5th International EHD Workshop, Poitiers, France

1. 5th International EHD Workshop, Poitiers, France On-Set of EHD Turbulence for Cylinder in Cross Flow Under Corona DischargesJ.S. Chang, D. Brocilo, K. UrashimaDept. of Engineering Physics, McMaster University, Hamilton, Ontario, Canada L8S 4L7J. Dekowski, J. Podlinski, J. MizeraczykInstitute for Fluid Flow Machinery, Polish Academy of Sciences, Gdansk, PolandG. TouchardLEA, University of Poitiers, Poitiers, France

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. Experimental Set-up(cylinder in a cross-flow geometry) grounded electrode needle (HV electrode ) u 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.

6. Additional Force and Energy Terms (i) Force density terms: 1st term: force density due to the space charge 2nd term: force density due to the charged particle motion 3rd term: force density due to the dielectric property change 4th term: force density due to the fluid permeability change 5th term: force density due to the electrostriction and magnetostriction (ii) Energy terms due to electromagnetic fields: 1st term: energygeneration 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 magnetic field such as energy storage in an electromagnetic system

7. Streamline Patterns without EHD Re=40 Steady laminar wake flow Unsteady laminar wake flow Re=200 Re=80 (Lee &Lin 1973) (Smith et al. 1970)

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 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

11. 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

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

13. Fluctuation Equation

14. Theoretical Analysis Based on Dimensionless Equations (i) Mass conservation (ii) Momentum equation (iii) Ion transport (iv) Poisson equation 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: • 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); • 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; • 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; • 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 • The electrical origin of instability leading to the on-set of turbulence can be estimated • from Ehd/Db2 > Re2 relation.