  In the stratified or partially premixed piloted jet flames, previous
experimental and priori studies have identified a strong correlation between
mixture fraction and progress variable. In the framework of large-eddy
simulation (LES) and flamelet-generated manifolds (FGM) approach, a joint
probability density function (PDF) method is constructed to characterize
subgrid correlations. To pave the way for high dimensional tabulation modeling,
a deep residual network (ResNet) is trained, dramatically reducing the memory
footprint of tabulation. The Message Passing Interface (MPI) shared memory
technique is applied to load the original chemical table during parallel
computations. Application of LES to a partially pre-vaporized ethanol spray
flame demonstrates good agreement with experimental results. Consideration of
the subgrid correlation results in a noticeable improvement in temperature
prediction. Calculations using ResNet show a notable consistency with those
using chemical tables. Visualization of enthalpy highlights the significance of
non-adiabatic tabulation in modeling liquid fuel combustion. The unscaled
progress variable is selected to better describe the chemical reaction rate in
the blending zone of an air stream and a pilot stream with the product of a
fully burnt lean fuel mixture. The impact of the source term due to evaporation
in the transport equation of the progress variable is validated. The
correlation coefficient is found to significantly influence the chemical
reaction rate. The subgrid-scale interaction between liquid fuel evaporation
and subgrid correlation is elucidated.
