Numerical analyses of deflagration initiation by a hot jet

Abstract

Numerical simulations of axisymmetric reactive jets with one-step Arrhenius kinetics\n\t\t\t\t are used to investigate the problem of deflagration initiation in a premixed fuel–air\n\t\t\t\t mixture by the sudden discharge of a hot jet of its adiabatic reaction products. For the\n\t\t\t\t moderately large values of the jet Reynolds number considered in the computations,\n\t\t\t\t chemical reaction is seen to occur initially in the thin mixing layer that separates the hot\n\t\t\t\t products from the cold reactants. This mixing layer is wrapped around by the starting\n\t\t\t\t vortex, thereby enhancingmixing at the jet head, which is followed by an annular mixing\n\t\t\t\t layer that trails behind, connecting the leading vortex with the orifice rim. A successful\n\t\t\t\t deflagration is seen to develop for values of the orifice radius larger than a critical\n\t\t\t\t value aϲ in the order of the flame thickness of the planar deflagration δL. Introduction\n\t\t\t\t of appropriate scales provides the dimensionless formulation of the problem, with\n\t\t\t\t flame initiation characterised in terms of a critical Damk¨ohler number ∆ϲ = (aϲ/δL)²,\n\t\t\t\t whose parametric dependence is investigated. The numerical computations reveal that,\n\t\t\t\t while the jet Reynolds number exerts a limited influence on the criticality conditions,\n\t\t\t\t the effect of the reactant diffusivity on ignition is much more pronounced, with the\n\t\t\t\t value of ∆ϲ increasing significantly with increasing Lewis numbers Le. The reactant\n\t\t\t\t diffusivity affects also the way ignition takes place, so that for reactants with Le ≳ 1 the\n\t\t\t\t flame develops as a result of ignition in the annular mixing layer surrounding the developing\n\t\t\t\t jet stem, whereas for highly diffusive reactants with Lewis numbers sufficiently\n\t\t\t\t smaller than unity combustion is initiated in the mixed core formed around the starting\n\t\t\t\t vortex. The analysis provides increased understanding of deflagration initiation processes,\n\t\t\t\t including the effects of differential diffusion, and points to the need for further\n\t\t\t\t investigations incorporating detailed chemistry models for specific fuel–air mixtures.