Pedergnana T, Noiray N
Department of Mechanical and Process Engineering, CAPS Laboratory, ETH Zürich, Sonneggstrasse 3, Zürich 8092, Switzerland.
Proc Math Phys Eng Sci. 2022 Mar;478(2259):20210851. doi: 10.1098/rspa.2021.0851. Epub 2022 Mar 9.
Thermoacoustic instabilities in can-annular combus-tors of stationary gas turbines lead to unstable Bloch modes which appear as rotating acoustic pressure waves along the turbine annulus. The multiscale, multiphysical nature of the full problem makes a detailed analysis challenging. In this work, we derive a low-order, coupled oscillators model of an idealized can-annular combustor. The unimodal projection of the Helmholtz equation for the can acoustics is combined with the Rayleigh conductivity, which describes the aeroacoustic coupling between neighbouring cans. Using a Bloch-wave ansatz, the resulting system is reduced to a single equation for the frequency spectrum. A linear stability analysis is then performed to study the perturbation of the spectrum by the can-to-can interaction. It is observed that the acoustic coupling can suppress or amplify thermoacoustic instabilities, raising the potential for instabilities in nominally stable systems.
固定式燃气轮机的罐环形燃烧室中的热声不稳定性会导致不稳定的布洛赫模式，这些模式表现为沿涡轮机环形空间传播的旋转声压波。整个问题的多尺度、多物理性质使得详细分析具有挑战性。在这项工作中，我们推导了一个理想化罐环形燃烧室的低阶耦合振荡器模型。罐声学的亥姆霍兹方程的单模投影与描述相邻罐之间气动声学耦合的瑞利传导率相结合。使用布洛赫波假设，将所得系统简化为频谱的单个方程。然后进行线性稳定性分析，以研究罐间相互作用对频谱的扰动。可以观察到，声耦合可以抑制或放大热声不稳定性，增加了名义上稳定系统中出现不稳定性的可能性。
