Ionization of air in flow around a blunt wedge at relatively low hypersonic speeds

Calculations are performed for investigation of air ionization near to surface of blunted wedges with half-angles φ = 3° and 9° and radii of blunting of Rn = 1.5 and 2.0 cm, moving at speeds of 3 ÷ 6 km/s in an air atmosphere with unperturbed gas parameters corresponding to altitudes of 20 ÷ 60 km.


Introduction
The movement of hypersonic aircraft leads not only to a strong heating of their constructive elements, but also to ionization of the gas in the compressed layer near the streamlined surface, which is a very important aspect of the hypersonic flight of an aircraft, since it leads to a radio communication disruption. At superorbital velocities of spacecraft returning to Earth ( 9 V   km/s) the kinetic energy of the colliding particles proves to be sufficient for direct shock ionization of gas particles. At relatively low hypersonic velocities ( 7 V   km/s) the question of the primary cause of the appearance in the gas flow of a significant number of electrons. In a number of computational and theoretical studies [1][2][3][4][5][6] it was established that the most probable cause of primary ionization is the process of associative ionization , which is at least the two-stage process and at this the atoms N and O appear as a result of the dissociation of air components, i.e. molecular nitrogen and molecular oxygen in a mutual collision. In this case, the dissociation of molecules is often not due just to their collision, but is accompanied by the excitation of internal degrees of freedom, in the first placethe vibrations of nuclei in molecules. Therefore, there is a complex multi-stage nature of this process.
Calculations and experiments [7] showed a high probability of realizing this scenario of ionization development at the surface of the body flying at moderate hypersonic speed. The experiments were performed on a shock tube for the velocities of shock waves in the range 4.7 6.7 V  km/s. These experiments showed a very high intensity of the radiation of a heated air plug behind the front of the shock wave in the region of the vacuum ultraviolet spectrum (wavelength ~190 220   nm) was detected, which confirms the appearance of NO molecules in the flow of excited electronic states  Numerical simulation results of the processes of physicochemical kinetics behind the front of the shock wave and the spectral emissivity of the air showed good agreement with the radiation intensity observed in the experiment. The used kinetic model of associative ionization [9], applied in [4,5], showed a high probability of associative ionization. This is the rationale for choosing a model of physicochemical kinetics for the study of ionization processes at relatively low hypersonic velocities. However, it should be borne in mind that the use of this model at two speeds of experimental hypersonic blunted cones ~ 7.4 km/s [4] and 5.6 km/s [4,10], has shown the necessity of modifying the rate constants of associative ionization with decreasing velocity.
Thus, the kinetic model underlying the study of ionization processes at the blunt wedge surface is based on the process of associative ionization, which includes the dissociation of N 2 and O 2 molecules, the formation of NO molecules as a result of chemical reactions (primarily due to collisional association of N and O atoms), the excitation of electronic states of NO* with the subsequent decomposition of NO* into NO + and e -.
This kinetic model is used in this work to analyze the gas ionization in the vicinity of a blunt wedge in a wide range of velocities 36 V  km with the parameters of the incident flow corresponding to altitudes 20 60 H km. Calculations are performed for wedges with half-angles

Results of numerical simulation of ionization processes in flow past a blunt wedge
The scheme of the problem being solved is shown in figure 1. The matrix of the calculated variants is given in table 1, where in addition to the initial data, the braking temperature is presented The author's computer code NERAT2D was used in the calculations. The method of integrating the system of Navier -Stokes equations for the motion of a viscous, heat-conducting, chemically reacting gas is described in detail in [4,10].  cm -3 were detected. Note that the critical electron concentration required to reflect the radio signal can be predicted from formula In the case considered in figure 2, c, the electron concentration in the compressed layer above the surface of the wedge reaches 11 10 e n cm -3 . In this case, the distribution of electron and NO + ion concentrations along the thickness of the compressed layer is shown in figure 4, a, from which it is clearly seen that the thickness of the ionized region reaches almost 10 cm, and the degree of ionization falls insignificantly along the wedge generatrix.
The distributions of the translational and vibrational temperatures N 2 over the height of the compressed layer in these same sections ( figure 4, b) show a good thermalization of the internal degrees of freedom. The distribution of the concentrations of atomic nitrogen (the result of N 2 dissociation) and NO molecules (formed as a result of the chain of chemical transformations) in figure  3, a, as well as the concentrations of O atoms and O 2 molecules in figure 3, b, give an idea of the degree of dissociation of air molecules and the configuration of the field of NO molecules, which serve as the primary source of electrons.  Figure 2. The fields of the translational temperature T(a, above) and the vibrational temperature V T of N 2 (a, from below), the longitudinal velocityVx u V   (b, from above) and the Mach number (b, from below), the electron concentration (c, from above) and NO + ions (c, from below). The temperature is in K, the concentration is in cm -3 ; 20    Figure 5. The fields of the translational temperature T (a, above) and the vibrational temperature V T of N 2 (a, from below), the longitudinal velocityVx u V   (b, from above) and the Mach number (b, from below), the electron concentration (c, from above) and NO + ions (c, from below). The temperature is in K, the concentration is in cm -3 ; 20 H  km, 3 V   km/s.    Figure 8. The fields of the translational temperature T (a, above) and the vibrational temperature V T of N 2 (a, from below), the longitudinal velocityVx u V   (b, from above) and the Mach number (b, from below), the electron concentration (c, from above) and NO + ions (c, from below). The temperature is in K, the concentration is in cm -3 ; 30km H  , 4 V   km/s.   Figure 11. The fields of the translational temperature T (a, above) and the vibrational temperature V T of N 2 (a, from below), the longitudinal velocity Vx u V   (b, from above) and the Mach number (b, from below), the electron concentration (c, from above) and NO + ions (c, from below). The temperature is in K, the concentration is in cm -3 ; 30 H  km,   Figure 14. The fields of the translational temperature T (a, above) and the vibrational temperature V T of N 2 (a, from below), the longitudinal velocity Vx u V   (b, from above) and the Mach number (b, from below), the electron concentration (c, from above) and NO + ions (c, from below). The temperature is in K, the concentration is in cm -3 ; 40 H  km, 5 V   km/s.   Figure 17. The fields of the translational temperature T (a, above) and the vibrational temperature V T of N 2 (a, from below), the longitudinal velocity Vx u V   (b, from above) and the Mach number (b, from below), the electron concentration (c, from above) and NO + ions (c, from below). The temperature is in K, the concentration is in cm -3 ; 40 H  km,    Figure 23. The fields of the translational temperature T (a, above) and the vibrational temperature V T of N 2 (a, from below), the longitudinal velocity Vx u V   (b, from above) and the Mach number (b, from below), the electron concentration (c, from above) and NO + ions (c, from below). The temperature is in K, the concentration is in cm -3 ; 50 H  km,   Figure 26. The fields of the translational temperature T (a, above) and the vibrational temperature V T of N 2 (a, from below), the longitudinal velocity Vx u V   (b, from above) and the Mach number (b, from below), the electron concentration (c, from above) and NO + ions (c, from below). The temperature is in K, the concentration is in cm -3 ; 50 H  km,    The distribution of the maximum electron concentrations along the generatrix of a blunt wedge in a wide range of heights and velocities is shown in figure 41. If the critical level of the electron density is 10 10 e n  cm -3 , then at an altitude 30 H  km and a velocity 3 V   km/s, the ionization level is low. However, as mentioned above, the critical concentration depends not only on the parameters of the ionized air, but also on the frequency of the probing electromagnetic wave.
As the resume, it can be stated that the presented results of a preliminary analysis of aerophysics over a blunted wedge over a wide range of heights and velocities make it possible to determine a program for further studies of the nonequilibrium effects accompanying gas motion at moderate hypersonic speeds.