A Nonlinear Frequency Domain Model for Limit Cycles in Thermoacoustic Systems with Modal Coupling
A Nonlinear Frequency Domain Model for Limit Cycles in Thermoacoustic Systems with Modal Coupling
复制标题
模态耦合热声系统极限环的非线性频域模型
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
W. Polifke
中科院分区：
文献类型：
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作者：
F. Selimefendigil;W. Polifke
为了预测线性不稳定热声系统的极限环振荡，开发了具有显式模态耦合的频域低阶系统。为此，从非定常计算流体动力学结合前馈神经网络辨识获得了非线性热源动力学模型。从神经网络中，导出了 Volterra 级数形式的输入输出关系的等效表示，其中 Volterra 核是根据神经网络的权重计算的。然后将核变换到频域以获得高阶传递函数，通过该函数耦合模态。通过这种方式，可以明确地描述模式之间的非线性能量交换。与伽辽金时域仿真的比较表明，可以正确捕获极限环中纯正弦行为的偏差，同时大大降低了计算成本。
For prediction of limit cycle oscillations of linearly unstable thermo-acoustic systems, a frequency-domain, low-order system with explicit modal coupling is developed. To this purpose, a model for the nonlinear heat source dynamics is obtained from unsteady computational fluid dynamics in combination with feed-forward neural network identification. From the neural network, an equivalent representation for the input-output relation in Volterra series form is derived, where Volterra kernels are computed in terms of the weights of the neural network. Then the kernels are transformed into the frequency domain to obtain the higher order transfer functions, through which the modes are coupled. In this way nonlinear energy exchange among the modes can be described explicitly. Comparison with a Galerkin time domain simulation shows that deviations from purely sinusoidal behaviour in the limit cycle are captured correctly, while the computational cost is drastically reduced.