Transcript Jean-Charles Matéo-Vélez - Institut de Mathématiques de Toulouse

Estimation of the ionic wind created by a wire-to-wire
corona discharge
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
Purpose: modelling the interaction between an electric
discharge and aerodynamics
air flow
• 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
• Possible applications:
EHD actuators for :
• drag reduction,
• flow control,
• shock waves reduction, ...
Sens de l'écoulement
Vitesse dans la couche
limite sans décharge
Vitesse dans la couche limite
derrière la décharge
efefgedg
Vent ionique
Anode
Cathode
Plaque plane
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.
Wire-to-wire discharge: Electrostatic field
– Electric field calculation: no space charge included (i.e. without discharge)
– Use of PDEtool library of Matlab®.
Anode : +22 kV,  = 0.7 mm
cathode : -10 kV,  = 2.0 mm
Electric potential (V)
– This highlights 3 characteristic zones:
two chemical active zones and 1 passive zone
The anode zone:
– 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,
Positive corona
+
+
e-
+
+
e-
e-
+
Moving positive
charges
+
u+
+
ra
E
– 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 cathode 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,
Electronic attachment
Negative corona
-
erc
-
e-
-
-
+
e-
Moving negative
charges
(ions)
u
e-
-
E
– 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).
The inter-electrodes space:
–
–
–
–
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
+
-
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:


f  eN net E
• Electric force model:
– force due to positive ions current:
– force due to negative ions current:
– total electric force:


f   j   x


f    j   x

f 

1 C
1 

 j  j x


C  1       
jI S
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.
The inter-electrodes space = force application:
Ue
h = 0,1-2 mm
f uniform
+22 kV
-10 kV
d = 4 cm
– h = height of the moving charges zone, h must be defined,
– for C = 2, + = 2.104 m2V-1s-1, - = 2,7.104 m2V-1s-1, I / l = 1 mA/m (Moreau, LEA):
h (mm)
f (N / m3)
0.1
0.5
1.0
1.5
2.0
21000
4200
2100
1400
1050
The height of the anode zone which is
the more efficient ionisation zone
Numerical simulation:
–
–
–
–
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.
slip
Subsonic inflow
Subsonic outflow
U = 15 m/s
P = 1 atm
T = 300 K
Force application
zone:
h = 0.1-2.0 mm
wall
Force application zone:
L = 4cm
Results:
flow velocity profiles
Y (mm)
J. Pons, Gas discharge, 2004
x = 6 cm
16
14
12
10
8
6
i = 0.3 mA/m
i = 0.6 mA/m
i = 0.9 mA/m
i = 1.2 mA/m
4
2
0
0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5
Velocity (m/s)
h (mm)
U (m/s)
* (µm)
0
0
334
0,1
1,7
266
0,5
7,4
56
1
6,0
14
1,5
4,4
21
2
3,4
28
Boundary layer thickness
Drag reduction
for h = 1.5 mm, the flow
boundary layer is 30%
more thin
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