## 7 Conclusions  
The effects of the chemical reactions on the discharge characteristics and energy of a plane to plane NS-DBD actuator have been studied by adopting a three-equation drift-diffusion model. 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-transport coefficients are obtained by using LMEA. The validity of the numerical model on the prediction of the discharge energy and gas heating also has been proved. The discharge energy in the repetitive NS-DBD reaches a periodic phase equality state after the second pulse following the discharge pulse, which is mainly balanced by the gas heating and energy stored in the heavy species. All the \(N_{2}/O_{2}\) mixture kinetic models over-predict almost the same discharge energy during the pulse. The simplified 4-species 4-reaction kinetic model under-predicts the discharge energy, but it is qualitatively similar to that in the other models. The discharge energy is mainly affected by the electronic excitation and the energy gain by ions from the electric field. The vibrational excitation, negative ions, associative ionization, dissociation of nitrogen and oxygen molecules have weak effects on the prediction of the discharge energy. The gas heating is mainly contributed by the ions and exothermic reactions. The contribution of ions is larger than that of the exothermic reactions. The dissociation of oxygen molecules, the quench of electronically excited oxygen atoms and nitrogen molecules are the dominant exothermic reactions in the low electric field zone (\(E/N\leq 200\) Td), and the dissociation of nitrogen molecules and positive ion conversation reactions are the main exothermic reactions in the high electric field region (\(E/N>400\) Td). The reduction of the negative ions, the vibrational excitation, and associative ionization reactions have very weak effects on the prediction of fast gas heating, but it has considerable effects on the slow gas heating. The gas heating mainly releases during the high voltage pulse and the fast gas heating efficiencies are in the range of 41%\(\sim\)47% predicted by all the reaction models, which is consistent with the results in the past. However, the simple 4-reaction model predicts unreasonable high gas heating efficiencies after the pulse due to the unreasonable exothermic reaction in the model. Based on the contributions of the different types of chemical reactions on discharge physics, specifically on discharge energy and gas heating, the present results can be used to reduce the chemical reactions for NS-DBD when different gas heating stages are specified. They can also be used to simplify chemical reactions in the flow-control applications, when fast gas heating is dominated, compromising the fidelity and the computational cost. Conceptualization, Z.C. ; supervision, Z.C. ; funding acquisition, Z.C. ; project administration, Z.C. ; writing--review and editing, Z.C. ; methodology, S.Z. ; investigation, S.Z. ; writing--original draft, S.Z. ; resources, Z.C., B.Z. and Y.C. This work is partially funded by the National Natural Science Foundation of China under Contract No. 11402211. The authors declare no conflict of interest.