Patent Publication Number: US-9408287-B2

Title: System and method for controlling plasma induced flow

Description:
BACKGROUND 
     The disclosure relates generally to Electro-hydrodynamic (EHD) devices and more particularly, to a system and method for controlling plasma induced flow in an EHD device, for example plasma actuators. 
     An Electro-hydrodynamic (herein also referred as “EHD”) device is used to ionize a gaseous medium to generate plasma. Typically, a charged ion (herein also referred as “a charged particle”) is separated from the plasma to transfer momentum to a neutral gaseous medium. The neutral gaseous medium is then ejected out of the EHD device. In general, the performance of the EHD devices, such as ion wind, and Dielectric Barrier Discharge (herein also referred as “DBD”) plasma actuator, is dependent on a flow velocity of the neutral gaseous medium, generated by such devices. The typical DBD plasma actuator is one-dimensional shape or has planar configuration having two large parallel plates. Such DBD plasma actuators may produce the flow velocity not exceeding 8 m/s. One reason for DBD plasma actuators not generating a velocity greater than 8 m/s is due to space charge limitation. 
     The space charge limitation is based on availability of the charged particles and an electric field applied for producing the charged particles. The electric field and amount of the charged ions are implicitly limited by the gaseous medium breakdown electric field value. In the conventional plasma actuators, the charged particles between one or more flat electrode may distort the applied electric field, and do not let more new charged particles to enter the plasma, thus limiting the electric current. 
     Thus, there is a need for an improved plasma actuator for efficiently reducing the space charge limitation. 
     BRIEF DESCRIPTION 
     In accordance with one exemplary embodiment, a plasma actuator system is disclosed. The plasma actuator system includes a first electrode having a first slit formed in a first peripheral section of the first electrode. The first slit is configured for directing flow of a gaseous medium along a radial direction of the first electrode. Further, the plasma actuator system includes a second electrode which is coupled to the first electrode and disposed concentrically around the first electrode. Further, the second electrode has a second slit in a second peripheral section of the second electrode. The second slit is configured for directing flow of the gaseous medium along the radial direction of the second electrode. Further, the plasma actuator system includes a power source coupled to the first electrode and the second electrode for supplying electric power to the first electrode and the second electrode. 
     In accordance with another exemplary embodiment, a method is disclosed. The method includes supplying electric power to a first electrode and a second electrode. The second electrode is coupled to the first electrode and is disposed concentrically around the first electrode. Further, the method includes receiving a gaseous medium into the first electrode and directing the gaseous medium along a radial direction via a first slit of the first electrode. The method includes ionizing the gaseous medium between the first electrode and the second electrode, to generate plasma. Further, the method includes directing the gaseous medium along the radial direction via a second slit of the second electrode, by imparting momentum to the gaseous medium using the generated plasma. 
     In accordance with yet another embodiment, an apparatus is disclosed. The apparatus includes an airfoil device, and a plasma actuator system coupled to the airfoil device. Further, the plasma actuator system includes a first electrode having a first slit formed in a first peripheral section of the first electrode. The first slit is configured for directing flow of a gaseous medium along a radial direction of the first electrode. Further, the plasma actuator system includes a second electrode which is coupled to the first electrode and disposed concentrically around the first electrode. Further, the second electrode has a second slit in a second peripheral section of the second electrode. The second slit is configured for directing flow of the gaseous medium along the radial direction of the second electrode. Further, the plasma actuator system includes a power source coupled to the first electrode and the second electrode for supplying electric power to the first electrode and the second electrode. 
    
    
     
       DRAWINGS 
       These and other features, aspects, and advantages of the present invention will become better understood when the following detailed description is read with reference to the accompanying drawings in which like characters represent like parts throughout the drawings, wherein: 
         FIG. 1  illustrates an isometric view of a cylindrical shaped plasma actuator system in accordance with one exemplary embodiment; 
         FIG. 2  is a diagrammatical representation of a plasma actuator in accordance with one exemplary embodiment; 
         FIG. 3 a    illustrates a cylindrical shaped plasma actuator system having a plurality of sectors in accordance with one exemplary embodiment; 
         FIG. 3 b    is a sector of a cylindrical shaped plasma actuator system in accordance with an embodiment; 
         FIG. 3 c    is a multi-sector of a cylindrical shaped plasma actuator system in accordance with an exemplary embodiment; 
         FIG. 4  illustrates an isometric view of a spherical shaped plasma actuator system in accordance with another exemplary embodiment; 
         FIG. 5 a    is a sector of the spherical shaped plasma actuator system in accordance with an exemplary embodiment; 
         FIG. 5 b    is a multi-sector of a spherical shaped plasma actuator system in accordance with an exemplary embodiment; 
         FIG. 6  is a radar chart representing a circumferential distribution of plasma induced pressure in a plasma actuator, in accordance with one exemplary embodiment; and 
         FIG. 7  illustrates an aircraft having an airfoil with a plasma actuator system in accordance with one exemplary embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     While only certain features of the invention have been illustrated and described herein, many modifications and changes will occur to those skilled in the art. It is, therefore, to be understood that the appended claims are intended to cover all such modifications and changes as fall within the true spirit of the invention. 
     Embodiments herein disclose an improved Electro-Hydrodynamic (herein also referred as an “EHD”) device. The EHD device may include an electrode, a power source, a gas source, and the like. The EHD device may be used for ionizing air and move a charged ion cloud to transfer momentum to the air, to produce an air jet. In a specific embodiment, although a plasma actuator is disclosed to describe the inventive techniques, it should not be construed as a limitation of the present system and techniques. In one embodiment, the plasma actuator system includes a power source to supply power to a pair of electrodes of the plasma actuator for ionizing a gaseous medium. Further, the system includes a plurality of slits on a peripheral section of both the electrodes for radially ejecting the gaseous medium from the plasma actuator. 
     More specifically, certain embodiments of the present system disclose a first electrode having a first slit formed on a peripheral section of the first electrode. Further, the system includes a second electrode having a second slit formed on a peripheral section of the second electrode. The second electrode is disposed concentrically around the first electrode. The system includes a gas source coupled to the first electrode for supplying the gaseous medium into the first electrode and directing the gaseous medium along a radial direction via the first slit of the first electrode. Further, the system includes a power source coupled to the first and second electrode, to supply power, so as to ionize the gaseous medium and to generate plasma. The second electrode directs the gaseous medium along the radial direction via the second slit. 
       FIG. 1  is an isometric illustration of a cylindrical shaped plasma actuator system  100 . In the illustrated embodiment, the cylindrical shaped plasma actuator system  100  includes a first electrode  102  having a first slit  106 , a second electrode  104  having a second slit  108 , a first layer  110 , a pair of side walls  112 , a power source  114 , and a gas source  116 . 
     The first electrode  102  is coupled to the second electrode  104  via the pair of side walls  112 . The pair of side walls  112  may be disposed on either side respectively of the first electrode  102  and the second electrode  104 . In this embodiment, the first electrode  102  and the second electrode  104  have a cylindrical shape. The diameter of the first electrode  102  is smaller than the diameter of the second electrode  104 . The second electrode  104  is disposed concentrically around the first electrode  102 . The first electrode  102  includes a first peripheral section  118  having an inner peripheral surface  122  and an outer peripheral surface  124 . The first slit  106  is formed in the first peripheral section  118  of the first electrode  102 . In the illustrated embodiment, a plurality of first slits  106  is formed spaced apart in the first peripheral section  118  of the first electrode  102 . The space between the plurality of first slits  106  may vary depending on the application and design criteria. In the illustrated embodiment, the first slit  106  is formed along an axial direction  107  of the first peripheral section  118 . In certain embodiments, the first slit  106  may be formed along a different direction of the first peripheral section  118  of the first electrode  102 . The orientation of the first slit  106  on the first peripheral section  118  of the first electrode  102  may vary depending on the application and design criteria. In the illustrated embodiment, the first slit  106  may be formed in at least a portion of the first peripheral section  118 . In this example, the first slit  106  is of three-fourth length, along the axial direction  107  of the first peripheral section  118 . The length of the first slit  106  may also vary depending on the application and design criteria. The first slit  106  is designed to direct a gaseous medium  137  along a radial direction  136  from the first electrode  102 . 
     The second electrode  104  includes a second peripheral section  120  having an inner peripheral surface  126  and an outer peripheral surface  128 . The second slit  108  is formed in the second peripheral section  120  of the second electrode  104 . In certain embodiments, a plurality of second slits  108  are spaced apart and formed in the second peripheral section  120  of the second electrode  104 . The space between the pluralities of the second slits  108  may vary depending on the application and design criteria. In the illustrated embodiment, the second slit  108  is formed along an axial direction  109  of the second peripheral section  120 . In certain embodiments, the second slit  108  may be formed along a different direction of the second peripheral section  120  of the second electrode  104 . The orientation of the second slit  108  on the second peripheral section  120  of the second electrode  104  may vary depending on the application and design criteria. In the illustrated embodiment, the second slit  108  may be formed in at least a portion of the second peripheral section  120 . In this embodiment, the second slit  108  is of three-fourth length, along the axial direction  109  of the second peripheral section  120 . The length of the second slit  108  may also vary depending on the application and design criteria. The second slit  108  is designed to eject the gaseous medium  137  along a radial direction  138  from the second electrode  104 . Further, the first layer  110  is disposed on the inner peripheral surface  126  of the second electrode  104 . In one embodiment, the first layer  110  is a first dielectric layer. In certain other embodiments, the first layer  110  is a first partially conductive layer. Based on the application and the design criteria, either the first dielectric layer  110  or the first partially conductive layer  110  may be disposed on the inner peripheral surface  126  of the second electrode  104 . In one embodiment, the dielectric layer may include polyimide film (for example “kapton”), and polytetrafluoroethylene (for example “Teflon”). The partially conductive layer may include any semi conductive material such as silicon, gallium, and arsenide. 
     In the illustrated embodiment, the first slit  106  and the second slit  108  have a rectangular shape. In certain other embodiments, the first slit  106  and the second slit  108  may be of square shape, circular shape, or oval shape, depending on the application and design criteria. 
     The side wall  112  discussed herein includes an inner peripheral surface  130  and an outer peripheral surface  132 . A second layer  134  is disposed on the inner peripheral surface  130  of the side wall  112 . In one embodiment, the second layer  134  is a second dielectric layer. In certain other embodiments, the second layer  134  is a second partially conductive layer. Based on the application and the design criteria, either the second dielectric layer  134  or the second partially conductive layer  134  may be disposed on the inner peripheral surface  130  of the side wall  112 . In certain embodiments, the side wall  112  may include a plurality of slits (not represented in  FIG. 1 ). The plurality of slits may be used for both feeding the gaseous medium  137  inside the plasma actuator  100 , and ejecting the gaseous medium  137  from the plasma actuator  100 . 
     The power source  114  is coupled to the first electrode  102  and the second electrode  104  for supplying electric power to the electrodes. In the illustrated embodiment, the negative end of the power source  114  is coupled to the first electrode  102  and the positive end of the power source  114  is coupled to the second electrode  104 . The power source  114  may supply a direct current, or an alternating current, or a pulsed current. 
     The gas source  116  is coupled to the first electrode  102 . In the illustrated embodiment, the gas source  116  is coupled to one end of the first electrode  102 . In one embodiment, the gas source  116  may supply the gaseous medium  137  such as air or the like. In certain other embodiments, the gas source  116  may be a compressor or the like. 
       FIG. 2  is a diagrammatical representation of functioning of the plasma actuator  200  in accordance with one embodiment of the present invention. The functioning of the plasma actuator  200  is explained in conjunction with the cylindrical shaped plasma actuator system  100  of  FIG. 1 . 
     In one embodiment, the gas source is used to supply a gaseous medium  210  into the first electrode  102 . The gaseous medium  210  is directed through the first slit  106  formed in the first peripheral section of the first electrode  102  along a radial direction  218  of the first electrode  102 . The power source is coupled to the first electrode  102  and the second electrode  104 . The power source is used for supplying electric power, preferably a high voltage electric power, to the first electrode  102  and the second electrode  104 . The supplied electric power ionizes the gaseous medium  210  in the vicinity of the first electrode  102  to generate plasma  216 . The ionization of the gaseous medium  210  results in generation of a positive ion(s)  212 , an electron(s) (not shown in  FIG. 2 ), and a negative ion(s)  214 . In one embodiment, the positive ions  212 , the negative ions  214  and the electrons may be referred to as charged particles. During the ionization process, the electrons in the vicinity of the first electrode  102  accelerate towards the first electrode  102 , and will break-down neutral molecules of a gaseous medium  210  into negative ion  214  and positive ions  212 . As a result, a cloud of the charged particles is generated (also referred to as the plasma  216 ) around the first electrode  102 . Subsequently, the positive ions  212  are separated out of the plasma  216  by the applied electric field and are pushed (also referred as a “drift”) towards the second electrode  104 . The positive ions  212  of the charged particles  212  transfer the momentum to the gaseous medium  210 . The positive ions  212  recombine on the inner peripheral surface of the second electrode  104 . The gaseous medium  210 , which had gained momentum from the protons  212  is ejected out of the plasma actuator  100  along the radial direction  220  via the second slit  108  of the second electrode  104 . 
     The first dielectric layer is disposed on the inner peripheral surface of the second electrode  104 , to prevent arcing between the first electrode  102  and the second electrode  104 . In one embodiment, to mitigate the charge build-up (i.e. the positive ions  212 , the electrons and the negative ions  214 ) on the dielectric surface of the second electrode  104 , the polarity of the high voltage power source may be switched periodically. In some embodiments, a first partially conductive layer may be disposed on the inner peripheral surface of the second electrode  104 , which may allow the plasma actuator to function with dc voltage 
     The cylindrical shaped plasma actuator  100  is designed to over-come the space charge limitation. According to Gauss&#39;s law, a charge acts as a source for an electric field, and adding more charge leads to higher electric field induced by the charge. In such cases, the electric field may not exceed a breakdown value. The charged particles in the ionization region separates, modifying the electric field until the electric field value drops below a breakdown value: 
                     div   ⁢           ⁢     E   _       =     ρ     ɛ   0               (   1   )               
where,
 
             div   =       ∂     ∂   x       +     ∂     ∂   y       +     ∂     ∂   z               
is a divergence operator,
 
               ∂     ∂   x       +     ∂     ∂   y       +     ∂     ∂   z             
are partial derivatives with respect to x, y, and z, where, x, y, and z represent Cartesian coordinates, {right arrow over (E)} is a vector of the electric field, ρ is electric charge density, ∈ 0 =8.85×10 −12  Farad/meter is a universal constant referred to as vacuum permittivity.
 
     The charged particles drift velocity is considered to be linear to the supplied electric field, and the coefficient of proportionality μ is referred to as mobility of ions. In cylindrical coordinates the Gauss&#39;s law, the continuity equation for the charged particles, and an expression for a drift velocity can be as represented as mentioned below: 
                       E   x     +       ⅆ   E       ⅆ   x         =     en     ɛ   0               (   2   )               J   =     2   ⁢   π   ⁢           ⁢   xenv             (   3   )               v   =     μ   ⁢           ⁢   E             (   4   )               
where Equation (2) represents Poisson equation, Equation (3) represents Continuity equation, and Equation (4) represents Drift approximation, dE is change in the electric field over the distance dx, e is an electric charge per particle, ∈ 0 =8.85×10 −12  Farad/meter is a universal constant called vacuum permittivity, J is linear current density i.e. amount of the electric charge crossing lateral area of cylinder with a unit height per second, n number of charged particles per unit volume, E is a radial component of the electric field, x is a distance from the centerline of the cylinder, π is a mathematical constant that is the ratio of a circle&#39;s circumference to circle&#39;s diameter, and μ is the ion mobility.
 
     From the above equations (2), (3), and (4), a drift velocity V(x), electric field E(x), electric potential U(x), and charged particles concentration n(x), can be determined as mentioned below: 
                     v   ⁡     (   x   )       =       3   2     ⁢       μ   ⁢           ⁢   U     L     ⁢       (     x   L     )       1   /   2                 (   5   )                 E   ⁡     (   x   )       =       3   2     ⁢     U   L     ⁢       (     x   L     )       1   /   2                 (   6   )                 U   ⁡     (   x   )       =     -       U   ⁡     (     x   L     )         3   /   2                 (   7   )                 n   ⁡     (   x   )       =         3   ⁢     ɛ   0     ⁢   U       4   ⁢           ⁢     eL   2         ⁢       (     x   L     )         -   1     /   2                 (   8   )                     9   ⁢     μɛ   0       8     ⁢     U   2       =       L   3     ⁢   J             (   9   )               
where, U is an electric potential, μ is the ion mobility, L is a gap between the electrodes which is the radii difference, x is a distance from the centerline of the cylinder, ∈ 0 =8.85×10 −12  Farad/meter is a universal constant called vacuum permittivity, J is linear current density i.e. amount of the electric charge crossing lateral area of cylinder with a unit height per second, and e is an electric charge per particle, the equation (9) represents Volt-amp characteristic of the discharge, i.e. relationship between the applied voltage and transmitted current.
 
     From the Equations (5), (6), (7), (8) and (9), Force F or flow velocity created by the charged particles can be derived, as mentioned below: 
     
       
         
           
             
               
                 
                   F 
                   = 
                   
                     
                       
                         9 
                         ⁢ 
                         
                           ɛ 
                           0 
                         
                         ⁢ 
                         
                           U 
                           2 
                         
                       
                       
                         8 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           L 
                           2 
                         
                       
                     
                     = 
                     
                       
                         
                           ɛ 
                           0 
                         
                         ⁢ 
                         
                           E 
                           2 
                         
                       
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     From the Equation (10), it is ascertained that even for relatively small sized exemplary cylindrical actuators (for example, r=1 mm, and R=20 mm), the created flow velocity of the gaseous medium is six times higher relative to an actuator having a plane configuration, where “r” is the radius of the first electrode  102 , and “R” is the radius of the second electrode  104 . 
       FIG. 3 a    illustrates a cylindrical shaped plasma actuator system  300  having a plurality of sectors  320  in accordance with one embodiment of the present invention. In the illustrated embodiment of the present invention, the plasma actuator system  300  includes a first electrode  302 , a second electrode  304 , a first slit  306 , a second slit  308 , and a pair of side walls  310 . 
     The cylindrical shaped plasma actuator system  300  including the first electrode  302 , the second electrode  304  and the pair of side walls  310  (In  FIG. 3 , the other side wall among the pair of the side walls  310  is not illustrated) are divided to form the plurality of sectors  320 . The width of the sector  320  gradually increases from one end  312  towards the other end  314 . The cylindrical shaped plasma actuator system  300  includes a power source  316  coupled to the first electrode  302  and the second electrode  304  for supplying a high voltage electric power to the electrodes. 
       FIG. 3 b    illustrates the sector  320  of the cylindrical shaped plasma actuator system  300  in accordance with an embodiment of  FIG. 3 a   . The sector  320  includes a portion  322  of the first electrode  302 , a portion  324  of the second electrode  304 , and pair of side walls  330 , 331 . 
     In the illustrated embodiment, the sector  320  has one first slit  306  formed in the portion  322  of the first electrode  302  and one second slit  308  formed in the portion  324  of the second electrode  304 . In certain embodiments, a plurality of first slits  306  and second slits  308  may be formed on the portion  322  of the first electrode  302  and the portion  324  of the second electrode  304  respectively depending on the application and design criteria. In some embodiments, the sector  320  may have a varied cross sectional area along the length of the sector  320 . Such a design facilitates to reduce the viscous losses of the gaseous medium flowing along the radial direction  338  from the first electrode  302  to the second electrode  304 . In the illustrated embodiment, a first dielectric layer  332  is disposed on an inner peripheral surface of the portion  324  of the second electrode  304 . Similarly, a second dielectric layer  334  is disposed on an inner peripheral surface of the pair of side walls  330 ,  331 . The second dielectric layer  334  is disposed on both the pair of side walls  330 ,  331 . The width of the sector  320  gradually increases from an end  321  towards the other end  323 . In the illustrated embodiment, the sector  320  includes a power source  336  coupled to the portion  322  of the first electrode  302  and the portion  324  of the second electrode  304  for supplying a high voltage electric power. In certain embodiments, the sector  320  may not be coupled to a separate power source  336 . In the illustrated embodiment, a gaseous medium is directed along a radial direction  325  through the first slit  306 . The ionization of gaseous medium leads to the formation of a plasma  329 , and the gaseous medium is ejected from the sector  320  of the cylindrical shaped plasma actuator  300 , through the second slit  308  along a radial direction  327 . 
       FIG. 3 c    is a diagrammatical representation of a multi-sector  340  of a cylindrical shaped plasma actuator system in accordance with an embodiment of the present invention. Such an actuator system may include a plurality of such multi-sectors  340 . The illustrated multi-sector  340  includes a first electrode portion  342 , a plurality of second electrode portions  343 ,  344 ,  345 , and a pair of side walls  350 ,  352  on either side respectively of the multi sector  340 . 
     In the illustrated embodiment, the multi-sector  340  has four first slits  307  formed in the first electrode portion  342 , four second slits  309  formed in the second electrode portion  343 ,  344 , and six second slits  309  formed in the second electrode portion  345 . In the illustrated embodiment, the multi-sector  340  has three sub-sectors  353 ,  354 ,  356 . The three sub-sectors  353 ,  354 ,  356  have different cross sectional areas. In the illustrated embodiment, the cross sectional area varies along the length of the each sector  340 . The sub-sectors  353 ,  354 ,  356  include the second electrode portions  343 ,  344 ,  345  respectively and also the pair of side walls  350 ,  352  respectively. A first dielectric layer  358  is disposed on an inner peripheral surface of the second electrode portions  343 ,  344 ,  345 . Similarly, a second dielectric layer  360  is disposed on an inner peripheral surface of the pair of side walls  350 ,  352 . Such a design facilitates to further reduce the viscosity of a gaseous medium flowing along the radial direction  364  from the first electrode  302  to the second electrode  304  respectively. In the illustrated embodiment, a power source  362  coupled to the first electrode portion  342  and the second electrode portions  343 ,  344 ,  345  for supplying a high voltage electric power. The power source  362  is used to supply power at different voltages across the sub-sectors  353 ,  354 ,  356 . In one example, the power source  362  may supply a higher voltage to the sub-sector  353 , a medium voltage to the sub-sector  354  and a low voltage to the sub-sector  356 . In certain other embodiments, the sub-sectors  353 ,  354 ,  356  of the multi-sector  340  may not be coupled to a separate power source. In this embodiment, the plurality of first slits  307  formed on the first electrode portion  342  directs the gaseous medium along a radial direction  361 . The power source  362  ionizes the gaseous medium leading to the formation of plasma  363 . A charged particle separated from the plasma  363  imparts momentum to the gaseous medium. The gaseous medium is ejected from through the second slits  309  along a radial direction  365 . 
       FIG. 4  illustrates an isometric view of a spherical shaped plasma actuator system  400  in accordance with another embodiment of the present invention. In the illustrated embodiment, the spherical shaped plasma actuator system  400  includes a first electrode  402 , a second electrode  404 , a power source  414 , and a gas source  416 . 
     The first electrode  402  is disposed around the second electrode  404 . The first electrode  402  is coupled to the second electrode  404  via a suitable connecting device. In the illustrated embodiment, the first electrode  402  is coupled to the second electrode  404  via the gas source  416 . Any possible variation of connecting device, for coupling the first electrode  402  with the second electrode  404  may be considered. In this embodiment, the first electrode  402  and the second electrode  404  have a spherical shape. The first electrode  402  includes a first peripheral section  418  having an inner peripheral surface  422  and an outer peripheral surface  424 . In the illustrated embodiment, a plurality of first slits  406  is spaced apart in the first peripheral section  418  of the first electrode  402 . The space between the plurality of the first slits  406  may vary depending on the application and design criteria. The orientation of the first slit  406  in the first peripheral section  418  of the first electrode  402  may vary depending on the application and design criteria. In the illustrated embodiment, the first slit  406  is formed in at least a portion of the first peripheral section  418 . The first slit  406  is designed to direct a gaseous medium from the gas source  416 , along a radial direction  436 . 
     The second electrode  404  includes a second peripheral section  420  having an inner peripheral surface  426  and an outer peripheral surface  428 . In the illustrated embodiment, a plurality of second slits  408  is spaced apart in the second peripheral section  420  of the second electrode  404 . The space between the plurality of second slits  408  may vary depending on the application and design criteria. The orientation of the second slit  408  in the second peripheral section  420  of the second electrode  404  may vary depending on the application and design criteria. In the illustrated embodiment, the plurality of second slits  408  may be formed in at least a portion of the second peripheral section  420 . The shape of the second slit  408  may also vary depending on the application and design criteria. Further, a first layer  410  disposed on the inner peripheral surface  426  of the second electrode  404 . In one embodiment, the first layer  410  is a first dielectric layer. In certain other embodiments, the first layer  410  is a partially conductive layer. Based on the application and the design criteria, either the first dielectric layer  410  or the first partially conductive layer  410  is disposed on the inner peripheral surface  426  of the second electrode  404 . The second slit  408  is designed to eject the gaseous medium along a radial direction  438  from the second electrode  404 . The shape of the first slit  406 , the second slit  408  may vary depending on the application and design criteria. In the illustrated embodiment, the first slit  406  and the second slit  408  have a circular shape. In certain other embodiments, the first slit  406  and the second slit may be of square shape, rectangular shape, or oval shape, depending on the application and design criteria. 
     The power source  414  is coupled to the first electrode  402  and the second electrode  404  for supplying electric power to the electrodes  402 ,  404 . In the illustrated embodiment, the positive end of the power source  414  is coupled to the first electrode  402  and the negative end of the power source  414  is coupled to the second electrode  404 . 
     In this embodiment, the gas source  416  couples the first electrode  402  to the second electrode  404 . Additionally, the gas source  416  feeds the gaseous medium into the first electrode  402 . In the illustrated embodiment, one end  415  of the gas source  416  (i.e. pipe) is coupled to the first electrode  402  and the other end  417  of the gas source is opened to the atmosphere. A second layer  434  is disposed on an outer peripheral surface  432  along a longitudinal direction  435  of the gas source  416 . In one embodiment, the second layer  434  is a second dielectric layer. In certain other embodiments, the second layer  434  is a second partially conductive layer. Based on the application and the design criteria, either the second dielectric layer  434  or the second partially conductive layer  434  may be disposed on the outer peripheral surface  432  of the gas source  416 . The flow velocity created by the spherical shaped plasma actuator  400  is up to three times higher compared to an actuator having a plane configuration. 
       FIG. 5 a    is a sector  520  of the spherical shaped plasma actuator system  400  in accordance with an embodiment of the present invention. The sector  520  is explained in conjunction with the spherical plasma actuator system  400  of  FIG. 4 . The spherical shaped plasma actuator system  400  having the first electrode  402 , the second electrode  404 , and the connecting device  416  is divided to form a plurality of sectors  520 . In the illustrated embodiment, the sector  520  includes a portion  522  of the first electrode  402 , a portion  524  of the second electrode  404 , and pair of side walls  530 , 531 . 
     In the illustrated embodiment, the sector  520  has one first slit  406  and one second slit  408 . In certain other embodiments, the plurality of first slits  406  and the second slits  408  may be formed on the portion  522  of first electrode  402  and the portion  524  of second electrode  404  respectively depending on the application and design criteria. The sector  520  has varied cross sectional area along the length of the sector  520 . The cross sectional area of the sector  520  facilitates to reduce the viscosity of the gaseous medium flowing along a radial direction  510  from the first electrode  402  to the second electrode  404 . A first dielectric layer  532  is disposed on an inner peripheral surface of the second electrode portion  524 . Similarly, a second dielectric layer  534  is disposed on an inner peripheral surface of the pair of side walls  530 ,  531 . The width of the sector  520  gradually increases from an end  540  towards the other end  538 . In the illustrated embodiment, a power source  536  is coupled to the portion  522  of the first electrode  502  and the portion  524  of the second electrode  504  for supplying a high voltage electric power. In the illustrated embodiment, a positive end  537  of the power source  536  is coupled to the second electrode portion  524  and a negative end  535  of the power source  536  is coupled to the first electrode portion  522 . In the illustrated embodiment, a gaseous medium is directed along a radial direction  542  through the first slit  406 . The ionization of gaseous medium leads to the formation of plasma  544 , and the gaseous medium is ejected from the sector  520  of the spherical shaped plasma actuator  400 , through the second slit  408  along a radial direction  546 . 
       FIG. 5 b    is a multi-sector  550  of a spherical shaped plasma actuator system in accordance with an embodiment of the present invention. The multi-sector  550  is explained in conjunction with the spherical plasma actuator system  400  of  FIG. 4 . The multi-sector  550  includes a first electrode portion  552 , a plurality of second electrode portions  553 ,  554 , and pair of side walls  560 ,  562  on either side of the multi-sector  550 . 
     In the illustrated embodiment, the multi-sector  550  has one first slit  507  formed on the first electrode portion  552 , and one second slit  509  formed in the second electrode portion  553 ,  554 . In certain other embodiments, a plurality of first slits  507  and a plurality of second slits  509  may be formed in the first electrode portion  552  and the second electrode portions  553 ,  554  respectively depending on the application and design criteria. In the illustrated embodiment, the multi-sector  550  has two sub-sectors  564 ,  566 . The two sub-sectors  564 ,  566  have different cross sectional areas. In another embodiment, the cross sectional areas of the two sub-sectors  564 ,  566  may be similar. The cross sectional area varies along the length of the each of the sub-sectors  564 ,  566 . The sub-sectors  564 ,  566  include the second electrode portions  553 ,  554  respectively. The cross sectional area of the multi-sector  550  facilitates to reduce the viscosity of the gaseous medium flowing along a radial direction  576  from the first electrode  402  to the second electrode  404 . A first dielectric layer  568  is disposed on an inner peripheral surface of the second electrode portions  553 ,  554 . Similarly, a second dielectric layer  570  is disposed on an inner peripheral surface of the side walls  560 ,  562 . In the illustrated embodiment, a power source  572  coupled to the first electrode portion  552  and the second electrode portions  553 ,  554  for supplying a high voltage electric power. The power source  572  is used to supply power at different voltages across the sub-sectors  564 ,  566 . In one embodiment, the power source  572  may supply a higher voltage to the sub-sector  564 , and a medium voltage to the sub-sector  566 . In this example, the plurality of first slits  507  directs the gaseous medium along a radial direction  574 . The power source  572  ionizes the gaseous medium leading to the formation of plasma  575 . A charged particle separated from the plasma  575  imparts momentum to the gaseous medium. The gaseous medium is ejected through the second slit  509  along a radial direction  578 . 
       FIG. 6  is a radar chart  600  representing a circumferential distribution of plasma induced pressure in a plasma actuator in accordance with an exemplary embodiment of the present invention. In one embodiment, a plurality of vectors  602 ,  604 ,  606 ,  608 ,  610 ,  612 ,  614 ,  616  represent a plurality of slits formed on a second electrode  618  of an exemplary plasma actuator  619 . A plurality of curves  620 ,  622 ,  624 ,  626 ,  628 ,  630 ,  632  are indicative of pressure of a gaseous medium ejected through the plurality of slits  602 ,  604 ,  606 ,  608 ,  610 ,  612 ,  614 ,  616  of the plasma actuator  619 . In the illustrated embodiment, the pressure of the gaseous medium ejected through the eight slits is represented by units of 10 Pascal up to 70 Pascal. A conventional planar configuration of a plasma actuator ejects the gaseous medium at a pressure of 40 Pascal as indicated by the curve  634 . In one embodiment, the results illustrated in the radar chat  600  are derived through one or more experiments using the exemplary plasma actuator  619 . The exemplary plasma actuator  619  may be cylindrical shaped or spherical shaped. The curve  636  is representative of the pressure of the gaseous medium attained using the cylindrical shaped plasma actuator  619 . Similarly, the curve  638  is representative of the pressure attained using a spherical shaped plasma actuator. From the radar chart, it is clearly evident that the cylindrical shaped plasma actuator  619  and the spherical shaped plasma actuator over comes the space charge limitation of the conventional one-dimensional plasma actuator. 
       FIG. 7  illustrates an aircraft  700  having a plasma actuator system  708  in accordance with one exemplary embodiment. The aircraft includes a nose  702 , a pair of wings  706  (the other wing among the pair of wings  706  is not shown), and a plurality of exemplary plasma actuators  708 . 
     In the illustrated embodiment, the plurality of plasma actuators  708  is disposed at a trailing end  710  of the wing  706  (herein also referred as an “airfoil”). In one embodiment, the plasma actuator  708  includes a first electrode, a second electrode, and a power source. The first electrode and the second electrode have at least one of a cylindrical shape, or a spherical shape, or combinations thereof. The first electrode may include a plurality of first slits and the second electrode may include a plurality of second slits. The first electrode of the plasma actuator  708  may receive a gaseous medium via the plurality of first slits. The power source may supply high voltage power to ionize the gaseous medium around the first electrode and generate plasma. The gaseous medium may then be ejected from the plasma actuator through the plurality of second slits along a radial direction. The aircraft  700  during flight may face the wind flowing along a longitudinal direction indicated by the reference numeral  712 . At least one among the plurality of the plasma actuator  708  disposed on the trailing end  710  of the airfoil  706  reduces the drag, by ejecting the gaseous medium along the horizontal direction  714  of the aircraft  700 . In another embodiment, at least one among the plurality of the plasma actuator  708  ejects the gaseous medium along a vertical direction  716  of the aircraft  700  i.e. along a plane  704  perpendicular to the airfoil  706 . 
     An exemplary EHD device having cylindrical and spherical shaped electrodes has advantages associated with overcoming the space charge limitation. Conventional ion wind and DBD plasma actuators have one dimensional geometries or planar configuration geometries, and thus subjected to the space charge limitation. The exemplary electrodes having cylindrical or spherical configuration overcomes the space charge limitation and generates higher flow velocities. The potential applications of the exemplary cylindrical or spherical shaped plasma actuators may include various flow control application, such as separation control, drag reduction, noise control, lift destruction, and the like. The drag reduction application may be used on airplane wings, wind and gas turbines, and the like. Additionally, the exemplary actuators may be used as a plasma thruster to propel small UAVs or be utilized in hair driers and fans to move the air.