Modeling of Lean Hydrogen Flames in Vertical Hele-Shaw Cells: The Boussinesq Limit

Ultra-lean near-limit hydrogen flames evolving in narrow gaps of Hele-Shaw cells may undergo a possibly unexpected propagation mode by breaking the reaction front into isolated flamelets forming fractal-like structures. The combined effect of diffusive-thermal instability and intense heat losses act as two main mechanisms that explain experimental observations. The current study offers an extension of the earlier buoyancy-free reaction–diffusion model over the Boussinesq formulation, accounting for the buoyancy effect present in recent experimental studies of vertical Hele-Shaw burners. It is found that for upward-propagating flames, the bouyancy markedly expands the limits of propagation ability and reduces the limits for downward-propagation.