Indian J.Sci.Res.1(2) : 803-814, 2014 ISSN : 0976-2876 (Print) ISSN : 2250-0138(Online) MODELING OF PLASMA ACTUATOR AND ITS EFFECT ON FLOW FIELD AROUND RECTANGULAR CYLINDER SAEED KAVOUSFAR a, HOSSEIN MAHDAVY-MOGHADDAM 1b, ESMAEIL ESMAEILZADEH c, a Department of Aerospace Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran Email: S.kavousfar@Gmail.com b Department of Aerospace Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran Email: Mahdavy@srbiau.ac.ir c Heat & Fluid Research Laboratory, Department of Mechanical Engineering, Tabriz University, Tabriz, Iran Email: Esmzadeh@tabrizu.ac.ir ABSTRACT Abstract-One the modern and useful method for controlling active flow field, is using of dielectric barrier discharge (DBD) plasma actuator. In this paper air flow field around a rectangular cylinder is simulated and effect of DBD plasma actuator on this flow field is analysed. One of the important phenomena in this field is separation of flow in leading edge of particular geometry. This separation is like a bubble and it s named bubble separation. In this research first plasma actuator is modelled and compared with similar consequences. So far model of plasma actuator is added on flow field around rectangular cylinder and its affection of bubble separation domain is studied. Results are shown as both location of electrodes and the intensity of electric field has huge affection on suction fluid flow in the space of bubble separation that in the consequences, it has changes on structure and dimension of bubble separation. KEYWORDS: Bubble Separation, Fluid Flow, Plasma Actuator, Electric Field Fluid flow control around the rigid body especially controlling of boundary layer separation is an important issue, which considered in researches of engineering field and technology and different studies about this issue has done. Flow separation from solid surfaces occurs in a variety of technical applications, such as expanding flow channels (diffusers) or car and train tails, in turbomachinery, on airfoils at high angles of attack etc. This inevitably leads to a significant decrease in efficiency (Brunn and Nitsche, 2006). Separation is almost always associated with losses of some kind, including loss of lift, drag increase, pressure recovery losses, etc. Consequently, engineers have been preoccupied, for almost a century, with altering its location or avoiding it entirely (Greenblatt and Wygnanski, 2000). In many practical situations, flow separation is triggered by a sharp edge. In the context of bluff body, edges can be advantageously smoothed to improve the aerodynamic characteristics of the body while better controlling the production of noise or vibrations. Despite the practical knowledge of these types of influence (especially in the car industry), there is no clear understanding of the physical mechanisms involved in the change of the resulting flow separation depending on the shape of the edge (Lamballais et al., 2010). Separation phenomena in the different parts of a geometry may accrue. The aim of research is controlling of separation on leading edge of blunt body which it is named bubble separation. In this method by using of high voltage electric field on the airflow field, causes the ionization of air and forming of plasma. This method of plasma formation is called dielectric barrier discharge (DBD). Friction of plasma with fluid causes the transformation of momentum to fluid and effects on separation phenomena. Primary application of plasma actuator for controlling of flow by Kossinov et al. (1990) for setup Tollmien schilichting wave mods on boundary layer an a surface. As part of a fundamental study on plasma actuators of this geometry, Post (2004) documented the flow induced by a single actuator in still air using both Particle Image Velocimetry (PIV) and Pitot probes. Orlov (2006) investigated the effects of voltage and ac frequency on the extent and propagation velocity of the discharge. 2D numerical simulation on flat plate by Jayaraman and Shyy (2008) and Matéo-Vélez et al. (2006) has accomplished and affection of plasma actuator on flow field parameters are studied. In this paper application of plasma actuator in low speed aerodynamics with Reynolds number in the order 10 4 up to 10 5 is studied. The main results can be pointed to modify the boundary layer velocity profile. Reynolds-averaged (rank 10 5 ), the flow field around a symmetric airfoil with the plasma actuator by Sosa et al. (2007) has been studied experimentally. DBD plasma actuator has a simple structure. This type of actuator is composed of two electrodes, one in the air and the other is covered with an insulating material. The sample configuration is shown in Figure 1. The electrodes are supplied with an alternating voltage is sufficiently high values of voltage and causes the air around the covered electrode is ionized. In a classical description, the air ionized "plasma" is called that because these methods are named as plasma actuators. 1 Corresponding author
Figure 1. The structure and arrangement of DBD plasma actuatoor electrodes (Jayaraman and Shyy, 2008) The problem studied in this paper, is the DBD plasma actuator simulation and use of this type of actuator to control the bubble separation on the front edge of a rectangular cylinder (Figure 2). In This type of actuator air flow field under high voltage electrical field located, resulting in, near the electrodes the air is ionized; the ionized air is called plasma. Contact with plasma with fluid causes momentum transfer to the fluid and generating body force. This body force can be used to change the structure of the flow separation phenomenon. Furthermore the plasma actuator modeling and simulation results are presented. The effect of this actuator on the flow around a rectangular cylinder with a simulation of the flow field is shown. Figure 2. The overall structure of the bubble separation around a rectangular cylinder MODELING OF PLASMA ACTUATORS One of the first works about one-dimensional modeling of load discharge dynamic with dielectric barrier was created by Massine et al. (1998). This model is based on the numerical solution of the momentum and continuity equations for electron and ion transport coupled with Poisson's equation. As the discharge is common at high pressure, electrons and ions equilibrium with the electric field is assumed. When applying a high voltage to the two electrodes separated by an insulating layer, air between the electrodes ionized and the plasma begins to take shape. The result of this plasma formation is Body Force, which is applied locally on the flow field. The plasma is an ionized quasi-neutral gas. In the general case, the system can be represented by a set of four Maxwell's equations given by 804 Indian J.Sci.Res.1(2) : 803-814, 2014
D H = J+ t B E = (1) t. D= ρ c. B = 0 Where H is the magnetic field strength, B is the magnetic induction, E is the electric field strength, D is the electric induction, J is the electric current, and ρ c is the charge density. It can be assumed that the charges in the plasma have sufficient amount of time to redistribute themselves in the region and the whole system is quasi-steady. In this case, the electric current, J, the magnetic field, H, and the magnetic induction, B, are all equal to zero. In addition the time derivatives of the electric induction, D, and the magnetic t induction, B are equal to zero. As a result (Orlov, 2006), the t amount of volume is equal to: f b = ρce = ρc ( φ) (2) Body force derived from this method the Suzen and Huang (2006) were used, the same model is used in this paper. Body force equation (2) should directly consider into the equations of motion. V = 0 ui u + u i j t xj 2 P u = + ν i + fb xj xj xi As a result, body force depends on the electric field and is independent of the flow field. In other words, the electric field in this problem unilaterally affects the flow field. To ensure proper use of the above model, the plasma actuator on a flat plate in still air and the simulation results are compared with available references. Geometric Model To compare the results of the present analysis with the references in this field, the geometry of the electrodes and the solution field is matched with the references. Geometry used in this analysis consists of an insulator, an upper electrode (exposed to air stream) and a bottom electrode (which is located inside the insulation) is shown in Figure 3. (3) Figure 3. The structure and geometry of the electrodes Flow Field Meshing For meshing of Solutions field, structural grid is being used. Due to high gradients near the electrodes, the cell density in these areas is higher than in the rest of the field. An example of this mesh, with magnification near the electrodes is shown in Figure 4. Indian J.Sci.Res.1(2) : 803-814, 2014 805
Figure 4. Meshing of the resolution field near electrodes Survey Results In this section, the results of modeling the electric potential field and its effects on the still air around electrodes, is compared with the results of Suzen - Huang models. Distribution of electric potential φ, body force (f b ), load density ρ and velocity fields are important parameters of comparison. In Figures 5, 6, 7 and 8, respectively, nondimensional electric potential (φ/φ max ) contours, body force vector, non-dimensional density of load (ρ c /ρ c max ) the streamlines and contours of the present analysis are compared with the results in the references. This comparison shows that the plasma actuator modeling with Suzen-Huang consistent and reliable simulation is performed. Therefore, this method of plasma actuator added to the flow field and its effect was investigated. One important result of this part is the most influential on the top edge of the plasma actuator is a basic covered electrode, because body force from actuator of this region has the highest value. 806 Indian J.Sci.Res.1(2) : 803-814, 2014
Figure 5. The contours of the non-dimensional electric potential (φ/φ max ) around the electrodes, A: Suzen and Huang (2006), B: Bouchmal (2011), C: The present analysis Figure 6. A body force vector (f b ) field, A: Bouchmal (2011), B: present analysis Indian J.Sci.Res.1(2) : 803-814, 2014 807
Figure 7. The non-dimensional load-density (ρ c /ρ c max ) contours around the electrodes, A: Suzen and Huang (2006), B: Bouchmal (2011), C: The present analysis Figure 8. A flow field streamlines, A:Suzen and Huang (2006), B: Bouchmal (2011), C: Experimental results (Jacob et al., 2005), D: Present analysis 808 Indian J.Sci.Res.1(2) : 803-814, 2014
Velocity Profiles Obtained By The Plasma Actuator After The verification of used technique in the simulation of plasma actuator, in this section the effect of plasma actuator on the velocity profile of the flow field on the flat plate is investigated. Figure 9 shows the velocity profile at the position x= 2. 5mm for different values of strength of electric and speed fields. The results for the flow velocity of zero, 1, 2 and 5 meters per second are done. Figure 9. The effect of plasma actuator on the flow field velocity profile for different values of strength of electric and velocity field According to the results in Figure 9 plasma actuator arrangement shown in Figure 1, leading to energy transfer and increased momentum of the flow field. So near the wall it has velocity increased and boundary layer structure changes. By Increase of electric field strength, performance of plasma actuator increased and it has a significant effect on the velocity profile. However, with increasing velocity field strength, decreases plasma actuator effect, as in the free-stream velocity u = 5m / s increasing the electric potential has not so much influence on velocity profile. determined. Now as an application, plasma actuator added to flow field around rectangular cylinder and its effect on the structure of this field is studied. The Geometric Model And Grid Generation Geometry of the desired object Selected as a rectangular cylinder that air flows around it in the way of 2D symmetric. The dimensions of an object are H = 50mm and L= 200mm. Figure 10 shows the geometric model with the electrodes position and zooming grid of field. FLOW FIELD AROUND A RECTANGULAR CYLINDER In the last section of the DBD plasma actuator modeling and verification of work in isolation was also Indian J.Sci.Res.1(2) : 803-814, 2014 809
In this analysis we have used the structural square grid. Due to high gradients near the electrodes, the cell density in these areas is higher than in the rest of the field. Because of the electric field s interaction with flow field and formation of strong gradients in the solution domain, the number of grid cells required for this field s type is large in quantity and the analysis of it needs more time. Due to time saving and the symmetry of the flow field, half of the field is analyzed. It should be noted that the presence of the electric field in both fluid and solid space, the part of solid object around the electrodes is meshed. ANALYSIS OF THE FLOW FIELD AND ITS RESULTS Figure 10. Geometric models with grid of solution field zooming an electric field analyzed and different values for these two fields are used. The free stream velocity of both 5 and 10 meters per second and the electric field voltage of 15, 25 and 30 kv are used. Flow Field Without Plasma Actuator The flow field around the body without the presence of an electric field analyzed and the result is displayed to the separation bubble formed, and its size is specified. This analysis is performed for a free-stream velocity equal to u = 5m / s. Streamlines of the field are shown in Figure 11. According to the fluid flow after a collision with an object due to the pressure gradient against the sharp edge of the object is formed on the surface of separation bubbles isolated. Reattachment point of flow on the body surface (bubble To evaluate electric field effects on the flow field around a rectangular cylinder with and without the presence of 810 Indian J.Sci.Res.1(2) : 803-814, 2014
separation length) located at position x R = 470mm and the thickness of the bubble separation is equal to h R = 49mm. Figure 11. Streamlines for u = 5m / s and without the electric field The Effect Of Plasma Actuators However, to the flow field, an electric field is applied. First, the dimensions and spacing of the electrodes (based on Figure 10) is chosen as it follows: Object's distance from the edge of the exposed electrode a= 5mm Length of the exposed electrode b= 10 mm The longitudinal distance between the electrodes c= 2mm Length the insulated electrode d = 50 mm The effect of electric field on the flow field is taken by producing a body force due to electrical gradient. By using of distribution of body force in analytical field, could specify its maximum values. In Figure 12, contours and body force vectors by applying the electric field intensity, φ max = 15 kv, is shown. Figure 12. Contours and body force vectors near the electrodes by applying electric field φ max = 15 kv We can see that the area around the electrodes, have relatively large amounts body force and far from the electrodes it limits to zero. Therefor the direction of body force vectors is from exposed electrode to insulated electrode, which the result would be the suction from left to the right (suction into the bubble). To determine the precise location of maximum body force, distribution of this force along the surface of the object is shown in Figure 13. Indian J.Sci.Res.1(2) : 803-814, 2014 811
Figure 13. Distribution of body force on body surface for φ max = 15 kv Maximum value of body force is created around the position x= 17. 6mm. This position is located on the primary points of insulated electrode, which it starts from to x= 17 mm x= 67mm, so in resulting for more affection of plasma actuator on bubble separation domain. It is better to apply maximum body force to start points of bubble separation. In the other word, insulated electrode should be closer to the leading edge of geometry. The streamlines of field analysis shows (Figure 14) reattachment point of flow on the body surface located at position x R = 450mm and the thickness of the bubble separation is equal to h R = 45mm. So electric field intensity of 15kV caused decrement of bubble separation dimensions. Figure 14. Streamlines for u = 5m / s and φ max = 15 kv Affection Of The Electrodes Position And Electric Field Intensity In the last section it was observed that maximum body force is created on the primary edge of insulated electrode. In the other hand the domain of formed plasma depends on length of insulated electrode. Therefor optimization of results and achieving of expected target, it is better to choose short length of exposed electrode so that position of maximum body force gets closer to the start point of separation. Therefore, the parameters related to the size and spacing of the electrodes (based on Figure 10) is amended as follows: Object's distance from the edge of the exposed electrode a= 0. 1mm Length of the exposed electrode b= 0. 5 mm The longitudinal distance between the electrodes c= 0. 1 mm 812 Indian J.Sci.Res.1(2) : 803-814, 2014
Length the insulated electrode d = 50 mm Also in this section electric field intensity is increased too and it equals to 25kV and 30kV. Streamlines obtained from specified field analysis is shown ordinary in figure 15 and 16. For φ max = 25 kv reattachment point of flow on the body surface located at position thickness of the bubble separation is equal to x R = 223mm and the h R = 9. 6mm. Thus new conditions (position and intensity of the electrodes) leading to a further reduction of the bubble separation dimensions. With increasing electric field intensity φ max = 30 kv bubble separation dimensions decreases again. According to the figure 16 it is observed that dimensions of the bubble change to x R = 50mm and h R = 3. 5mm. Figure 15. Streamlines for u = 5m / s and φ max = 25 kv with new position of the electrodes Figure 16. Streamlines for u = 5m / s and φ max = 30 kv with new position of the electrodes Increasing Of Free Stream Velocity However flow field studied for different value of free stream velocity and same as previous situation in position of electrodes and body dimensions. Flow field with velocity u = 10m / s is placed in the electric field with intensity φ max = 30kV and φ max = 35 kv. In both cases where the reattachment point of flow on surface is placed at position x R = 380mm and x R = 350mm. Given these results, it is observed with increasing Reynolds number flow, the intensity of separation and bubble separation domain is large and applied electric field has not noticeably changed. CONCLUSION In this paper the flow field around a blunt body with a sharp edge and the effect of the electric field that acts as a plasma actuator was examined. According to results which they were electric field through the plasma formation, to enter the body force to fluid molecules and it accelerates air fluid Indian J.Sci.Res.1(2) : 803-814, 2014 813
flow. Thus, maximum value of body force is created on the top of primary edge of second electrode (insulated electrode). For further accelerating the flow and follow it to shrink or even complete loss of separation bubble, need a second electrode was placed near the edge of body. Besides increasing the intensity of the electric field has a significant impact on reducing the bubble separation domains. In order to completely imitation of bubble separation, it needs to apply strong electric field that its results would be much energy consumption; it seems that using of composed method is useful. Sosa, R., Artana, G., & Moreau, E. (2007). Stall control at high angle of attack with plasma sheet actuators. Experiments in Fluids, 42, 143-167. Suzen, Y.B., & Huang, P.G. (2006). Simulations of Flow Separation Control using Plasma Actuators. 44th AIAA Aerospace Sciences Meeting and Exhibit. REFERENCES Bouchmal, A. (2011). Modeling of Dielectric-Barrier Discharge Actuator. Master of Science Thesis, Delft University of Technology. Brunn, A., & Nitsche, W. (2006). Active control of turbulent separated flows over slanted surfaces. International Journal of Heat and Fluid Flow, 27, 748 755. Greenblatt, D., & Wygnanski, J. (2000). The control of flow separation by periodic excitation. Progress in Aerospace Sciences, 36, 487-545. Jacob, J.D., Ramakumar, K., Anthony, R., & Rivir, R.B. (2005). Control of laminar and turbulent shear fows using plasma actuators. Fourth International Symposium on Turbulence and Shear Flow Phenomena. Jayaraman, B., & Shyy, W. (2008). Modeling of dielectric barrier discharge-induced fluid dynamics and heat transfer. Progress in Aerospace Sciences, 44, 139-191. Kosinov, A., Maslov, A., & Shevelkov, S. (1990). Experiments on the stability of supersonic laminar boundary layers. J. Fluid Mech., 219, 621-633. Lamballais, E., Silvestrini, J., & Laizet, S. (2010). Direct numerical simulation of flow separation behind a rounded leading edge: Study of curvature effects. International Journal of Heat and Fluid Flow, 31, 295 306. Massines, F., Rabehi, A., Decomps, P., BenGadri, R., Segur, P., & Mayoux, C. (1998). Experimental and theoretical study of a glow discharge at atmosperic pressure controlled by dielectric barrier. Journal of Applied Physics, 83, 2950-2957. Matéo-Vélez, J.C., Rogier, F., Thivet, F., & Degond, P. (2006). Numerical Modeling of Plasma - Flow Interaction. ICCS 2006, Part II, LNCS 3992, 1 9. Orlov, D.M. (2006). Modelling and Simulation of Single Dielectric Barrier Discharge Plasma Actuators, PhD thesis, University of Notre Dame. Post, M.L. (2004). Plasma actuators for separation control on stationary and unstationary airfoils, PhD thesis, University of Notre Dame. 814 Indian J.Sci.Res.1(2) : 803-814, 2014