Features of numerical simulation of the equilibrium shock adiabat using the equation of state for a real gas
The article presents physico-mathematical models of equilibrium one-dimensional detonation with account for the real gas state equation. An original computational algorithm is presented for plotting an equilibrium detonation adiabat employing a simplified real gas state virial equation. Specifics of the numerical simulation algorithm implementation employing the real gas state virial equation are analyzed. Single-fluid approximation, according to which the extra additive, associated with the existence of the intermolecular interaction, appears in the equations of the real gas thermo-dynamic functions for transition from the pure gas state equation to the combustion products as a model of mixture was employed. The results of comparing the problem solution on the equilibrium parameters computing of the stoichiometric methane-air mixture combustion products at the constant specific volume and internal energy with the known literature data are presented for the developed algorithms verification. The difference was less than 1%. The perfect gases model application at high initial pressure may lead to the pressure dissimilarity from the real gas model by more than 30%. A study of equilibrium adiabat characteristics detonation products of a stoichiometric mixture of methane and air for initial pressures up to 50 atm was conducted. In this case, the perfect gas model application leads to the pressure decrease behind the detonation front up to 13%. The Chapman-Jouguet detonation velocity at the increased initial pressures may exceed the one calculated by the ideal model by more than 10%. The need to account for the properties of a real gas for detonating mixtures in the high-pressures region was confirmed based on the analysis of the numerical modeling results.