Real gas effect on steady planar detonation and uncertainty quantification

Abstract

The steady planar detonation in hydrogen/air mixture was simulated at elevated pressure. The real gas effect was incorporated by considering the Peng-Robinson equation of state (EoS), nonideal thermodynamic functions and reaction kinetic laws. The nonideal EoS and corresponding thermodynamic functions increase the Chapman-Jouguet (CJ) velocity but decrease the post-shock temperature compared to the ideal gas model, which induces a change of the induction time and distance. The effect of the nonideal reaction rate law depends on the amplitude of compressibility factor and fugacity coefficient and tends to shorten both the induction time and induction distance. These effects counterbalance each other in the complete real gas model which lead to induction time and distance close to the ideal model results. The total heat release was also found to be reduced for the complete model, but the key reactions and their relative importance remain the same as when using the ideal gas model. The nonideal portion of heat release is minor compared with its ideal portion as temperature increases and pressure drops in the reaction zone. The uncertainty of the real gas model, originating from the uncertainty of the parameters in the EoS, was quantified using a Monte Carlo sampling approach. The uncertainty increases linearly with initial pressure and is mainly determined by the species with higher uncertainty factor, larger mole fraction weighted molecular attraction and covolume parameters. Compared to the uncertainty caused by the chemical reaction model, real gas model uncertainty is negligible at low pressure, but becomes of the same order of magnitude at elevated pressure.