The complete sets of state-to-state transition rate coefficients for both target and projectile molecules of hydrogen are derived from the predicted response surface designed by the ordinary Kriging model. A system of master equations is constructed for bound-bound and bound-free transitions with these designed transition rate coefficients, and the rovibrational number densities are numerically evaluated by implicitly integrating a system of master equations. In these master equation studies, relaxation of rotation and vibration modes, number density relaxation, reaction rate coefficients, and average rotational and vibrational energy losses due to dissociation are each considered in strong nonequilibrium conditions. A system of master equations is coupled with one-dimensional flow equations to analyze the relaxations of hydrogen in post-normal shock and nozzle expanding flows. In post-normal shock flows, at high temperature, the relaxation of the rotational mode is similar to the relaxation of the vibrational mode. In nozzle expanding flows, the relaxations of both rotational and vibrational modes appear to be frozen.
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