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首页> 外文期刊>Journal of Engineering for Gas Turbines and Power >Nonlinear Phenomena in Thermoacoustic Systems With Premixed Flames
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Nonlinear Phenomena in Thermoacoustic Systems With Premixed Flames

机译:预混火焰在热声系统中的非线性现象

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Nonlinear analysis of thermoacoustic instability is essential for the prediction of the frequencies, amplitudes, and stability of limit cycles. Limit cycles in thermoacoustic systems are reached when the energy input from driving processes and energy losses from damping processes balance each other over a cycle of the oscillation. In this paper, an integral relation for the rate of change of energy of a thermoacoustic system is derived. This relation is analogous to the well-known Rayleigh criterion in thermoacoustics, however, it can be used to calculate the amplitudes of limit cycles and their stability. The relation is applied to a thermoacoustic system of a ducted slot-stabilized 2-D premixed flame. The flame is modeled using a nonlinear kinematic model based on the G-equation, while the acoustics of planar waves in the tube are governed by linearized momentum and energy equations. Using open-loop forced simulations, the flame describing function (FDF) is calculated. The gain and phase information from the FDF is used with the integral relation to construct a cyclic integral rate of change of energy (CIRCE) diagram that indicates the amplitude and stability of limit cycles. This diagram is also used to identify the types of bifurcation the system exhibits and to find the minimum amplitude of excitation needed to reach a stable limit cycle from another linearly stable state for single-mode thermoacoustic systems. Furthermore, this diagram shows precisely how the choice of velocity model and the amplitude-dependence of the gain and the phase of the FDF influence the nonlinear dynamics of the system. Time domain simulations of the coupled thermoacoustic system are performed with a Galerkin discretization for acoustic pressure and velocity. Limit cycle calculations using a single mode, along with twenty modes, are compared against predictions from the CIRCE diagram. For the single mode system, the time domain calculations agree well with the frequency domain predictions. The heat release rate is highly nonlinear but, because there is only a single acoustic mode, this does not affect the limit cycle amplitude. For the twenty-mode system, however, the higher harmonics of the heat release rate and acoustic velocity interact, resulting in a larger limit cycle amplitude. Multimode simulations show that, in some situations, the contribution from higher harmonics to the nonlinear dynamics can be significant and must be considered for an accurate and comprehensive analysis of thermoacoustic systems.
机译:热声不稳定性的非线性分析对于预测极限循环的频率,幅度和稳定性至关重要。当来自驱动过程的能量输入和来自阻尼过程的能量损失在整个振荡周期内相互平衡时,就达到了热声系统的极限周期。本文推导了热声系统能量变化率的积分关系。该关系类似于热声学中众所周知的瑞利准则,但是,它可以用于计算极限环的幅度及其稳定性。该关系适用于管道槽稳定的二维预混火焰的热声系统。使用基于G方程的非线性运动学模型对火焰进行建模,而管中平面波的声学则由线性动量和能量方程式控制。使用开环强制模拟,可以计算出火焰描述函数(FDF)。来自FDF的增益和相位信息与积分关系一起使用,以构建一个循环积分能量变化率(CIRCE)图,该图指示极限循环的幅度和稳定性。该图还用于识别系统出现的分叉类型,并找到从单模热声系统的另一线性稳定状态达到稳定极限循环所需的最小激励幅度。此外,该图准确显示了速度模型的选择以及增益和FDF相位的幅度相关性如何影响系统的非线性动力学。耦合热声系统的时域仿真通过Galerkin离散化进行,用于声压和声速。将使用单一模式以及二十种模式的极限循环计算与来自CIRCE图的预测进行比较。对于单模系统,时域计算与频域预测非常吻合。放热率是高度非线性的,但是因为只有一个声学模式,所以不会影响极限循环幅度。但是,对于二十模系统,热量释放速率和声速的高次谐波相互作用,从而导致更大的极限循环幅度。多模仿真表明,在某些情况下,高次谐波对非线性动力学的贡献可能很大,必须对热声系统进行准确而全面的分析时才应考虑。

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