Premixed flames in stagnating turbulence part II. The mean velocities and pressure and the Damköhler number

We extend to premixed flames an earlier asymptotic analysis of constant density stagnating turbulence by introducing a specified distribution of mean density, e.g., one obtained from experimental data for the mean progress variable. The small parameter providing the basis for the analysis is again the relative intensity of the turbulence exiting from the jet. The first moment equations are shown to predict the mean velocity components and the mean pressure. Comparison is made with four experiments involving turbulent reactants impinging on a wall and with one involving reactants in opposed streams. A range of rates of strain is covered in these experiments so that we treat flames either adjacent to a wall or to a stagnation plane as well as freestanding flames, i.e., those removed from the wall or stagnation plane. Quantitative agreement is found in three cases and only qualitative agreement in the other two. Conjectural explanations of the absence of quantitative agreement in these latter cases are provided. The first movement equation for the mean progress variable is shown to yield a distribution of a turbulent Damköhler number. Having validated the theory by comparisons with experiment, we then calculate systematically the characteristics of a range of flames: those adjacent to walls and stagnation planes and those which are freestanding. Features of the two classes of flames are found to differ significantly; for example, freestanding flames involve a pressure drop, whereas the pressure is either constant or increasing through flames adjacent to walls or stagnation planes. The Damköhler number is nearly constant in the latter flames, but significantly increases through freestanding flames. The implications of these findings are discussed.