A numerical method for the chemical reaction and a plasma actuator (PA) for a cannon combustor were developed using the compressible Navier Stokes (CNS) equation. Due to the massive CPU requirement for the PA, we introduced the Reynolds averaged diffusion model to the electron-ion density distribution equations. The computation was stable, and we extracted the interaction line of the sound from the wake of the jet and the sound from the dipole of the PA using the fluctuating density gradient correlation.