ASYMPTOTIC HIGH-SPEED OVERSHOOT EFFECT VALUE IN A SHOCK-COMPRESSED GAS MIXTURE

Abstract

Aim. We have found asymptotically exact values for the distribution function of pairs of molecules in a shock-compressed, binary mixture of gases with a strong difference in the concentrations and molecular weights of its components. Methodology. The research relies on the mathematical methods of theoretical physics related to the calculation of the threshold frequency of collisions based on the kinetic Boltzmann equation. Results. Asymptotically exact analytical expressions are found for the distribution functions of pairs of molecules by the absolute values of their relative velocities. The maxima of these functions are also determined in pairs: light–light, light–heavy and heavy–heavy components. These maxima correspond to the greatest intensities of the effects of high-speed overshoot in the components of the shock-compressed gas mixture. Research implication. The effect of high-speed overshoot in the components of a shock-compressed gas mixture is realized by experimentally modeling it in shock pipes (for example, in the processes of pyrolysis of carbon and carbon-hydrogen compounds). The results obtained in this work are essential for the optimal performance of such experiments.