The main focus of the review is on dynamics and kinetics of near-surface discharge plasmas, such as surface dielectric barrier discharges sustained by AC and repetitively pulsed waveforms, pulsed DC discharges, and quasi-DC discharges, generated in quiescent air and in the airflow. A number of technical issues related to plasma flow control applications are discussed in detail, including discharge development via surface ionization waves, charge transport and accumulation on dielectric surface, discharge contraction, different types of flow perturbations generated by surface discharges, and effect of high-speed flow on discharge dynamics. In the first part of the manuscript, plasma morphology and results of electrical and optical emission spectroscopy measurements are discussed. Particular attention is paid to dynamics of surface charge accumulation and dissipation, both in diffuse discharges and during development of ionization instabilities resulting in discharge contraction. Contraction leads to significant increase of both the surface area of charge accumulation and the energy coupled to the plasma. The use of alternating polarity pulse waveforms accelerates contraction of surface dielectric barrier discharges and formation of filamentary plasmas. The second part discusses the interaction of discharge plasmas with quiescent air and the external airflow. Four major types of flow perturbations have been identified: (1) low-speed near-surface jets generated by electrohydrodynamic interaction (ion wind); (2) spanwise and streamwise vortices formed by both electrohydrodynamic and thermal effects; (3) weak shock waves produced by rapid heating in pulsed discharges on sub-microsecond time scale; and (4) nearsurface localized stochastic perturbations, on sub-millisecond time, detected only recently. The mechanism of plasma-flow interaction remains not fully understood, especially in filamentary surface dielectric barrier discharges. Localized quasi-DC surface discharges sustained in a high-speed flow are discussed in the third part of the review. Although dynamics of this type of the discharge is highly transient, due to its strong interaction with the flow, the resultant flow structure is stationary, including the oblique shock and the flow separation region downstream of the discharge. The oblique shock is attached to a time-averaged, wedge-shaped, near-wall plasma layer, with the shock angle controlled by the discharge power, which makes possible changing the flow structure and parameters in a controlled way. Finally, unresolved and openended issues are discussed in the summary.

A physical and numerical model for surface dielectric barrier discharge evolution in atmospheric air was developed and tested against experimental data for discharge parameters. Both discharge formation and relaxation phases were simulated successfully using a new approach of non-local air ionization by electron impact and ab initio boundary conditions on the electrode and dielectric surface. The main features of the physical and numerical model of the discharge simulation have been discussed. It was shown that discharge relaxation phase contributes primarily to momentum and heat sources relevant for flow control. The momentum source spatial distribution has a complex structure with the regions of upstream and downstream body force direction and qualitatively depends on applied voltage polarity and voltage pulse waveform. For different conditions it could lead to either near-surface flow acceleration or vortex generation.

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Surface dielectric barrier discharge, initiated by a high-voltage pulse of negative polarity in atmospheric pressure air, is studied numerically and experimentally. At a pulse duration of a few tens of nanoseconds, two waves of optical emission propagate from the high-voltage electrode corresponding to the leading and trailing edges of the high-voltage pulse. It is shown by means of numerical modeling that a glow-like discharge slides along the surface of the dielectric at the leading edge of the pulse, slowing down on the plateau of the pulse. When the trailing edge of the pulse arrives to the high-voltage electrode, a second discharge starts and propagates in the same direction. The difference is that the discharge corresponding to the trailing edge is not diffuse and demonstrates a well-pronounced streamer-like shape. The 2D (in numerical modeling) streamer propagates above the dielectric surface, leaving a gap of about 0.05 mm between the streamer and the surface. The calculated and experimentally measured emission picture, waveform of the electrical current, and deposited energy, qualitatively coincide. The sensitivity of the numerical solution to unknown physical parameters of the model is discussed.

This paper analyses numerical efforts regarding nanosecond (NS) surface dielectric barrier discharge (SDBD) modelling in atmospheric air. Numerical results of the discharge structure for positive and negative applied voltage pulse polarity, and the features of the physical models and boundary conditions used, are discussed. The results of 2D simulations of the quasi-uniform SDBD mode are presented and compared with the results of other research teams, and with experimental data, to reveal the most appropriate approaches. New results of numerical simulations and analytical estimations of the energy into gas deposition due to NS SDBD driven by a single NS voltage pulse are presented. The problems relating to NS SDBD modelling are discussed.