Onset of global instability in a premixed annular V-flame

TL;DR

This study analyzes the linear and nonlinear dynamics of a premixed V-flame, identifying conditions for global instability and oscillations through eigenmode analysis and simulations, revealing complex nonlinear feedback mechanisms.

Contribution

It provides the first detailed linear eigenmode analysis of a premixed V-flame in an annular jet and explores nonlinear subcritical oscillations and hysteresis phenomena.

Findings

Eigenmodes exhibit strong oscillations at the flame tip.

Instability increases with Reynolds number.

Nonlinear simulations show hysteresis and subcritical limit cycles.

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. 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, attributed to the fundamentally nonlinear dynamics of the subcritical V-flame instability, where the dichromatic, non-local interaction cannot be approximated as a simple distortion of the mean flow.