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Propagation speed of inertial waves in cylindrical swirling flows

Published online by Cambridge University Press:  19 September 2019

Alp Albayrak Open the ORCID record for Alp Albayrak [Opens in a new window] ,
Matthew P. Juniper Open the ORCID record for Matthew P. Juniper [Opens in a new window]  and
Wolfgang Polifke Open the ORCID record for Wolfgang Polifke [Opens in a new window]
Alp Albayrak
Affiliation:
Faculty of Mechanical Engineering, Technical University of Munich, D-85748 Garching, Germany
Matthew P. Juniper
Affiliation:
Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, UK
Wolfgang Polifke*
Affiliation:
Faculty of Mechanical Engineering, Technical University of Munich, D-85748 Garching, Germany
*
†Email address for correspondence: polifke@tum.de
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Abstract

Thermo-acoustic combustion instabilities arise from feedback between flow perturbations and the unsteady heat release rate of a flame in a combustion chamber. In the case of a premixed, swirl stabilized flame, an unsteady heat release rate results from acoustic velocity perturbations at the burner inlet on the one hand, and from azimuthal velocity perturbations, which are generated by acoustic waves propagating across the swirler, on the other. The respective time lags associated with these flow–flame interaction mechanisms determine the overall flame response to acoustic perturbations and therefore thermo-acoustic stability. The propagation of azimuthal velocity perturbations in a cylindrical duct is commonly assumed to be convective, which implies that the corresponding time lag is governed by the speed of convection. We scrutinize this assumption in the framework of small perturbation analysis and modal decomposition of the Euler equations by considering an initial value problem. The analysis reveals that azimuthal velocity perturbations in swirling flows should be regarded as dispersive inertial waves. As a result of the restoring Coriolis force, wave propagation speeds lie above and below the mean flow bulk velocity. The differences between wave propagation speed and convection speed increase with increasing swirl. A linear, time invariant step response solution for the dynamics of inertial waves is developed, which can be approximated by a concise analytical expression. This study enhances the understanding of the flame dynamics of swirl burners in particular, and contributes physical insight into the inertial wave dynamics in general.

JFM classification

Geophysical and Geological Flows: Waves in rotating fluids
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 879 , 25 November 2019 , pp. 85 - 120
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Copyright
© 2019 Cambridge University Press 

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