  Large Eddy Simulation with a Perfectly Stirred Reactor model (LES-PSR) is
developed to simulate supersonic combustion with high-enthalpy flow conditions.
The PSR model considers the viscous heating and compressibility effects on the
thermo-chemical state, through correcting the chemical source term for progress
variable and incorporating absolute enthalpy as the control variable for the
look-up table. It is firstly validated by using a priori analysis of the
viscous heating and compressibility effects. Then an auto-igniting hydrogen
flame stabilized in supersonic vitiated co-flowing jet is simulated with
LES-PSR method. The results show that the shock wave structure, overall flame
characteristics, flame-shock interaction and lift-off height are accurately
captured. Good agreements of the velocity and mixture fraction statistics with
the experimental data are observed. The results also show that the LES-PSR
model can predict the mean temperature and mole fractions of major species
quite well in both flame induction and stabilization zones. However, there are
some under-predictions of temperature RMS by about 100-150 K, which may be due
to the chemical non-equilibrium in the H2/O2-enriched combustion product of the
co-flowing jet. The scatter plots of two probe locations respectively from
induction and flame zones show that the respective flame structures in mixture
fraction space are captured well. However, the flucturations of the temperature
and species mole fractions are under-predicted in the flame zone. The
shock-induced auto-igniting spots are captured by the PSR model. These spots
are highly unsteady and play an important role in flame stabilization. It is
also shown that the intense reactions are initiated at mixture fractions around
the stoichiometry or fuel-lean values, corresponding to local elevated pressure
(1.5-2.0 atm) due to shock compression.
