CUED Publications database

Weakly nonlinear analysis of thermoacoustic bifurcations in the Rijke tube

Orchini, A and Rigas, G and Juniper, MP (2016) Weakly nonlinear analysis of thermoacoustic bifurcations in the Rijke tube. Journal of Fluid Mechanics, 805. pp. 523-550.

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In this study we present a theoretical weakly nonlinear framework for the prediction of thermoacoustic oscillations close to Hopf bifurcations. We demonstrate the method for a thermoacoustic network that describes the dynamics of an electrically heated Rijke tube. We solve the weakly nonlinear equations order by order, discuss their contribution on the overall dynamics and show how solvability conditions at odd orders give rise to Stuart-Landau equations. These equations, combined together, describe the nonlinear dynamical evolution of the oscillations' amplitude and their frequency. Because we retain the contribution of several acoustic modes in the thermoacoustic system, the use of adjoint methods is required to derive the Landau coefficients. The analysis is performed up to fifth order and compared with time domain simulations, showing good agreement. The theoretical framework presented here can be used to reduce the cost of investigating oscillations and subcritical phenomena close to Hopf bifurcations in numerical simulations and experiments and can be readily extended to consider, e.g. the weakly nonlinear interaction of two unstable thermoacoustic modes.

Item Type: Article
Uncontrolled Keywords: bifurcation low-dimensional models nonlinear instability
Divisions: Div A > Energy
Div A > Turbomachinery
Depositing User: Cron Job
Date Deposited: 17 Jul 2017 19:29
Last Modified: 21 Jun 2018 02:34