  A zero-dimensional (volume-averaged) and a pseudo-one-dimensional (plug-flow) model are developed to investigate atmospheric-pressure plasma jet devices operated with He, He/O$_2$, He/N$_2$ and He/N$_2$/O$_2$ mixtures. The models are coupled with the Boltzmann equation under the two-term approximation to self-consistently calculate the electron energy distribution function (EEDF). The simulation results are verified against spatially resolved model calculations and validated against a wide variety of measurement data. The nitric oxide (NO) concentration is thoroughly characterized for a variation of the gas mixture ratio, helium flow rate and absorbed power. The concentration measurements at low power are better captured by the simulation with a larger hypothetical "effective" rate coefficient value for the reactive quenching N$_2$(A$^3\Sigma$,B$^3\Pi$) + O($^3$P) $\to$ NO + N($^2$D). This suggests that the NO production at low power is also covered by the species N$_2$(A$^3\Sigma$,B$^3\Pi$;v>0) and multiple higher N$_2$ electronically excited states instead of only N$_2$(A$^3{\Sigma}$,B$^3{\Pi}$;v=0) in this quenching. Furthermore, the O($^3$P) density measurements under the same operation conditions are also better predicted by the simulations with a consideration of the aforementioned hypothetical rate coefficient value. It is found that the contribution of the vibrationally excited nitrogen molecules N$_2$(v$\geqslant$13) to the net NO formation rate gains more significance at higher power. The vibrational distribution functions (VDFs) of O$_2$(v<41) and N$_2$(v<58) are investigated. The sensitivity of the zero-dimensional model with respect to a variation of the VDF resolutions, wall reaction probabilities and synthetic air impurity levels is presented. The simulated plasma properties are sensitive to the variation especially for a feeding gas mixture containing nitrogen. 
Zero-dimensional and pseudo-one-dimensional models of   atmospheric-pressure plasma jet in binary and ternary mixtures of oxygen and   nitrogen with helium background