1 NUMERICAL ANALYSES OF A VISCID COMPRESSIBLE IONIC FLOW C. Tulita, S.Raghunathan, E. Benard 1

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NUMERICAL ANALYSES OF AVISCID COMPRESSIBLE IONIC FLOW

C. Tulita, S.Raghunathan , E. Benard

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PLASMA FLOW CONTROL

OBJECTIVES

•Prevent Separation•Reduce Drag

PLASMA TECHNIQUES

•Corona Discharge

•Glow Discharge

By creating an important electriccharge distribution in a particular region

of the flow.

It occurs near sharp points, whereit creates a localized electric fieldgreater than the breakdown electric field of the medium surrounding it.

It operates at the Stoletow point, atwhich the energy cost of an ion-electron

pair is the minimum theoretically possible.

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Case: M=0.147, Re=2.8106, =0°

CORONA DISCHARGE EFFECT ON AN AEROFOIL IN SUBSONIC FLOW

Local electric field

Electricpotential

Plasma on

Plasma off

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Aerofoil wallWake cut Wake cut

NUMERICAL STRATEGY

C-Grid TransformationCFD mesh

Electro-dynamic grid

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cii ,

gradE

0, iiic vkE

0, iiv

0

ngradn

kV25

kV10

ELECTRODYNAMIC PROBLEM

mmAJvEk cc /40

Poisson equation

Conservation of the electric charge

Patankar control-volume method

Leger-Moreau-Touchard 2001

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CORONA EXPERIMENTAL CORRELATIONAT ANODE. Peek (1929) & Cobine(1958)

The initiating voltage for corona

MVa

daEV si

ln

m

MV

amEs

0308.0

11.3

1;67.0m The empirical surface roughness factor

11,298298

atmpKTT

p The relative atmospheric density factor

rVV i 0

dar

Plasma Active Volume

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ELECTRODYNAMIC RESULTATS

sE

BE

cm

kVE

cm

kVE

B

s

27

31

ijjiij EEET

2

2

Electric potential

Electric field

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0

0

0

,,

,,

,,,

ijijiit

jijijjiti

iit

vqhve

pvvv

v

RTp

FLUIDE PROBLEM

e , iv

iv 0jijn 0, iine

Inflow: given and extrapolated

Outflow: given and

T

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MASS-AVERAGED NAVIER-STOKES EQUATIONS IN TWO DIMENSIONAL

CONSERVATION FORM

0

y

G

x

F

t

U

e

v

uU

~

~

~

y

TkkuTvTe

Tv

Tvu

v

G

tyxyxyxyyy

yyy

yxyxyx

~)(~~~~~~~

~~~

~~~~

~

2

x

TkkvTuTe

Tvu

Tu

u

F

txyyxyxxxx

xyxyxy

xxx

~)(~~~~~~~

~~~~

~~~

~

2

2

2

~2

~~~~

~~~~~~

~2

~~~~

vy

v

y

v

x

up

vux

v

y

u

ux

u

y

v

x

up

yy

yxyxxyxy

xx

2

~~~)1(

22 vuep

TC

vue

v~~2

~~~~

22

02

1

3

2~3

2~~

,

,,,

ik

tjjijij

ijijkkijjitji

Kvvvv

Kuuuuu

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Tow dimensional thin-layer, mass-averaged Navier-Stokes code

NUMERICAL METHOD

Upwind implicit MacCormack predictor/corrector cell-centered finite-volume method

Flux Splitting method of Van Leer

Mulder’s continuous differentiable flux limiter

Gauss-Seidel line relaxation iterative procedure

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Modified version of the Baldwin-Lomax turbulence model,using a non-linear formulation of the wall region anisotropy

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AERODYNAMIC RESULTATS

Case: M=0.147, Re=2.8106, =0°

Plasma off Plasma on

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SKIN FRICTION COEFFICIENT

Plasma onPlasma off

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PRESSURE COEFFICIENT DISTRIBUTIONS

Plasma onPlasma off

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CONCLUDING REMARKS

Reduces drag

Enhance the mass and heat transfer between the aerofoil and surrounding flow 13

SUBSONIC REGIME

CORONA DISCHARGE TECHNIQUE

Prevents separation

The ionic charge distribution depends strongly on:

•The anode electrode radius•The empirical surface roughness factor•The relative atmospheric density factor•The potential difference between anode and cathode

PLASMA CHEMISTRY FROM THE ACTIVE VOLUME

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Electric fieldElectric potential

mmAJvEk cc /3

Possible Electric Results

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