On-Set of EHD Turbulence for Cylinder in Cross Flow Under Corona Discharges J.S. Chang, D. Brocilo,...
-
Upload
dorthy-warner -
Category
Documents
-
view
218 -
download
0
Transcript of On-Set of EHD Turbulence for Cylinder in Cross Flow Under Corona Discharges J.S. Chang, D. Brocilo,...
On-Set of EHD Turbulence for Cylinder in Cross Flow Under Corona Discharges
J.S. Chang, D. Brocilo, K. UrashimaDept. of Engineering Physics, McMaster University, Hamilton, Ontario, Canada L8S 4L7
J. Dekowski, J. Podlinski, J. MizeraczykInstitute for Fluid Flow Machinery, Polish Academy of Sciences, Gdansk, Poland
G. TouchardLEA, University of Poitiers, Poitiers, France
5th International EHD Workshop, Poitiers, France
G D A Ń S K
P A N
2
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
3
50x40
60
6
40
Experimental Set-up(cylinder in a cross-flow geometry)
needle (HV electrode )
grounded electrode
u
270
400
180
7575
500
150 0
60
Figure 1. Schematic of (a) experimental flow channel, and (b) details of cylindrical and electrodes arrangements.
4
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)
5
Conservation Equations Under Electromagnetic Field
(i) Mass conservation
(ii) Momentum equation
(iii) Energy conversation
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.
0)(
U
tg
EBfUPTTUUt
UDDs
])[()()(
EMQTC
kTU
t
T
P
2
6
Additional Force and Energy Terms
(i) Force density terms:
1st term: force density due to the space charge2nd term: force density due to the charged particle motion3rd term: force density due to the dielectric property change4th term: force density due to the fluid permeability change5th term: force density due to the electrostriction and magnetostriction
(ii) Energy terms due to electromagnetic fields:
1st term: energy generation due to the flow of charged particles such as ohmic heating2nd term: energy generation due to the polarization such as electromagnetic hysteresis
loss3rd term: energy generation due to the displacement current and time varying
magnetic field such as energy storage in an electromagnetic system
])(2
1)(
2
1[
2
1
2
1 2222TTieEB HEHEBJEF
)]()([)()())((B
dt
dH
D
dt
dEDUHBUEBUEUJQ ieEB
7
Streamline Patterns without EHD
Steady laminar wake flow
(Smith et al. 1970)
Re=40
Re=80
Unsteady laminar wake flow
Re=200
(Lee &Lin 1973)
8
Typical flow patterns for cylinder in a cross-flow with EHD
a) Re=35; V=0[kV] b) Re=35; V=4.5[kV]
c) Re=35; V=5[kV] d) Re=35; V=5.5[kV]
10
Typical PIV Images for Wire-plate Geometry with EHD
a) V=0 [kV];Rew=28; Ehdw=0; Recw=2800; Ehd-cw=0
b) V=-24kV; Rew=28; Ehdw=2.3106; Recw=2800; Ehd-cw=8.4106
c) V=-30kV; Rew=28; Ehdw=5.7106; Recw=2800; Ehd-cw=2.1107
Flow direction
Laminar flow
EHD laminar wake flow
EHD turbulent flow
11
Typical PIV Images for Wire-plate Geometry with EHD
d) EHD Von-Karman vortex at Rew=22.4; Ehdw=8105; Recw=2240; Ehd-cw=3.1106
Flow direction
e) Fully developed vortex at Rew=5.6; Ehdw=2.3106; Recw=560; Ehd-cw=8.4106
12
Navier-Stokes equation:
Time fluctuating (‘) and averaged components (< >) of velocity and pressure:
Reynolds Equation:
Reynolds Equation
0';;'
0';;'
0';;'
EBEBEBEBEBEB
iiiiii
ffFfFf
ppPpPp
uuUuUu
EBfUPUUt
U
21
)(
EBEB ffuux
U
xPUU
t
Uji
j
i
j
')','(1
)(
13
Fluctuation Equation
.),Re()/('')''
(?)'''
'''
'1
'''
''
2
'''
)2(
'''''';''
'''
'''
'1)''''('
'''
32
22
2
22222/12
2
constforLqdxx
uu
xx
uud
diffusionrelaxationsource
fup
uyy
u
y
up
y
Uu
Dt
uuD
upq
yd
y
Uuu
Dt
qD
uuuuuqqq
t
uuu
t
uuu
t
xx
u
x
puuuu
xx
Uu
x
uU
t
uf
Mij
ji
ij
ji
Exyyx
yyx
yyx
zyxji
jij
iji
ji
i
ijiji
jj
ij
j
jj
iE
14
Theoretical Analysis Based on Dimensionless Equations
(i) Mass conservation
(ii) Momentum equation
(iii) Ion transport
(iv) Poisson equation
0)( u
unE
puuu
ihd 2
2
~
Re
1
Re
~-
~
0~
)(~
F ~
2
ReSc 2i iiEi nnnu
iibE nDF ~
EhdRe2EHD dominant
laminar flow
[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>Rec
2 Space charge generated turbulence 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.
15
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.