Moderate or intense low-oxygen dilution (MILD) combustion is a novel combustion technique that can simultaneously improve thermal efficiency and reduce emissions. This paper focuses on the differences in statistical behaviours of the surface density function (SDF = magnitude of the reaction progress variable gradient) between conventional premixed flames and exhaust gas recirculation (EGR) type homogeneous-mixture combustion under MILD conditions using direct numerical simulations (DNS) data. The mean values of the SDF in the MILD combustion cases were found to be significantly smaller than those in the corresponding premixed flame cases. Moreover, the mean behaviour of the SDF in response to the variations of turbulence intensity were compared between MILD and premixed flame cases, and the differences are explained in terms of the strain rates induced by fluid motion and the ones arising from flame displacement speed. It was found that the effects of dilatation rate were much weaker in the MILD combustion cases than in the premixed flame cases, and the reactive scalar gradient in MILD combustion cases preferentially aligns with the most compressive principal strain-rate eigendirection. By contrast, the reactive scalar gradient preferentially aligned with the most extensive principal strain-rate eigendirection within the flame in the premixed flame cases considered here, but the extent of this alignment weakened with increasing turbulence intensity. This gave rise to a predominantly positive mean value of normal strain rate in the premixed flames, whereas the mean normal strain rate remained negative, and its magnitude increased with increasing turbulence intensity in the MILD combustion cases. The mean value of the reaction component of displacement speed assumed non-negligible values in the MILD combustion cases for a broader range of reaction progress variable, compared with the conventional premixed flames. Moreover, the mean displacement speed increased from the unburned gas side to the burned gas side in the conventional premixed flames, whereas the mean displacement speed in MILD combustion cases decreased from the unburned gas side to the middle of the flame before increasing mildly towards the burned gas side. These differences in the mean displacement speed gave rise to significant differences in the mean behaviour of the normal strain rate induced by the flame propagation and effective strain rate, which explains the differences in the SDF evolution and its response to the variation of turbulence intensity between the conventional premixed flames and MILD combustion cases. The tangential fluid-dynamic strain rate assumed positive mean values, but it was overcome by negative mean values of curvature stretch rate to yield negative mean values of stretch rate for both the premixed flames and MILD combustion cases. This behaviour is explained in terms of the curvature dependence of displacement speed. These findings suggest that the curvature dependence of displacement speed and the scalar gradient alignment with local principal strain rate eigendirections need to be addressed for modelling EGR-type homogeneous-mixture MILD combustion.
Effect of equivalence ratio on premixed flame response to unsteady strain-rate and curvature