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Numerical simulation of nanosecond-pulse electrical discharges

Recent experiments with a nanosecond-pulse, dielectric barrier discharge at the stagnation point of a Mach 5 cylinder flow have demonstrated the formation of weak shock waves near the electrode edge, which propagate upstream and perturb the bow shock. This is a promising means of flow control, and understanding the detailed physics of the conversion of electrical energy into gas motion will aid in the design of efficient actuators based on the concept. In this work, a simplified configuration with planar symmetry was chosen as a vehicle to develop a physics-based model of nanosecond-pulse discharges, including realistic air kinetics, electron energy transport, and compressible bulk gas flow. A reduced plasma kinetic model (23 species and 50 processes) was developed to capture the dominant species and reactions for energy storage and thermalization in the discharge. The kinetic model included electronically and vibrationally excited species, and several species of ions and ground state neutrals. The governing equations included the Poisson equation for the electric potential, diffusion equations for each neutral species, conservation equations for each charged species, and mass-averaged conservation equations for the bulk gas flow. The results of calculations with this model highlighted the path of energy transfer in the discharge. At breakdown, the input electrical energy was transformed over a time scale on the order of 1 ns into chemical energy of ions, dissociation products, and vibrationally and electronically excited particles. About 30% of this energy was subsequently thermalized over a time scale of 10 µs. Since the thermalization time scale was faster than the acoustic time scale, the heat release led to the formation of weak shock waves originating near the sheath edge, consistent with experimental observations. The computed translational temperature rise (40 K) and nitrogen vibrational temperature rise (370 K) were of the same order of magnitude as experimental measurements (50 K and 500 K, respectively), and the approach appears promising for future multi-dimensional calculations. The effectiveness of flow control actuators based on nanosecond-pulse, dielectric barrier discharges is seen to depend crucially on the rapid thermalization of input energy, in particular the rate of quenching of excited electronic states and the rate of electron–ion recombination.