Prediction of shock standoff distance with modified rotational relaxation time of air mixture

Abstract

The rotational relaxation time of an air mixture is modified as an approach to improve accuracy when predicting hypersonic shock standoff distance. A novel atomistic quasi-classical trajectory (QCT) method with a modified approach is devised to drastically reduce computational cost, and rigorously model the rotational relaxation time of N2 in N2–N and N2–N2 collisions. The calculated full sets of rotational state-to-state transition rates obtained by the QCT method are fed into the rotational state-resolved master equations to determine the rotational relaxation time of N2. Clear discrepancies are observed when the present rotational relaxation time is compared with existing empirical data for N2. The existing empirical model is utilized to determine the rotational relaxation time of other atmospheric gas species. Then the present set of rotational relaxation times for the air mixture is employed to predict the hypersonic shock standoff distance over a blunt body of the ground and flight experiments. Compared with the results from the two-temperature model, the rotational nonequilibrium enlarges the hypersonic shock standoff distance. This increase in shock standoff distance by the rotational nonequilibrium is attributed to the delay in chemical reactions inside the shock layers. The accuracy of the predicted measured shock standoff distance is improved by considering the present rotational relaxation time of the air mixture.