A fitting formula for radiative cooling based on non-local thermodynamic equilibrium population from weakly-ionized air plasma

Abstract

Abstract.A fitting formula for radiative cooling with collisional-radiative population for air plasma flowfield has been developed. Population number densities are calculated from rate equations in order to evaluate the effects of nonequilibrium atomic and molecular processes. Many elementary processes are integrated to be applied to optically-thin plasmas in the number density range of 10 12 /cm 3 ≤ N ≤ 10 19 /cm 3 and the temperature range of 300 K ≤ T ≤ 40,000 K. Our results of the total radiative emissivity calculated from the collisional-radiative population are fitted in terms of temperature and total number density. To validate the analytic fitting formula, numerical simulation of a laser-induced blast wave propagation with the nonequilibrium radiative cooling is conducted and successfully reproduces the shock and plasma wave front time history observed by experiments. In addition, from the comparison between numerical simulations with the radiation cooling effect based on the fitting formula and those with a gray gas radiation model that assumes local thermodynamic equilibrium, we find that the displacement of the plasma front is slightly different due to the deviation of population probabilities. By using the fitting formula, we can easily and more accurately evaluate the radiative cooling effect without solving detailed collisional-radiative rate equations. IntroductionIn most aerospace applications of air plasma flow (hypersonic flow around a reentry body [1-4], laser-driven blast wave [5][6][7][8], and plasma processing techniques using electric discharges), plasma internal states do not achieve local thermodynamic equilibrium (LTE). It is necessary to consider nonequilibrium properties of population distribution into each plasma internal state. The nonequilibrium properties directly affect radiative emissivities and opacities, partition functions of internal energy modes, and thermal relaxations. These effects of nonequilibrium processes are still a problem that remains to be solved in those applications.For instance, we take a gas-driven laser-propulsion system whose thrust power is obtained through interaction with a propellant gas heated by external laser beam irradiation. After a focused laser breaks down the propellant gas, a blast wave is formed by the laser-produced plasma and propagates to the projectile through the surrounding gas. The performance of a gas-driven laser propulsion system depends heavily on the blast-wave dynamics and the plasma states sustaining it. Our previous work [8] numerically simulated a laser-driven blast wave