Transient growth of flow disturbances in triggering a Rijke tube combustion instability
Author
Zhao, Dan
Date of Issue
2012School
School of Mechanical and Aerospace Engineering
Abstract
Combustion instabilities in a Rijke tube could be triggered by the transient growth of flow disturbances,
which is associated with its non-normality. In this work, a Rijke tube with three different temperature
configurations resulting from a laminar premixed flame are considered to investigate its non-normality
and the resulting transient growth of flow disturbances in triggering combustion instabilities. For this, a
general thermoacoustic model of a Rijke tube is developed. Unsteady heat release from the flame is
assumed to be caused by its surface variations, which results from the fluctuations of the oncoming flow
velocity. Coupling the flame model with a Galerkin series expansion of the acoustic waves present
enables the time evolution of flow disturbances to be calculated, thus providing a platform on which
to gain insights on the Rijke tube stability behaviors. Both eigenmodes orthogonality analysis and transient
growth analysis of flow disturbances are performed by linearizing the flame model and recasting it
into the classical time-lag N-τ formulation. It is shown from both analyses that Rijke tube is a non-normal
thermoacoustic system and its non-normality depends strongly on the temperature configurations
and the flame position. Furthermore, the most ‘dangerous’ position at which the flame is more susceptible
to combustion instabilities are predicted by real-time calculating the maximum transient growth rate
of acoustical energy.
Type
Journal Article
Series/Journal Title
Combustion and flame
Collections
http://dx.doi.org/10.1016/j.combustflame.2012.02.002
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