LABORATOIRE PLASMA ET CONVERSION D’ENERGIE - UMR5213

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Accueil du site > Groupes de recherche > Groupe de Recherche Energétique, Plasmas et Hors Equilibre > Projets en cours > Actionneurs plasma pour le contrôle d’écoulement

PLASMA ACTUATORS FOR FLOW CONTROL

5 avril 2008

Participants

Students : Y. Lagmich (2004-2007) , T. Unfer

Permanents : T. Callegari, L. Pitchford, J.P. Boeuf

Partners, collaboration and contracts

Collaboration with ONERA/DMAE, ONERA/DTIM, LEA (E. Moreau et al.), LAPLACE/MPP

This work is partly supported by AFOSR (EOARD) and partly by the EADS Foundation

T. Unfer benefits from a fellowship from the EADS Foundation.

Y. Lagmich has benefited from a fellowship of the French Ministry of Research

Context

Surface dielectric barrier discharges (DBDs) at atmospheric pressure can generate a flow or modify the boundary layer of a flow and have been proposed as actuators for flow control. The momentum transfer from charged particles to neutral molecules generates an ElectroHydroDynamic (EHD) force that can be used to modify the airflow profile within the boundary layer in order to control the laminar-turbulent transition, reduce the drag, and re-attach or stabilize the flow.

Surfaces DBDs or corona discharges have been shown to be able to generate flows of a few m/s, but their potential application as actuators for flow control will be taken much more seriously if larger flow velocities can be demonstrated. It is therefore essential to understand the limits of the force that can be generated by a surface discharge and to look for conditions (discharge and electrode geometry, voltage waveform) that could increase this force. There is still a lack of clear understanding of the qualitative effect of these surface discharges on the flow, and the potential and limits of this effect need to be quantified.

Objectives

The objectives of our work on plasma actuators are :
to better understand the nature of the ElectroHydroDynamic force in Dielectric Barrier Discharges
to quantify the EHD force and to understand the limits of this force
to look for surface discharge conditions (electrode configurations, voltage waveforms etc…) optimizing the EHD force

The research described here is based fluid models of the DBD and simple optical and electrical diagnostics of the DBDs.

EHD force and discharge model

The EHD force per unit volume, f, in electric discharges is due to momentum transfer from charged particles to neutral particles and can be written (for species s colliding with neutrals and neglecting the neutral velocity) :

$f = n_s \nu_{ms}m\s\textbf{u}_s$

$n_s$ is the charged particle density, $\nu_{ms}$ is the momentum transfer collision frequency of a particle s colliding with neutrals, $m_s$ is the mass of s, and $\textbf{u}_s$ is the drift velocity of species s.

The charged particle mobility $\mu_s$ is defined as :

$\mu_s=\frac{e} {m_s\nu_{ms}}$

Combining the above equations and summing the contributions of positive ions (index "i"), electrons ("index "e"), and negative ions (index "n"), the EHD force per unit volume can be written as :

$f = \frac {j_i} {\mu_i}-\frac {j_e} {\mu_e}-\frac {j_n} {\mu_n}$

As a first approximation, the current density of the charged particles of type s can be written, in a collisional plasma :

$j_s=\pm n_s\mu_s E$ where $\mu_s$ is the charged particle mobility and E the electric field.

Therefore :

$f = e(n_i-n_e-n_n)E$

The force per unit volume acting on the neutral molecules is therefore equal to the Coulomb force acting on the charged particles, which means that the momentum gained by the charged particles on the electric field is exactly and locally balanced by collisions, and entirely transmitted to neutral molecules. One consequence of the above equation is that the EHD force is zero in a first approximation for a quasi-neutral plasma (see Ref. [1] for a more explicit discussion). The EHD force is large in regions of the discharge with large electric field and where the space charge is non-zero (positive or negative). This is the case, for example, in the cathode sheath regions of glow discharges or in the drift region of corona discharges. Electrons are supposed to be generated on the dielectric surface by ion impact secondary electron emission.

The space and time variations of the EHD force per unit volume can be deduced from a fluid model of the surface DBD, where electron and ion fluid equations are coupled with Poisson’s equation. The charging of the dielectric surface is taken into account self-consistently.

Results

The geometry of DBD plasma actuators can be seen on the simulation domain shown in the figure below.

DBB geometry

The results shown below have been obtained in air for a L=8mm, w=1 mm, h=3 mm (dielectric permittivity 5). The space and time variations of the charged parcticel densities are shown for linearly increasing or decreasing voltage waveforms (with a slope of $\pm 300 V/\mu s$ )

Results for a positive ramp voltage (anode above the dielectric surface)

A positive ion cloud forms and expands along the surface. When the positive ion cloud reaches a critical size and density, breakdown occurs. Breakdown is characterized by a large current pulse and the progation of a filamentary discharge along the surface. The maximum extension of the ion cloud is limited by breakdown. The EHD force during this positive discharge is due to positive ions and is directed away from the tip of the top electrode. The EHD force is important during the low current phase between current pulses (similar to ion wind in corona discharges) and is not significant during the current pulses.

electron density
positive ion density
negative ion density
current

Results for a negative ramp voltage (cathode above the dielectric surface)

In the case of a negative discharge, the current exhibits pulses at a higher frequency and lower amplitude than in the positive case. A negative ion space charge forms above the surface and continuously expands. At each current pulse the electrons spreads a little further along the surface, ahead of the negative ion cloud (and generate more negative ions by attachment ahead of the cloud). The EHD force in this phase is due to negative ions and is in the same direction as in the positive phase.

electron density
positive ion density
negative ion density
current

Publications

Y. Lagmich, T. Callegari, L. Pitchford, and J.P. Boeuf, Model description of surface dielectric barrier discharges for flow control J. Phys. D : Appl. Phys. 41 095205 (2008)

Y. Lagmich, Th. Callegari, Th. Unfer, L. C. Pitchford, and J. P. Boeuf, Electrohydrodynamic force and scaling laws in surface dielectric barrier discharges, Appl. Phys. Lett. 90, 051502 (2007)

J.P. Boeuf, Y. Lagmich, Th. Unfer, Th. Callegari, L.C. Pitchford, Electrohydrodynamic Force in Dielectric Barrier Discharge Plasma Actuators, J. Phys. D : Appl. Phys. 40, 652 (2007)

J.P. Boeuf and L.C. Pitchford, Electrohydrodynamic force and aerodynamic flow acceleration in surface dielectric barrier discharge, J. Appl. Phys. 97 103307 1-9 (2005)