Mathematical modelling of premixed laminar methane-air flames

Abstract

Two mathematical models have been developed to simulate two-dimensional, premixed, laminar, stationary, axisymmetric methane-air flames, and successfully validated with non-intrusive Coherent Anti-Stokes Raman Spectroscopy (CARS) temperature measurements. With the first model, the heat releaser ate model, volumetric heat release rate was generalised from one-dimensional computations. This approximation greatly simplified the set of governing equations that need to be solved. However, it cannot describe the effects of high stretch rates or of negative stretch rate. The second model made use of a number of reduced chemical kinetic schemes, with realistic elementary reactions. These were drawn from the literature and realistic transport properties have been included. With this model, based on the work of Peters (1985), the effects of stretch are automatically accounted for. Practical experimental validation was obtained with a multiple slot burner, supplied by the collaborating body, British Gas p1c. Temperature fields, obtained with the CARS technique, partially validated the reduced chemical kinetic scheme model. Some uncertainty arose in the prediction of heat loss to the burner tube. A numerical algorithm based upon the SUVIPLE method was employed,with a fully staggered grid. Various discretisation schemes were examined with the heat release model. Based on these tests, the hybrid scheme was selected for use in the reduced model. With this approach, a few reduced kinetic schemes have been selected and implemented. The most successfuol ne was the Peters( 1985) scheme. This consisted of 4 global reaction steps with 18 elementary reactions and 7 non-steady chemical species. The scheme has been employed in all the detailed computations in the present study. With this scheme, two-dimensional field solutions, for methane-air mixtures with equivalence ratios of 0.75,0.84 and 1.0, with slot widths of 2 mm, and 3 mm, and mean inlet velocities ranging from 0.3 m/s to 2.8 m/s have been obtained. Detailed flame structures have been obtained for all these conditions. Under these conditions, a number of parameters, essential in burner design and stability analysis, have been investigated. These includes flame height, flame thickness, and heat loss to the burner tube. The loss can range between 3% and 32% of the chemical energy in the premixture. The computations reveal the stretch rates acting on the flame and their effects on the burning velocity. At low flow rates the base of the flame has a negative stretch rate, while the flame tip is positively stretched. These effects are reversed at high flow rates. From the localised relationships between stretch rate and burning velocity, Markstein lengths have been evaluated,for different mixtures and the values compared with those obtained experimentally by other researchers. In general, there was good agreement despite the large scatter in the experimental values. The results further showed that the effects of the two components of flame stretch, namely flame curvature and aerodynamic straining, on burning velocities were very different. It seems appropriate to introduce two Markstein lengths to correlate burning velocity and the two components of stretch and these have been evaluated. Aerodynamic straining has a significantly larger effect on burning velocity than has flame curvature