A test of conditioned balance equation approach

Abstract

To model the effect of a premixed flame on turbulent scalar transport, new balance equations for mass and velocities conditioned either on unburned or burned mixture were recently derived by the author. The goal of this work is to test the equations by simulating various measurements of countergradient scalar transport in premixed turbulent flames stabilized in impinging jets. To do so, standard balance equations for (i) mass, (ii) the Favre-averaged combustion progress variable, and (iii) the Favre-averaged axial velocity and new balance equations for (iv) the difference between axial velocities conditioned on unburned and burned mixture and for radial velocities conditioned on (v) unburned and (vi) burned mixture were numerically solved. To place the focus of testing on the conditioned equations, some model parameters were adjusted in order for the computed axial profiles of the mean combustion progress variable and the mean axial velocity to agree well with experimental data. In contrast, the model parameters directly relevant to the conditioned equations (iv)–(vi) were neither varied nor tuned. The computed axial profiles of the axial conditioned velocities and axial scalar flux agree well with experimental data, thus indicating that the conditioned balance equation approach is a promising tool. The numerical results also show that: (i) in the front zone of the flames studied here, countergradient scalar transport is mainly caused by the pressure drop across flamelets, while (ii) the mean pressure gradient plays a more important role in the middle of the flame brush, and (iii) the magnitude of countergradient scalar flux is limited by chemical reactions in flamelets.