In this paper, we develop a linear technique that predicts how the stability of a thermoacoustic system changes due to the action of a generic passive feedback device or a generic change in the base state. From this, one can calculate the passive device or base state change that most stabilizes the system. This theoretical framework, based on adjoint equations, is applied to two types of Rijke tube. The first contains an electrically heated hot wire, and the second contains a diffusion flame. Both heat sources are assumed to be compact, so that the acoustic and heat release models can be decoupled. We find that the most effective passive control device is an adiabatic mesh placed at the downstream end of the Rijke tube. We also investigate the effects of a second hot wire and a local variation of the cross-sectional area but find that both affect the frequency more than the growth rate. This application of adjoint sensitivity analysis opens up new possibilities for the passive control of thermoacoustic oscillations. For example, the influence of base state changes can be combined with other constraints, such as that the total heat release rate remains constant, in order to show how an unstable thermoacoustic system should be changed in order to make it stable.
A Theoretical Approach for Passive Control of Thermoacoustic Oscillations: Application to Ducted Flames
Contributed by the Controls, Diagnostics and Instrumentation Committee of ASME for publication in the Journal of Engineering for Gas Turbines and Power. Manuscript received June 27, 2013; final manuscript received July 8, 2013; published online August 21, 2013. Editor: David Wisler.
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Magri, L., and Juniper, M. P. (August 21, 2013). "A Theoretical Approach for Passive Control of Thermoacoustic Oscillations: Application to Ducted Flames." ASME. J. Eng. Gas Turbines Power. September 2013; 135(9): 091604. https://doi.org/10.1115/1.4024957
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