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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 2 Experimental Set-up (cylinder in a cross-flow geometry) 0 10 grounded electrode 39 0m m 500 40 180 75 270 60 75 1500 50 x40 400 6 u 60 needle (HV electrode ) Figure 1. Schematic of (a) experimental flow channel, and (b) details of cylindrical and electrodes arrangements. 3 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) 4 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 C P 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. 5 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 6 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) 7 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] 8 Time Averaged Current-Voltage Characteristic 9 Typical PIV Images for Wire-plate Geometry with EHD Flow direction b) V=-24kV; Rew=28; Ehdw=2.3106; Recw=2800; Ehd-cw=8.4106 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=5.7106; Recw=2800; Ehd-cw=2.1107 10 Typical PIV Images for Wire-plate Geometry with EHD Flow direction d) EHD Von-Karman vortex at Rew=22.4; Ehdw=8105; Recw=2240; Ehd-cw=3.1106 e) Fully developed vortex at Rew=5.6; Ehdw=2.3106; Recw=560; Ehd-cw=8.4106 11 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 12 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 D(q 2 ) 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 2 ui ' u j ' ) 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 .) 13 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 EhdRe2 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. 14 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. 15