Laminar mixing in diluted and undiluted fuel jets upstream from lifted flames

Abstract

The boundary-layer approximation is used to describe the frozen mixing process taking place when a fuel jet of radius a discharges into stagnant air. The results are applicable to the calculation of lifted flames stabilized in round laminar jets with relatively large Reynolds numbers, Re, for which the proposed formulation provides a detailed description for the velocity and composition fields encountered by the propagating triple flame formed at the base of the lifted flame. The problem is integrated for relevant values of the flow parameters, including values of the stoichiometric air-to-fuel mass ratio S of order unity, when the lifted flame is located in the region of jet development, corresponding to distances from the injector of order Re a. Further attention is given to the relevant case S ≫ 1, corresponding to typical conditions of undilute hydrocarbon-air flames, for which the resulting lifted flames are stabilized at relatively large distances from the injector, of order S Re a. It is seen that Schlichting asymptotic solution, which corresponds to a point source of momentum, is then applicable to describe the mixing process upstream from the lifted flame. Improved accuracy is sought by introducing expansions for the velocity components and for the reactant mass fractions in powers of S-1. The resulting development shows in particular that the first-order correction to the leading-order solution is equivalent to the introduction of a virtual origin for the axial coordinate. It is shown that the magnitude of the required translation, which is equal for the velocity and composition fields, must be determined from continuity considerations. As an illustrative example, the resulting description is used to calculate flame fronts with S ≫ 1 in the thermal-diffusive approximation.