## 1 Introduction
Different models have been proposed to simulate the discharge, which mainly include particle-in-cell (PIC) model [12; 13; 14; 15], Monte Carlo model [16; 17], five-moment fluid model [7; 18], three-equation drift-diffusion fluid model [4; 6; 7; 8; 10], two-equation drift-diffusion fluid model [19; 20; 21; 22; 23; 24; 25], and some other analytical models according to the fidelity of the physical principles. The PIC and Monte Carlo models based on the principle of particle collisions, typically involve the solution of the Boltzmann equation, which is computation expensive, requiring a long computation time. In a normal NS-DBD plasma discharge under working pressure (\(>\)0.5 Torr) [26], the plasma can be assumed as a continuum fluid. It is reasonable to adopt the fluid models, which compromise the fidelity and computational cost. In the plasma flow control application, the speed of the gas heating and the amount of the discharge energy is transferred to the gas heating are the major concerns. The discharge energy is the total energy of the charged species (electron and ions) gained from the electric field, which is calculated by different methods. In the experiment [27], the discharge power and energy are calculated by the load voltage and the current. In the quasi-one-dimensional analytical model [28], the discharge energy is the sum of energy in the plasma and the energy stored in the capacitor, which is formed by the sheath and the dielectric layers. The gas heating is the energy that transfers from the discharge energy to the thermal energy of the gas, which is also considered by different methods. [PERSON] et al. [4] put all the charged species energy to the fluid. [PERSON] et al. [23] and [PERSON] et al. [24] assumed the ions' energy obtained from the electric field fully transfer to the fast gas heating, but a fraction of the electron'senergy contributes to the gas heating. [PERSON] et al. [8] assumed that the electrons contribute to the gas heating through the quenching of the excited neutrals, and the ions' energy is totally transferred into the gas heating instantaneously. [PERSON] et al. [20] and [PERSON] et al. [22] predicted the electron energy release to the gas heating through electronic excitation, vibrational excitation, and the elastic and rotational collisions at different timescales. The ions' energy totally contributes to the gas heating instantaneously. Although the past studies have adopted different chemical reaction models in the NS-DBD investigations, the effects of the chemical reactions on the discharge characteristics, in particular on the discharge energy and gas heating, have not been studied systemically. In addition, there are few numerical studies concerning the vibrational-translational relaxations that are crucial to the slow gas heating. Therefore, the detailed vibrational-translational relaxation reactions are included in the present reaction models. In the present investigation, the objectives are, on the one hand, to figure out the effects of chemical reactions on the discharge characteristics and energy of a plane to plane high-voltage repetitive NS-DBD actuator. On the other hand, foundations are built to simplify chemistry reactions for further researches on the plasma flow control. A three-equation drift-diffusion model is used to reduce the computational cost, the model is adopted in the previous works [29; 30; 31]. Four sets of the \(N_{2}/O_{2}\) mixture reduced kinetic models (31-species 99-reaction, 28-species 85-reaction, 23-species 50-reaction and 15-species 42-reaction) and a simplified \(N_{2}/O_{2}\) mixture averaged 4-species 4-reaction kinetic model are adopted. The electron-impact reaction-rate coefficients and the electron drift and diffusion coefficients are calculated by the Local-mean-energy approximation (LMEA). Because the initial states, i.e., the species number densities and the electric field, are different in each repetitive pulses, the discharge needs at least two periods to reach a statistical periodic state.