  This work presents a numerical study of a diffusion flame in a reacting,
two-dimensional, turbulent, viscous, multi-component, compressible mixing layer
subject to a large favorable streamwise pressure gradient. The boundary-layer
equations, coupled with the SST turbulence model, are solved using a sub-grid,
turbulence-aware flamelet model. The flamelet model employs a 13-species,
32-elementary reaction, methane-air reaction mechanism and a flamelet progress
variable (FPV) approach. The model is applied to both pure air and vitiated
air, the latter being particularly relevant in turbine-burner scenarios.
Boundary-layer results, when compared to Navier-Stokes solutions, consistently
under-predict mixing layer Navier-Stokes growth in upstream locations due to
reduced accuracy locally. Thus, mixing layer and flame locations are shifted
towards the fuel-side. A comparison is made with results obtained using a
simplified one-step reaction mechanism to provide insights in flow and flame
structure differences resulting from the detailed reaction mechanism. The FPV
solutions with the more detailed reaction mechanism show faster chemistry
compared to the one-step reaction approach and report shorter ignition delays.
Furthermore, the FPV solutions show considerable carbon monoxide production in
the reaction zone and significantly reduced peak temperatures. Ignition delay
causes oxygen to be entrained from the air-side to the fuel-side. Effects of
vitiated air on the flow and combustion process are observed with a weak flame
characterized by lower peak temperature and impeded development.
