Transcript Design of Plasma Treatment System for Simultaneous Control

5th International EHD Workshop, Poitiers, France
On-Set of EHD Turbulence for Cylinder in Cross Flow
Under Corona Discharges
J.S. Chang, D. Brocilo, K. Urashima
Dept. of Engineering Physics, McMaster University, Hamilton, Ontario, Canada L8S 4L7
J. Dekowski, J. Podlinski, J. Mizeraczyk
Institute for Fluid Flow Machinery, Polish Academy of Sciences, Gdansk, Poland
G. Touchard
LEA, University of Poitiers, Poitiers, France
P
A
N
GDAŃSK
Objectives
•Conduct experimental and theoretical investigations to study the on-set of EHD
turbulence for:
•
cylinder in cross flow, and
•
wire-plate geometry.
•Develop theoretical models based on the mass, momentum, and charged particle
conservation equations coupled with the Poisson's equation for electric field.
•Evaluate instability in a flow system based on the time dependent term of the
momentum equations.
•Demonstrate the EHD origin of the on-set of turbulence by the charge relaxation
and electric fields using dimension analyses and experimental observations.
•Determine the criteria for the on-set of turbulence based on dimensionless
numbers
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Experimental Set-up
(cylinder in a cross-flow geometry)
0
10
grounded electrode
500
39
0m
m
40
180
75
270
60
75
1500
5 0 x40
400
6
u
60
needle (HV
electrode )
Figure 1. Schematic of (a) experimental flow channel, and (b) details of cylindrical and electrodes arrangements.
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Experimental Set-up
(wire-plate geometry)
Figure 2. Schematic of PIV system used in wide wire-plate geometry set-up.
(Flow channel dimensions are as follows: plate- to-plate distance A=10cm, plate length B=60cm , and plate width C=20cm)
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Conservation Equations Under
Electromagnetic Field
(i) Mass conservation
 g
t

   ( U )  0
(ii) Momentum equation



 
U

  (U  )U    (T  Ts )  P    [( D   D )U ]  f EB
t
(iii) Energy conversation
T 
k
 U  T 
 2T  Q EM
t
CP
ρg is the gas density, U is the gas velocity, is the coefficient of thermal expansion of the fluid, k is the thermal conductivity, T is the
temperature, P is the pressure, D and εD are dynamic and eddy viscosities, Ts is the reference temperature, Cp is the specific heat, fEB
and QEB are the momentum and energy change due to the presence of electric and magnetic fields, respectively.
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Additional Force and Energy Terms
(i) Force density terms:
1
1
1

1

F EB  ie E  J  B  E 2  H 2  [ E 2 ( )T  H 2 ( )T ]
2
2
2

2

1st term:
2nd term:
3rd term:
4th term:
5th term:
force density due to the space charge
force density due to the charged particle motion
force density due to the dielectric property change
force density due to the fluid permeability change
force density due to the electrostriction and magnetostriction
(ii) Energy terms due to electromagnetic fields:
QEB  ( J  ieU )(E  U  B)    ( E  U  B)  ( H  U  D)  [ E
d D
d B
( )  H ( )]
dt 
dt 
1st term: energy generation due to the flow of charged particles such as ohmic heating
2nd term: energy generation due to the polarization such as electromagnetic hysteresis
loss
3rd term: energy generation due to the displacement current and time varying
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magnetic field such as energy storage in an electromagnetic system
Streamline Patterns without EHD
Re=40
Steady laminar wake flow
Unsteady laminar wake flow
Re=80
(Smith et al. 1970)
Re=200
(Lee &Lin 1973)
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Typical flow patterns for
cylinder in a cross-flow with EHD
a) Re=35; V=0[kV]
c) Re=35; V=5[kV]
b) Re=35; V=4.5[kV]
d) Re=35; V=5.5[kV]
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Time Averaged
Current-Voltage Characteristic
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Typical PIV Images for
Wire-plate Geometry with EHD
Flow direction
b) V=-24kV; Rew=28; Ehdw=2.3106; Recw=2800; Ehd-cw=8.4106
a) V=0 [kV];Rew=28; Ehdw=0; Recw=2800; Ehd-cw=0
Laminar flow
EHD laminar wake flow
EHD turbulent flow
c) V=-30kV; Rew=28; Ehdw=5.7106; Recw=2800; Ehd-cw=2.1107
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Typical PIV Images for
Wire-plate Geometry with EHD
Flow direction
d) EHD Von-Karman vortex at
Rew=22.4; Ehdw=8105; Recw=2240; Ehd-cw=3.1106
e) Fully developed vortex at
Rew=5.6; Ehdw=2.3106; Recw=560; Ehd-cw=8.4106
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Reynolds Equation
Navier-Stokes equation:



 
U
1
2
 (U  )U   P   U  f EB
t

Time fluctuating (‘) and averaged components (< >) of velocity and pressure:
ui  U i  ui ' ;
U i  ui ;
 ui '  0
p  P  p' ;
f EB  FEB  f EB ' ;
P  p ;
FEB  f EB ;
 p'  0
 f EB '  0
Reynolds Equation:





U i
U
1

 (U  )U   P 
(
  ui ' , u j ' )  f EB '   f EB
t

x j
x j
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Fluctuation Equation
u j '
ui '
U i
 2 ui

1 p '
f E '
U j
 u j '

(ui ' u j '  ui ' u j ' )  

t
x j
x j x j
 xi
xi x j
u j '
ui '

 ui ' u j ' 
 u j '  ui '
t
t
t
q '  q '2 1/ 2 ; q '2  ui ' u j '  u x '2 u y '2 u z '2
2
q
D(
)
2  u ' u '  U  d  
x
y
Dt
y
y
D  u x ' u y ' 
Dt
 q' p' 
  u y '
2 
 u ' u y ' 
U 1

 

p '  x 
y 
y  y
 y
 source relaxation diffusion
 u y '2 
 ui ' u j ' )
 2  ui ' u j '  

d 

 x j xi
x j xi 

 2 p' 
 u y '  u x '  f E ' (?)


d   (q 3 / LM )
( for Re ,   const.)
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Theoretical Analysis
Based on Dimensionless Equations
(i) Mass conservation
  (u)  0
(ii) Momentum equation
Ehd
u
1 ~2
~
~
 u  u  - p  2 ni  
 u

Re
Re
(iii) Ion transport
ReSc i ~
~
~2
u  ni  FE   (ni  )   ni  0
2
EhdRe2
EHD dominant
[Ehd/Re2]wire
EHD dominant near wire
[Ehd/Re2]channel
EHD dominant even near
flow channel
Ehd>Rec2
Maximum EHD
enhanced flow above
critical Reynolds number
Ehd/Db2>Rec2
Space charge generated
turbulence flow
(iv) Poisson equation
~
FE   Dbi ni
laminar flow
Sci is the ion Schmidt number, FE is the electric field number, Dbi is the Debye numbers,
u is the dimensionless velocity vector, η is the dimensionless electric field, and ni is the dimensionless ion density.
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Concluding Remarks
Based on simple charge injection induced EHD flow model and experimental observations,
we concluded that:
1. No significant flow modifications will be observed when
Electric Rayleigh Number Ehd << Re2;
2. Forward wake is observed when Ehd  Re2 due to the charge injection (EHD flow);
3. Small recirculation will be generated along the surface of cylinder
from front to real stagnation points;
4. Flow wake deformation is observed when Ehd  Re2;
5. Fully developed EHD wakes are observed when Ehd >> Re2;
6. On-set of vortex stream tails normally observed at Re > 80
can be generated even at lower Reynolds number when Ehd > Re2;
7. On-set of EHD turbulence is usually initiated downstream of the near real-stagnation
point;
8. EHD turbulence can be generated even when Reynolds numbers based on the
cylinder diameter are less than 0.2, if the EHD number is larger than Reynolds
number square (Ehd > Re2) and the local Reynolds number based on velocity
maximum exceeds critical Reynolds number based on flow channel (Recw >> 2300); and
9. The electrical origin of instability leading to the on-set of turbulence can be estimated
from Ehd/Db2 > Re2 relation.
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