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]

9

Time Averaged Current-Voltage Characteristic

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.