In this study, we examine the structure and existence of state relationships in unsteady partially premixed flames (PPFs) subjected to buoyancy-induced and external perturbations. A detailed numerical model is employed to simulate the steady and unsteady two-dimensional PPFs established using a slot burner under normal and zero-gravity conditions. The coflow velocity is parametrically varied. The methane-air chemistry is modeled using a fairly detailed mechanism that contains 81 elementary reactions and 24 species. Validation of the computational model is provided through comparisons of predictions with nonintrusive measurements. The combustion proceeds in two reaction zones, one a rich premixed zone and the other a nonpremixed zone. These reaction zones are spatially separated, but involve strong interactions between them due to thermochemistry and scalar transport. The fuel is mostly consumed in the premixed zone to produce CO and H2, which are transported to and consumed in the nonpremixed zone. The nonpremixed zone in turn provides heat and H-atoms to the premixed zone. For the range of conditions investigated, the zero-g partially premixed flames exhibit a stable behavior and a remarkably strong resistance to perturbations. In contrast, the corresponding normal-gravity flames exhibit oscillatory behavior at low coflow velocities but a stable behavior at high coflow velocities, and the behavior can be explained in terms of a global and convective instabilities. The effects of coflow and gravity on the flames are characterized through a parameter VR, defined as the ratio of coflow velocity to jet velocity. For VR ≤ 1 (low coflow velocity regime), the structures of both 0- and 1-g flames are strongly sensitive to changes in VR, while they are only mildly affected by coflow in the high coflow velocity regime (VR > 1). In addition, the spatio-temporal characteristics of the 0- and 1-g flames are markedly different in the first regime, but are essentially similar in the second regime. A more significant difference in the first regime between these flames is the presence of a flow instability that manifests itself through the self-excited oscillations of the 1-g flame and the concomitant flickering of the nonpremixed reaction zone. For VR ≤ 1, as the coflow velocity is increased, the oscillation amplitude decreases and the oscillation frequency increases, both of which are in accord with previous experimental and computational results concerning 1-g jet diffusion flames. The modified conserved scalar approach is found to be effective in characterizing the flame structure and developing state relationships for both steady and unsteady partially premixed flames. This is demonstrated by the fact that the temperature as well as the major and minor species profiles follow similar state relationships in terms of the modified mixture fraction for the 0- and 1-g flames, even though these flames have markedly different spatio-temporal characteristics.
A priori investigation of subgrid correlation of mixture fraction and progress variable in partially premixed flames
