution strategy implemented in a finite element framework: Firstly, the steady state, low-Mach number, Navier–Stokes equations with Arrhenius type one-step reaction mechanism are solved by Newton’s method. The flame impulse response is then computed by transient solution of the analytically linearized reactive flow equations in the time domain, with mean flow quantities provided by the steady-state solution. The corresponding flame transfer function is retrieved by fitting a finite impulse response model. This approach is validated against experiments for a perfectly premixed, lean, methane-air Bunsen flame, and then applied to a laminar swirling flame. This academic case serves to investigate in a generic manner the impact of an inertial wave on the flame response. The structure of the inertial wave is characterized by modal decomposition. It is shown that axial and radial velocity fluctuations related to the eigenmodes of the inertial wave dominate the flame front modulations. The dispersive nature of the eigenmodes plays an important role in the flame response.

中文翻译：

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旋流火焰对惯性波的响应

穿过旋流器的声波在旋转流中产生惯性波。在本研究中，仔细研究了预混火焰对惯性波的响应，重点是基本的流体动力学和火焰运动学相互作用机理。该分析依赖于线性化的反应流方程，并在有限元框架中实现了两部分的求解策略：首先，牛顿方程求解了具有Arrhenius型单步反应机理的稳态，低马赫数，Navier-Stokes方程。方法。然后，通过时域中解析线性化的无功流方程的瞬态解来计算火焰脉冲响应，其中平均流量由稳态解提供。通过拟合有限脉冲响应模型来检索相应的火焰传递函数。该方法已针对完全预混合，稀薄的甲烷-空气本生火焰进行了实验验证，然后应用于层流涡旋火焰。该学术案例用于以一般方式研究惯性波对火焰响应的影响。惯性波的结构以模态分解为特征。结果表明，与惯性波本征模有关的轴向和径向速度波动主导着火焰前调制。本征模的分散性在火焰响应中起重要作用。惯性波的结构以模态分解为特征。结果表明，与惯性波本征模有关的轴向和径向速度波动主导着火焰前调制。本征模的分散性在火焰响应中起重要作用。惯性波的结构以模态分解为特征。结果表明，与惯性波本征模有关的轴向和径向速度波动主导着火焰前调制。本征模的分散性在火焰响应中起重要作用。