REDUCED-ORDER MODELING AND DYNAMICS OF NONLINEAR ACOUSTIC WAVES IN A COMBUSTION CHAMBER
REDUCED-ORDER MODELING AND DYNAMICS OF NONLINEAR ACOUSTIC WAVES IN A COMBUSTION CHAMBER
复制标题
燃烧室内非线性声波的降阶建模和动力学
DOI：
10.1080/00102200590900219
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发表时间：
2005
影响因子：
1.9
通讯作者：
F. Culick
中科院分区：
文献类型：
--
作者：
N. Ananthkrishnan;S. Deo;F. Culick
摘要为了理解燃烧室非定常运动的基本性质，以及主动反馈控制的应用，降阶模型占有独特的重要地位。存在一个将一组无限维偏微分方程表示一般行为转化为一组有限的非线性二阶常微分方程的框架。该过程依赖于在模态函数或基函数中展开压力场和速度场，然后进行空间平均以得到时间上的一组二阶方程。非线性气体动力学得到了明确的解释，但所有其他贡献过程都需要建模。通过将模态展开截断到所需的项数，可以简单地获得腔室动力学全局行为（最重要的是压力）的降阶模型。程序的核心是确定必须保留多少模态才能给出准确结果的标准。解决这个问题是本文的主要目的。我们的分析表明，在纵向模态的情况下，第一模态失稳问题在模态截断中至少需要四个模态，而对于第二模态失稳问题，至少需要保留前八个模态。第二个重要的问题涉及线性稳定系统在足够大的扰动下变得不稳定的条件。先前的工作给出了部分答案，表明非线性气体动力学本身不能产生脉冲或“触发”的真正非线性不稳定性，这一建议现在在理论上得到了证实。此外，已知燃烧过程的某种形式的非线性能量添加会导致线性稳定系统中的稳定极限环。第二种形式的非线性燃烧动力学与一个新的速度耦合函数，自然地显示一个阈值特征，这里也显示了产生触发的极限环行为。
ABSTRACT For understanding the fundamental properties of unsteady motions in combustion chambers, and for applications of active feedback control, reduced-order models occupy a uniquely important position. A framework exists for transforming the representation of general behavior by a set of infinite-dimensional partial differential equations to a finite set of nonlinear second-order ordinary differential equations in time. The procedure rests on an expansion of the pressure and velocity fields in modal or basis functions, followed by spatial averaging to give the set of second-order equations in time. Nonlinear gasdynamics is accounted for explicitly, but all other contributing processes require modeling. Reduced-order models of the global behavior of the chamber dynamics, most importantly of the pressure, are obtained simply by truncating the modal expansion to the desired number of terms. Central to the procedures is a criterion for deciding how many modes must be retained to give accurate results. Addressing that problem is the principal purpose of this paper. Our analysis shows that, in the case of longitudinal modes, a first-mode instability problem requires a minimum of four modes in the modal truncation, whereas, for a second-mode instability, one needs to retain at least the first eight modes. A second important problem concerns the conditions under which a linearly stable system becomes unstable to sufficiently large disturbances. Previous work has given a partial answer, suggesting that nonlinear gasdynamics alone cannot produce pulsed or “triggered” true nonlinear instabilities, that suggestion is now theoretically established. Also, a certain form of the nonlinear energy addition by combustion processes is known to lead to stable limit cycles in a linearly stable system. A second form of nonlinear combustion dynamics with a new velocity coupling function that naturally displays a threshold character is shown here also to produce triggered limit-cycle behavior.