Low-Order Modelling of Thermoacoustic Limit Cycles
Low-Order Modelling of Thermoacoustic Limit Cycles
复制标题
热声极限环的低阶建模
DOI：
--
复制
发表时间：
2004
期刊：
影响因子：
--
通讯作者：
A. Dowling
中科院分区：
文献类型：
--
作者：
S. Stow;A. Dowling
稀薄预混预汽化 (LPP) 燃烧可以减少燃气轮机的氮氧化物排放，但通常会导致燃烧不稳定。声波会产生热量释放的波动，例如通过扰动燃料空气比。这些热波动反过来会产生更多的声波，并且在某些情况下会形成自持振荡。由此产生的极限环可能具有很大的振幅，导致结构损坏。热声振荡最初将具有低振幅。因此，线性模型可以给出稳定性预测。不稳定的线性模式的幅度将增长，直到非线性效应变得重要并实现极限环。虽然线性模式的频率可以很好地近似所得极限环的频率，但线性理论无法预测其幅度。描述了 LPP 燃烧器中热声极限环的低阶模型。该方法基于以下事实：主要非线性在于对流动扰动的燃烧响应。在 LPP 燃烧中，入口燃油空气比的波动已被证明是不稳定燃烧的主要原因：出现这种情况是因为预混管道中的速度扰动导致燃油空气比随时间变化，然后在下游对流。如果速度扰动变得与平均流量相当，则对进入燃烧器的当量比波动以及因此对热释放速率将存在依赖于振幅的影响。针对这种依赖性开发了一个简单的非线性火焰模型，并假设这是对极限环的主要非线性影响。由于马赫数较低，速度扰动可以与平均流相当，甚至发生反向流，而扰动在声学上仍然是线性的，因为压力扰动仍然远小于平均值。因此，在其他地方，扰动被视为线性的。在这个非线性火焰模型中，描述燃烧对入口流量变化的响应的火焰传递函数是频率和幅度的函数。非线性火焰传递函数被纳入平面波的线性热声网络模型中。将频率、幅度和振型预测与大气试验台的结果进行比较。该方法扩展到薄环形几何形状中的周向波，其中非线性导致模态耦合。版权所有 © 2004 ASME
Lean premixed prevaporised (LPP) combustion can reduce NOx emissions from gas turbines, but often leads to combustion instability. Acoustic waves produce fluctuations in heat release, for instance by perturbing the fuel-air ratio. These heat fluctuations will in turn generate more acoustic waves and in some situations self-sustained oscillations can form. The resulting limit cycles can have large amplitude causing structural damage. Thermoacoustic oscillations will have a low amplitude initially. Thus linear models can give stability predictions. An unstable linear mode will grow in amplitude until nonlinear effects become important and a limit cycle is achieved. While the frequency of the linear mode can provide a good approximation to that of the resulting limit cycle, linear theories give no prediction of its amplitude. A low-order model for thermoacoustic limit cycles in LPP combustors is described. The approach is based on the fact that the main nonlinearity is in the combustion response to flow perturbations. In LPP combustion, fluctuations in the inlet fuel-air ratio have been shown to be the dominant cause of unsteady combustion: these occur because velocity perturbations in the premix ducts cause a time-varying fuel-air ratio, which then convects downstream. If the velocity perturbation becomes comparable to the mean flow, there will be an amplitude-dependent effect on the equivalence ratio fluctuations entering the combustor and hence on the rate of heat release. A simple nonlinear flame model for this dependence is developed and is assumed to be the major non-linear effect on the limit cycle. Since the Mach number is low, the velocity perturbation can be comparable to the mean flow, with even reverse flow occurring, while the disturbances are still acoustically linear in that the pressure perturbation is still much smaller than the mean. Hence elsewhere the perturbations are treated as linear. In this nonlinear flame model, the flame transfer function describing the combustion response to changes in inlet flow is a function of both frequency and amplitude. The nonlinear flame transfer function is incorporated into a linear thermoacoustic network model for plane waves. Frequency, amplitude and modeshape predictions are compared with results from an atmospheric test rig. The approach is extended to circumferential waves in a thin annular geometry, where the nonlinearity leads to modal coupling.Copyright © 2004 by ASME