Assessment of model assumptions and budget terms of the unsteady flamelet equations for a turbulent reacting jet-in-cross-flow

An a priori analysis of the flamelet model for diffusion flames is conducted to systematically assess model assumptions that are associated with the asymptotic expansion, the omission of higher-order expansion terms, the consideration of preferential diffusion effects, and the one-dimensional flamelet representation. For this, a recent direct numerical simulation database of a reacting hydrogen/air jet-in-cross-flow (JICF) by Grout et al. [15,16] is used. The full flamelet equation for temperature, exact to the order of the Eulerian transport equation and general to different definitions of the mixture fraction, is derived. Analysis of mixture fraction conditioned profiles of temperature and scalar dissipation rate along the jet trajectory identified different ignition and flame stabilization scenarios on the windward and leeward sides of the reacting JICF. A balance analysis of the temperature flamelet equation is conducted to quantify contributions in flame-aligned and flame-orthogonal directions. Consistent with the flamelet assumption, it is shown that terms arising from scalar diffusion, heat-release, and species-diffusion-induced enthalpy flux are the dominant contributions, while the flame-aligned preferential diffusion promotes entrainment of heat into the flamelet structure. For the current JICF-configuration, it is found that contributions along the flame-orthogonal direction are on average negligible.