Investigation of fluid flow around a cylinder with EHD actuation on inclined plates behind the cylinder

Transcription

1 Investigation of fluid flow around a cylinder with EHD actuation on inclined plates behind the cylinder S. Reza-zadeh Department of Mechanical Engineering, Hakim Sabzevari University (HSU), Sabzevar, Iran s.rezazadeh@hsu.ac.ir Abstract- In this work, the compound flow control method (passive-active) has been applied around a cylinder with a splitter plate. The wire-plate electrodes (active) and the splitter plate (passive) were used simultaneously. Simulations consist of the interaction between the electric field and the fluid flow. Modeling conditions included different arrangements of the splitter plates (γ) and position of the wire is α=±90º. Corona wind is more effective for low Reynolds numbers so the Reynolds number of flow is 40. Pressure distribution over the surface of the cylinder has been calculated and flow patterns have been visualized. Results show the effects of two corona wind over the cylinder and the splitter. The first corona wind is between the wires and the cylinder and the second one is between the wires and the splitter plate. These winds acted simultaneously and by increasing γ, the second corona wind got stronger. I. INTRODUCTION The fluid flow around a cylinder, because of complicated phenomena such as vortex shedding and flow separation behind the cylinder, has been studied by many researchers and scientists. They applied some methods and devices to control this flow. Most of these techniques are changing the Boundary layer and the wake zone to obtain the best efficiency. Methods are classified in three groups: (1) passive control, (2) active control and (3) compound control. Passive control techniques do not need any external energy during application. Additional devices in the fluid flow or changing the geometry of the bluff body such as splitter plate, base bleed and roughness are applied in this method. Active control techniques such as EHD actuators and vibrators need external energy to affect the fluid flow. When Active and passive techniques are applied simultaneously, it is called compound method. The Splitter plate is widely used for flow control as a passive method. Using a circular cylinder with a connected splitter plate was reported by [1]. Then others used it for different cases. Ref.[2,3] performed some experiments by the splitter plate and the second cylinder in the wake zone.his experiments included different length and asymmetrically arranged splitter plate. He used detached splitter plate at different gap distances. It was found that when the splitter was arranged asymmetrically, vortex shedding was critically suppressed and there was an ideal gap distance. Ref.[4,5] considered the fluid flow that the splitter plate was placed at various locations downstream of the cylinder. They found out the splitter plate significantly reduced drag force and lift fluctuation and there was an ideal location of the splitter for the maximum reduction. Ref.[6] investigated heat transfer around the cylinder with the splitter plate. They remarked a reduction in the size of wake zone. The splitter plate was an extra fin area for conduction, so heat transfer increased. Ref.[7] studied the fluid flow around the cylinder with a hinged-splitter plate in the wake zone. Their experiments showed that the splitter plate oscillation increases with Reynolds number at low Reynolds numbers. Application of electrohydrodynamic (EHD) actuators was reported some decades ago. EHD is the interaction of electric and flow fields. High field strength around sharp emitter produces ions and accelerates ions to opposite electrode.energy transfer between charges and fluid molecules leads to flow motion which called ionic wind or corona wind. The Corona wind was reported by [8] then others used this phenomenon for various applications and developed it. Ref.[9,10] could reduce wake zone behind a plate by EHD actuators and found out the kinetic energy induced by the ionic wind inside the boundary layer allows a drag reduction for low Reynolds numbers. Ref.[11] explored the fluid flow around a cylinder by wire-plate electrodes and adjusted the size of mean recirculation region behind the cylinder. Ref.[12] performed some experiments to examine the effect of distance between electrodes. They found out the pressure drag can be affected by imposing corona wind. Onset of EHD turbulence was reported in cross flow around a cylinder [13]. They produced EHD turbulence even at low Reynolds numbers. Ref. [14] used dielectric barrier discharge (DBD) plasma actuator to control flow around a cylinder. In present work, the compound method (passive and active) is applied to control the fluid flow around a cylinder with a splitter plate. In this approach, a splitter plate, as a passive technique and EHD actuators (wireplate), as an active technique, are used simultaneously. Investigation included different arrangements of the splitter plates (γ= 0º, ±5º, ±10º, ±15º, ±20º, ±25º, ±30º, ±35º, ±40º, ±45º), H=R (H: distance between the wires and the cylinder surface), position of the wires (α=±90º) and the Reynolds number of flow is 40. Pressure and velocity of Flow were calculated. Results show the effects of the corona winds for various arrangements of the splitter plates. 212

2 C p Proceedings of the 2013 International Conference on Applied Mathematics and Computational Methods in Engineering II. METHOD OF ANALYSIS The physical basis of much electrically enhanced momentum lies in the EHD force F per unit volume, generated by electric field strength E, in a fluid of dielectric permittivity ε, density ρ at temperature T; this can be expressed as : F = qe- E + E q( ) (1) 2 2 Where q is the space charge density in the fluid, qe is the Coulomb force exerted by an electric field upon the free charge in high voltage electric field. For the single phase, Coulomb force is predominate mechanism for EHD and qe should then be included in the momentum equation. The Poisson equation for the electric potential and the current continuity equation can be written as follows: 2 V q 0 (2) Where ε 0 is the dielectric permittivity of free space. The electric potential is defined: E V (3) Electric current is included: (1) conduction (ions motion because of electric field), (2) convection (transport of charges with airflow), and diffusion. Current density J is: J Eq Uq D q (4) E E Where μ E is the mobility, D E is diffusion coefficient and U is velocity vector of flow. Because of DC Current continuity condition, current continuity equation is:.j 0 (5) Fluid flow is steady-state incompressible flow and continuity equation is:.u 0 (6) And.Navier-Stokes equation is: 2 U. U p U q V (7) Where ρ is the air density, p is the air pressure, and μ is the air dynamic viscosity. By substituting and modifying equations could be found new equation for current density as follow:.( D q Vq) U. q 0 (8) E So we should solve equations (2,6,7,8).As observed all equation are coupled,therefore they are solved simultaneously. We used COMSOl code to simulate twodimensional flow around the cylinder. The geometry of present work were shown in fig(1). Between wire and collecting electrodes, there are ionization zone and drifting zone. At the boundary between them,ions started to move. The electric field strength is equal to breakdown in this boundary. electric field strength in air E 0 = V/m according to Kaptsov s assumption [15].For the positive corona, by empirical Peek s formula for air at standard conditions, the electric field strength E W at surface of a smooth corona wire was given: 2 E E R (9) W 0 W Where R W is wire radius. It found out that electrical potential on the boundary of ionization zone is: V V E R ln E E 0 W W W W 0 And radius of this zone is: 2 (10) R R R W 0 W (11) So, we modified q 0 till to obtain an acceptable amount of V 0 at boundary of ionization zone. At the surface of the stationary cylinder, the usual no-slip boundary condition is applied. For electrical boundary conditions, the gradients of voltage and electric charge density in far fields are considered zero. In order to determine the electric charge density, the tryand-error method starts by an initial guess of charge density on the surface of the electrode, and then the current in the wire electrode is calculated. Considering experimental values, this current must be in the microampere scale. This method continues to reach the desired value. The electrode potential on the wire electrode was 10, 15, and 20 kv and the cylinder surface and the splitter plate electrodes were ground electrodes. Fig. 1. The schematic diagram of geometry III. RESULTS AND DISCUSSION For evaluation of our simulation, we compared the pressure coefficient of present work with existing experimental work that was shown in fig Exp Re=36 Exp Re=45 Re=40, No EHD Angle ( degree ) Fig. 2. Comparison of the pressure coefficient Fig.3 reveals the External forces around the cylinder schematically for various position of the splitter plate. Two corona winds were recognized in this geometry. The first corona wind was between the wires and the cylinder 213

3 and the second one was between the wires and the splitter plate. 214

4 Fig 3 Schematic diagram of electric forces: (a) No splitter plate,(b) G=0, (c) G=0.5d, (d) G=d, (e) G=2d The results that will report in this paper included the applied voltage=10kv and Re number=40. Fig 4 shows the relative pressure coefficient Cp/ Cpo (Cpo is the pressure coefficient of stagnation point when there is no EHD actuation for the single cylinder) over the cylinder for various locations of the splitter and the wires. As observed, for α (angle of wire electrode) =0º and ±30º, the presence of the splitter plate behind the cylinder doesn t play an important role but for α=±90º, Cp/Cpo decreased considerably and for α=±150º, this effect is notable because for α=±90º, ±150º, the distance between the wires and the splitter is short and the second corona wind is more effective. Fig 5 illustrates the contours of velocity around the cylinder without EHD actuation and splitter plate. There are two stationary vortexes behind the cylinder as we predicted. When a splitter plate was set behind the cylinder, we observed the velocity contours as fig 6. Two pair of vortexes are predicted behind the cylinder. When EHD actuation was applied and the wire was set at α=0º, the velocity contours is shown in fig 7. EHD actuation caused to increase the momentum and velocity of flow that made the wake zone get smaller and just a pair of vortexes is observed behind the cylinder. 215

5 Fig. 4. Relative pressure coefficient=10kv Fig. 5. Velocity contours for single cylinder Fig. 7 Velocity contours for cylinder-splitter, α=0 For different arrangements of wires, some flow patterns were observed. When α=±30º, As shown in fig 8,,the recirculation zones were appeared in front of the cylinder as reported [12],[16].The vortexes behind the cylinder were became smaller because the wires are near the splitter plate and the wake zone were affected more. As observed in fig 9, when α =±90º, the recirculation zones were grown up and effect of EHD actuation is strong for wake zone and made the vortexes be disappeared behind the cylinder. By setting wires at α =±150º, as shown in fig 10a, there were two pairs of vortexes in front of the cylinder because the Columb force is a resistance for flow and the vortexes behind the cylinder were grown up considerably. By setting the splitter plate behind the cylinder, the wake zone was affected more and the second corona wind play an important role. The vortexes that were in front of the cylinder, disappeared and we can observe three pairs of vortexes behind the cylinder. By increasing the gap distance (G: distance between the splitter plate and the cylinder), the size of these vortexes were changed as observed in fig 10a,b,c,d,e. Fig. 8. Velocity contours for cylinder-splitter, α=30 Fig. 9. Velocity contours for cylinder-splitter, α=90 (a) (b) (c) (d) Fig. 6. Velocity contours for cylinder-splitter (e) Fig. 10. Velocity contours for cylinder-splitter, α=150,(a) no splitter,(b) G=0, (c) G=0.5D,(d) G=D, (e) G=2D Fig 11 shows the drag coefficient Cd for different arrangements of wires and different gap distances. as observed, for α=0º, ±30º, ±90º, increasing of gap distance 216

6 is not important but for α=±150º,the presence of the splitter caused the increasing of Cd. [12] Hyun, K.T., Chun, C.H., (2003) The wake flow control behind a circular cylinder using ion wind, Experiments in Fluids, 35, pp [13] Chang, J.S., Brocilo, D., Urashima, K., Dekowskib, J., Podlinskib, J. (2006) On-set of EHD turbulence for cylinder in cross flow under corona discharges, Journal of Electrostatics, 64, pp [14] Jukes, T.N., Choi, K.S, (2009) Flow control around a circular cylinder using pulsed dielectric barrier discharge surface plasma, Physics of Fluids, 21, [15] N. A. Kaptsov, Elektricheskie Yavleniya v Gazakh i Vakuume, Moscow, OGIZ, [16] Reza-zadeh, S., Masumi H., Esmaeilzadeh E., (2010), Experimental study of heat transfer around cylinder in presence of electric field, JAST, 6(2),pp Fig. 11. Drag coefficient for different arrangments IV.CONCLUSION The compound method (passive and active) was applied to control hydrodynamic around a cylinder. The splitter plate, as a passive technique, and EHD actuators (wireplate), as an active technique, applied simultaneously. Two corona winds were recognized around the cylinder. By increasing α, the second corona wind got strong and affects the wake zone more. REFERENCES [1] Roshko, A. (1954) On the drag and shedding frequency of twodimensional bluff bodies, National Advisory Committee for Aeronautics, Technical Note 3169, pp [2] Ozono, S. (1999) Flow control of vortex shedding by a short splitter plate asymmetrically arranged downstream of a circular cylinder, Physics of Fluids, 11, pp [3] Ozono, S. (2000) Flow control of vortex shedding by asymmetrically arranged plates, Theoretical and Applied Mechanics. 49, pp [4] Hwang, J.Y., Yang, K.S., Sun, S.H., (2003) Reduction of flowinduced forces on circular cylinder using a detached splitter plate, Physics of Fluids, 15(8), pp [5] Hwang J.Y., Yang K.S., (2007) Drag reduction on a circular cylinder using dual detached splitter plates, Journal of Wind Engineering and Industrial Aerodynamics, 95, pp [6] Tiwari, S., Chakraborty, D., Biswas, G., Panigrahi, P.K. (2005) Numerical prediction of flow and heat transfer in a channel in the presence of a built-in circular tube with and without an integral wake splitter, International Journal of Heat and Mass Transfer, 48, pp [7] Shukla, S., Govardhan, R.N., Arakeri, J.H. (2009) Flow over a cylinder with a hinged-splitter plate, Journal of Fluids and Structures, 25, pp [8] Hauksbee, F., (1719) Physico-mechanical experiments on various subjects, London, pp: [9] Leger, L., Moreau, E., Artana, G., Touchard, G. (2001) Influence of a DC corona discharge on the airflow along an inclined flat plate, Journal of Electrostatics, 51/52, pp [10] Leger, L., Moreau, E., Gerard, G., Touchard, G. (2002) Effect of a DC Corona Electrical Discharge on the Airflow along a Flat Plate, IEEE Transactions on Industry Applications, 38, pp [11] Artana, G., Sosa, R., Moreau, E., Touchard, G. (2003) Control of the near-wake flow around a circular cylinder with electrohydrodynamic actuators, Experiment in Fluids, 36, pp