Mathematical modelling of diffusion flames with continuous geometric variation between counterflow and coflow regimes

Abstract

This work presents a model of diffusion flames that continuously change from the counterflow regime to the coflow regime. In addition, the hydrodynamic aspects of this system are examined by means of scale modelling, asymptotic analysis and numerical simulation. The continuous change of the flame is imposed by the flow field, which is the composition of a radial fuel ejection from a cylindrical porous burner in the middle of two opposed impinging flows of oxidiser. The counterflow diffusion flame is located in the axis parallel to the incoming flows and the coflow diffusion flame, in the axis parallel to the outgoing flow. A scaling model shows that the flame length depends linearly on the stoichiometric oxidiser-fuel ratio (S), on the Péclet number based on the fuel ejection (Peb) and inversely proportional to the square root of the Péclet number based on the impinging flows (Pec), i.e., the parameter N:=cSPeb/Pec1/2 is appropriate to measure the flame length (c depends on the flame shape). A potential flow is assumed to allow analytical investigations of the flow field and flame properties. The results unveil the streamlines crossing the flame from the oxidiser side to the fuel side (oxidiser carried to the flame), up to approximately 60% of the flame length, and, from the fuel side to the oxidiser side (oxidiser carried to the flame), from this position to the flame tip. Moreover, the Navier–Stokes flow is also assumed in the analysis and the results show that the potential flow describes well the diffusion flame in the proposed geometric configuration. This result corroborates the consistency of the results and the adequate physical description provided by the potential flow model.