Theoretical and numerical study of the binary scaling law for electron distribution in thermochemical non-equilibrium flows under extremely high Mach number

Abstract

The binary scaling law is a classical similarity law used in analysing hypersonic flow fields. The objective of this study is to investigate the applicability of the binary scaling law in thermochemical non-equilibrium airflow. Dimensional analysis of vibrational and electron–electronic energy conservation equations was employed to explore the theoretical reasons for the failure of the binary scaling law. Numerical simulation based on a multi-temperature model (translational–rotational temperature T, electron–electronic excitation temperature ${T_e}$ and the vibrational temperatures of ${\textrm{O}_2}$ and ${\textrm{N}_2}$ , $\; {T_{{v_{{\textrm{O}_2}}}}}$ and ${T_{{v_{{\textrm{N}_2}}}}}$ ) with two chemical models (the Gupta model and the Park model) was adopted to study the accuracy of the binary scaling law for electron distribution at high altitude with extremely high Mach number. The results of theoretical analysis indicate that the three-body collision reactions and the translation–electron energy exchange from collisions between electrons and ions, ${Q_{t - e\_ions}}$ , can cause the failure of the binary scaling law. The results of numerical simulation show that the electron-impact ionization reactions are the main reasons for the invalidation of the binary scaling law for electron distribution at high altitude with high Mach number. With an increase of free-stream Mach number, the negative effect on the binary scaling law caused by ${Q_{t - e\_ions}}$ cannot be ignored.