Calculation of the structure and extinction limit of a methane-air counterflow diffusion flame in the forward stagnation region of a porous cylinder

The paper addresses itself to the numerical representation of the structure of counterflow methane-air diffusion flames, with the use of complex chemistry and detailed formulation of the transport fluxes. A similarity solution is briefly outlined which allows the problem to be treated as one-dimensional in space. Following this, discretization and solution of the resulting algebraic equations has been achieved by five different methods. Although there are some differences between the results of the separate computations, these results agree within the probable experimental error with the observations of Tsuji and Yamaoka as regards the temperature and species mole fraction profiles in a particular flame. The more detailed chemical models are able to predict the profiles of C 2 hydrocarbons with reasonable precision; but even somewhat less detailed models are able satisfactorily to predict the major structural features. Despite this agreement, the system overall does not behave as a straightforward boundary layer flow, and in order fully to match the solution to the experimental results it was necessary to modify the measured velocity gradient of 100 s −1 for the cold flow to near 130 s −1 in the flame region. The discrepancy is probably caused by modification of the pressure field due to apparatus effects or to the flame itself, and a full solution requires a two-dimensional treatment to include this effect. As the velocity gradient which characterises these flames is increased, the increased strain in the flame reaction zone (or flame stretch) may lead to extinction. The effect of increasing strain on the flame structure and position near the porous cylinder is examined. There are differences between the two available predictions of the quenching velocity gradient, but both predictions are consistent with the measured, nominal gradient. It is shown that thermal quenching effects at the cylinder do not contribute appreciably to the observed limits. The significance of the extinction limits in the context of non-premixed turbulent combustion is briefly discussed.