CUED Publications database

Bypass transition to sustained thermoacoustic oscillations in a linearly stable rijke tube

Juniper, MP and Waugh, IC (2010) Bypass transition to sustained thermoacoustic oscillations in a linearly stable rijke tube. 16th AIAA/CEAS Aeroacoustics Conference (31st AIAA Aeroacoustics Conference).

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In this paper we examine triggering in a simple linearly-stable thermoacoustic system using techniques from flow instability and optimal control. Firstly, for a noiseless system, we find the initial states that have highest energy growth over given times and from given energies. Secondly, by varying the initial energy, we find the lowest energy that just triggers to a stable periodic solution. We show that the corresponding initial state grows first towards an unstable periodic solution and, from there, to the stable periodic solution. This exploits linear transient growth, which arises due to nonnormality in the governing equations and is directly analogous to bypass transition to turbulence. Thirdly, we introduce noise that has similar spectral characteristics to this initial state. We show that, when triggering from low noise levels, the system grows to high amplitude self-sustained oscillations by first growing towards the unstable periodic solution of the noiseless system. This helps to explain the experimental observation that linearly-stable systems can trigger to self-sustained oscillations even with low background noise. © 2010 by University of Cambridge. Published by the American Institute of Aeronautics and Astronautics, Inc.

Item Type: Article
Divisions: Div A > Energy
Depositing User: Cron Job
Date Deposited: 17 Jul 2017 19:46
Last Modified: 18 Feb 2021 16:17
DOI: 10.2514/6.2010-3856