1. 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 5th International EHD Workshop, Poitiers, France

2. 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. 3 Experimental Set-up (cylinder in a cross-flow geometry) needle (HV electrode ) grounded electrode u Figure 1. Schematic of (a) experimental flow channel, and (b) details of cylindrical and electrodes arrangements.

4. 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. 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 ε D are dynamic and eddy viscosities, T s is the reference temperature, Cp is the specific heat, f EB and Q EB are the momentum and energy change due to the presence of electric and magnetic fields, respectively.

6. 6 Additional Force and Energy Terms (i) Force density terms: 1 st term:force density due to the space charge 2 nd term: force density due to the charged particle motion 3 rd term:force density due to the dielectric property change 4 th term: force density due to the fluid permeability change 5 th term:force density due to the electrostriction and magnetostriction (ii) Energy terms due to electromagnetic fields: 1 st term:energy generation due to the flow of charged particles such as ohmic heating 2 nd term: energy generation due to the polarization such as electromagnetic hysteresis loss 3 rd term:energy generation due to the displacement current and time varying magnetic field such as energy storage in an electromagnetic system

7. 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. 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. 9 Time Averaged Current-Voltage Characteristic

10. 10 Typical PIV Images for Wire-plate Geometry with EHD a) V=0 [kV];R ew =28; E hdw =0; Re cw =2800; E hd-cw =0 b) V=-24kV; Re w =28; E hdw =2.3  10 6 ; Re cw =2800; E hd-cw =8.4  10 6 c) V=-30kV; Re w =28; E hdw =5.7  10 6 ; Re cw =2800; E hd-cw =2.1  10 7 Flow direction Laminar flow EHD laminar wake flow EHD turbulent flow

11. 11 Typical PIV Images for Wire-plate Geometry with EHD d) EHD Von-Karman vortex at Re w =22.4; E hdw =8  10 5 ; Re cw =2240; E hd-cw =3.1  10 6 Flow direction e) Fully developed vortex at Re w =5.6; E hdw =2.3  10 6 ; Re cw =560; E hd-cw =8.4  10 6

12. 12 Navier-Stokes equation: Time fluctuating (‘) and averaged components ( ) of velocity and pressure: Reynolds Equation: Reynolds Equation

13. 13 Fluctuation Equation

14. 14 Theoretical Analysis Based on Dimensionless Equations (i) Mass conservation (ii) Momentum equation (iii) Ion transport (iv) Poisson equation E hd  Re 2 EHD dominant laminar flow [E hd /Re 2 ] wire EHD dominant near wire [E hd /Re 2 ] channel EHD dominant even near flow channel E hd >Re c 2 Maximum EHD enhanced flow above critical Reynolds number E hd /D b 2 >Re c 2 Space charge generated turbulence flow Sc i is the ion Schmidt number, F E is the electric field number, Db i is the Debye numbers, u is the dimensionless velocity vector, η is the dimensionless electric field, and n i is the dimensionless ion density.

15. 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 E hd << Re 2 ; 2.Forward wake is observed when E hd  Re 2 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 E hd  Re 2 ; 5.Fully developed EHD wakes are observed when E hd >> Re 2 ; 6.On-set of vortex stream tails normally observed at Re > 80 can be generated even at lower Reynolds number when E hd > Re 2 ; 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 (E hd > Re 2 ) and the local Reynolds number based on velocity maximum exceeds critical Reynolds number based on flow channel (Re cw >> 2300); and 9.The electrical origin of instability leading to the on-set of turbulence can be estimated from E hd /Db 2 > Re 2 relation.