Asymptotic Analysis of the Ignition of Hydrogen by a Hot Plate in a Boundary Layer Flow

Abstract

In this paper we have analyzed the steady-state process leading to ignition of a combustible mixture of hydrogen, oxygen and nitrogen by a hot flat plate in a boundary layer flow. For plate temperatures larger than the crossover temperature dictated by the competition between the chain branching reaction H + 0₂ → OH + O and the chain breaking reaction H + 0₂ + M → H0₂ + M, the ignition event corresponds to a typical chain branching explosion with negligible heat release, in a first approximation. The boundary layer equations are solved using the fact that the activation energy of the chain branching reaction H + 0₂ → OH + O is relatively large, employing the reduced kinetic mechanism appropriate for this regime. The equations reduce to a single integro-differential equation for the concentration of atomic hydrogen. The ignition condition can be assumed to be reached when one of the shuffle reactions reaches partial equilibrium. On the other hand, for low plate temperatures, the ignition event is characterized by a thermal runaway. The governing equations reduce to a single one-parameter integro-differential equation, to be solved numerically.