Jean-Charles Matéo-Vélez, Frédéric Thivet, Pierre Degond *

ONERA - Centre de Toulouse

* CNRS - Mathématiques pour l'Industrie et la Physique, Toulouse

Summer school on Mathematical modelling and computational challenges in plasma physics and applications,

Cargese, october 2004

Estimation of the ionic wind created by a wire-to-wire corona discharge

Purpose: modelling the interaction between an electric discharge and aerodynamics

• Some previous experimental works:– Roth (Univ. Tenessee, 1998):

• AC discharge with dielectric barrier

– Moreau (LEA, 1998): corona discharge• 2 thin electrodes on a plate• DC or pulsed current• atmospheric pressure• ionic wind about 3-4 m/s

air flow

Anode Cathode

Vitesse dans la couchelimite sans décharge

Vitesse dans la couche limite derrière la décharge

Vent ionique

Plaque plane

Sens de l'écoulement

efefgedg

• Possible applications:EHD actuators for :

• drag reduction,• flow control,• shock waves reduction, ...

Wire-to-wire discharge

• Several regimes - a lot of influencing parameters: – electric potential difference, – shapes of the electrodes, their positions upon or in the dielectric plate,– composition of the dielectric plate,– humidity degree of the air,– air flow,– etc …

• Present simplified study:– "high spot" regime, the most efficient: many luminescent points on the electrodes,– two corona discharges: one positive corona and one negative corona.

Electric potential (V)

– Electric field calculation: no space charge included (i.e. without discharge)– Use of PDEtool library of Matlab®.

– This highlights 3 characteristic zones:

two chemical active zones and 1 passive zone

Wire-to-wire discharge: Electrostatic field

Anode : +22 kV, = 0.7 mm

cathode : -10 kV, = 2.0 mm

– electronic avalanche if E > Ed, where Ed is the disruptive electric field in air at atmospheric pressure,

– the radius ra is defined by E(ra) = Ed,

– if r < ra, gas ionisation,

– if r > ra, no more ionisation,

+e-

e-

+

E

++

+++e-

+

u+

ra

Positive coronaMoving positive charges

– The calculation of the electric field indicates that ra 1.5 mm,

– This order of magnitude is confirmed by two analytical calculations inspired by the works of Raizer(1994) and Li (2004).

The anode zone:

– electronic avalanche if E > Ed,

– if r < rc, E > Ed, gas ionisation, the positive ions are absorbed by the cathode (secondary emission due to ionic bombardment),

– if r > rc, E < Ed, the electrons are evacuated, they rapidly attach to neutrals,

– the negative charges (negative ions) are accelerated because of the strong electric field,

– The electric field calculation indicates that rc 1 mm.

– This order of magnitude is also confirmed by an approximated analytic calculation inspired by the exact solution for one unique wire (Raizer).

-

E

+

e- -

u-

rc

Negative corona Moving negative charges (ions)

e-

e-

e-

Electronic attachment

-

--

-

The cathode zone:

– acceleration of positive and negative ions due to the strong electric field (Lorentz force),– collisions with the neutral molecules of air,– ionic wind effect,– competition between positive and negative ionic wind.

+ -

Ures

The inter-electrodes space:

1st wire-to-wire discharge model: Objectives

– Verifying the corona discharges hypothesis:• both positive and negative ions currents provoke ionic wind,• evaluation of positive and negative currents,• use of experimental data such as the total current,

– Developing the simplest discharge-aerodynamics interaction model,

– Analysing the results so as to develop a second model if necessary.

1st wire-to-wire discharge model:

• Lorentz force: EeNf net

• Electric force model:

– force due to positive ions current:– force due to negative ions current:– total electric force:

xjf

xjf

xjjC

Cf

SIj

1

1

1

C: ratio of positive ions and negative ions density currents

The electric force is linked to the discharge current I, experimentally obtained,

The section S on which the force is exerted must be determined.

– h = height of the moving charges zone, h must be defined,

d = 4 cm

f uniformh = 0,1-2 mm

+22 kV -10 kV

Ue

h (mm) 0.1 0.5 1.0 1.5 2.0

f (N / m3) 21000 4200 2100 1400 1050

The height of the anode zone which is the more efficient ionisation zone

– for C = 2, + = 2.104 m2V-1s-1, - = 2,7.104 m2V-1s-1, I / l = 1 mA/m (Moreau, LEA):

The inter-electrodes space = force application:

– Use of CEDRE: ONERA code for fluid mechanics,– adding of an external volumetric force in agreement with the model, – Calculation of a laminar flow above a plate,– refined mesh near the wall.

Numerical simulation:

slip

Subsonic inflow

U = 15 m/s

T = 300 K

Subsonic outflow

P = 1 atm

wall

Force application zone:

L = 4cm

Force application zone:

h = 0.1-2.0 mm

h (mm) 0 0,1 0,5 1 1,5 2U (m/s) 0 1,7 7,4 6,0 4,4 3,4* (µm) 334 266 56 14 21 28

Results: flow velocity profiles

0

2

4

6

8

10

12

14

16

0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5

i = 0.3 mA/m i = 0.6 mA/m i = 0.9 mA/m i = 1.2 mA/m

Velocity (m/s)

Y (

mm

)

J. Pons, Gas discharge, 2004

x = 6 cm

for h = 1.5 mm, the flow boundary layer is 30% more thin

Boundary layer thickness Drag reduction

for h = 1.5 mm, the drag reduction is about 70% at the end of the plate

Conclusion:

– this simple model is in agreement with experimental data,– the effects on the aerodynamics are important,– it encourages us to continue this study, by developing a predictive tool for the calculation of

discharge-aerodynamics interaction.

Perspectives:

– a more precise model of the discharge is being developed,– it takes into account the momentum equation of the fluid, the Poisson equation and

conservation equations for the species of the plasma,– an asymptotic analysis enables to simplify the problem,– the most difficult issue is to determine the chemistry of the wire-to-wire corona discharge.

THANK YOU