**1. Introduction**

The interest in flow control in the fluid dynamic domain has showed a quick growth in last 15 years [1] due to rapid development of sensors and actuators technologies. Even though passive control techniques are still attractive since they do not require an energy input, active control

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strategies have recently received more attention since they can be used in a selective way and canbeoperatedonlywhenitiseffectivelyrequested.Amongdifferentactivetechniques,plasma aerodynamic actuators are attractive because they present high dynamic responses due to the absence of moving parts, are characterized by low weight, are easy to build, are backward compatible with existing aerodynamic surfaces, and generate negligible aerodynamics interferences when they are switched off. When actuated, they can significantly modify the status of the boundary layer developing on the body surfaces. For this reason, they have been extensively studied for aeronautical applications to prevent flow separation enhancing lift and reducingdrag [2, 3].More recently,theyhave beenusedalso to controlfrictiondrag bydelaying transition [4, 5] or by oscillating the flow in spanwise direction [6], and to control global instabilities of the flow [2, 3, 7]. Due to these characteristics, the potential of plasma actuators has been extended to many other applications like for instance tip clearance flow control of turbines [8, 9], and wind turbine blades and holder [10, 11].

This brief review about DBD aerodynamic actuators is all but exhaustive. The main goals of this work are to give to the reader some basic knowledge about the physics of plasma actuators and to show most important applications of these devices into the active flow control domain.

## **2. DBD aerodynamic actuators: basic principles**

Plasma aerodynamic actuators are based on the electrohydrodynamic (EHD) interaction generated by the so-called ionic wind. High electric fields can locally ionize the air. The produced heavy-charged species are accelerated by the applied electric field and, by means of collisions, they can yield momentum to the surrounding neutral gas. The force *f* per unit volume within the discharge can be yield by the following expression:

$$\mathbf{f} = (\mathbf{n}\_i - \mathbf{n}\_e)\overline{\mathbf{E}} \tag{1}$$

where *E* is the electric filed and *ni* and *ne* are ion and electron number density respectively.

First studies were conducted by using direct current (DC) corona discharges [2]. Main disadvantages of these actuators are low flexibility in electrodes configuration and in the supply system, and the transition into spark regime producing irreversible damage of the actuator itself.

Nowadays, the largest part of plasma aerodynamic actuators is based on the surface dielectric barrier discharge (SDBD). This typology of discharge allows to use several electrodes geome‐ try, different supply voltage waveforms, and it prevents the transition into the arc regime due to the presence of the dielectric material. DBD actuators generate non-thermal plasmas [12], limiting power consumption and allowing their use over heat sensitive surfaces.

A classical DBD aerodynamic plasma actuator is constituted by a dissymmetric electrode pair separated by a dielectric slab (**Figure 1**). When high voltages (typically 10–50 kV at 1–100 kHz) are applied to the electrodes, a surface discharge is produced (**Figure 2**). Discharge appears to be macroscopically homogeneous to the unaided eye, but it is constituted by a sequence of micro-discharges [13] lasting typically for tens of nanoseconds with a repetition rate of several hundreds of megahertz. Fast ignition and quenching of the discharge can be inferred by voltage-current time behavior reported in **Figure 3**.

**Figure 1.** Schematic of a SDBD actuator for flow control.

strategies have recently received more attention since they can be used in a selective way and canbeoperatedonlywhenitiseffectivelyrequested.Amongdifferentactivetechniques,plasma aerodynamic actuators are attractive because they present high dynamic responses due to the absence of moving parts, are characterized by low weight, are easy to build, are backward compatible with existing aerodynamic surfaces, and generate negligible aerodynamics interferences when they are switched off. When actuated, they can significantly modify the status of the boundary layer developing on the body surfaces. For this reason, they have been extensively studied for aeronautical applications to prevent flow separation enhancing lift and reducingdrag [2, 3].More recently,theyhave beenusedalso to controlfrictiondrag bydelaying transition [4, 5] or by oscillating the flow in spanwise direction [6], and to control global instabilities of the flow [2, 3, 7]. Due to these characteristics, the potential of plasma actuators has been extended to many other applications like for instance tip clearance flow control of

This brief review about DBD aerodynamic actuators is all but exhaustive. The main goals of this work are to give to the reader some basic knowledge about the physics of plasma actuators and to show most important applications of these devices into the active flow control domain.

Plasma aerodynamic actuators are based on the electrohydrodynamic (EHD) interaction generated by the so-called ionic wind. High electric fields can locally ionize the air. The produced heavy-charged species are accelerated by the applied electric field and, by means of collisions, they can yield momentum to the surrounding neutral gas. The force *f* per unit

First studies were conducted by using direct current (DC) corona discharges [2]. Main disadvantages of these actuators are low flexibility in electrodes configuration and in the supply system, and the transition into spark regime producing irreversible damage of the

Nowadays, the largest part of plasma aerodynamic actuators is based on the surface dielectric barrier discharge (SDBD). This typology of discharge allows to use several electrodes geome‐ try, different supply voltage waveforms, and it prevents the transition into the arc regime due to the presence of the dielectric material. DBD actuators generate non-thermal plasmas [12],

A classical DBD aerodynamic plasma actuator is constituted by a dissymmetric electrode pair separated by a dielectric slab (**Figure 1**). When high voltages (typically 10–50 kV at 1–100 kHz)

limiting power consumption and allowing their use over heat sensitive surfaces.

**f n nE** = - ( **i e** ) (1)

and *ne* are ion and electron number density respectively.

turbines [8, 9], and wind turbine blades and holder [10, 11].

**2. DBD aerodynamic actuators: basic principles**

where *E* is the electric filed and *ni*

58 Recent Progress in Some Aircraft Technologies

actuator itself.

volume within the discharge can be yield by the following expression:

**Figure 2.** Top view image of SDBD discharge [14].

**Figure 3.** Voltage-current time behavior of a SDBD [15].

The presence of the plasma and the particular electrode configuration induce a jet tangential to the actuator wall, similar to a classic blowing technique [13]. These jets can modify the aerodynamic boundary layer, increasing flow momentum, at least in the near-wall region above the surface. A large number of experimental [14–25] and numerical [26–47] works have been done in last decade to understand basic physical phenomena involved in the EHD interaction.

A typical velocity profile induced by the tangential wall jet is shown in **Figure 4**. Measurements have been carried out by a glass Pitot tube positioned 2 mm downstream with respect plasma extension and moved parallel to the actuator surface. Maximum velocity of about 5–6 m/s are usually reached.

**Figure 4.** Typical pitot velocity profile of a DBD plasma actuator (red line). Blue lines represent standard deviation [48].

Fast dynamics of these actuators is underlined in **Figure 5** where Schlieren images of the induced jet developing during ignition of the discharge are shown. Steady state (d) is typically reached after 400 ms after discharge ignition.

**Figure 3.** Voltage-current time behavior of a SDBD [15].

60 Recent Progress in Some Aircraft Technologies

interaction.

usually reached.

[48].

The presence of the plasma and the particular electrode configuration induce a jet tangential to the actuator wall, similar to a classic blowing technique [13]. These jets can modify the aerodynamic boundary layer, increasing flow momentum, at least in the near-wall region above the surface. A large number of experimental [14–25] and numerical [26–47] works have been done in last decade to understand basic physical phenomena involved in the EHD

A typical velocity profile induced by the tangential wall jet is shown in **Figure 4**. Measurements have been carried out by a glass Pitot tube positioned 2 mm downstream with respect plasma extension and moved parallel to the actuator surface. Maximum velocity of about 5–6 m/s are

**Figure 4.** Typical pitot velocity profile of a DBD plasma actuator (red line). Blue lines represent standard deviation

**Figure 5.** Schlieren images of induced wall jet during ignition phase of the discharge (a, b, and c) and steady state oper‐ ation (d) [48].

As already introduced [26–47], EHD interaction produced by DBD plasma actuators has been numerically investigated a well. Main issues are related to the simulation of the discharge and its interaction with surrounding gas. A 'realistic' simulation of a DBD streamer should take into account gas ionization, plasma chemistry, thermal fluxes, diffusion of neutral and charged species, and charge deposition over dielectric surfaces. Time steps of about tens of picoseconds and mesh size in the order of few micrometers are usually required to reproduce the formation of a plasma filament lasting for tens of nanoseconds and featured with characteristic length of about few millimeters. Several coefficients related to diffusion, secondary electrons emission, reaction rates, and electrons attachment are often not easy to estimate or to recover from existing literature. The numerical model leads to the temporal/spatial evolution of the body force produced by the discharge. The second step is the coupling between the discharge and the surrounding gas. This is another numerical challenge because characteristic times and lengths of the discharge are several orders of magnitude smaller with respect those related to the fluid-dynamic domain. Several authors [26–36] followed this computational strategy obtaining interesting results in good agreement with experimental fluid-dynamic effects. In **Figure 6a**, integrated horizontal body force as a function of the applied voltage is shown [36]. The two half periods produce different force dynamics and magnitude. In **Figure 6b**, the timeaveraged horizontal force distribution above the actuator surface is depicted [33]. Highest values have been obtained close to plasma end.

**Figure 6.** Time evolution of the EHD body force (a) [36], and spatial distribution of the average horizontal force (b) [33].

A simpler approach is to estimate the electron number density [37–42], on the basis of experimental measurements or theoretical calculations, and to evaluate EHD body force using Equation 1. This force is subsequently utilized as input parameter in the Navier-Stokes equation solver. A spatial/temporal average value of the body force can also be obtained by means of experimental results [43–47]. This method allows to use standard fluid-dynamic solvers avoiding difficulties arising from the couple between plasma and surrounding gas.

Both numerical and experimental works demonstrated the capability of plasma actuators to produce a thrust able to move surrounding gas in a desired direction. In order to increase both induced speed and region in which the actuator manifests its influence, a series of DBD actuators can be manufactured (**Figure 7**). Each actuator of this multi-electrode arrangement contributes to increase the induced speed.

**Figure 7.** Horizontal velocity profile (*y* = 0.5 mm) above four DBD actuators in series [13].

On a parallel plane, voltage waveform shape (arbitrary or nanopulsed signals) can enhance thrust of the induced jet, increasing effectiveness of actuators [15, 49–56]. The use of arbitrary waveforms can enhance plasma ignition phases in which induced thrust is higher. In this way, induced speed (**Figure 8**) and efficiency (**Figure 9**) can be both increased [15]. Nanopulsed discharges are able to generate energetic plasmas lasting for few nanoseconds. During the ignition of the discharge, a high amount of energy is deposited within the gas inducing local shock waves able to significantly modify the boundary layer of an incoming flow [56].

**Figure 6.** Time evolution of the EHD body force (a) [36], and spatial distribution of the average horizontal force (b)

A simpler approach is to estimate the electron number density [37–42], on the basis of experimental measurements or theoretical calculations, and to evaluate EHD body force using Equation 1. This force is subsequently utilized as input parameter in the Navier-Stokes equation solver. A spatial/temporal average value of the body force can also be obtained by means of experimental results [43–47]. This method allows to use standard fluid-dynamic solvers avoiding difficulties arising from the couple between plasma and surrounding gas.

Both numerical and experimental works demonstrated the capability of plasma actuators to produce a thrust able to move surrounding gas in a desired direction. In order to increase both induced speed and region in which the actuator manifests its influence, a series of DBD actuators can be manufactured (**Figure 7**). Each actuator of this multi-electrode arrangement

[33].

contributes to increase the induced speed.

62 Recent Progress in Some Aircraft Technologies

**Figure 7.** Horizontal velocity profile (*y* = 0.5 mm) above four DBD actuators in series [13].

**Figure 8.** Pitot velocity profiles obtained close to plasma extension for different supplying voltage waveforms [15].

**Figure 9.** Electric into kinetic conversion efficiency for a DBD actuator driven with different voltage waveforms [15].

Another possibility to increase actuator performance is the adoption of a third exposed electrode supplied with high-voltage DC fields. In this way, a sliding DBD is generated. Depending on the sign of the DC field, it is possible to modify the morphology of the induced ionic wind [57, 58].

DBD actuators can be arranged to produce normal or vectorized jets, too. These devices can be used to mimic classical synthetic jets and are usually called plasma synthetic jet actuators (PSJA). Typical geometries are annular and linear one [48, 59–62]. In both cases, tangential wall jets collide merging in a unique-induced jet able to generate perturbations far away from the actuator surface (**Figures 10** and **11**). When the linear configuration is adopted, by supplying exposed electrodes with different voltages, it is possible to produce an induced jet with an arbitrary inclination. Three-dimensional flows can be also produced by using a classical DBD actuator, but with an exposed electrode characterized with serpentine or serrated geometries, instead of the usual linear one [63, 64]. This particular electrode geometry generates small tangential jets that collide and propagate downstream pushed by the EHD interaction body force.

**Figure 10.** Induced normal jet of linear (left-hand side) and annular (right-hand side) PSJA.

**Figure 11.** Schlieren images of PSJAs of linear (a) and annular (b) geometries. Electrode distance (a) and diameter (b) is 30 mm.
