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.

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Computational and theoretical studies of a Mach 5 flow over a hemisphere were carried out to validate a new computer code for magnetogasdynamic simulation, and to examine the possibility of heat transfer mitigation through magnetic control. Sample calculations were made using a local solution developed by W. B. Bush [J. Aerosp. Sci. 25, 685 (1958); 28, 610 (1961)] for the stagnation point flow over an axisymmetric blunt body with an imposed dipole magnetic field. Numerical computations, which obviated many of the simplifications inherent in the Bush theory, were carried out employing the low magnetic Reynolds number approximation. Both models indicate that an imposed dipole field can slow the flow in the conductive shock layer and consequently reduce the wall heat flux in the vicinity of the stagnation point. The theoretical model predicts a slightly higher level of heat transfer than that obtained computationally, but there is good agreement between the two models in the fractional change in heat transfer with increasing strength of the applied magnetic field. For both models, nonuniform electrical conductivity was found to reduce the effectiveness of a given applied field. Magnetic flow control is seen to have a sound physical basis, and may prove to be a useful technology for heat transfer mitigation.

The present work develops a computationally efficient one-dimensional subgrid embedded finite element formulation for plasma-sheath dynamics. The model incorporates space-charge effect throughout the whole plasma and the sheath region using multifluid equations. Secondary electron emission is not considered. A third-order temperature dependent polynomial is used to self-consistently calculate the rate of ionization in the plasma dynamic equations. The applications include dc and rf sheath inside a glow discharge tube where the noble gas is immobile, and a partially ionized plasma sheath inside an electric propulsion thruster channel in which the gas flows. The electron and ion number densities of the numerical solution decrease in the sheath region as expected. The ion velocity and electron temperature profiles also exhibit the expected behavior. The computed sheath potential compares well with the available experimental data.