We show that the spatio-temporal electrohydrodynamic (EHD) force production in surface alternative current-dielectric barrier discharge (AC-DBD) actuators is strongly influenced by both the streamer regime during the positive phase and the micro-discharge regime during the negative phase. Focusing on the spatial EHD force profiles, we demonstrate that the ionic wind spatial distribution can only be explained by the positive contribution of the streamer regime. The location of maximum ionic wind is found to be directly linked with the maximum elongation of the streamers at several millimeters from the exposed electrode. In both positive and negative phases of the AC-DBD operation, residual volumetric and surface charges once again linked to the streamer formation and afterburn, result to a variety of positive EHD force zones which, when time-averaged in one AC period, contribute to the generation of the experimentally observed induced thin wall jet. Through a thorough elaboration of our numerical results, we provide an illustrative explanation of the EHD force spatio-temporal evolution, showcase the importance of streamers and retrieve a correct representation of the ionic wind spatial profiles when compared to experiments.

We report on a detailed numerical study of the two-phase operation of a surface alternating current dielectric barrier discharge actuator. We showcase that when the quasi-periodic regime has been established, residual volume and surface charges play an important role on the discharge evolution strongly coupling the positive and negative phases. It is shown that the quasi-neutral streamer discharge found on the positive phase serves as both a positive and negative charge generator and acts as a virtual anode. As the streamer is not attached to the dielectric surface, most of the surface charging occurs during its after-burn (relaxation) phase. The positive surface charge leads to an distant zone of high electric field and thus ion drift but also interacts majorly with the negative discharge phase. During the latter, microdischarges form near the active electrode and an intense cathode layer feeds with charges the discharge volume. Each microdischarge is followed by a plasma layer formation attached to the dielectric layer expanding further at each repetition until it occupies a volume linked to the streamer elongation length and positively charged surface portion. The strong coupling between the positive and negative phases along with the strong impact of the streamer discharge on both suggest implications that have been ignored so far in terms of electrohydrodynamic force production and its spatiotemporal distribution.

N umerical simulation of active flow control using plasma actuators is dependent upon the development of models accounting for the effects of the actuators on the flow. These can be obtained either by using experimental results coupled with strong assumptions regarding the plasma force distribution, or through numerical simulation. The objective of this paper is to investigate the characteristics of DBD plasma source terms obtained using direct numerical simulation. Using ONERA's in-house plasma solver COPAIER, we propose an insight of a complete chain of numerical models, ranging from the plasma discharge description to the computation of a DBD-induced ionic wind.

Summary form only given. Microwave discharges can be used for efficient remote energy deposition. They can be created at the intersection of microwave beams, in the focus of microwave radiation or next to a metallic initiator (see Ref.[1] and references therein). Some possible applications of these discharges include flow control and combustion control. If the microwave electric field is overcritical in a localized region at atmospheric pressure, a microwave filament or streamer forms around seed electrons and elongates in a direction parallel to the electric field. Depending on the conditions, a pattern of parallel filaments can form and move in the direction of the source 2 . Complex structures of interconnected filaments can also develop under subcritical conditions in the presence of a metallic initiator 1 . Recent simulation works have been able to reproduce the formation and dynamics of microwave filament patterns 3 and of single microwave streamers over short periods of time 4 .Since the energy absorbed per unit volume in a microwave streamer can be considerable, gas heating arises, leading to the formation of a shock wave which can significantly affect the development and dynamics of microwave streamers. In this paper we present a fully self-consistent model combining Maxwell equations coupled with a simple description of the plasma and with inviscid Navier Stokes equations to study the energy deposition, gas heating and shockwave formation in a single microwave discharge generated at the intersection of two microwave beams at atmospheric pressure. We show that the gas temperature in the streamer can reach 5000 K in about 300 ns at the intersection of two beams of 2.5 MV/m field amplitude. Gas heating and the subsequent shockwave formation and gas density redistribution can lead to a complex dynamics of the streamer and to a limitation of its length to values on the order of λ/2 where O is the wavelength, as observed in some experiments1.

In the past years, the plasma synthetic jet actuator has been proven as promising for aeronautical applications of aerodynamic flow control. In this paper, the plasma synthetic jet actuator's operation is numerically modeled. Results of this simplified coupled numerical approach are presented, along with parametric studies that have been performed concerning geometrical and operational criteria, providing insights of its performance. The results of its pulsed mode have been coupled in a computational fluid dynamics solver via source terms, and basic simulations over a flat plate illustrate the main expected effect of the actuator for aerodynamic flow control: the vortices' generation.

Recent experiments have demonstrated that a freely localized 100 GHz microwave discharge can propagate towards the microwave source with high speed, forming a complex pattern of self-organized filaments. We present three-dimensional simulations of the formation and propagation of such patterns that reveal more information on their nature and interaction with the electromagnetic waves. The developed three-dimensional Maxwell-plasma solver permits the study of different forms of incident field polarization. Results for linear and circular polarization of the wave are presented and comparisons with recent experiments show a good overall agreement. The three dimensional simulations provide a quantitative analysis of the parameters controlling the time and length scales of the strongly non-linear plasma dynamics and could be useful for potential microwave plasma applications such as aerodynamic flow and combustion control. (C) 2014 AIP Publishing LLC.

A crucial aspect for supersonic flights is the strong shock wave that forms in front of the air vehicle. By modifying the supersonic incoming flow, one can adjust this wave -which is the most contributing factor of the drag coefficient of an aircraft- and have consequently positive effects on the fuel consumption and on the noise produced by the object due to the sonic boom. Lately, plasma associated flow control actuators have been in the center of flow control research and especially of supersonic applications.

This paper deals with the numerical modelling of corona discharges induced by electrohydrodynamic actuators. A specific numerical method is proposed and discussed to compute the multiscale nature observed in the modelling of corona discharges. The idea consists in a domain decomposition of the computational domain where each subdomain is described with a specific modelling well adapted to the phenomenon expected. Numerical results and comparisons on a wire-to-wire corona are shown and illustrate the ability of the multiscale method.

A mechanical spike is a device used to mechanically act on the bow shock ahead of an airplane in supersonic flight. This action results in improved flight conditions. We will investigate here the eects of the axial generation of a two-hundred-micrometer width cylindrical plasma ahead a quasi-realistic nose profile of centimeter width. The device is named plasma spike by analogy to the above-cited mechanical device. This plasma spike is a source of both momentum and energy for the neighboring fluid.

In this paper, we present a hybrid method to solve the 2D Maxwell-Vlasov system. The idea is to use a domain computational decomposition method with buffer zone’s presence [1]-[2]. The solution of the Maxwell equations on the global domain is obtained by the sum of the solutions on each subdomain. These equations are solved on the global domain by introducing an artificial connecting function. Contrary to these equations, the Vlasov equation is solved on the global domain to take into account the solution of the Maxwell equations on each subdomain. Some numerical examples have been added to validate the method.

The PROTO-SPHERA experiment (under construction in Frascati inside the START vacuum vessel) aims to study the properties of a spherical torus (ST), where a hydrogen force-free screw pinch (SP, with open field lines and fed by electrodes) replaces the central rod of the standard spherical tokamak experiments: PROTO-SPHERA, with a central screw pinch current Ie = 60 kA, aims at producing a spherical torus (with closed field lines) of diameter 2Rsph = 70 cm, and aspect ratio R/a = A = 1.2–1.3, carrying a toroidal current Ip = 120–240 kA. Such a configuration is an evolution of the flux core spheromak (FCS) concept, first proposed by Taylor. The formation mechanism of the configuration will be the one successfully developed by the TS-3 team at the University of Tokyo. The spherical torus toroidal current should be sustained by helicity injection from the screw pinch, therefore some level of resistive instability with toroidal mode numbers n = 1 and/or n = 2 is requested after the formation and during the sustainment phase; nevertheless, the configuration should be operated such as to maintain it stable from an ideal MHD point of view. The ideal MHD stability limits of PROTO-SPHERA have been analysed by a numerical code able to handle magnetic configurations endowed with both closed and open magnetic field lines. The results of such an analysis are presented in terms of the main parameter, which is the ratio between the currents in the spherical torus and in the central screw pinch, Ip/Ie, and of other relevant parameters of the ST (elongation, aspect ratio, total beta and the toroidal plasma current profile). A comparison with the TS-3 results is also shown.

The purpose of this paper is to propose a new model based on an asymptotic analysis for the modelling of steady wire-to-wire corona discharges. The concept consists in dividing the discharges into regions of two kinds: two thin ionization layers at the vicinity of the electrodes and a much larger ion-drift region. Introducing the length of the ionization layer ε and using an asymptotic analysis to define a truncated system, a simplified kinetic can be considered for each region which allows finding quasi-analytical solutions. The method is validated by comparison with a classical scheme and the results show good agreement with experiments. Finally, an example of parametric study of the discharge is presented. Indeed, the ability of the model to provide solutions at low computational cost allows quickly performing such a study and could be useful to experimenters in order to suggest new geometric settings or experimental setups.

In this paper, we present a discontinuous Galerkin (DG) method to solve the Maxwell equations in time domain. This method allows us to treat efficiently in terms of CPU-time and memory storage electromagnetic compatibility (EMC) problems, by a using high order spatial approximation and a local time-stepping strategy on unstructured meshes. To improve its capacity to solve EMC problems, some physical models have been added to the method. In particular, a composite material model is presented in this paper.

The purpose of this paper is to propose a simple model for plasma generation and effect on fluids at atmospheric pressure. Experiments are conducted using a wire-to-wire corona discharge actuator in a subsonic boundary layer flow. Velocity gains of several metres per second are observed. A quasi-2D numerical model of the discharge is proposed and explains the creation of two corona discharges around the electrodes. A one-way approach of the plasma aerodynamics coupling gives access to the ionic wind. It is confirmed that the actuator accelerates the flow from the anode to the cathode. Order of magnitudes of the ionic wind and flow velocity profiles are close to experiments. A first attempt to perform a 2D simulation of the wire-to-wire discharge is presented as the starting point of future works.

A discontinuous Galerkin (DG) method and some physical models added to this method to treat electromagnetic compatibility problems are presented. This method is very efficient in terms of CPU-time and memory usage because of the use of a high-order spatial approximation on general unstructured meshes. Some comparisons with other schemes are presented to validate the proposed models and to point out the advantages of the DG method. In particular, some improvements of the method like the use of a local time-stepping strategy have been studied.

Surface dielectric barrier discharges (DBDs) have been proposed as actuators for flow control. A two-dimensional fluid model of the DBD is used to describe the plasma dynamics and to quantitatively estimate the electrohydrodynamic (EHD) force. This problem is computationally expensive due to the various time scales at stake. A numerical investigation is made to compare semi-implicit Poisson/transport coupling with Scharfetter and Gummel scheme with a asynchronous MUSCL scheme in pure Nitrogen. Besides, the semi-implicit scheme has been used to estimate the EHD force distribution in air with simplified plasma chemistry. The induced airflow is then evaluated thanks to steady state coupling with a computational fluid dynamic code.

In the calculation of the ideal magnetohydrodynamic free-boundary stability of magnetoplasma equilibria, the integration of the perturbed magnetic energy in the vacuum region that can exist between the plasma edge and nearby conducting shells is extended to axisymmetric configurations composed in part by closed and in part by open field lines. Examples of such equilibria are flux-core-spheromaks and spherical tori with a plasma central column, where a magnetic separatrix divides a spherical torus—with closed field lines—from a central screw pinch discharge—with open field lines that end on the sustaining electrodes. These configurations pose two problems: their plasma-vacuum interface is composed of multiple flux surfaces (i.e., they enclose different values of toroidal and poloidal flux) and their plasma extends up to the symmetry axis. A Green’s function method based on two-dimensional finite elements is used to solve both problems, and an application to the experimental results of the Tokyo University Spherical Torus No. 3 flux-core-spheromak experiment [N. Amemiya, A. Morita, and M. Katsurai, J. Phys. Soc. Jpn. 63, 1552 (1993)] is illustrated.

The ideal magnetohydrodynamic (MHD) stability analysis of axisymmetric plasma equilibria is simplified if magnetic coordinates, such as Boozer coordinates (ψT radial, i.e., toroidal flux divided by 2π, θ poloidal angle, ϕ toroidal angle, with Jacobian g∝1∕B2), are used. The perturbed plasma displacement ξ⃗ is Fourier expanded in the poloidal angle, and the normal-mode equation δWp(ξ⃗*,ξ⃗)=ω2δWk(ξ⃗*,ξ⃗) (where δWp and δWk are the perturbed potential and kinetic plasma energies and ω2 is the eigenvalue) is solved through a 1D radial finite-element method. All magnetic coordinates are however plagued by divergent metric coefficients, if magnetic separatrices exist within (or at the boundary of) the plasma. The ideal MHD stability of plasma equilibria in the presence of magnetic separatrices is therefore a disputed problem. We consider the most general case of a simply connected axisymmetric plasma, which embeds an internal magnetic separatrix—ψT=ψTX, with rotational transform ι̷(ψTX)=0 and regular X-points (B⃗≠0)—and is bounded by a second magnetic separatrix at the edge—ψT=ψTmax, with ι̷(ψTmax)≠0—that includes a part of the symmetry axis (R=0) and is limited by two singular X-points (B⃗=0). At the embedded separatrix, the ideal MHD stability analysis requires the continuity of the normal plasma perturbed displacement variable, ξψ=ξ⃗∙∇⃗ψT; the other displacement variables, the binormal ηψ=ξ⃗∙(∇⃗θ−ι̷∇⃗ϕ) and the parallel μ=−gξ⃗∙∇⃗ϕ, can instead be discontinuous everywhere. The permissible asymptotic limits of (ξψ,ηψ,μ) are calculated for the unstable (ω2<0) eigenvectors, imposing the regularity of δWp, δWk, and ξ⃗ at the embedded separatrix and at the edge separatrix. An intensified numerical radial mesh following Boozer magnetic coordinates is set up; it requires a logarithmic fit to the rotational transform near the embedded magnetic separatrix, a minimum distance between the radial mesh and both separatrices, and finally an extended spectrum of poloidal mode numbers in the Boozer angle. The numerical results are compared “a posteriori” with the permissible asymptotic limits for the perturbed displacement: the radial displacement variable ξψ is found to be always near its most unstable asymptotic limit, while the full range of permissible asymptotic behaviors can be obtained for the binormal and the parallel displacement variables.

The design study of PROTO-SPHERA, a novel compact torus configuration, has been completed. It is composed of a spherical torus (ST) (with closed flux surfaces) and a force-free screw pinch (SP) (with open flux surfaces and fed by electrodes). PROTO-SPHERA is formed at spherical-tokamak-like densities (similar to 10(19) M-3) with low voltage (similar to 200 V) between the electrodes. The idea of replacing the metal centrepost current (I-tf) of the spherical tokamaks with the SP plasma electrode current (I-e) is aimed mainly at getting rid of the rod at the centre of the plasma configuration, which is the most critical component of spherical tokamak design. As a consequence it should be possible to decrease the aspect ratio A = R/a (R = ST major radius, a = ST minor radius) in the course of experiment and to increase the ratio between the toroidal plasma current (I-ST) and the plasma electrode current, I-ST/I-e >> 1. Matching two plasma configurations, i.e. an open flux-surface SP and a closed flux-surface ST, brings to life several radically new issues. The purpose of this paper is to analyse the equilibrium, the ideal MHD stability and the formations and modelling issues of such a combined magnetic confinement system. The MULTI-PINCH experimental setup, which is being assembled inside the START vacuum vessel (now in Frascati), will represent the first phase of PROTO-SPHERA: its goal is to prove the feasibility of a stable disc-shaped SP around the electrodes.