Triggering in the horizontal Rijke tube: non-normality, transient growth and bypass transition
Triggering in the horizontal Rijke tube: non-normality, transient growth and bypass transition
复制标题
DOI：
10.1017/s0022112010004453
复制
发表时间：
2011-01-25
影响因子：
3.7
通讯作者：
Juniper, Matthew P.
中科院分区：
文献类型：
--
作者：
Juniper, Matthew P.
只要有足够大的脉冲，热声系统即使在线性稳定的情况下也能达到自持续振荡，这一过程被称为触发。本文提出了一种求能引起自持续振荡的最低初始能量和相应初始状态的方法。这就是所谓的“最危险”初始状态。该程序基于非线性控制方程的伴随环，并结合优化程序。它是为一个简单的热声系统模型，水平Rijke管开发的，并且可以扩展到更复杂的热声模型。观察到，最危险的初始状态在向稳定周期解发展之前，会短暂地向不稳定周期解发展。触发这些自持续振荡所需的初始能量远低于振荡本身的能量，略低于不稳定周期解的最低能量。结果表明，这种暂态增长是由控制方程的非正态性引起的。这类似于在流体机械系统的旁路过渡到湍流中观察到的事件序列，并且具有相同的根本原因。最危险的初始状态作为放热参数的函数来计算。发现自持续振荡可以在大约一半的线性稳定域内实现。实际热声系统的瞬态增长是这个简单模型的10(5)-10(6)倍。一个实际的结论是，即使在线性稳定状态下，通过本文描述的机制，真正的热声系统可能需要很少的初始能量来触发高振幅的自持续振荡。
With a sufficiently large impulse, a thermoacoustic system can reach self-sustained oscillations even when it is linearly stable, a process known as triggering. In this paper, a procedure is developed to find the lowest initial energy that can trigger self-sustained oscillations, as well as the corresponding initial state. This is known as the 'most dangerous' initial state. The procedure is based on adjoint looping of the nonlinear governing equations, combined with an optimization routine. It is developed for a simple model of a thermoacoustic system, the horizontal Rijke tube, and can be extended to more sophisticated thermoacoustic models. It is observed that the most dangerous initial state grows transiently towards an unstable periodic solution before growing to a stable periodic solution. The initial energy required to trigger these self-sustained oscillations is much lower than the energy of the oscillations themselves and slightly lower than the lowest energy on the unstable periodic solution. It is shown that this transient growth arises due to non-normality of the governing equations. This is analogous to the sequence of events observed in bypass transition to turbulence in fluid mechanical systems and has the same underlying cause. The most dangerous initial state is calculated as a function of the heat-release parameter. It is found that self-sustained oscillations can be reached over approximately half the linearly stable domain. Transient growth in real thermoacoustic systems is 10(5)-10(6) times greater than that in this simple model. One practical conclusion is that, even in the linearly stable regime, it may take very little initial energy for a real thermoacoustic system to trigger to high-amplitude self-sustained oscillations through the mechanism described in this paper.