The flamelet/progress variable model for supersonic turbulent reacting flows was developed based on Pierce's model for low Mach number flows

in consideration of the compressibility effects and shock waves.The present model solved the mixture fraction and progress variable transport equations

and employed three solution branches of flamelet equation:the steady burning branch

the unstable branch of partially extinguished states and the complete extinction state.The performance of the flame/progress variable model was compared to the steady flamelet model for predicting the product and temperature field of a hydrogen-air supersonic combustion ramjet engine in DLR (Deutsches Zentrum für Luft- und Raumfahrt) for which experimental data are available.With capturing of extinction and lifted flame

the present model is good agreement with the experimental data

and outperforms the steady flamelet model which predicts an attached flame.