Nonlinear Phenomena in Thermoacoustic Systems With Premixed Flames
Nonlinear Phenomena in Thermoacoustic Systems With Premixed Flames
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DOI：
10.1115/1.4023305
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发表时间：
2013-06-01
影响因子：
1.5
通讯作者：
Juniper, Matthew P.
中科院分区：
文献类型：
--
作者：
Kashinath, Karthik;Hemchandra, Santosh;Juniper, Matthew P.
热声不稳定性的非线性分析对于极限环的频率、振幅和稳定性的预测是必不可少的。当驱动过程的能量输入和阻尼过程的能量损失在振荡周期内相互平衡时，热声系统达到极限循环。本文导出了热声系统能量变化率的积分关系式。这种关系类似于热声学中众所周知的瑞利准则，然而，它可以用来计算极限环的振幅及其稳定性。将该关系式应用于导管槽稳定二维预混火焰热声系统。火焰模型采用基于g方程的非线性运动学模型，而平面波在管内的声学特性由线性化的动量和能量方程控制。利用开环强迫模拟，计算了火焰描述函数（FDF）。从FDF中获得的增益和相位信息与积分关系一起用于构造循环积分能量变化率（CIRCE）图，该图表示极限环的幅度和稳定性。该图还用于识别系统所显示的分岔类型，并找到从单模热声系统的另一个线性稳定状态达到稳定极限环所需的最小激励幅度。此外，该图精确地显示了速度模型的选择以及增益和FDF相位的幅值依赖性如何影响系统的非线性动力学。采用伽辽金离散法对声压和声速进行了时域模拟。使用单一模态的极限环计算，以及20个模态，与CIRCE图的预测进行比较。对于单模系统，时域计算结果与频域预测结果吻合较好。热释放率是高度非线性的，但是，因为只有一个单一的声学模式，这并不影响极限环振幅。然而，对于二十模系统，放热率和声速的高次谐波相互作用，导致更大的极限环幅值。多模态模拟表明，在某些情况下，高次谐波对非线性动力学的贡献可能是显著的，必须考虑到对热声系统进行准确和全面的分析。
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.