Flash-back, blow-off, and symmetry breaking of premixed conical flames

Hydrodynamic and thermal-diffusive effects subject premixed flames to intrinsic instabilities that strongly influence their shape and propagation/stabilization characteristics. However, the interaction and coupling of intrinsic flame dynamics with background flow gradients and boundary conditions remain poorly un-derstood. This paper presents a global nonlinear bifurcation analysis of burner-stabilized laminar pre-mixed conical flames with varying reaction rates and reactant diffusivities, respectively parameterized by the Damkohler number Da and the Lewis number Le . Using a dimensionless formulation of the reacting, weakly-compressible Navier-Stokes equations, the dynamics of flash-back, blow-off, and cellular instabil-ity are explored in a fully-coupled framework. Our analysis identifies steady conical flame states over a finite range of Da and Le , limited by saddle-node bifurcations corresponding to spontaneous blow-off of the axisymmetric flame below a Le-dependent lower critical Da value and spontaneous boundary-layer flash-back beyond a higher critical Da value. Furthermore, the analysis reveals that the conical flame loses its axisymmetry via circle-pitchfork bifurcations as Le or Da decrease or increase beyond respective critical values. These bifurcations are shown to correspond to stationary three-dimensional global modes describing steady polyhedral or tilted flame structures, each associated with distinct azimuthal periodic-ities. Statement of Significance: This work presents a bifurcation analysis of laminar premixed conical flames within a fully-coupled flame/flow model. By considering variations in reaction rate and reactant diffusiv-ity, the analysis identifies saddle-node bifurcations corresponding to spontaneous flash-back and blow-off of the axisymmetric flame. It also identifies axisymmetry breaking bifurcations associated with transitions to steady three-dimensional polyhedral and tilted flame states. These global instabilities indicate that hy-drodynamic and thermal-diffusive effects strongly influence a flame's steady structure in the azimuthal dimension even when no instabilities appear in the plane of symmetry. As such, future analyses of flame dynamics should rule out symmetry-breaking behaviors before adopting a two-dimensional computa-tional framework.(c) 2023 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Automated summary

This paper presents a global nonlinear bifurcation analysis of burner-stabilized laminar premixed conical flames, exploring the dynamics and steady structures of the flame. The analysis reveals saddle-node bifurcations corresponding to spontaneous flash-back and blow-off of the axisymmetric flame, as well as axisymmetry breaking bifurcations associated with transitions to steady three-dimensional polyhedral and tilted flame states.