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Onset of global instability in a premixed annular V-flame

Published online by Cambridge University Press:  28 October 2024

Chuhan Wang Open the ORCID record for Chuhan Wang [Opens in a new window] ,
Christopher M. Douglas Open the ORCID record for Christopher M. Douglas [Opens in a new window] ,
Yu Guan Open the ORCID record for Yu Guan [Opens in a new window] ,
Chunxiao Xu Open the ORCID record for Chunxiao Xu [Opens in a new window]  and
Lutz Lesshafft Open the ORCID record for Lutz Lesshafft [Opens in a new window]
Chuhan Wang*
Affiliation:
AML, Department of Engineering Mechanics, Tsinghua University, 100084 Beijing, PR China LadHyX, CNRS, École Polytechnique, Institut Polytechnique de Paris, 91120 Palaiseau, France
Christopher M. Douglas
Affiliation:
LadHyX, CNRS, École Polytechnique, Institut Polytechnique de Paris, 91120 Palaiseau, France Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC, USA
Yu Guan
Affiliation:
Department of Aeronautical and Aviation Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong
Chunxiao Xu
Affiliation:
AML, Department of Engineering Mechanics, Tsinghua University, 100084 Beijing, PR China
Lutz Lesshafft
Affiliation:
LadHyX, CNRS, École Polytechnique, Institut Polytechnique de Paris, 91120 Palaiseau, France
*
†Email address for correspondence: [email protected]
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Abstract

We investigate self-excited axisymmetric oscillations of a lean premixed methane–air V-flame in a laminar annular jet. The flame is anchored near the rim of the centrebody, forming an inverted cone, while the strongest vorticity is concentrated along the outer shear layer of the annular jet. Consequently, the reaction and vorticity dynamics are largely separated, except where they coalesce near the flame tip. The global eigenmodes corresponding to the linearised reacting flow equations around the steady base state are computed in an axisymmetric setting. We identify an arc branch of eigenmodes exhibiting strong oscillations at the flame tip. The associated eigenvalues are robust with respect to domain truncation and numerical discretisation, and they become destabilised as the Reynolds number increases. The frequency of the leading eigenmode is found to correspond to the Lagrangian disturbance advection time from the nozzle outlet to the flame tip. The essential role of this convective mechanism is also supported by resolvent analysis, which finds that the same flame-tip disturbance structure and frequency are optimally amplified when the flame is subjected to external white noise forcing. Strong non-modal effects in the form of pseudo-resonance are not found. Nonlinear time-resolved simulation further reveals notable hysteresis phenomena in the subcritical regime prior to instability. Hence, even when the flame is linearly stable, perturbations of sufficient amplitude can trigger limit-cycle oscillations and higher-dimensional dynamics sustained by nonlinear feedback. A Monte Carlo simulation of passive tracers in the unsteady flame suggests a nonlinear non-local instability mechanism. Notably, linear analysis of the subcritical time-averaged limit-cycle state yields eigenvalues that do not match the nonlinear periodic oscillation frequencies. This mismatch is attributed to the fundamentally nonlinear dynamics of the subcritical V-flame instability, where the dichromatic, non-local interaction between the heat release rate along the flame surface and the vortex dynamics in the jet shear layer cannot be approximated as a simple distortion of the mean flow.

JFM classification

Instability: Shear-flow instability Reacting Flows: Flames Wakes/Jets: Jets
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 998 , 10 November 2024 , A23
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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