Kinetic modeling of detonation and effects of negative temperature coefficient

The kinetic modeling and simulation of reactive flows, especially for those with detonation, are further investigated. From the theoretical side, a new set of hydrodynamic equations are deduced, where the viscous stress tensor and heat flux are replaced by two non-equilibrium quantities that have been defined in our previous work. The two non-equilibrium quantities are referred to as Non-Organised Momentum Flux (NOMF) and Non-Organised Energy Flux (NOEF), respectively, here. The numerical results of viscous stress (heat flux) have a good agreement with those of NOMF (NOEF) near equilibrium state. Around sharp interfaces, the values of NOMF (NOEF) deviate reasonably from those of viscous stress (heat flux). Based on this hydrodynamic model, the relations between the two non-equilibrium quantities and entropy productions are established. Based on the discrete Boltzmann model, four kinds of detonation phenomena with different reaction rates, including Negative Temperature Coefficient (NTC) regime, are simulated and investigated. The differences of the four kinds of detonations are studied from three aspects: hydrodynamic quantities, non-equilibrium quantities and entropy productions. It is found that, the effects of NTC on hydrodynamic quantities are to lower the von-Neumann peaks of density, pressure, and velocity, to broaden the reaction zone, and to subdue the chemical reaction. It may also vanish the peak of temperature. Consequently, the effects of NTC are to widen the non-equilibrium regions and reduce the amplitude of the non-equilibrium effects in the reaction zone. Besides, it is also found that the (local) entropy production has three sources: the chemical reaction, NOEF and NOMF. As for the global entropy production in the system, the portion caused by reaction is much larger than the other two, and the portion caused by NOMF is larger than that by NOEF. Furthermore, the effect of NTC is to widen the region with entropy production caused by reaction and lower the global entropy productions caused by reaction, NOMF and NOEF, which means that NTC drives detonation closer to an isentropic process.