DBD Plasma Actuators for Aerodynamic Flow Control: A Review

Abstract

Dielectric barrier discharge (DBD) plasma actuators (PAs) are devices used to control airflow. DBD actuators generate an electric field that accelerates ionized air particles, inducing localized flow modifications. Among other applications, they are particularly effective for enhancing cooling, for aerodynamic drag reduction, and for lift enhancement, therefore capable of improving stall characteristics. In addition, they offer several distinct advantages, such as rapid response time, low power consumption, and no moving parts. The present review paper aims to summarize the main governing equations associated with the most common phenomenological PA Computational Fluid Dynamics (CFD) models, Shyy and Suzen-Huang, as well as highlight the major applications to flat plates, wind turbine airfoils and entire wind turbines. The application of DBD plasma actuators on individual wind turbine blades, as well as dynamic horizontal and vertical axis wind turbines, is reviewed, drawing from key numerical and experimental investigations. The simulated performance of various configurations of single and multiple PAs on representative airfoils at different chordwise locations is discussed. The overall findings indicate that the chordwise location of the actuators on airfoils and their optimum spanwise placement on small and large wind turbine blades, along with the geometry and excitation parameters of the actuators, play a crucial role in their performance, affecting the boundary layer and the flow pattern. The reader shall obtain an overall idea of the most recent aerodynamic applications of PAs as well as their expected efficiency.

1. Introduction

The ability to manipulate flow by implementing passive or active flow control methods is of immense technological importance. After the discovery of the boundary layer (BL) by Ludwig Prandtl in 1904, the concept of flow control arose. Manipulation of this boundary layer and the turbulent structures within it allows for precise control of several key aspects of the flow field. Of particular interest is the control of the flow field in order to reduce drag and/or enhance lift on any bluff body, thereby increasing the efficiency of industrial applications such as wind turbine power generation or airplane flight control. As a result, significant research efforts have focused on the utilization and improvement of these types of flow control mechanisms.

In general, the technology of flow control focuses on modifying the natural boundary layer state to generate a more desired status. Passive flow control (PFC) techniques do not need any use of energy [1] and typically utilize static devices such as leading edge protuberances [2], vortex generators [3], gurney flaps [4], winglets [5], microtabs [6], boundary layer trips [7], bumps [8] and leading edge slots [9] to modify the flow structure. Active flow control (AFC) techniques require a source of energy for implementation. Cattafesta et al. [10] classify all active flow control strategies into the following functional categories:

• Fluidic actuators such as suction and blowing slots/holes, and synthetic jets.
• Electromagnetic/magnetohydrodynamic actuators.
• Moving/rotating Surface actuators such as variable pitch blades and morphing blades.
• Plasma actuators.

A typical flow control mechanism is based on using these aforementioned devices to promote/delay the separation of the boundary layer. This form of AFC implementation is often based on injecting or sucking flow momentum into/from the boundary layer. The different AFC devices can operate in open- or closed-control loops, depending on whether the injected/sucked flow is continuous or periodic. One of the most well known advantages of using periodic forcing versus constant blowing or suction is that it interacts with the natural instabilities of the boundary layer, and therefore a smaller amount of energy is required to delay the separation of the boundary layer [11].

From the different active flow control devices, plasma actuators offer many unique benefits, including ease of implementation, solid-state functionality, fast response, and relatively low power consumption. The most common plasma actuators can be classified as follows [10]:

• Corona discharge.
• Local arc filament.
• Sparkjet.
• Dielectric barrier discharge (DBD).

Classifications can also be made according to the pressure generated in the plasma region [12] as follows:

• Low-pressure plasma such as DC discharge, RF discharge, and microwave discharge.
• Atmospheric pressure plasma such as corona discharge, arc discharge, DBD, and atmospheric pressure glow discharge.

Dielectric barrier discharge (DBD) plasma actuators are designed to generate a glow discharge [13], which is characterized by a uniform, homogeneous, and stable plasma. A DBD plasma actuator typically consists of two electrodes that are separated by a dielectric material. One of the electrodes is exposed to the air, and the other one is encapsulated and fully covered by the dielectric material [14]. The dielectric barrier discharge material is generally glass, quartz, or polyamide (Kapton), or ceramic [15]. When a voltage is applied to the electrodes and when asymmetric actuators are considered, the plasma region is generated on one side of the exposed electrode; the plasma region appears on both sides of the exposed electrode when symmetric actuators are employed. For this second case, a continuous encapsulated electrode covering both plasma regions is needed; see Figure 1. For the remainder of this review, when mentioning plasma actuators (PAs), we will refer to DBD flow control devices. In fact, this is the usual nomenclature commonly used in current literature (see, for example, [16]). Note that these devices are widely used in the field of aerodynamics for active flow control applications (see [17,18,19]).

1.1. Aim of the Study

The aim of the present review is to analyze the aerodynamic performance of DBD plasma actuators (PAs) when applied to flat plates and airfoils employed in wind turbines, such as the NACA and S-series families, among others, at various wind speeds and angles of attack (AoA). Their use on entire wind turbines (WTs) is also evaluated. This study considers the impact of excitation parameters on PA discharge, the appropriate chordwise location of the PA for implementation on airfoil surfaces and WTs, the essential PA design considerations, and the application of current theoretical knowledge in numerical and experimental investigations. To clarify how this review differs from the previous existing ones, the most recent and representative research articles summarizing earlier AFC-PA applications on flat plates, airfoils and full wind turbines are presented below.

Previous review articles have mostly evaluated the aerodynamic performance improvements obtained when using flow control techniques; however, the focus was put on one of the following specific areas, such as generating wall jets [21], ice mitigation on aircraft and wind turbines [22], or shock wave control and boundary layer interference at high-speed flows [23].

Omidi [24] reviewed the PAs’ applications focused on improving the aerodynamic performance and power output of some airfoils and entire wind turbines. The review highlighted the plasma actuators’ potential in enhancing power generation, reducing torque fluctuations, and enabling self-starting, particularly in horizontal axis wind turbines (HAWTs).

Karthikeyan and Harish [23] highlighted the effectiveness of DBD plasma actuators in aerodynamic flow control, including drag reduction, lift enhancement, and turbulence management on airfoils.

In the review performed by Saemian and Bergada [20], they highlighted the different AFC actuators used in wind turbines, including synthetic jet actuators (SJAs), suction and blowing actuators and dielectric barrier discharge (DBD) plasma actuators (PAs).

Sato and Ohnishi [25] examined the development and performance enhancement of dielectric barrier discharge (DBD) plasma actuators for active airflow control in aerospace applications. Emphasis was placed on understanding the mechanisms of surface discharge and electrohydrodynamic (EHD) force.

The present review seeks to identify key trends, inconsistencies, and influencing factors related to optimal actuator geometry, location and excitation parameters. Ultimately, the goal is to synthesize the findings into a deep understanding that highlights and the aerodynamic characteristics in different studies, providing a foundation for future research and practical applications.

This paper is divided into five main chapters. It begins with a review of governing equations, including phenomenological models such as the Shyy and Suzen–Huang (S-H) models, along with discussions on thrust, power consumption, and empirical methods. The following section focuses on highlighting the novel applications of PAs on flat plates. The next section explores the application of dielectric barrier discharge (DBD) plasma actuators (PAs) on wind turbine airfoils, covering both numerical simulations and experimental investigations under periodic and pulsating actuation modes. Subsequently, the use of PAs on wind turbines (WTs) is examined in the context of both vertical-axis wind turbines (VAWTs) and horizontal-axis wind turbines (HAWTs), including analyses at different operational scales and conditions. The main conclusions of the study are summarized in the final part of the document.

1.2. Concept Behind the Plasma Actuators (PAs)

A gas discharge is created on the DBD unit when an electric field of sufficient amplitude is applied between the two electrodes. The electric field ionizes the neutral gas by electron impact ionization, a process in which energetic electrons interact with the gas molecules to produce ions [26]. In a single PA discharge, during one half of the alternating current (AC) cycle, electrons are emitted from the metal electrode (exposed electrode) and accumulate on the surface of the dielectric unit. In the opposite half of the cycle, the dielectric unit releases the electrons, which then travel back towards the exposed electrode; see Figure 2. The timescale of this process is influenced by factors such as gas composition, excitation frequency, and other operating conditions, but typically occurs within a few tens of nanoseconds [27].

During the first half cycle, the exposed electrode is negatively charged, and electrons move forward and away from the electrode. During the second half cycle, the electrons return to the exposed electrode, and at this moment, the electrode is positively charged. In the course of the forward discharge, where the exposed electrode is negative, the discharge will glow (Townsend-type discharge), whereas the back discharge characteristic of a positively charged electrode will appear more filamentary/streamer-like.

Figure 2 shows the flow of charged particles (ions and electrons) generated by the discharge effect of the DBD plasma actuator. DBD plasma actuators differ from other discharges such as arc filament and corona discharge because a dielectric layer between the electrodes prevents arcing. This layer causes surface charge accumulation, creating a memory effect that shapes how discharges propagate and influence subsequent discharges. This is the key effect to generate an ionic wind in DBD plasma actuators [29]. Indeed, charged particles generated by the discharge are accelerated by a high-voltage electric field, and collide with neutral particles, transferring momentum and producing airflow through the electrohydrodynamic (EHD) effect. The EHD body force is an electrostatic force acting on the charged particle. An asymmetric electrode design (see Figure 1a) ensures a unidirectional EHD force, allowing the actuator to actively control airflow.

DBD plasma actuators influence the incoming flow mainly through momentum injection driven by the EHD effect, or by generating compression waves resulting from rapid local Joule heating [30]. In reality, the EHD force is generated in both configurations, but is particularly weak in the second one [31,32]. Both mechanisms are summarized in this review.

2. Numerical Models and Empirical Methods

2.1. Main Concept Behind the Numerical Methods

The research undertaken by Kosinov et al. [33] was among the first ones to use ionized air (i.e., plasma) as a mechanism of flow control. They used an AC glow discharge to excite disturbances in the boundary layer. Additional experimental studies involving plasma for aerodynamic flow control were carried out by Cavalier [34] in 1995 and Cork and Cavalier [35] in 1997. A glow discharge technique, in which a gas breaks down and transitions from higher to lower resistance following the application of a critical voltage between two exposed electrodes, was employed. According to Paschen’s law, Equation (1), the voltage required for breakdown depends on the geometry of the electrodes, the distance between the exposed and covered electrodes, and the properties and conditions of the gas [36].

$$V_{bd}={\displaystyle \frac{BPd}{ln\left(Pd\right)-ln\left[\frac{A}{ln\left(1+\frac{1}{{\gamma }_{se}}\right)}\right]}}$$

(1)

where $V_{bd}$ represents the breakdown voltage, P is the pressure of the gas, d characterizes the distance between the electrodes, and ${\gamma }_{se}$ is the secondary electron emission coefficient (that is, the number of secondary electrons produced per incident positive ion). A and B are constants that depend on the type of gas, where A stands for the saturation ionization of the gas and B is related to the excitation and ionization energies. These two constants can be used to obtain Townsend’s first ionization coefficient $\alpha$, defined as

$$\alpha =A·P·e^{-{\displaystyle \frac{B·P}{E}}}$$

(2)

where $\alpha$ represents the number of ionizing collisions per unit length made by an electron, and E is the applied electric field. In the ionization process, the neutral gas is transported due to the Lorentzian collisions. This effect is presented as an electrostatic body force $\overrightarrow{F}$,

$$\overrightarrow{F}={\displaystyle \frac{1}{2}}{\epsilon }_0\nabla E^2$$

(3)

where ${\epsilon }_0$ is the permittivity of air (free space).

There are several methods available to simulate the plasma actuator and the resulting flow field [37], including the following:

(1)

Phenomenological or simplified modeling such as the Shyy (a linear electric field model) [38], the Suzen–Huang [39,40], and the Lumped-Element Circuit model (LEC) by Orlov [41]. The main advantage of these models resided in their simplicity and ease of simulation; in the next subsections, these models are explained in detail.

(2)

Fluid models are first-principles-based modeling approaches, and represent electrons, neutral particles, and ions (either both positive and negative or only positive) [42,43].

(3)

A third approach consists of kinetic models, which represent macroscopic properties of fluids by analyzing their molecular composition and motion [44,45]. Kinetic models generally involve solving the Boltzmann equation or using particle-based simulations, such as the Monte Carlo method. The Monte Carlo method simultaneously follows numerous simulated particles to replicate the collective behavior of real atoms and molecules within the flow [46]. Each computational particle corresponds to thousands or even millions of charged particles of a single species (ion or electron).

(4)

Hybrid models mix fluid and kinetic approaches to balance accuracy and computational efficiency. This model is efficient in low-pressure discharges, and charged particles are typically not in local thermodynamic equilibrium [47,48,49].

A large number of numerical models and research works have simulated the PAs performance without directly modeling the ionization physics and chemistry associated (see, for example, [37,38,39,40,50,51,52,53]). In fact, the work on plasma modeling can be classified into the following approaches, noting that some models may fall into more than one category [54]. These categories are as follows:

(1)

Analytical models.

(2)

Semi empirical models (theoretical foundations with experimental observations).

(3)

Empirical models (derived directly from experimental data).

(4)

Computational Fluid Dynamics (CFD), which uses numerical methods such as RANS, LES, and DNS.

In the following subsections, the main characteristics of the most common numerical (Shyy and Suzen-Huang) and empirical models developed for PAs are summarized. These numerical models are computationally efficient and can be easily integrated into RANS codes. In these numerical methods (Shyy and Suzen-Huang), the influence of the plasma actuator on the external flow is represented in the Navier–Stokes computations as a body force vector. The Navier–Stokes equations for incompressible flow incorporating the plasma actuator as an external force term are represented as

$${\displaystyle \frac{\partial \mathbf{u}}{\partial t}}+(\mathbf{u}·\nabla )\mathbf{u}=-{\displaystyle \frac{1}{\rho }}\nabla p+\nu {\nabla }^2\mathbf{u}+{\mathbf{F}}_{\mathbf{plasma}}$$

(4)

2.2. Suzen and Huang (S-H) Model

Based on the Lorentz body force formulation introduced by Enloe et al. [55], Suzen et al. [39,40] generated their electrostatic model. In this theoretical model, the body force was represented with a Gaussian charge distribution, and was determined by solving two elliptic equations. The plasma region follows the Maxwell equations, assuming that the whole system remains quasi-steady and plasma charges have adequate time for redistribution. The magnetic field, the magnetic induction, and the electric current are zero; therefore, the electrohydrodynamic (EHD) force per unit volume $\overrightarrow{F}$ can be given as

$$\overrightarrow{F}={\rho }_{pl}\overrightarrow{E}$$

(5)

$\overrightarrow{E}$ represents the electric field and ${\rho }_{pl}$ characterizes the net charge density; both terms (${\rho }_{pl}$ and $\overrightarrow{E}$) must be determined individually. Under the quasi-steady assumptions, the Maxwell equations take the form $\nabla \times \overrightarrow{E}\approx 0$, which involves that the electric field can be derived from the gradient of a scalar potential,

$$\overrightarrow{E}=-\nabla \Phi$$

(6)

$\Phi$ represents the potential term, determined by the summation of the potential of the net charge density $\phi$, and the potential external electric field $\varphi$,

$$\Phi =\phi +\varphi$$

(7)

Following Gauss’s law, it can be said that

$$\nabla ·(ϵ\overrightarrow{E})={\rho }_{pl}$$

(8)

The parameter $ϵ$ characterizes the total permittivity, and ${\rho }_{pl}$ can be expressed as a function of the potential term $\Phi$ and the Debye length ${\lambda }_d$,

$${\rho }_{pl}=-{\displaystyle \frac{{ϵ}_0}{{\left({\lambda }_d\right)}^2}}\Phi$$

(9)

In this model, the Debye length, and the charge on the wall (DBD surface) are assumed to be small; the distribution of charged particles within the domain is governed by the potential generated by the electric charge on the wall, which is considered rather unaffected by the external electric field. Based on these assumptions, independent equations can be obtained for the external electric field $\varphi$ due to the applied AC voltage at the upper electrode, and for the potential of the plasma net charged density $\phi$.

$$\nabla ·({ϵ}_r\nabla \phi )=-{\displaystyle \frac{{\rho }_{pl}}{\left({ϵ}_0\right)}}$$

(10)

$$\nabla ·({ϵ}_r\nabla \varphi )=0$$

(11)

where ${ϵ}_r$ represents the material permittivity and ${ϵ}_0$ characterizes the permittivity of the free space, or vacuum permittivity.

The permittivity of the DBD unit ${ϵ}_d$, is given by

$${ϵ}_d={ϵ}_0{ϵ}_r$$

(12)

Combining Equations (7) and (9)–(11), and after some rearrangement, the following is obtained:

$$\nabla ·({ϵ}_r\nabla {\rho }_{pl})={\displaystyle \frac{{\rho }_{pl}}{{\left({\lambda }_d\right)}^2}}$$

(13)

From this equation, with an established boundary condition on the surface over the encapsulated or lower electrode, ${\rho }_{pl}$ can be obtained.

The resulting body force vector takes the form

$$\overrightarrow{F}={\rho }_{pl}\overrightarrow{E}=-{\rho }_{pl}(\nabla \varphi )$$

(14)

The boundary conditions required to determine the net charge density and the potential external electric field are summarized in Figure 3.

The boundary conditions in the S-H model, Figure 3, can be summarized as Neumann and Dirichlet types. Dirichlet boundary conditions for the electrical potential $\varphi$ are applied on the exposed electrode, while Neumann boundary conditions are used on the outer boundaries (air). The electrical potential $\varphi$ of the lower electrode is set to zero. The net charge density ${\rho }_{pl}$ is defined based on Dirichlet boundary conditions on the outer boundaries and on the DBD surface. The permittivity of the surface where plasma is forming is given as a Dirichlet boundary condition and it is taken as the average of the permittivity of the air and the dielectric material.

Although its derivation falls outside the scope of this review, it is important to remember that the Suzen et al. [52] model was improved more recently in order to expand its use to more complicated actuator geometries.

2.3. Shyy Model

Another phenomenological model is the one developed by Shyy [38], which is based on the empirical model introduced by Roth in 1998 [56]. In this model, the electric field generated by the actuator is simplified as a triangular area, and it forms on the DBD surface. The force near the vertex of the left-angled plasma region is maximum, while no force exists outside this region; see Figure 1a. The main mathematical equations associated with the Shyy model are as follows:

The electric field distribution $\left|E\right|$ in the triangle region is represented as

$$\left|\overrightarrow{E}\right|=E_s-K_1\left(x\right)-K_2\left(y\right)$$

(15)

$K_1\left(x\right)$ and $K_2\left(y\right)$ represent the linear distribution of the field force in the X and Y directions, respectively, which can be determined by

$$K_1\left(x\right)={\displaystyle \frac{E_s-E_b}{l_{pl}}}$$

(16)

$$K_2\left(y\right)={\displaystyle \frac{E_s-E_b}{h_{pl}}}$$

(17)

Here, $l_{pl}$, and $h_{pl}$ represent the length and the height of the plasma region, respectively. $E_b$ and $E_s$ represent the breakdown and strength of the electric field,

$$E_s=V_{pl}/D_{pl}$$

(18)

Here, $D_{pl}$ characterizes the distance between the two electrodes measured along the X direction, which is kept constant in the Shyy model ($D_{pl}$ = 0.25 mm). $V_{pl}$ represents the voltage applied to the upper and lower electrodes. The electric field component in the X direction (${\overrightarrow{E}}_x$) takes the form

$${\overrightarrow{E}}_x={\displaystyle \frac{\overrightarrow{E}{K}_1\left(x\right)}{\sqrt{K_1{\left(x\right)}^2+K_2{\left(y\right)}^2}}}$$

(19)

The component in Y direction (${\overrightarrow{E}}_y$) can be expressed as

$${\overrightarrow{E}}_y={\displaystyle \frac{\overrightarrow{E}{K}_2\left(y\right)}{\sqrt{K_1{\left(x\right)}^2+K_2{\left(y\right)}^2}}}$$

(20)

Finally, the electric field force inside the plasma region (triangle area) is given by

$$\overrightarrow{F}=\overrightarrow{E}{\alpha }_{pl}{e}_{pl}{\rho }_{pl}\delta \Delta t$$

(21)

The component of the electric field force in X direction can be expressed as

$${\overrightarrow{F}}_x={\overrightarrow{E}}_x{\alpha }_{pl}{e}_{pl}{\rho }_{pl}{f}_{pl}\delta \Delta t$$

(22)

The corresponding force component in Y direction takes the form

$${\overrightarrow{F}}_y={\overrightarrow{E}}_y{\alpha }_{pl}{e}_{pl}{\rho }_{pl}{f}_{pl}\delta \Delta t$$

(23)

In the body force equations, $f_{pl}$ represents the voltage frequency and ${\alpha }_{pl}$ characterizes the collision efficiency. In Shyy model, $\Delta t$ is the discharge time ($67 \mathsf{\mu }$s), $e_{pl}$ defines the charge of the electron (1.602 × ${10}^{-19}$), ${\rho }_{pl}$ represents the net charge density per unit volume (1 $\times {10}^{11}{\mathrm{C}\mathrm{o}\mathrm{u}\mathrm{l}\mathrm{o}\mathrm{m}\mathrm{b}\mathrm{s}/\mathrm{c}\mathrm{m}}^3$), and all these variables are assumed to remain constant. Voltage and frequency are treated as variable parameters. In addition, $\delta$ defines the Dirac function; when $\overrightarrow{E}$ < ${\overrightarrow{E}}_b$ the Dirac function takes a value of $\delta$ = 1, and when ${\overrightarrow{E}}_b$ < $\overrightarrow{E}$, the value is $\delta$ = 0.

2.4. Lumped-Element Circuit (LEC) Model

Orlov et al. [53] developed a Lumped-Element Circuit (LEC) model to describe the behavior of the aerodynamic plasma actuator. This electrostatic model is more complex than the S-H and Shyy models, and it consists of several capacitive elements and one resistive element representing the plasma and the plasma region divided into n domains; see Figure 4.

Each of these elements in Figure 4a varies with time because the plasma changes during each half-cycle of the applied AC voltage. The air and DBD capacitors are given by

$$C_{\mathrm{a}\mathrm{i}\mathrm{r}}={\displaystyle \frac{{ϵ}_0{ϵ}_r{A}_n}{L_n}}$$

(24)

And

$$C_{\mathrm{DBD}}={\displaystyle \frac{{ϵ}_0{ϵ}_r{A}_d}{T_{pl,i}}}$$

(25)

$A_n$ denotes the cross section of the air capacitor, $A_d$ the total number of the sub-circuits, and $L_n$ determines the length of the air capacitor in sub-circuit n. And finally, the resistance in the n-th sub-circuit is given by

$$R_{\mathrm{n}\text{-}\mathrm{t}\mathrm{h}}={\displaystyle \frac{L_n{\rho }_r}{A_n}}$$

(26)

where, ${\rho }_r$ is resistivity of the air.

2.5. Equations to Determine Thrust and Power Consumption

A different EHD body force model for the induced wall-jet velocity was proposed by Yoon and Han [51]; they estimated the resulting thrust based on classical electrostatic theory and experimental observations. The thrust $T_{pl}$ and power consumption $P_{\mathrm{p}\mathrm{l}\mathrm{a}\mathrm{s}\mathrm{m}\mathrm{a}}$ are given by

$$T_{pl}={\alpha }_t{w}_{pl}{C}_{eq}{\left(V_{pl}-V_{bd}\right)}^2$$

(27)

Here, ${\alpha }_t$ represents a constant associated with the thrust, $V_{pl}$ is the voltage applied to the electrodes and $w_{pl}$ is the angular frequency of the AC circuit; see Thomas et al. [15].

$$P_{\mathrm{p}\mathrm{l}\mathrm{a}\mathrm{s}\mathrm{m}\mathrm{a}}=2\pi l_{\mathrm{p}\mathrm{l}}{C}_{\mathrm{e}\mathrm{q}}{\left(V_{pl}-V_{\mathrm{b}\mathrm{d}}\right)}^2$$

(28)

where $V_{bd}$ and $C_{\mathrm{e}\mathrm{q}}$ represent the breakdown voltage and the equivalent capacitance of the actuator, respectively. The $C_{\mathrm{e}\mathrm{q}}$ can be calculated as

$$C_{\mathrm{e}\mathrm{q}}={\displaystyle \frac{C_1{C}_2}{C_1+C_2}}$$

(29)

$C_1$ and $C_2$ are capacitor-equivalent properties. $C_1$ represents the capacitor between the end of the upper electrode and the DBD unit and $C_2$ is composed of the upper electrode and the plasma region.

$$C_1={\displaystyle \frac{2\pi {ϵ}_0}{ln\left(\frac{0.5T_{pl,e}+{\lambda }_d}{0.5T_{pl,e}}\right)}}$$

(30)

and

$$C_2={\displaystyle \frac{\pi {ϵ}_d}{ln\left(\frac{0.5T_{pl,e}+2T_{pl,i}}{0.5T_{pl,e}}\right)}}$$

(31)

where $T_{pl,i}$ and $T_{pl,e}$ represent the thickness of the dielectric barrier and the exposed electrode, respectively; see Figure 1.

The Debye length ${\lambda }_d$, in this theory can be determined as a function of the voltage applied to the electrodes,

$${\lambda }_d=0.2\left(0.3\times {10}^{-3}{V}_{pl}\right)-\left(7.42\times {10}^{-4}\right)$$

(32)

2.6. Concept of Duty Cycle (Dc)

In plasma actuators, the duty cycle (Dc) is commonly used in both numerical and experimental investigations and it is a main flow control parameter. This parameter characterizes the operation of the actuator under pulsating mode, and it is defined as the ratio of the discharge duration (when plasma is on) to the total period of the actuation cycle. It is expressed as

$$Dc=T_{on}/T_{pu}$$

(33)

where $T_{on}$ represents the time at which plasma is active within a cycle and $T_{pu}=T_{on}+T_{off}$ characterizes the pulse modulation period of a given PA; see Figure 5. Based on these assumptions, the pulsating frequency can be represented as

$$f_{pu}=1/T_{pu}={\displaystyle \frac{f_{pl}Dc}{N_{pl}}}$$

(34)

The term $N_{pl}$ defines the number of pulsating cycles in the active period of the plasma actuator, $T_{on}=N_{pl}T$. For a periodic actuation mode, $Dc=1$.

2.7. Overview and Evolution of the Main Empirical and Semi Empirical Methods

Stability experiments involving compressible boundary layer flows were initially conducted on flat plates by [57] (1960) and on conical surfaces by [58] (1975). The studies were performed at a range of Mach numbers from 1.6 to 5.6 on flat plates, and considering Mach numbers of 5.5 [58], 7 [59] and 8 [60,61] on sharp cones. Various techniques have been employed to introduce periodic disturbances in boundary layers, including vibrating metallic ribbons in the subsonic regime [62] and a resistive heating wire in the subharmonic regime [63]. Although this phenomenon was first discovered in 1857 [64], it was not until 1995 that Cavalieri [34] explored how a corona-discharge perturbation system could be used to deliberately excite boundary-layer instabilities on a sharp cone under supersonic flow at Mach numbers from 3.5 to 6. The first piezoelectric devices operated at desired frequencies but at low amplitudes, whereas the glow discharge technique, developed by Corke in 1997 [35], could operate at higher amplitudes. The glow discharge technique generated a plasma region between two exposed electrodes in a gas environment, introducing controlled disturbances to excite oblique waves with a specified initial amplitude, frequency, and azimuthal wavenumber. Glow discharge actuators were based on two main configurations: the flush-mounted electrodes and below-surface electrodes. The latter configuration was applied by [35] to generate controlled disturbances in hypersonic boundary layers at Mach numbers ranging from 3.5 to 6.0.

In the late 1990s, Roth [56] presented the EHD body force as a flow control device. In a different study [65], he used a simplified model to estimate the body force, assuming it to be proportional to the electric field and the vacuum permittivity. Through a one-dimensional analysis, he demonstrated that the induced aerodynamic pressure was proportional to the electrostatic one. Shyy et al. [38] modified the models of Roth et al. [66] and Thomas et al. [67] and considered a further simplification for the electric field assuming a weakly ionized plasma. In order to better understand the momentum coupling mechanism between the plasma region and the fluid flow, Jayaraman and Shyy [68] presented a model of flow control and heat transfer using discharge-based effects in both the laminar and transitional turbulent regimes. Later, Grundmann et al. [50] conducted an experimental-numerical investigation, and used experimental data to calibrate the numerical phenomenological model of Shyy et al. [38]. An electrostatic model for plasma characteristics based on the formulation of the Lorentz force was presented by Enloe et al. [55] in 2004. In their model, they assumed a quasi-steady plasma generation and ignored the effect of magnetic forces; therefore, the Maxwell equations were accordingly simplified to a single equation. In fact, the theory developed by Suzen and Huang [39,40] was based on the research performed by [55]. In a following study, Enloe et al. [69] used experimental data to create a one-dimensional Gaussian charge distribution able to compute the plasma field generated on a DBD unit. Furthermore, the electrical field could be decoupled from the flow field; therefore, it could be calculated prior to flow computations. The main disadvantage of this model resides in that it is applicable only for a single voltage and frequency and a fixed DBD plasma geometry. In fact, the model requires experimental data for each given voltage, frequency and actuator configuration. More recently, a further model was presented by Post and Corke [70], where a very thin layer for cover and encapsulated electrodes in pulsating mode was considered. In this model a PA with steady and unsteady modes is operated in open- and closed-loop control systems.

Orlov et al. [41,53] in 2006 and Jayaraman et al. [37] in 2008 introduced glow discharge models of a single DBD plasma actuator operating during both half-cycles and while at atmospheric pressure. Orlov et al. [41,53] proposed a lumped-circuit model to calculate the electric potential and plasma volume. In their approach, the actuator is represented as a network of discrete circuits, each comprising an air capacitor, a dielectric capacitor, a resistive plasma element, and Zener diodes. Jayaraman et al. [37] simulated the physics of a 2-D PA operating in helium gas by using a high-fidelity first principles-based numerical modeling approach, and analyzed the effect of the DBD geometry, electrode materials, and species transport properties on the momentum coupling between the ionized jet and the incoming flow. A similar study, although using nitrogen, was undertaken by Orlov et al. [28]. Thomson and Moeller [71] (2012) developed a full Maxwell solver as an extension of the S-H model. In their study, the flow separation control, magnetic field effects, and pre-ionization of the flow were investigated.

It is important to realize that the PA’s numerical development [38,39,40,41] is based on previous experimental studies [53,55,56], which collectively provide a solid foundation for understanding the capabilities and limitations of plasma actuators, forming the basis for the detailed discussion that follows.

3. DBD Plasma Actuators (PAs) on Flat Plates

This section presents experimental investigations conducted on a flat plate configuration using both alternating current (AC) and direct current (DC) dielectric barrier discharge (DBD) plasma actuators. Three main designs are considered: asymmetric (traditional) DBD plasma actuators, which produce pulsating and periodic (continuous) aerodynamic body forces; sliding DBD plasma actuators (S-PA), which are three-electrode DBD actuators that work with AC and DC current; and DC-pulsed plasma actuators (D-PA).

The section focuses on characterizing the fundamental differences in flow behavior, discharge properties, and induced aerodynamic effects between the two excitation modes. In particular, the following section highlights the influence of plasma actuation on boundary layer modification, details the performed electrical diagnostics, and elaborates on the various flow visualization techniques that are employed to capture the discharge characteristics and their interaction with the boundary layer. Moreover, research on skin-friction drag reduction associated with quasi-streamwise vortices in the turbulent boundary layer is discussed, as it has attracted a great deal of attention due to its potential benefits in various engineering applications. In addition, the plasma-actuated wall-jet control technique for reduction in skin-friction drag in a boundary layer on flat plates is explained.

3.1. Asymmetric DBD Plasma Actuator (PA)

In this section, experimental parametric studies of asymmetric DBD plasma actuators on flat plates (PA), performed to evaluate the influence of design geometry and excitation parameters, such as voltage and frequency, with the objective of identifying their optimal configuration, are introduced. The actuator is powered by an AC voltage supply. In all studies, the lower electrode is grounded.

Forte et al. [72] optimized the geometry and excitation parameters to implement single and multiple PAs on a flat plate. They observed that the optimal gap between the exposed and the encapsulated electrodes is between 0 and 5 mm. In addition, an increase in the length of the encapsulated electrode, the voltage, and the frequency results in a rise in the ionized velocity until a plateau is reached. According to the results, the maximum ionic wind velocity reached 7 m/s with a single PA and 8 m/s with four PAs.

Seraudie et al. [73] studied the gap between the electrodes from 0 to 5 mm on a flat plate. Investigations were carried out at a fixed frequency of 1 kHz and an applied voltage of 20 kV. When the gap increased, the density of the current peaks decreased; however, the amplitude of these current peaks concurrently increased (see Figure 6). An optimum gap between the electrodes was found to be 2 ≤ $D_{pl}$ ≤ 3 mm, and in such condition, the momentum thickness was reduced by about 30%, resulting in lower friction drag.

Thomas et al. [15] optimized the geometry, waveform and excitation parameters of a single PA implemented on a flat plate. For a given frequency of 2 kHz, a positive ramp waveform required a lower voltage to achieve a given force than the sinusoidal waveform. The thrust reached by the actuator with a positive ramp waveform was nearly twice as high as with a sinusoidal waveform. A similar result is observed in [72], which implemented three PAs in multiple configurations. Furthermore, this study also found that increasing the width of the encapsulated electrode in the multiple PA configuration had a greater positive influence on the generated force when compared to increasing the electrode width in a single PA configuration. In this multiple PAs strategy the distance between the exposed electrodes was 12.7 mm with a maximum width of 25.4 mm.

A later study by Yu et al. [74] applied a single PA on a flat plate. In the actuated case, the maximum velocity at the leading edge of the lower electrode reached 5.5% of freestream velocity ($U_{\infty }$), with an applied voltage of 20 kV and a frequency of 5.5 kHz. The experimental results were compared with the ones generated by the Shyy model, showing that the peak velocity obtained in the simulation agreed well with the one obtained in the experiments. In a following numerical study, Yu et al. [75] applied PAs on a flat plate by using the Shyy model. Actuation strengths (a ratio of electrical force to the kinetic energy per unit volume of the flow) $D_c^{*}={\displaystyle \frac{\overrightarrow{E}{e}_{pl}{\rho }_{pl}C}{{\rho }_{\infty }{U}_{\infty }^2}}$ of 25, 30, 35, and 50 at 10 m/s were considered. The maximum induced velocity reached 1.8$U_{\infty }$, a ratio of electrical force to the kinetic energy per unit volume of the flow. Al-Sadawi et al. [76] applied a PA on a flat plate using three configurations, each characterized by the direction of the induced body force. The PAs were implemented near the trailing edge of a flat plate with a range of voltages from 2.4 to 4.2 kV and a frequency of 8 kHz; see Figure 7. Investigations were carried out at Reynolds numbers from $75\times {10}^3$ to $400\times {10}^3$. According to the results at the lowest wind speed, the PA2 and PA3 configurations achieved reductions in vortex shedding tonal noise by 14.5 dB at 4.2 kV and 12 dB at 3.6 kV, respectively. The exposed electrodes in PA3 were 15 mm long, making them significantly shorter in the spanwise direction compared to the ones employed in PA1 and PA2 configurations.

Nati et al. [77] applied PAs to suppress the vortex shedding in a truncated trailing edge of a flat plate. The PAs were placed on both sides of the flat plate at the trailing edge, either symmetrical or anti-symmetrical with respect to the wake centerline; see Figure 8. The PAs were operated with a voltage of 18 kV and a frequency of 2 kHz. A transverse plasma actuation configuration, which acted across the shear layers to disrupt circulation during vortex roll-up, was the most effective design across the studied configurations. The transverse plasma actuator markedly decreased the contribution of the first two eigenmodes (corresponding to the Von Karman Vortex shedding phenomena) to the total kinetic energy, from 89.1% down to 37.8%.

Yan et al. [78] reduced the vortex shedding and the aerodynamic noise generated by a slit using PAs. Experimental investigations were performed at wind speeds between 10 and 20 m/s. Based on the results, combining the slit and the PA significantly reduced the vortex shedding frequency and the aerodynamic noise at all wind speeds. They also found that this positive effect was greater at lower wind speeds. For a wind speed of 10 m/s, the plasma-generated jet produced a blowing rate of 4.5% of the wind speed, resulting in a total noise reduction of 8 dB.

Cheng et al. [79] installed streamwise PAs on a flat plate to create streamwise vortical structures. The PAs were implemented by three configurations at a wind speed of 2.5 m/s; see Figure 9. They were actuated with a range of peak-to-peak (P-P) voltages from 3.5 to 6.75 kV and a constant frequency of 11 kHz. The first and second configurations respectively achieved the largest drag reduction of 20% and 26%, using a voltage of 5.75 kV. The best control performance was achieved when the maximum spanwise velocity was approximately 4 times the friction velocity. Actuating the PAs with voltages higher than 5.75 kV increased vortex-induced shear stresses and the drag in the boundary layer, causing the generated vortical structures to grow rapidly. The structure flow was modified by PA; see Figure 10.

Wei and Zhou [80] applied PAs by using a multiple PA implementation strategy to generate a near-wall spanwise flow. The PAs design followed the configuration b from [79]; see Figure 9. The voltage applied ranged from 1.2 to 6 kV (P-P), and Mylar (used in [79]) was replaced with Mica as the DBD material. Investigations were carried out at 564 ≤ $R{e}_{\tau }$ ≤ 811, which corresponds to the range of voltages applied. In the baseline case, the drag increased logarithmically with increasing spanwise flow, but in the actuated case, drag reduction depended on the voltage applied, $R{e}_{\tau }$ and the distance between the upper electrodes (${\lambda }_z$). The vorticity circulation, ${\Gamma }_{0.8}^{+}$, obtained when applying the specified range of voltages was 1.604, 0.988, and 0.657, which led to a drag reduction of 70%, 32%, and 18%, respectively.

This section has focused on experimental parametric studies of asymmetric DBD plasma actuators (PAs) implemented on flat plates, in order to enhance momentum force and reduce drag. In the following section, the applications of sliding DBD actuators (S-PAs) on flat plates are reviewed.

3.2. Sliding DBD Plasma Actuator (S-PA)

The concept of sliding DBD plasma actuators (S-PAs) was first developed for laser-pumping applications [81]. Sliding DBD utilizes a two-step process, where first an alternating current (AC) is applied to weakly ionize the air, and then a DC potential is superposed to establish a corona discharge between spatially separated electrodes. The S-PA configuration is composed of two exposed and one encapsulated electrode; see Figure 11. The design may be interpreted as an asymmetric DBD device with an additional exposed electrode supplied with a DC voltage.

Depending on the polarity of the DC voltage, one can produce either a luminescent plasma sheet or a discharge. If the voltage is negative, it creates a luminescent plasma sheet that fills the entire space between the upper electrodes. If the voltage is instead positive, the plasma generated more closely resembles that of a traditional DBD (PA); see Figure 12. The third, DC activated, electrode works to extend the discharge region and increase the ion drift velocity between the exposed electrodes [83]. The advantage of this updated configuration is that large stable plasma sheets can be produced, with no glow-to-arc transition, except when the DC component is above the DC breakdown limit for the air [14].

Moreover, a S-PA can achieve a variety of discharge dynamics dependent on the waveform of the power supplied and the configuration of the actuator. Their many distinct mechanisms and performance characteristics are often examined in the context of flow control and boundary layer manipulation. For example, studies on flat plates with an acceptable pressure gradient were performed by implementing an S-PA with an elliptical leading-edge shape based on the modified super ellipse (MSE) proposed by Lin et al. [85]. This design has been applied in several subsequent studies [86,87].

One of the pioneering studies on implementing S-PA on a flat plate, performed by Louste et al. [88], demonstrated the potential of combining AC/DC voltages to control plasma behavior and flow manipulation. In their work, two strategies were employed to study micro discharges. In the first one, a negative AC voltage was applied to the upper and lower electrodes, while a positive DC voltage was applied to the third electrode. In the second strategy, the first upper electrode was removed. Results showed that the discharge current was distinct between tests, dependent on three factors: the capacitive effect of the DBD material, the discharge between the exposed and encapsulated electrodes, and the sliding discharge between the two exposed electrodes. The influence of the DBD material on discharge current could be limited or controlled by changing its thickness. The study found that the DC current significantly altered the discharge characteristics, indicating enhanced and directional plasma activity versus the typical asymmetrical PA; see Figure 13.

Moreau et al. [89] applied the S-PA on a flat plate at low frequency. In their work, the first exposed electrode was actuated with a high AC voltage of 20 kV and a frequency of 1 kHz. The encapsulated and second exposed electrodes were operated with a negative and positive voltage of −/+10 kV. Three strategies were applied for the latter electrodes, including where both electrodes were positive (10 kV), both were negative (−10 kV), and where the encapsulated electrode was at −10 kV while the exposed electrode was operated at 19 kV. The study found that the discharge characteristics depend strongly on the polarity (positive or negative) of the DC electrode and the voltage of the AC one. The ionic wind in the X direction, between the two upper electrodes, was the fastest by the last strategy. This maximum ionic wind speed was localized at a distance greater than 1 mm above the wall, and it was at this location where the discharge produced the most efficient effect on the boundary layer. In this study, they also observed that decreasing the AC voltage and increasing its operating frequency greatly accelerated the S-PA wind velocity. As a result, in a further study by Moreau et al. [84], they employed similar strategies for operation of S-PA on a flat plate; however, applied high actuation frequencies. The strategies were the same as in [89], with DC voltages instead ranging from +/−17 to +/−20 kV applied to the second and third electrodes. These results were compared with a study of a traditional PA with a high frequency of 11.7 kHz, operating at AC voltages from 7 to 12 kV. This study found that when the DC voltage applied to the third electrode is increased, the ion drift of the space charge between electrodes was enhanced, resulting in a faster electric wind. Actuating the first electrode at a high frequency resulted in a faster electric wind versus the one observed by [89]. Downstream of the third (second exposed) electrode, the effect of the S-PA on the flow field was considerable. When the DC voltage was negative, the current generated increased (versus the typical AC-PA) during the positive half cycle, and then decreased during the negative half. The ionic wind direction of the S-PA was found to be dependent on the value of the AC voltage, and may be perpendicular to or inclined against the plate wall.

Seney et al. [90] considered the effect of the S-PA by evaluating three strategies. In the first one, the encapsulated electrode was supplied by a negative DC voltage, while one exposed electrode (electrode 3) was grounded. In the second strategy, the encapsulated electrode was grounded and the exposed electrode (electrode 3) was supplied with a negative DC voltage. In the last strategy, both the encapsulated and exposed electrodes (electrodes 2 and 3) were supplied with negative DC voltages. The S-PA injected momentum into the flow field with significant directionality, not only in the horizontal direction. In fact, when the AC-actuated exposed electrode was supplied by a voltage of 13 kV, and the other exposed and encapsulated (second and third) electrodes were supplied by a DC voltage of −2 kV, the optimal condition for generating a jet with an inclination angle of approximately ${60}^{\circ }$ from the horizontal plane was found. However, the flow structure induced by the S-PA remained unchanged.

Zheng et al. [91] applied a S-PA on a flat plate to modify the ionized jet inclination angle. In their work, one upper electrode (electrode 1) was actuated with a pulsating frequency and the other one (electrode 3) was operated with a DC voltage in the range of −18 to 18 kV. When the ratio of the DC voltage to the AC one was −1, the peak value of the jet velocity was found to be maximum at this Y = 3.3 mm vertical position.

A further investigation of the effects of S-PA on a flat plate was performed by Chen et al. [87]. The first upper electrode was actuated with a voltage of 40 kV and a frequency of 5 kHz, the encapsulated electrode was grounded, and the second upper electrode was operated with a DC voltage of −10 kV. The S-PA generated vorticity from the middle position of the actuator (between the consecutive upper electrodes) and lifted the vorticity volume from the wall surface, bringing momentum into the upper portion of the boundary layer. As a result, flow velocity significantly increased within the boundary layer and the mean peak velocity notably increased at a downstream location 120 mm from the DC-supplied exposed electrode.

Guo et al. [86], by employing a methodology analogous to that utilized by Chen et al. [87], studied the physical mechanism and the influence of the S-PA on a flat plate. Results demonstrated that the S-PA had a strong perturbation degree to the flow field between the electrodes, and the induced ionized flow direction was vertical upward. In addition, a non-uniformity disturbance to the flow field in the boundary layer was observed at the leading edge of the second exposed electrode (third electrode in Figure 11). And, a mixing effect between the upper and lower regions of the flow field was enhanced by the vertical momentum injection, near the second exposed electrode. As a result of the directional momentum injection of the S-PA on the boundary layer upper region, the velocity characteristics in this region were enhanced from the leading edge of the exposed electrode to downstream. Causing the upper flow field to squeeze the lower flow, which mainly leads to the fluctuation of the velocity partition layer in the lower region, moving downwards the boundary between the upper and lower layers. This combined effect is summarized in Figure 14.

The various strategies employed to activate the electrodes used in S-PAs are presented in

Table 1. S-PA main operational parameters when applied to a flat plate, and the main focus of the study.

Ref.	Electrode 1	Electrode 2	Electrode 3	Aim of Study
[88]	AC −18 kV	AC −18 kV	DC 11 kV	Micro discharge
	1 kHz	1 kHz		currents
[89]	AC 20 kV	DC 19 kV	DC −10 kV	Accelerate the ionic wind
	1 kHz
[84]	AC 12 kV	DC 20 kV	DC 20 kV	Accelerate the ionic wind
	11.7 kHz
[90]	AC 13 kV	DC −2 kV	DC −2 kV	Flow direction
	10 kHz
[91]	AC 18 kV	DC −18 kV	DC −18 kV	Flow direction
	AC 8 kHz DC = 5%
[86,87]	AC 40 kV	Grounded	DC −10 kV	Accelerate the ionic wind
	5 kHz

. The primary focus of each individual study is highlighted in the last column of the table.

The previous section focused on analyzing the S-PA configurations that enhance the plasma region and influence the ionic wind direction on flat plates. The following section reviews studies that utilize some combination of sliding DBD and nanosecond-DC-Pulsed DBD plasma actuators on flat plates via experimental investigations.

3.3. Combination of Nanosecond-DC-Pulsed DBD Actuator and Sliding DBD Plasma (PS-PA)

Combination DBD actuators integrate features of nanosecond pulsed voltage excitation and sliding dielectric barrier discharge plasma (PS-PA). Unlike the conventional approach for sliding DBD actuators presented in Section 3.2, where an AC voltage drives the first exposed electrode, this configuration employs a nanosecond pulsed voltage to that exposed electrode. Meanwhile, the encapsulated and second exposed electrodes operate in the manner of a traditional sliding DBD plasma system, enabling the generation and propagation of surface plasma along the dielectric layer. More detailed information on nanosecond-AC/DC-pulsed DBD actuators is introduced in Section 4.3.

Song et al. [92] studied a PS-PA particular design, see a schematic view in Figure 15. The first pulsed, exposed electrode was supplied with a positive DC voltage of 7.2 kV, while a negative DC voltage was applied to the second exposed electrode. The encapsulated electrode was grounded. The induced body force resulting from this configuration increased significantly with the decrease from −8 kV to −12 kV of the DC voltage applied to the second exposed electrode. The maximum ionized jet velocity induced by the PS-PA was 1.75 m/s, which is considerably larger than the one generated by a conventional PA, which is around 1.05 m/s.

Bayoda et al. [93] examined the actuator energy consumption by evaluating the energy deposition on the DBD surface. The deposited energy produced local heat mainly from vibrational excitation, leading to pressure waves whose strength increased linearly with the consumed energy. The first exposed electrode was actuated with a pulsating frequency of 1 kHz and a voltage of 20 kV. It was observed that luminescent plasma formed only when the electrode was supplied by a sufficiently high negative voltage. When a DC voltage of −16 kV was applied to the other exposed electrode (electrode 3 from Figure 11), the ionized channels crossed over the inter electrode distance (see Figure 16) and modified the heated gas region above the discharge. The S-PA configuration generates a rather long plasma extension, therefore extending the linear part between the semi-spherical pressure waves; see Figure 17. Both hemispherical waves propagated at ≈360 m/s, but the weaker pressure wave was associated with reduced local heating since most energy was deposited near the pulsed exposed electrode. Overall, the heated gas region was enlarged and heat deposition was extended by the negative DC component, which is expected to enhance flow control effectiveness.

Bayoda et al. [82] studied the boundary layer and the pressure wave generated by a PS-PA. The pulsed, exposed electrode was supplied with a positive DC voltage from 10 to 18 kV. At voltages ≤ 14 kV, the current peaks split into two parts (capacitive and discharge), but at higher voltages, the discharge current dominated the capacitive current and then two bumps were superimposed. In addition, the PS-PA produced a pressure wave with two main regions: a circular region and a planar region matching the plasma size. As a result, the PS-PA discharges enhanced the pressure wave over a longer distance, with a maximum pressure appearing above the ionizing electrode. This also increased heat deposition on the DBD surface, indicating stronger local heating and gas density changes.

In the following section, the main applications of nanosecond-Pulsed-DC DBD plasma actuators on flat plates via experimental investigations will be summarized.

3.4. Nanosecond-DC-Pulsed DBD Plasma Actuator (D-PA)-McGowan Approach

One of the first studies on the boundary structures appearing in the viscous sublayer is the one from Kline et al. [94]. They found that in the vicinity of a wall, turbulent flow forms long and thin streaks of slow-moving fluid. These streaks interact with the faster flow above them are lifted and become unstable, and then suddenly break apart in a process called bursting, which enhances turbulence. In the present subsection it will be seen that, to suppress this bursting mechanism and control the boundary-layer dynamics, DBD plasma actuators are applied on a flat plate. An initial review of the viscous drag reduction in turbulent boundary layers using flow control methodologies was performed by Corke and Thomas [95]. They focused either on modifying the large-scale outer motions or the small-scale motions near the wall that are particularly associated with low-speed wall streaks on flat plates. Subsequent experimental attempts using plasma actuators have highlighted the importance of properly targeting these motions. For instance, one of the earliest plasma designs created by [96] was ineffective in reducing the drag; they stated it was because the actuator did not induce sufficiently strong oscillatory motion in the flow, or at the right speed, where drag reduction was expected based on earlier studies.

One of the initial micro-pulsed-DC actuators, developed by McGowan et al. [97] was intended as a hybrid approach that combines the advantages of both AC and DC plasma actuators. In their design, the DC source is supplied to both electrodes; see Figure 18. A resistor (R) limits the current to the encapsulated electrode, which is also connected to a fast-acting solid-state switch that, when closed, reduces the voltage applied between the encapsulated electrode (lower electrode) and the power supply ground. A periodic trigger signal consisting of a TTL pulse is supplied to activate the solid-state switch.

Through this process, the DC applied voltage in the upper electrode remains constant in time while the encapsulated electrode is periodically grounded for extremely short instances of time ($20 \mathsf{\mu }$s). This gives rise to a transient plasma formation and an associated body force. In addition, the DBD unit in this design was made with an Ultem film [97], which is a PolyEtherImide (PEI) that is not affected by exposure to $O_3$.

In the following work undertaken by Duong et al. [98] they experimentally applied a D-PA on a flat plate (22.86 × 22.86 cm²) to create a plasma-induced spanwise region. The upper electrode of the actuator was operated with a DC voltage while the lower one was periodically grounded. An important characteristic from an application standpoint was that, over most of the cycle, the current-voltage product (power applied) was extremely small when compared to typical AC plasma actuator configurations. Two D-PA configurations, asymmetric and symmetric, were considered. In both configurations, the electrodes were located along the streamwise direction (X); see Figure 19. The actuators were operated in Mach numbers between 0.05 and 0.5. According to the results, the degree of drag reduction achieved was a function of two parameters: the viscous unit between electrodes defined as ${\lambda }_z^{+}={\displaystyle \frac{{\lambda }_z{u}_{\tau }}{\nu }}$, ${\lambda }_z$ being the distance in the vertical direction between the electrodes, and the ratio of maximum plasma-induced spanwise velocity defined as $W_{max}/u_{\tau }$, where $u_{\tau }$ stands for the friction velocity. The optimum values of both parameters ($W_{max}/u_{\tau }$ and ${\lambda }_z^{+}$) were found to vary with the applied voltage. The study found that the D-PA could be applied to reduce viscous drag at all studied wind speeds. They also found that reducing the number of viscous units between the upper electrodes (a smaller ${\lambda }_z^{+}$) increased the drag reduction. Drag reduction at low Mach numbers (0.05) was most significant when ${\lambda }_z^{+}$ and $W_{max}/u_{\tau }$ were 1000 and 1.65, respectively, under a high voltage of 8 kV. At a higher Mach number of 0.5, drag reduction up to 46% was achieved when ${\lambda }^{+}$ was 900. At the lowest Mach number, the effect of the D-PA on the logarithmic region of the boundary layer was insignificant; however, closer inspection near the plate revealed a notable effect in the viscous sublayer and the buffer zone. Both configurations achieved unprecedented levels of friction drag reduction in the turbulent boundary layer. As observed in Figure 20, the spanwise near-wall flow induced by the plasma actuator array serves to suppress streak lift-up, thereby reducing the bursting instabilities first observed by Kline et al. [94] that enhance turbulence within the boundary layer.

Thomas et al. [99] implemented D-PAs on the same flat plate used by [98] to induce spanwise flow and prevent the lift-up mechanism of low-speed streaks in the boundary layer (BL) near the wall. The PAs were designed as in [98] with two different distances between the electrodes, ${\lambda }_z$ = 19 and 23 mm, for the configurations b and a, respectively; see Figure 19. A pulsating frequency of 500 Hz, and a DC voltage range from 4 to 8 kV were used for both configurations. Experimental investigations using configuration b were conducted at wind speeds in the range 0.05 ≤ $M_{\infty }$ ≤ 0.1; configuration A was employed at wind speeds between 0.05 ≤ $M_{\infty }$ ≤ 0.15. Baseline results indicated that the number of low-speed streaks in the boundary layer increased as a function of the Mach number, from observing approximately 8 streaks at $M_{\infty }=0.05$ to 15 at $M_{\infty }=0.15$. In the actuated case, the greatest change in drag occurred when viscous wall units were between 800 ≤ ${\lambda }_z^{+}$ ≤ 1000 (8–10 streaks), regardless of the configuration used. Maximum drag reductions occurred with configuration B operating at 6 kV, resulting in up to 68% drag reduction at the lowest wind speed and 17% at maximum wind speed. Moreover, at high Mach numbers, when using the first configuration and when $W_{max}/u_{\tau }$ ≥ 1 and ${\lambda }_z^{+}$ ≈ 1000, drag reduction increased by increasing the voltage applied. However, at some particular wind speeds, increasing the voltage (7 kV ≥ DC voltage) resulted in higher drag. Figure 21 presents a series of shadowgraph images obtained at the indicated delay times after the DC pulse.

Duong et al. [100] studied the effect of the D-PA injecting momentum into the boundary layer. To reduce the wall-normal vorticity component, the D-PA with the same design as in [98,99] was implemented on a flat plate with a pulsating frequency of 500 Hz, ${\lambda }_z$ = 28 mm, and a range of voltage from 4 to 8 kV at Reynolds number $725\times {10}^3$. The results showed a reduction in both components of turbulent velocity fluctuations, and thereby a resulting drag reduction. The drag reduction had a greater effect on decreasing the wall-normal turbulence intensity ${\nu }^{\prime }$ than on the streamwise turbulence intensity, $u^{\prime }$. This is due to the fact that the fluctuations of ${\nu }^{\prime }$ depend on the energy transfer from the reduced $u^{\prime }$ fluctuations via pressure strain rate terms. The largest reduction in turbulent fluctuations occurred nearest to the wall, and the effect of the drag reduction at distances y/$\delta$ = 0 to y/$\delta$ = 0.8 from the wall was particularly significant. For a voltage of 5 kV and ${\lambda }_z^{+}$$=300$, a drag reduction of 68% was observed, and an average decrease in turbulence intensity ${\nu }^{\prime }$ and $u^{\prime }$ of 22% and 16% across the log layer was respectively reported.

In another study to produce a spanwise near-wall flow by D-PAs, Meyers et al. [101] modified the BL by applying the PAs configuration A, on the same flat plate as in [99,100]; see Figure 19. The Reynolds numbers considered ranged between 2.8 × ${10}^6$ and 8.1 × ${10}^6$. The D-PAs were operated with a pulsating frequency of 500 Hz and with a range of voltages from 4 to 8 kV. In addition, a range of viscous units between electrodes ranging between 200 ≤ ${\lambda }_z^{+}$ ≤ 3000 were evaluated, where ${\lambda }_z$ was 22 mm. When operating at the highest Reynolds number, the shear velocity tended to decrease with the increase in the voltage applied to the actuator. However, at the lower Reynolds numbers tested (Reynolds numbers based on the momentum thickness 6230 ≤ $R{e}_{\theta }$ ≤ 8735) the shear velocity would instead increase when the highest actuator voltage was applied, the same result was observed in [99]. In the actuated case, at ${\lambda }_z^{+}$/$R{e}_{\theta }$ ≤ 0.3, the optimum value of $W_{max}/u_{\tau }$ was 0.5 and 71% drag reduction was obtained at the lowest Reynolds number where ${\lambda }_z^{+}$ = 1000 and at maximum voltage of 8 kV. The boundary layer thickness ranged from 55 to 40 mm, depending on the incoming wind speeds. The largest effect across the buffer layer was on turbulence intensity ${\nu }^{\prime }$.

The previous section focused on application of D-PA configurations to enhance the plasma region and induce viscous drag reduction on flat plates. In all these studies, electrodes were placed along the wind direction. The D-PAs were actuated with a pulsating frequency of 500 Hz and a very small duty cycle of 1% (pulse width $20 \mathsf{\mu }$s), which created an extremely short current spike of ($10\times {10}^{-7}$ A). Note that, the applied frequency was not related to any outer or inner characteristic time scales of the baseline turbulent boundary layer (TBL). As such, the actuation mechanism employed is very similar to the activation mechanism used in nanosecond-AC/DC-pulsed PAs presented in Section 4.3.

• Summary of the achievements of DBD plasma actuators applied to Flat plates.

The plasma actuators implemented in both single and multiple configurations on flat plates effectively enhanced flow control by increasing momentum transfer, mitigating vortex shedding, and reducing aerodynamic drag and noise. The performance of the actuators was strongly dependent on a combination of factors, such as DBD/electrode materials, electrode geometry, and excitation parameters, in particular, the type and frequency of the driving waveform. Optimizing these parameters is critical to maximizing the effectiveness of the actuators in aerodynamic applications as follows:

• Three parameters are particularly relevant when considering the efficiency of plasma actuators performance: the DBD material (i.e., thickness and permittivity), the geometry of the exposed electrodes [15], and the length of the encapsulated electrode. These parameters should be optimized for maximizing actuator performance [15,72]. At higher voltages ($V_{pl}$ ≥ 20 KV), materials with lower permittivity (i.e., ${ϵ}_r=2$) demonstrated greater efficiency compared to others, whereas the opposite trend was observed at lower voltages. The thinnest DBD produced the highest velocity within a specific voltage range; however, at high voltages, the thickest DBD yielded the highest velocity while maintaining a non-filamentary discharge [15,72]. An increase in voltage reduces the boundary layer thickness $\left(\delta \right)$, leading to a decrease in displacement thickness ${\delta }^{*}$, momentum thickness ${\delta }_{\theta }$, and shape factor H (${\delta }^{*}$/${\delta }_{\theta }$) [73,74].
• In the PA, when the distance (gap) between the electrodes exceeds a certain threshold, the electric field dropped down. When the distance was negative (i.e., part of the upper electrode was located above the lower one), the symmetric distribution of the electric field did not accelerate the ionic wind.
• Parasitic ionization (spurious plasma formation) was observed when the spacing between exposed electrodes was determined to be insufficient when considering the multiple strategy with conventional plasma actuators (PA). An optimal electrode spacing was found to minimize parasitic discharge and produce the highest induced flow velocity.
• As the actuator voltage increased, more energy was injected into the boundary layer. The plasma actuation configuration, which acted across the shear layers to disrupt circulation during vortex roll-up, was the most effective design for aerodynamic noise [76] and drag reduction enhancement in the boundary layer [77,79,80]; see parts a and b in Figure 9. In addition, a sinusoidal waveform was chosen for most experiments because, compared to other waveforms, it produces the least distortion from capacitance and inductance effects in the plasma actuator circuit [15].
• In conventional plasma (asymmetric DBD actuators), the DBD unit produces very high power peaks, which may induce problems of electromagnetic hazards. Consequently, researchers began to focus on developing actuators that can achieve a more stable discharge [88]. Turning to the S-PA configuration led to a more homogeneous plasma with DC < 0 and a higher induced velocity than the typical DBD (PA). In S-PA, the application of a positive DC voltage component (VDC > 0) did not significantly change the DBD current. The velocity of the electric wind created by the three-electrode S-PAs with VDC > 0 is always greater than when VDC < 0. As such, to increase the velocity of the ionized wind, a positive DC voltage has to be applied to the downstream exposed electrode. These actuators changed the direction of the flow downstream in the boundary layer.
• In S-PA, the AC-actuated, exposed electrode mainly produces ions, while the DC-activated, exposed electrode collects them. As a result, the total current in the sliding discharge is a combination of three parts: capacitive, discharge, and sliding currents. In addition, the DC-actuated electrode had a strong influence on the velocity of the flow field. Moreover, the deposition energy of the actuator increased when compared against the typical plasma actuator (PA). The combination of the sliding DBD with nanosecond DC pulsed discharge (PS-PA), effectively enhanced the pressure wave generation [82,93].
• In previous studies surrounding D-PA, the actuators were implemented to produce a spanwise near-wall flow of sufficient magnitude to inhibit the lift-up of the near-wall streaks, resulting in drag reduction at high wind speeds. The degree of the drag reduction highly depended on two parameters, ${\lambda }_z^{+}={\displaystyle \frac{{\lambda }_z{u}_{\tau }}{\nu }}$, $W_{max}/u_{\tau }$, and the optimum value of both parameters ($W_{max}/u_{\tau }$ and ${\lambda }_z^{+}$) was found to vary with the applied voltage. The first parameter describes the non-dimensional distance between electrodes and characterizes how many near-wall streaks can be controlled, which indicates the overall potential to reduce drag. The second one describes the level of spanwise plasma-induced flow required relative to the local friction velocity. The lift-up of the low-speed streaks gave rise to a flanking wall-normal vorticity ($w_y$). The high level of $w_y$ is critical for streaks’ transient growth within the boundary layer. Regardless of the D-PA configuration considered, when applying an optimal ${\lambda }_z$ and optimal excitation parameters, the streak lift-up at high Reynolds numbers was suppressed.

4. DBD Plasma Actuators (PAs) on Wind Turbine Airfoils

In the present section, numerical and experimental studies on the implementation and effects of PAs on single airfoils are discussed. In all studies, the actuators may be positioned at a single or multiple chordwise locations.

4.1. Numerical Studies

The following section presents the main numerical studies concerning the PAs implementation on airfoils, which are based on the phenomenological models such as Shyy and S-H models.

Ebrahimi and Hajipour [102] used the Shyy model to implement two traditional PAs on a NACA 4415 airfoil. The PAs were placed at two locations, $19\%C$ (chordwise location) on the suction surface of the airfoil and at $99\%C$ on the pressure surface. Three distinct strategies were implemented to actuate the PAs with an applied voltage of 4 kV. A Reynolds number of $5.5\times {10}^5$ and an angle of attack (AoA) of ${18}^{\circ }$ were employed. In addition, two non-dimensional frequencies, $F^{+}={\displaystyle \frac{f_{pl}C}{U_{\infty }}}=0.8$ and $4.8$, were applied to the actuators. In the first and second strategies, the PAs placed at $19\%C$ and $99\%C$ were actuated simultaneously, and with respective non-dimensional frequencies of $F^{+}=0.8$ and $F^{+}=4.8$. In the third strategy, a single actuator was actuated with $F^{+}=0.8$. Based on the first, second, and third strategies, the efficiency of the airfoil was improved by 127%, 75%, and 89%, respectively, as compared with the no-actuation case.

Giorgi et al. [103] applied PAs on an oscillatory airfoil. Three PAs, based on the Shyy model and with an applied voltage of 4 kV and frequency of 3 kHz, were installed from $76\%C$ to the trailing edge on each side of a NACA 23012 airfoil; see Figure 22. At a Reynolds number of $6\times {10}^5$, the PAs were actuated under pitching state with a mean AoA of 7.$7^{\circ }$, an amplitude of $\pm 7^{\circ }$, and pitching circular frequencies of 20, 60, and 100 rad/s. The PAs were operated simultaneously in two groups, defined by the blue and red arrows in Figure 22. Results showed that, by increasing the pitching frequency, the effect of the PAs decreased. At low pitching frequencies, a small improvement of the lift coefficient, versus the non actuated case, was observed when activating the red actuators configuration.

Karthikeyan and Harish [104] enhanced the aerodynamic performance of a NACA 4412 airfoil by using a combination of a PA and a Gurney flap. The PA was designed based on the Shyy model; it was located at $2\%C$ and actuated with three applied voltages of 5.66 kV, 5.67 kV, and 6 kV, with a constant pulsating frequency of 5 kHz. In addition, a Gurney flap with heights of $1\%C$, $2\%C$, and $3\%C$ and a width of 2 mm was installed at the trailing edge of the airfoil. Numerical investigations were performed at a Reynolds number of $3.1\times {10}^6$ and at AoAs from $0^{\circ }$ to ${20}^{\circ }$. According to the results, at the stall AoA, the lift coefficient was increased by 35%, 58%, and 82% versus the clean case when Gurney flaps with heights of 1%C, 2%C, and 3%C were applied on the airfoil, respectively. In addition, when the PA was activated at the stall AoA and for the respective Gurney flap heights, the lift coefficient was increased by 94%, 118%, and 140% versus the clean case. It was observed that, to suppress flow separation, the voltage applied to the PA had to be increased when increasing the stall AoA.

Xu et al. [105] applied PAs on an EPPLER555 airfoil, equipped with a rudder with several deflection angles from $3^{\circ }$ to $9^{\circ }$. A single PA was operated at a Reynolds number of 410,752 with an applied voltage of 5 kV, a frequency range of 4 to 8 kHz, and at two AoAs of $0^{\circ }$ and ${15}^{\circ }$. At the AoA of $0^{\circ }$, when the PA was operated with the maximum frequency and for a deflection angle of $4^{\circ }$, the lift coefficient was prominently increased by 76.5% versus the no-actuation case. However, when the PA was operated with the maximum frequency, the effect of the PA at an AoA of ${15}^{\circ }$ and for a deflection angle of $8^{\circ }$ was significantly greater (over ≈24,000%) than at $0^{\circ }$.

Table 2. Different parameters considered for PAs in Shyy model on wind turbine airfoils.

Ref.	Theory	Geometry	Voltage	Location	Airfoil
[103]	Shyy	$l_{pl,e}$ = 0.5 mm	$V_{pl}$ = 4 kV	76%C to	NACA 23012
	2D	$l_{pl,c}$ = 3 mm	$f_{pl}$ = 3 kHz	100%C	Chord = 30 cm
		$T_{pl,e}$ = 0.1 mm			(pitching)
[105]	Shyy	$l_{pl,e}$ = 0.5 mm	$V_{pl}$ = 5 kV	16.5%	EPPLER555
	2D	$l_{pl,c}$ = 0.01 C	$f_{pl}$ = 8 kHz		Chord = -
[102]	Shyy	$T_{pl,e}$ = 0.1 mm	$V_{pl}$ = 4 kV	19%C	NACA 4415
	3D	$l_{pl,e}$ = 0.5 mm	$F^{+}$ = 0.8		Chord = 40 cm
		$l_{pl,c}$ = 3 mm
[104]	Shyy	Total length = 10 mm	$V_{pl}$ = 6 kV	2%C	NACA 4412
	3D	$T_{pl,e}$ = 0.1 mm	$f_{pl}$ = 5 kHz		Chord = 6.5 cm
		$T_{pl,i}$ = 0.8 mm

illustrates the corresponding geometry and location parameters of PAs that have been applied on wind turbine airfoils using the Shyy model; the corresponding voltage (rms) and frequency is also presented. Some of these parameters were determined optimal for the corresponding application.

Fukumoto et al. [106] investigated the aerodynamic effects on a NACA $63\left(3\right)-618$ airfoil by implementing a PA. The PA, based on the S-H model, was placed at the airfoil leading edge, at 10%C, and at 60%C. They were operated with a pulsating frequency of 500 Hz, a Duty Cycle (Dc) of 10%, and a ratio of electrical force to the kinetic energy per unit volume of the flow $D_c^{*}={\displaystyle \frac{\overrightarrow{E}{e}_{pl}{\rho }_{pl}C}{{\rho }_{\infty }{U}_{\infty }^2}}=10\%$, being the PA force. The numerical investigations were performed at a Reynolds number of $84\times {10}^3$ and under a pitching state with an amplitude AoA of ${\pm 15}^{\circ }$. Results show that actuating the PA at the downstream location of 60%C enhanced the aerodynamic efficiency ($C_l/C_D$) of the airfoil by 3% as compared with the clean case.

Guoqiang and Shihe [107] designed a PA based on the S-H model and implemented it at the leading edge of an S809 airfoil in order to control the dynamic stall. The PA was located at 2%C, actuated with a pulsating frequency between 25 and 200 Hz and a Dc in the range of 1% to 100%. The numerical investigations were evaluated at $Re=1\times {10}^6$ and under a dynamic pitching state with an amplitude AoA of $\pm 7^{\circ }$. The results showed that the PA affected the suction distribution on the upper surface of the airfoil and improved the aerodynamic performance of the airfoil when the plasma was actuated with a pulsating frequency of 50 Hz ($F^{+}={\displaystyle \frac{f_{pu}C}{U_{\infty }}}$ = 1.5) and Dc = 80%. Similarly to the plasma actuator modeled after Shyy’s formulation, the non-dimensional pulsating frequency and the non-dimensional periodic frequency in the range of 1 to 1.5 demonstrated the ability to enhance the actuator’s performance.

In Fadaei et al. [108], a PA was designed based on the S-H model, operated at three Reynolds numbers of $142\times {10}^3$, $285\times {10}^3$, and $427\times {10}^3$ and a range of AoAs from ${12}^{\circ }$ to ${30}^{\circ }$. Three PA locations, namely the leading edge, 2%C, and 15%C, were considered. When the PAs were activated at the stall AoA of ${21}^{\circ }$, the lift coefficient was improved across all Reynolds numbers. The impact of the PAs at Reynolds number $285\times {10}^3$ was most significant when the PA was located at the leading edge and activated with an applied voltage of 12 kV and a frequency of 12 kHz. Under these conditions the airfoil aerodynamic performance improved, versus the baseline case, by 300%.

In a further paper, Fadaei et al. [109] applied genetic algorithms to maximize the effect of the PA on the same airfoil previously analyzed in [108]. The PA locations and the range of AoAs were the same as in their previous paper [108], two Reynolds numbers of $142.5\times {10}^3$ and $427\times {10}^3$ were considered. In addition, a range of frequencies from 2.17 to 12 kHz and five applied voltages from 6 to 12 kV were employed. The location of the PA changed with the Reynolds number and AoA, and had a significant impact on flow separation. At a Reynolds number of $142.5\times {10}^3$, operating the PA at the leading edge had the highest effect at all AoAs. For the rest of the Reynolds numbers, the location of 2%C was more effective. The effect of the location in suppressing the flow at post-stall condition was minor, and maximum effectiveness was obtained at stall AoAs of 12.$9^{\circ }$ and ${12}^{\circ }$.

The geometry of a PA and associated parameters implemented on a DU 25 airfoil were optimized by Omidi and Mazaheri [110] using genetic algorithms. Instead of following a Gaussian distribution [39,40], the PA was modeled with a different boundary condition, in which the charge density distribution on the electrode boundary surface was proportional to the electric potential [54,111]. The PA was operated at a Reynolds number of $1\times {10}^6$ and an AoA of ${13}^{\circ }$. A range of frequencies from 1 to 10 kHz and five applied voltages of (7, 9, 11, 13, and 15 kV) were considered. The geometry of the encapsulated electrode ranged between ($0.01\%C\le l_{pl,c}\le 0.05\%C$), DBD thicknesses ranged between ($0.001\%C\le t_{pl,i}\le 0.012\%C$), and several DBD permittivities were also studied. It was observed that longer electrodes and higher permittivity resulted in a higher body force; however, the energy consumption of the actuators increased. Increasing the DBD thickness initially affected the body forces and aerodynamic performance, but beyond a certain point, further increases had a minimal effect.

Omidi and Mazaheri [112] applied a PA at the middle of a DU21 airfoil. The PA was designed based on the S-H model and operated with an applied voltage and frequency of 12 kV and 5 kHz, respectively. Four parameters, including the encapsulated electrode length ($0.01\%C\le l_{pl,c}\le 0.09\%C$), electrode thickness ($0.00001\%C\le T_{pl,e}\le 0.00055\%C$), DBD thickness ($0.001\%C\le t_{pl,i}\le 0.01\%C$), and DBD relative permittivity ($1\le {ϵ}_r\le 10$), were considered. Investigations were carried out at a Reynolds number of $1\times {10}^6$ and at the stall AoA of ${16}^{\circ }$. The generated PA body force improved as the length of the encapsulated electrode and the permittivity of the DBD unit increased and as the thickness of the electrodes and the DBD unit decreased.

Table 3. Different PAs parameters considered in S-H model on wind turbine airfoils.

Ref.	Theory	Geometry	Voltage	Location	Airfoil
[108]	S-H	$T_{pl,e}$ = 0.0254 mm	$V_{pl}$ = 12 kV	0%C	-
	2D	$T_{pl,i}$ = 0.127 mm	$f_{pl}$ = 12 kHz		Chord = 25 cm
		$l_{pl,e}$ = 10 mm
		$l_{pl,c}$ = 15 mm
[112]	S-H	$l_{pl,c}$ = 0.035%C	$V_{pl}$ = 12 kV	50%C	DU21
	2D	$l_{pl,e}$ = 0.032%C	$f_{pl}$ = 5 kHz		Chord = 100 cm
		$T_{pl,i}$ = 0.001%C
		${ϵ}_r$ = 6
		$D_{pl}$ = 0.002%C
[109]	S-H	$T_{pl,e}$ = 0.0254 mm	$V_{pl}$ = 11.7 kV	0%C	-
	2D	$T_{pl,i}$ = 0.127 mm	$f_{pl}$ = 11.9 kHz		Chord = 25 cm
		$l_{pl,e}$ = 10 mm
		$l_{pl,c}$ = 15 mm
[107]	S-H	$T_{pl,i}$ = 0.15 mm	$f_{pu}$ = 50 Hz	2%C	S809
	3D	$l_{pl,e}$ = 4 mm	$V_{pl}$ = 5 kV		Chord = 45 cm
		$D_{pl}$ = 0	Dc = 80%
		${ϵ}_r$ = 2.7	$F^{+}$ = 1.5
			$f_{pl}$ = 1 kHz
[106]	S-H	$l_{pl,c}$ = $0.01\%C$	$f_{pu}$ = 500 Hz	60%C	NACA ${63}_3-618$
	3D	$l_{pl,e}$ = $0.06\%C$	Dc = 10%		Chord = 20 cm
		$T_{pl,e}$ = $0.0005\%C$	$F^{+}$ = 1.3		(pitching)
		$T_{pl,i}$ = $0.0005\%C$	$D_c^{*}$ = 10%

illustrates the various PA parameters that have been investigated when applied on wind turbine airfoils and under the S-H model. The corresponding maximum (Peak) voltage and frequency is also presented. Across these studies, several of the listed parameters were found to yield optimal performance.

4.2. Experimental Investigations

The following section details some of the most relevant experimental investigations conducted on PA integrated into WTs airfoil configurations.

4.2.1. PA-Periodic Forcing on Airfoils

In this section, the experimental investigation of WT airfoils is discussed under continuous plasma actuation in periodic mode.

Guoqiang et al. [113] used a traditional PA to experimentally control the dynamic stall on an airfoil. A single PA was operated with an applied voltage of 22.5 kV and a frequency of 5.6 kHz; it was located at 8.3%C on the suction side of an S809 airfoil. The experimental investigations were evaluated at wind speeds of 10, 15 and 20 m/s and under a dynamic pitching state with an amplitude AoA of ${\pm 7}^{\circ }$. According to the results at 10 m/s, the effect of the PA at a low pitching frequency of 0.5 Hz was significant and decreased the average drag coefficient by 44.5%, increased the lift coefficient by 7.1%, and decreased the hysteresis loop by 4.5%. Similar effects for wind velocities of 15 and 20 m/s were observed.

In the study of Patel et al. [114], they applied a PA on S827 and S822 airfoils to suppress flow separation. The PA was placed at 78%C and actuated over a small range of AoAs and at a wind speed of 20 m/s. Compared to the non-actuated case, the lift increased at all AoAs. In addition, they considered the effect of water (see Figure 23b), and sand (see Figure 23c) on the PA. Water shut down the PA temporarily, but just for a few seconds while most of the water either evaporated or was pushed away by the PA. With regard to the sand experiment, there were no negative effects observed.

Unal et al. [115] improved the aerodynamic performance of a NACA 0015 airfoil by performing experimental and numerical studies. A range of applied voltages from 4 to 10 kV, with frequencies from 1.5 to 5.5 kHz and at AoAs of $0^{\circ }$, $5^{\circ }$, ${10}^{\circ }$, ${12}^{\circ }$, and ${14}^{\circ }$ were evaluated at a Reynolds number of 150 × ${10}^3$. The PAs were located on the airfoil upper surface at 10%C, 20%C, 50%C, and 95%C and actuated considering four strategies based on single and multi chordwise PAs locations. When considering the first strategy, just a single PA placed at 10%C was energized, and for the second one, the PAs were operated simultaneously at 10%C and 20%C. In the third strategy, three PAs were operated simultaneously at 10%C, 20%C and 50%C, and in the last strategy, all PAs were actuated simultaneously. Results showed that the applied voltages of 4 to 8 kV were ineffective, generating minor flow variations versus the clean case. Actuating the PAs by using the first and second strategies had a negative effect on the aerodynamic performance of the airfoil, but actuating them considering the last strategy, with the maximum applied voltage of 10 kV and with a frequency of 3.5 KHz, improved the aerodynamic performance of the airfoil.

Walker and Segawa [116] mitigated the flow separation using DBD plasma actuators on a NACA 0024 airfoil. The PAs were located at the leading edge and at 25%C on the airfoil suction surface. They were actuated with a voltage of 8 kV and a frequency of 9 kHz at three AoAs ($8^{\circ }$, ${12}^{\circ }$, and ${16}^{\circ }$) and three wind speeds ($U_{\infty }$ = 2.5, 5, and 10 m/s). The effectiveness of the plasma actuation was observed to change with AoA and wind speed. For a wind speed of $U_{\infty }$ = 2.5 m/s, the maximum effectiveness was obtained at an AoA = ${12}^{\circ }$ and when the PA was operated at the leading edge. For the same AoA and at a wind speed of 10 m/s, the optimum position of the PA was at 25%C.

Joseph et al. [117] implemented a PA on a NACA ${65}_4-421$ airfoil, taking advantage of the Coanda effect. Two PAs were actuated on the trailing edge of the airfoil with two applied voltages (15 kV and 18 kV) and a fixed frequency of 1 kHz. A Reynolds number of $2\times {10}^5$ and a range of AoA from $-7^{\circ }$ to $5^{\circ }$ were considered. A slight improvement in the lift coefficient was observed across all AoAs when both PAs were activated and regardless of the voltage applied.

Brownstein et al. [118] implemented PAs at 50%C and 70%C on a GOE 735 airfoil. Double PAs were operated with applied voltages between 1 and 9.9 kV and frequencies from 2 to 6 kHz, at a Reynolds number of $15\times {10}^3$, and for a wide range of AoAs. The lift coefficient of the airfoil at particular AoAs significantly improved when the PAs were actuated with a voltage of 9.9 kV and a minimum frequency of 2 kHz.

Karadag et al. [119] applied the PAs on a NACA 4412 airfoil. The PAs were operated in four strategies based on the PA location; see Figure 24. Investigations were carried out at a fixed Reynolds number of 35,000 and at three AoAs of ${10}^{\circ }$, ${20}^{\circ }$, and ${30}^{\circ }$. It was found that, actuating the PA at the AoA of ${20}^{\circ }$ by the third (multiple electrode spanwise) and fourth strategies (double electrode streamwise), delayed the stall angle by $6^{\circ }$ versus the clean case.

In

Table 4. Main PAs parameters of wind turbine airfoils under periodic (continuos) mode of operation (Experimental).

Ref.	Dimension	Methodology	Voltage	Location	Airfoil
[114]	$l_{pl,c}$ = 50 mm	Ramps	$V_{pl}$ = 35 kV	78%C	S822
	$T_{pl,i}$ = 6.4 mm	Impact of Rain and Sand	$f_{pl}$ = 2.3 kHz		Chord = 30 cm
	$l_{pl,e}$ = 50 mm
	$T_{pl,e}$ = 0.0254 mm	∗Copper ∗Teflon
[116]	$T_{pl,e}$ = $35 \mathsf{\mu }$m	PIV	$V_{pl}$ = 22.5 kV	8.3%C	NACA 0024
	$T_{pl,i}$ = $125 \mathsf{\mu }$m	∗Copper ∗Polyimide	$f_{pl}$ = 5.6 kHz		Chord = 7 cm
[113]	$l_{pl,c}$ = 5 mm	PIV	$V_{pl}$ = 22.5 kV	8.3%C	S809
	$T_{pl,i}$ = 0.07 mm	Car-sticker	$f_{pl}$ = 5.6 kHz		Chord = 30 cm
	$l_{pl,e}$ = 3 mm				(Pitching)
	$D_{pl}$ = 0	∗Copper ∗Polyamide
[115]	$T_{pl,e}$ = 0.3 mm	Smoke visualization	$V_{pl}$ = 10 kV	10, 20, 50, and 95%C	NACA 0015
	$T_{pl,i}$ = 0.03 mm	Titanium dioxide ($Ti{O}_2$)	$f_{pl}$ = 3.5 kHz		Chord = 12.5 cm
	$l_{pl,c}$ = 3 mm
	$l_{pl,e}$ = 3 mm	*Copper *Polyamide
[118]	$T_{pl,i}$ = 4.62 mm	Smoke visualization	$V_{pl}$ = 9.9 kV (rms)		GEO 735
	$l_{pl,c}$ = 19.05 mm		$f_{pl}$ = 2 kHz		Chord = 17.5 cm
	$l_{pl,e}$ = 19.05 mm
	$T_{pl,e}$ = 0.0736 mm
	$D_{pl}$ = 0	*Copper *Macor

, the dimensions and material properties of the PA, along with its excitation parameters, are presented for both single and multiple actuation strategies. In most studies, the applied voltages are specified in terms of peak-to-peak (P–P) values, and the optimal placement of the actuator is identified on the suction side of the airfoil.

4.2.2. PA-Pulsating Forcing on Airfoils

In this section, experimental investigations of plasma actuators operating under a pulsating mode on WT airfoils are discussed

In Suzuki et al. [120] a PA was actuated at the leading edge of an airfoil at a Reynolds number of 550,000 and with a range of AoAs from $0^{\circ }$ to ${30}^{\circ }$. The PA was actuated with an applied voltage in the range of 3.8 ≤ $V_{pl}$ ≤ 7 kV, a range of pulsating frequencies from 14 to 500 Hz, and a duty cycle (Dc) range of 0–50%. When the PA was operated with a maximum voltage of 7 kV, a pulsating frequency of 90 Hz, and a Dc of 5%, the PA had a positive effect at AoAs ranging from ${10}^{\circ }$ to ${30}^{\circ }$ and significantly controlled the stall AoA of ${20}^{\circ }$.

Gnapowski et al. [121] applied a PA on a SD 7003 airfoil. The PA was operated near the leading edge with voltages ranging from 7 to 12 kV, and a pulsating frequency of 50 Hz. The experimental investigations were carried out at Reynolds numbers from 87,500 to 240,000, and at AoAs from $0^{\circ }$ to ${15}^{\circ }$. At the lowest Reynolds number, and at a AoA of $5^{\circ }$, the lift coefficient was improved by 17%, compared to the no-actuation case.

Sekimoto et al. [122] applied a PA on a NACA 0015 airfoil. The PA was located at 5%C of the airfoil, and actuated with voltages of 3 and 6 kV, non-dimensional pulsating frequencies $F^{+}={\displaystyle \frac{f_{pu}C}{U_{\infty }}}$ from 0.1 to 20, and a Dc of 16%. The experimental investigations were performed at a Reynolds number of 63,000, and at AoAs from $8^{\circ }$ to ${15}^{\circ }$. According to the results, the optimal frequency and voltage changed as a function of the AoA. A $F^{+}$ = 1 and a low input voltage were effective at high AoAs, whereas $F^{+}$ = 6 or 10 along with high voltages were effective at low AoAs.

Table 5. Main experimental parameters of PAs operating under (Pulsating mode) on wind turbine airfoils.

Ref.	Reynolds	Power Supply	Excitation Parameters
[120]	550,000	Battery (≈110 g)	$V_{pl}$ = 9.9 kV
			$f_{pu}$ = 90 Hz
			Dc = 5%
[121]	87,500	Autotransformer	$V_{pl}$ = 12 kV
			$f_{pu}$ = 50 Hz
			Dc = -
[122]	63,000	Function generator	$V_{pl}$ = 4–6 kV
			$F^{+}$ = 1 @Low AoA
			$F^{+}$ = 6–10 @High AoA
			Dc = 16%

summarizes the main PAs’ experimental operating parameters when activated under pulsating mode.

4.3. Nanosecond-AC/DC-Pulsed DBD Actuator on Airfoils

Another design of pulsed dielectric barrier discharge actuator is a plasma-based flow control device in which nanosecond pulses produce negligible direct gas acceleration. In the past two decades, atmospheric pressure nonthermal plasma devices using direct current (DC) or alternating current (AC) have been developed. Corresponding research work, involving the experimental and theoretical studies of their discharge characteristics has been undertaken by [123,124].

The construction of these actuators is analogous to the PAs, but the discharge is driven by repetitive nanosecond-duration pulses (≈5–100 ns). Instead of inducing a steady ionic wind, its effectiveness relies on boundary-layer tripping and periodic forcing of the flow. During operation, the discharge energy is rapidly thermalized, leading to strong localized heating in the near-wall region. Peak temperatures of up to ≈70, 200, and 400 K have been reported for pulse durations of around 7, 12, and 50 nanoseconds [125]. This rapid heating generates a pressure disturbance that evolves into a shock wave, accompanied by secondary vortex structures that interact with it and disturb the main flow [126].

Roupassov et al. [127] suggested that the primary influence of the plasma on the flow results from rapid and localized heat generation within the actuator rather than from EHD flow acceleration. In support of this, they observed compression waves in quiescent air produced by localized heating during the nanosecond pulse discharge in the DBD actuator; see Figure 25. The nanosecond discharge generates intense local heating near the exposed electrode edge, producing compression waves or even shock waves [128,129,130]. The overall compression waves come from many small contributions, not a single uniform source [131,132]. Thermal perturbations in these actuators excite shear layer instabilities and generate coherent flow structures (spanwise vortices) [31,133,134].

The discharge patterns of nanosecond plasma actuators are typically categorized into four modes: diffuse (including the idealized uniform case), quasi-diffuse, separated-channel, and filamentary mode [135]. This design produces very low, if any, velocity in the neutral species. Instead, a thermal effect such as Joule heating generates a local compression wave that works as the control mechanism. Pressure waves are commonly employed to trigger fluid instabilities, such as the Kelvin–Helmholtz type, within separated shear layers [136]; as a result, separation of the flow can be suppressed.

Overall, the interaction between plasma and the flow is explained by two approaches, one of which is the thermal mechanism resulting from the energy released in the discharge, the second one being the momentum transfer from the electric field to the gas flow.

4.3.1. Nanosecond-DC-Pulsed DBD Actuator (P-PA) on Airfoils

Benard et al. [137] applied a P-PA on a NACA 3506 airfoil. In order to apply the P-PA, several parameters, such as positive and negative voltages (±4 kV, ±8 kV), pulse width, and a range of rise/decay time from 25 to 200 ns, were considered. Based on the deposited energy per plasma length, and regardless of the value of the voltage, the positive voltage pulse was more efficient than the negative one. In addition, two peaks of current corresponding to the rise and decay of the voltage pulse were observed. The first current peak was the main contributor to the energy deposited on the wall surface. Reducing the rise time of the voltage pulse enhanced the pressure wave due to faster energy deposition. When the rise time increased from 25 to 50 ns, the deposited energy decreased by 56%, leading to greater energy dissipation and, consequently, a higher potential for conversion into gas heating. The P-PAs were located at the leading edge and at the middle of the NACA 3506 airfoil chord, and actuated with an applied voltage of 15 kV. This device generated pressure waves, which were employed to control flow separation. Experimental investigations were carried out at a Mach number of 0.76 and an AoA of $4^{\circ }$. The results showed that the propagation speed normal to the plasma surface was about 330 m/s.

The energy deposited is defined as the time integral of the power $P\left(t\right)$ applied to the P-PA, and it is represented as

$$E_{\mathrm{i}\mathrm{n}\mathrm{s}\mathrm{t}}\left(t\right)={\int }_0^{t}P\left(t\right)dt$$

(35)

In nanosecond plasma actuators, the current peaks are mainly produced during the rise time and decay time. When the rise time increases, the amplitude of the current peak decreases and multiple peak currents are observed on the current waveform. Xie et al. [138] studied a range of voltage rise times (between 25 and 100 ns) applied to a P-PA, and considered its effect on the deposited energy and the pressure wave. The pressure wave was induced by the rapid release of energy, and the intensity of the pressure wave was stronger with shorter rise times. For a rise time of 50 ns, the induced pressure wave reached a maximum speed of 408 m/s. The gas-heating phenomenon occurring in a nanosecond pulse discharge was considered an important process in determining the performance of nanosecond plasma actuators.

4.3.2. Nanosecond-AC-Pulsed DBD Actuator (A-PA) on Airfoils

Although the typical plasma actuators (PA) produce a body force vector field that acts on the neutral air, the nanosecond-AC-Pulsed DBD actuators (A-PAs) generate short duration localized heating to produce expanding hemispherical pressure waves [32,139]. The voltage waveform employed in this actuator is markedly different from that utilized in the AC plasma actuator. Actually, the waveform consisted of positive voltage pulses of tens of nanosecond duration.

Roupassov et al. [127] applied the A-PA near the leading edge of a NACA 0015 airfoil. The P-PA was operated with a voltage of 25 kV, and a range of frequencies between 0.1 and 10 kHz. Experimental studies were conducted at wind speeds of 86 and 110 m/s, and at AoAs from ${17}^{\circ }$ to ${25}^{\circ }$. Actuating the A-PA with a pulsating frequency $f_{pu}$ of 1 kHz increased the lift coefficient at all AoAs and at both wind speeds, particularly at AoAs of ${19}^{\circ }$ and ${21}^{\circ }$.

Similarly to the previous study [127], Rethmel et al. [134] installed the A-PA on the same airfoil and at the same location. The PA was actuated with a range of non-dimensional frequency $F^{+}={\displaystyle \frac{f_{pu}C}{U_{\infty }}}$ and a voltage of 8.4 kV. The PA was operated at Mach number of 0.26 and at an AoA of ${14}^{\circ }$. The best results were obtained when the A-PA was operated with a $F^{+}$ = 1.9.

Zheng et al. [140] installed the A-PA, near the leading edge of same airfoil [127,134], at Mach number of 0.3. In this study, the PA was actuated with $F^{+}$ = 2.7, a range of voltages from 12 to 20 kV, and at an AoA of ${20}^{\circ }$. According to the result, the separated boundary layer was fully reattached by the actuator when operating at the maximum voltage of 20 kV.

Kelley et al. [141] compared the effect of a P-PA and a typical PA on an airfoil at Mach numbers from 0.1 to 0.4. The PA was operated at the leading edge, with an AC voltage of 30 kV and a frequency of 2.3 kHz. The P-PA was operated with an AC voltage of 11.9 kV (P-P), Dc of 50%, a pulse width of 100 ns, and a pulsating frequency of 1 kHz. Non-dimensional frequencies ($F^{+}={\displaystyle \frac{f_{pu}C}{U_{\infty }}}$) from 0.5 to 4 were applied for the A-PA. Both actuators were operated at Mach numbers from 0.1 to 0.4 and AoAs from ${10}^{\circ }$ to ${16}^{\circ }$. At a Mach number of 0.1 and a stall AoA of ${11}^{\circ }$, the application of the A-PA with $F^{+}=1$ increased the lift coefficient by 30%. At Mach numbers of 0.2 and 0.4, and at a post stall AoA of ${15}^{\circ }$, operating the PA resulted in an average increase of 120%, and 10% in lift coefficient, respectively.

Komuro et al. [142] implemented a P-PA on a NACA 0015 airfoil. The P-PA was located at leading edge with a voltage of 7.8 kV, and operated at a wide range of pulsating frequency $F^{+}={\displaystyle \frac{f_{pu}C}{U_{\infty }}}$ from 0.1 to 20. Actuating the P-PA with from $F^{+}$ = 1 to 2, enhanced the lift coefficient.

The nanosecond plasma actuators are particularly attractive for high-speed flow control and supersonic flow because they enable rapid, localized energy deposition into the boundary layer. Some studies at high Mach numbers investigated the effect of the P-PAs by CFD [143,144].

Table 6. Main experimental parameters of Nanosecond-AC/DC-Pulsed operating on aerodynamic application.

Ref.	Method	Mach	Voltage	Pulse Width	Rise Time	Power/Pulse
[137]	Exp.	0.76	15 kV(DC)	200 ns	30 ns	0.3 mJ/cm
[143]	CFD	2.5	10 kV(DC)	20 ns	-	50 mJ
[144]	CFD	4	50 kV(AC)	10 ns	4 ns	0.5 mJ
[141]	Exp.	0.4	11.9 kV(AC)	100 ns	-	-
[127]	Exp.	0.3	25 kV(AC)	12 ns	1.3 ns	1 mJ/cm
[134]	Exp.	0.26	8.4 kV(AC)	100 ns	-	-
[140]	Exp.	0.3	20 kV(AC)	-	4 ns	30 mJ
[141]	Exp.	0.4	11.9 kV(AC)	100 ns	-	-
[142]	Exp.	0.05	7.8 kV(AC)	100 ns	40 ns	42 mJ/m

summarizes the experimental and numerical studies by nanosecond-AC/DC-Pulsed DBD actuator at different Mach numbers.

• Summary of the achievements of DBD plasma actuators applied to Airfoils

Based on numerical and experimental investigations of PAs on single airfoils, actuator effectiveness primarily depends on chordwise placement and excitation parameters as follows:

• The optimum location of PAs is closely related to the boundary layer separation point on a given airfoil, which in turn depends on the Reynolds number, AoA, and the airfoil profile. Using the Shyy model, the maximum Reynolds number ever studied was 600,000; moreover, combining PAs with passive methods such as a Gurney flap can improve the airfoil’s efficiency at higher Reynolds numbers [104]. The Shyy model is a voltage-dependent theory, where increasing the voltage leads to an expansion of the plasma region. Furthermore, an increase in frequency enhances the force in both the X and Y directions [104,105]. Therefore, it must be considered that, in any active flow control (AFC) application, an energy assessment needs to be performed.
• For each given application, a parametric analysis considering the PA non-dimensional frequency $F^{+}$ (in both continuous [102] and pulsating modes [106,107]), its duty cycle [106,107], as well as the voltage applied, appear to be essential to maximize the PA efficiency while minimizing the energy required. The optimization of the PA parameters is particularly relevant in full three-dimensional simulations. When the operational frequency of the plasma actuator matches the baseline case vortex shedding frequency, flow control becomes significantly more energetically efficient.
• In order to improve the PAs’ performance via the S-H model, the boundary conditions were modified, and, rather than following a Gaussian distribution [39,40], the PAs were modeled with a different boundary condition in which the charge density distribution on the electrode surface was proportional to the electric potential [54,111]. Compared to the Shyy model, the Suzen–Huang (S-H) model enabled the investigation of several additional parameters, including the permittivity of the DBD unit, electrode dimensions (thickness and length), Debye length, and gap between the electrodes.
• To maximize the effect of plasma actuation under a static AoA or under dynamic pitching state on airfoils, a parametric optimization and a generic Algorithms (GA) based one were conducted. A range of PA essential parameters as well as the PA optimal chordwise location were analyzed [109,110].
• Considering the experimental research, parametric studies focused on evaluating a range of applied voltages and frequencies, as well as chordwise locations, in both single and multiple configurations were performed by [115,119]. As a result, the parameters resulting in an improved aerodynamic performance of the airfoils were established. In addition, the separation point in the baseline case was used to identify the optimal location of the plasma actuator, enhancing its effectiveness [115,116]. Furthermore, non-optimal excitation parameters, particularly frequency, provide little to no aerodynamic improvement while increasing energy consumption [118].
• Application of water droplets on an a PA temporarily disrupted functionality; however, the PA recovered within seconds as the water was evaporated or pushed away by the PA [114]. Some methodologies, including Smoke and Titanium-dioxide ($Ti{O}_2$) visualization, were used to study the boundary layer in baseline and actuated cases.
• In experimental studies conducted under pulsating mode, using pulsating frequencies and duty cycles enabled through DC to AC power converters, offered a significant advantage in energy consumption [120,121,122]. Compared to continuous operation (periodic), this approach was effective in controlling flow in the boundary layer while substantially reducing power consumption. A developed compact high-voltage AC power supply for the PA [120] demonstrated that miniaturization was achievable without compromising performance. A battery could function as the primary power source and was capable of efficiently powering the entire circuit, including the power supply board, main control board, and DC/AC converter.
• In nanosecond pulsed actuators, the deposited energy was the key metric for characterizing the actuators, and pressure wave intensity was directly correlated with the amplitude of the deposited energy. The rise time of the high-voltage pulse was critical for energy deposition and pressure wave formation. A shorter rise time leads to faster energy delivery in a smaller volume, resulting in significantly higher deposited energy, stronger gas heating, and more intense, faster streamers. Positive voltage pulses generate stronger, filamentary streamers with higher energy deposition, whereas negative voltage pulses produce more diffuse, weaker discharges with lower energy deposition. In addition, the positive voltage pulse was more efficient than the negative one, and a sharper voltage pulse made the discharge faster and stronger and established a higher streamer propagation speed. Reducing the rise time of the pulse enhanced the pressure wave due to faster energy deposition.

5. DBD Plasma Actuators (PAs) Applied on Wind Turbines

This section provides a detailed review of numerical and experimental studies on the application of PAs in single and multiple wind turbines configurations.

By synthesizing findings from computational simulations and experimental measurements, the present section aims to demonstrate the effectiveness and scalability of PA technologies in improving wind turbines efficiency.

5.1. Horizontal Axis Wind Turbine (HAWT)

In this section, single and multiple PAs are applied on the upper and lower surfaces of the blades and at various spanwise locations. All numerical studies are conducted as full three-dimensional (3D) simulations.

5.1.1. Large-Scale Wind Turbines

Two numerical studies and one experimental investigation related to large-scale horizontal-axis wind turbines are presented in this subsection.

Ebrahimi and Movahedi [145], numerically implemented typical plasma actuators (PAs) at different chordwise strategies to increase the aerodynamic performance of an offshore 5 MW WT blade. The PAs were located at a fixed spanwise location near the rotor (from $22\%$ to $29\%r/R$) and operated based on three chordwise strategies, whether activating the actuators placed at 41%C and 42%C, or the ones placed at 41%C, 42% and 43%C, or the previous three plus another one located at 45%C. All investigations were performed at a TSR = 7.56, $U_{\infty }$ = 9 m/s, and results indicated that the turbine power improvement (versus the clean blade) generated by all three strategies was insignificant ($0.66\%$, $0.77\%$, $0.85\%$).

In the numerical study from Omidi and Mazaheri [146] and using a modified S–H model proposed by [54], they studied the performance of an offshore 6 MW WT by implementing single (a PA located at 30%C) and multiple (two PAs located at 30%C and at 40%C, respectively) PAs configurations. The spanwise location was from $46\%$ to $56\%r/R$, which is rather far from the rotor hub in comparison with the location employed in [145]. The actuators used in the single and multiple configurations were operated at two sets of conditions: $U_{\infty }=12$ m/s with a pitch angle of $\theta =0^{\circ }$, and $U_{\infty }=6$ and 10 m/s with pitch angles ranging from $\theta =0^{\circ }$ to ${10}^{\circ }$. Based on the results obtained when employing the first condition, the output power of the wind turbine, when compared with the results from [145], was enhanced by 61 and 95 kW when using the single and multiple PAs configurations, respectively. Similar improvements were achieved when employing the second condition, where a maximum pitch angle of ${10}^{\circ }$ was applied. They noted for the actuated case that the velocity contours observed along the blade span were modified, delaying the boundary layer separation; see Figure 26.

Differently than in the two previous studies, Matsuda et al. [147] experimentally installed PAs on a large 1.75 MW WT. The PAs were installed along the leading edge of the WT blades near the rotor, covering a length of 8 m. A pulsating frequency $F^{+}={\displaystyle \frac{f_{pu}C}{U_{\infty }}}$ of 1, and a tiny Dc of 1% were used to activate each actuator. The PAs were operated simultaneously, at various wind speeds between 4 m/s and 17 m/s, over 6 days. During the experiments, a 4.9% of the average WT power (versus the baseline case) was reported.

The optimum chordwise and spanwise locations of the PAs for both single and multiple location strategies are summarized in

Table 7. Main parameters associated with the PAs implementation on large scale HAWTs.

Ref.	Plasma Design	Spanwsie and Chordwsie Location	Voltage and Frequency
[146]	Modified S-H	$46\%$ to $56\%r/R$	$V_{pl}$ = 12 kV
CFD	$T_{pl,e}=0.0025\%C$	Single $30\%C$	$f_{pl}$ = 5.5 kHz
	$T_{pl,i}=0.01\%C$	Multiple $30\%C$ and $40\%C$
	$l_{pl,e}=0.07\%C$
	$l_{pl,c}=0.13\%C$
[145]	S-H	$22\%$ to $29\%r/R$	$V_{pl}$ = 20 kV
CFD	${\rho }_{pl}$ = $0.0054$	41%C, 42%C, 43%C, and 45%C	$f_{pl}$ = 2 kHz
	${\lambda }_d$ = 0.1 m
	$l_{pl,e}$ = 20 mm
	$T_{pl,e}$ = 0.1 mm
[147]	-	Near the rotor	$F^{+}=1$
Exp.	$l_{pl,e}$ = 8 m	Leading edge	Dc = 1%

.

5.1.2. Reducing Damage Equivalent Load (DEL) in Onshore and Offshore Wind Turbines

The present subsection outlines numerical methodologies to redesign offshore wind turbines equipped with PAs, controllable Gurney flaps (CGF) and Microtabs, aimed at reducing the damage equivalent load (DEL); see the mathematical definition in [148]. In all studies, the Microtabs and CGFs are installed on the pressure surface of the blade, and at particular spanwise locations (r/R).

In all studies, the WT was redesigned numerically, and spanwsie and chordwise locations were considered fixed. As one of the earliest studies, Govindan and Santiago [149], redesigned an offshore 5 MW wind turbine by actuating the PAs on Microtabs. The PAs on the Microtabs, and at particular spanwise direction (see Table 8) were operated with a fixed frequency of 24 kHz, and a Dc = 90%. A range of applied voltages from 3 to 7 kV was evaluated. Two optimizers (NSGAII and MOPSO) were added to the simulations, which were performed at a $U_{\infty }$ = 20 m/s (wind speed). Based on the results from the optimizations, at a voltage of 7 kV and using the NSGAII and the MOPSO optimizers, the DEL of the redesigned wind turbine was improved by 55.7% and 52.84% (versus the non actuated blade), respectively.

Sakib et al. [150] studied the design space and aero-structural performance of a 3.4 MW WT with PAs and controllable Gurney flaps (CGFs) [151]. In order to decrease the Levelized Cost of Energy (LCOE), three strategies were implemented, including using CGFs on the WT to decrease the DEL (similar to what was performed in [152]), designing the WT model with different rotor radii, and using several genetic algorithms optimization methods [153] to produce higher annual energy production (AEP). Aerodynamic design was performed using the Blade Element Momentum (BEM) theory, and the structural design was adjusted by the use of a semiautomated tool (AutoNuMAD). Results showed that the DEL of the redesigned WT decreased, and longer blades yielded higher AEP and lower LCOE.

To enhance the DEL reduction, Gupta et al. [154] applied the same device reported by [150] on a 3.4 MW WT, see Figure 27. A feedback control algorithm, and a controller system were incorporated into the simulations. The PAs were actuated with a frequency of 2.9 kHz (much smaller than what was used in [149]), and a voltage of 10 kV. Simulations were performed at a wide range of wind speeds from 4 to 25 m/s. The reduction in the DEL by the redesigned WT was between 4% and 8% under wind speed lower than 9.8 m/s, and between 8% and 12% at wind speed higher than 9.8 m/s (compared to the non-actuated blade). In addition, the LCOE was decreased between 3.5% and 5.9%.

In the numerical research from Chetan et al. [152], they achieved an enhanced reduction in the DEL on the wind turbine previously examined by [154]. PAs were placed on the CGFs and actuated using the same procedure already employed in [154]. For the redesign of the wind turbine incorporating CGFs and the activation of PAs, the numerical investigations employed a feedback control system, as reported in [154], in combination with a sequential-iterative procedure. A range of wind speeds, from cut-in, 5 m/s to cut-out 25 m/s were considered. The redesigned WT achieved a considerable DEL reduction, under wind conditions higher than 9.8 m/s the reduction varied between 15% and 18%. Consequently, the LCOE was reduced between 1.16% and 3.11%.

Another numerical study aiming to reduce the damage equivalent load on an offshore wind turbines is the one performed by Liu et al. [155], where they redesigned the same device previously studied by [152,154]. The PAs configuration, along with the applied actuation parameters (voltage and frequency), were the same as reported in [152,154]. Actuation of the PAs on the CGFs at $U_{\infty }$ = 9.8 m/s was achieved by integrating a gust alleviation controller into the numerical investigations, and a controller architecture employing Multi-Blade Coordinate transformations (the same was used in [154]). Thanks to the actuation, the DEL of the redesigned WT was reduced by 23% (versus the baseline case).

Table 8 shows a summary of the PAs implementations on HAWTs based on 3D numerical investigations aimed at decreasing DEL and LCOE. The DEL and LCOE values shown in the table characterize the maximum performance from each particular design.

Table 8. Summary of the main parameters of PAs implementation on large scale HAWTs to decrease the DEL and the LCOE in onshore and offshore WTs.

Ref.	WT’ Scale	Spanwsie	Chordwsie	Device	DEL/LCOE
[149]	NREL-5 MW	80–100%r/R	90%C	Microtabs	55.7%/-
[154]	IEA-3.4 MW	76–100%r/R	95%C	CGF	12%/5.9%
[155]	IEA-3.4 MW	77–100%r/R	95%C	CGF	23%/-
[152]	IEA-3.4 MW	75–100%r/R	95%C	CGF	18–3.11%
[150]	IEA 3.4 MW	75–100%r/R	95%C	CGF	AEP boosts

Table 8. Summary of the main parameters of PAs implementation on large scale HAWTs to decrease the DEL and the LCOE in onshore and offshore WTs.

Ref.	WT’ Scale	Spanwsie	Chordwsie	Device	DEL/LCOE
[149]	NREL-5 MW	80–100%r/R	90%C	Microtabs	55.7%/-
[154]	IEA-3.4 MW	76–100%r/R	95%C	CGF	12%/5.9%
[155]	IEA-3.4 MW	77–100%r/R	95%C	CGF	23%/-
[152]	IEA-3.4 MW	75–100%r/R	95%C	CGF	18–3.11%
[150]	IEA 3.4 MW	75–100%r/R	95%C	CGF	AEP boosts

5.1.3. Small-Scale Wind Turbines

This section presents one numerical and three experimental studies related to PA implementation on small-scale horizontal-axis wind turbines.

Aono et al. [156] numerically suppressed the flow separation by implementing PAs on the blades of a small HAWT. The PAs were actuated at the leading edge and along the entire length of the blades. Two pulsating frequencies $F^{+}={\displaystyle \frac{f_{pu}C}{U_{\infty }}}$ of 1 and 6 with a Dc of 10%, and two values of $D_c^{*}$ = 12.5% and 50% (the electrical force of the fluid to its inertial force), were considered. Wind velocity was fixed at 10 m/s. The maximum performance of the PAs was obtained when the PAs were activated with a $D_c^{*}$ = 50% and $F^{+}$ = 1, and the WT torque was enhanced by 19% (versus the baseline case).

The effects of PAs on a single blade from a 660 kW WT were experimentally studied by Maleki et al. [157]. As it was previously performed in [156], the PAs were positioned at the blade’s leading edge, following the NACA airfoil geometry, and actuated using a pulsating mode strategy. A pulsating frequency of 2.17 kHz, an applied voltage of 16 kV, and a duty cycle of 29.6% were examined, at a fixed Reynolds number of 2.8 ×${10}^5$, and AoAs from $4^{\circ }$ to ${36}^{\circ }$. Actuating the PAs on the blade before stall AoA ≤ ${20}^{\circ }$ had a negligible impact relative to the non-actuated case. While at AoAs of ${20}^{\circ }$, and ${25}^{\circ }$, the blade’s aerodynamic efficiency $\left({\displaystyle \frac{C_l}{C_d}}\right)$ increased by 120%, and 64%, (compared to the non-actuated case).

Tanaka et al. [158] implemented PAs on a 300kW WT, keeping active the yaw and pitch control systems. The PAs with a voltage of 13 kV (P-P), a Dc of 5% and a non-dimensional pulsating frequency $F^{+}=1$ were operated at the leading edge of the three WT blades. The three PAs were simultaneously activated/deactivated every 10 min. Three different pitch angles of $\theta$ = $0^{\circ }$, $1^{\circ }$, and ${90}^{\circ }$ were considered. Experimental studies were carried out over six days. The WTs operated under wind speeds ranging from 2 to 6 m/s. Activating the PAs, improved the lift coefficient, but only when flow separation occurred at the leading edge. In addition, plasma actuation demonstrated an effective control of airflow over WT blades at Reynolds numbers of 1.6–1.8 ×${10}^6$.

In the last study presented in this section, Jukes [159] experimentally installed PAs on the suction surface of a small WT with two blades. The PAs with continuous and pulsating modes and also with two different configurations (based on the direction of the plasma force), were installed in spanwise locations ranging from 27% ≤ r/R ≤ 77%; see Figure 28. An applied voltage of 6.5 kV, a frequency of 14 kHz for continuous mode, and a pulsating frequency of 60 Hz (Dc = 25%) for pulsating mode, were considered. In both operational modes, the actuators were activated over the blades (with a pitch angle of $\theta$ = 7.$3^{\circ }$), at a wind velocity $U_{\infty }$ = 2 m/s (TSRs from 3.7 to 6). Actuating the PAs with the symmetry design (first configuration) in continuous mode proved to be more efficient than when using a pulsating one, increasing the turbine power coefficient by 11–24% at all TSRs.

Table 9. PA on small scale HAWTs.

Ref.	Plasma Model	Spanwsie and Chordwsie Location	Voltage
[156]	S-H	Entire the blades	$D_c^{*}$ = 50%
LES	$T_{pl,e}=0.0005\%C$	Multiple-leading edge	Dc = 10%
	$T_{pl,i}=0.0005\%C$		$F^{+}$ = 1
	$l_{pl,e}=0.06\%C$
	$l_{pl,c}=0.01\%C$
[157]	Enloe	Entire the blade	$V_{pl}$ = 16 KV
PIV	$T_{pl,e}$ = 0.08 mm	Single-leading edge	$f_{pu}$ = 2.17 KHz
	$T_{pl,i}$ = 0.127 mm		Dc = 29.6%
[159]	-	27% ≤ r/R ≤ 77%	$V_{pl}$ = 6.5 KV
PIV	$T_{pl,e}$ = $35 \mathsf{\mu }$m	Multiple-$1\%C$ to $38\%C$	$f_{pl}$ = 14 KHz
	$T_{pl,i}$ = $0.125 \mathsf{\mu }$m		$f_{pu}$ = 60 Hz
			Dc = 25%
[158]	-	30% ≤ r/R ≤ 78.8%	$V_{pl}$ = 13 KV
	$T_{pl,e}$ = 2 mm	Single-leading edge	$f_{pl}$ = 15 kHz
	$T_{pl,i}$ = 2 mm		Dc = 5%
	$l_{pl,e}$ = 60 mm
	$l_{pl,c}$ = 60 mm

presents a summary of the PAs implementations on small HAWTs based on 3D numerical investigations aimed at improving the aerodynamic performance.

• Summary of the achievements of DBD plasma actuators applied to HAWTs

This subsection highlights that PAs operating under pulsating and continuous modes may be implemented in wind turbines ranging from small scale to large ones to enhance their aerodynamic performance by suppressing flow separation. Based on numerical and experimental studies conducted on small and large HAWTs, the aerodynamic effectiveness of plasma actuators was found to depend strongly on their placement along the blade. Additionally, the reviewed results highlighted the important role of the non-dimensional frequency ($F^{+}$) in both periodic and pulsating actuation modes, offering valuable insights for enhancing aerodynamic performance as follows:

• The PAs work well and are efficient when placed at or just upstream of the separation point, where they can meaningfully delay stall AoA [157,160,161,162]. In contrast, installing the PAs near the inboard region of the rotor of the large HAWTs, even with multiple strategy (actuating the four PAs simultaneously) had insignificant aerodynamic effect [145] due to the low aerodynamic contribution of that area. Implementing the PAs at an optimum spanwise location along the blade had a larger impact on WT performance than adjusting their single and multiple chordwise placement.
• Redesigning large turbines by combining PAs with devices such as Microtabs or CGF placed at a particular spanwise location near the blade tip, significantly reduced the DEL and improved the LCOE, particularly at wind speeds ≤ 9.8 m/s [149,152,154]. To properly implement PAs with CGF, a control system [154] or a gust alleviation controller [155] were required. In addition, the S-H model as a phenomenological method, successfully enhanced the aerodynamic performance across both small [156], and large scale [146] HAWTs, also contributing to a reduction in DEL [149,152,155]. Modifying the boundary condition for the charged surface, proposed as an alternative to the commonly used Gaussian distribution in this model [54], outperforming the Shyy model, specially at high wind speeds (10 and 12 m/s).
• Observations from experiments on small turbines showed that, an array of symmetric PAs distributed across the entire blade and actuated in periodic mode, produced a stronger aerodynamic effect than employing PAs with an asymmetric configuration [159]. In this case, the plasma-induced vortex generators produced more streamwise vortices compared to the asymmetric design.

5.2. Vertical Axis Wind Turbines (VAWTs)

The application of PAs to single and multiple configurations of small-scale Savonius and Darrieus VAWTs is reviewed. The specifications of the actuator models, along with the optimum parameters for wind turbine (WT) airfoils (blades), are examined across a range of Tip Speed Ratios (TSR) $\lambda =\mathrm{T}\mathrm{S}\mathrm{R}={\displaystyle \frac{R\Omega }{U_{\infty }}}$. In VAWTs azimuth angles from $0^{\circ }$ to ${180}^{\circ }$ are referred to upwind region, and from ${180}^{\circ }$ to ${360}^{\circ }$ are referred to downwind region. These wind turbines can operate at a fixed TSR or across a wide range of TSRs; low TSRs are typically associated with high AoAs and vice versa. It should be mentioned that, in VAWTs, the suction and pressure surfaces of the blade vary with the azimuth angle. The inner surface acts as the suction surface in the upwind region and acts as the pressure surface in the downwind one, while the outer surface behaves oppositely, experiencing pressure in the upwind region and suction in the downwind one. All numerical simulations discussed herein were conducted in two-dimensions (2D).

5.2.1. Numerical Studies

This section analyzes the power output improvement achieved via PAs implementation on VAWTs of laboratory scale and when employing phenomenological approaches such as the Shyy and S-H models. In each study, the main PA parameters are highlighted.

Darraee and Abbasi [163] implement PAs to enhance the output power of a Darrieus-WT with three blades. They investigated the effect of the chordwise placement of the actuators on individual blades. In addition, actuation timing based on azimuth angle in both downwind and upwind regions was evaluated, while keeping the excitation parameters constant. Actuating the PAs on the inner surfaces of the blades, and at specific actuation timing, increased the net power coefficient of the turbine by 29%, versus the non-actuated case. Optimum actuation timing (optimum azimuth angle in upwind/downwind regions to turn on the actuators), blade location and excitation parameters, are clarified in Table 10. In a second study from the same authors [164] and using the same WT previously employed in [163], they investigated different PA excitation waveforms; see Figure 29. Results showed that the cosine and sinusoidal waveforms achieved the highest rate of improvement for the WT, and when using the cosine waveform, the net WT power improved by 52.64%, at specific azimuth angular positions.

Ma et al. [165] evaluated the aerodynamic effect of the PAs implementation under pulsating mode on the same WT and using the same methodology to enhance the aerodynamic performance previously employed in [163,164]. They evaluated a range of chordwise placements (from 5%C to 90%C) and different actuation timings in both upwind/downwind regions based on the azimuth angle. Results showed that when the actuators were operated on the inner surfaces, and just in upwind region, turbine’s net power output was enhanced by (34%) compared with the non-actuated case.

Chavoshi and Ebrahimi [166] implemented PAs based on the Suzen and Huang model on a WT similar to the one used in [163,165], although they used a different airfoil type. In this study, the actuators were installed near the blades’ leading edge on either side, and their aerodynamic impact was investigated based on the three strategies (actuating the PAs on the inner, outer, or both airfoil surfaces). According to the results, actuating on both sides was very effective; however, the actuation on the inner surface was slightly better, achieving a 10% power improvement with respect to the clean case. In addition, actuating the PA in azimuth angles from ${115}^{\circ }$ to ${245}^{\circ }$ had a profound impact on the aerodynamic performance of the WT.

Yu et al. [167] studied the effect of PAs on a Darrieus-WT with two blades. They investigated a narrow range of chordwise placements near the leading edge (0.002, 0.02, and 0.05%C), and at various TSRs from 1.37 to 2.5. The actuators were activated on the suction side of the blades in both upwind/downwind regions. According to the results, the optimum placement to apply the PAs changed as a function of the TSR. At low TSRs, the AoA was higher, causing flow separation, which required a shift in the actuator location to obtain maximum effectiveness. The power coefficient was enhanced by 110%, and 500% at TSRs of 1.37 and 2 (optimum TSR) against the clean case, respectively.

The structure of Savonius VAWTs is simple and robust but suffers from low aerodynamic efficiency due to high drag and significant flow separation. In fact, the propulsion of these WTs is based on drag reduction [168]. Xu et al. [169] increased the efficiency of a Savonius-WT with two blades. In their work, the actuator was modeled based on the Shyy approach, and several excitation conditions, plasma actuation directions, PA placements, and a range of TSRs (from 0.233 to 1.080) were investigated. Actuating the PAs in pairs (${\mathrm{P}\mathrm{o}\mathrm{s}}_2$, and ${\mathrm{P}\mathrm{o}\mathrm{s}}_5$) changed the optimum TSR from 0.992 to 0.687, and significantly enhanced the power coefficient by 43.8%, at the TSR 0.687, against the clean case. Increasing the voltage and frequency increased the plasma force; see Figure 30. At low TSRs (0.233), actuating the plasma region against the wind proved more effective than actuation aligned with the rotor’s rotation. Figure 30 illustrates the direction and different placement of the pairs of actuators analyzed.

Benmoussa and Pascoa [170] studied the impact of typical plasma actuators (PAs) on a Darrieus-WT with six blades, under both conventional and dynamic pitching states; see Figure 31. In this initial study, they evaluated the actuation timing and blade location of the PAs on the WT. The optimum actuator position on each blade (chordwise placement) and also its actuation timing varied with the azimuth angle in the upwind or downwind regions, resulting in a 1.5% increase in overall thrust of the WT (compared to the non-actuated case), during dynamic pitching. In further numerical research [171], they studied the effect of the actuators placed in multiple locations. The PAs were symmetrically placed on both blade surfaces near the leading edge (the first pair was installed at 2%C, and two other pairs were positioned behind the initial one.) Simultaneously activating the three pairs of PAs on the pressure surfaces of the blades under variable pitch conditions, increased the turbine thrust by $2.3\%$ (versus the non-actuated case). In a third study from Benmoussa and Pascoa [172], they implemented the PAs on the suction surface of the same WT blade presented in [170,171]. In this work, the PA was operated at a fixed position of $20\%C$ of the blades and actuated at a $U_{\infty }=6.28$ m/s (a low TSR $=1$), under both conventional and variable pitch conditions. The computational domain inlet turbulence intensity (TI) was 5%. When the PAs were actuated on the suction surface of the blade and combined with a dynamic pitching state, the power coefficient of the WT was improved by 38% when the conventional pitch angle was set to zero ($\beta =0^{\circ }$).

Table 10 summarizes the specifications of the PAs implemented in 2D numerical simulations of small-scale vertical-axis wind turbines (VAWTs). The applied voltage is expressed in terms of its root mean square (RMS) value. The third column illustrates the excitation parameters, such as voltage, frequency, Dc (in pulsating mode), and collision efficiency. The fourth column shows the optimal blade location to apply the single PA, and the fifth column reports the optimum azimuth angle in upwind/downwind regions to turn on the actuators. In the last column, it is explained at which azimuth angular position the PAs are activated. The airfoil surface where the actuation is performed, whether the pressure or suction surfaces, or the inner or outer ones, is also clarified in this column. The asterisk ∗ sign indicates that the output power was obtained based on an energy assessment.

Table 10. Main characteristics of PAs when applied on micro scale VAWTs (Numerical).

Ref.	Theory	Excitation	Airfoil	TSR/$\mathbf{\Omega }$	Azimuth Angle and PA Location
[170]	Shyy	$V_{pl}$ = 4 kV	NACA 0016	200 rpm	Specific angular positions
∗	$h_{pl}$ = 1.5 mm	$f_{pl}$ = 3 kHz	Chord = 30 cm
	$l_{pl}$ = 3 mm	${\alpha }_{pl}$ = 1	Opt = 20%C		Both Surfaces
[171]	Shyy	$V_{pl}$ = 4 kV	NACA 0016	200 rpm	$0^{\circ }$–${360}^{\circ }$
	$h_{pl}$ = 1.5 mm	$f_{pl}$ = 3 kHz	Chord = 30 cm
	$l_{pl}$ = 3 mm	${\alpha }_{pl}$ = 1	Opt = 2%C		Pressure surfaces
[172]	Shyy	$V_{pl}$ = 4 kV	NACA 0016	1	$0^{\circ }$–${360}^{\circ }$
	$h_{pl}$ = 1.5 mm	$f_{pl}$ = 3 kHz	Chord = 30 cm
	$l_{pl}$ = 3 mm	${\alpha }_{pl}$ = 1	Opt = 20%C		Suction Surfaces
[163]	Shyy	$V_{pl}$ = 4 kV	NACA 0022	2.15	${55}^{\circ }$–${145}^{\circ }{/175}^{\circ }$–${265}^{\circ }$ and ${285}^{\circ }$–${15}^{\circ }$
∗	$h_{pl}$ = 1.5 mm	$f_{pl}$ = 3 kHz	Chord = 10 cm
	$l_{pl}$ = 3 mm	${\alpha }_{pl}$ = 0.3	Opt = 10%C		Inner surfaces
[164]	Shyy	$V_{pl}$ = 4 kV	NACA 0022	2.15	$0^{\circ }$–${30}^{\circ }{/240}^{\circ }$–${360}^{\circ }$
∗	$h_{pl}$ = 1.5 mm	$f_{pl}$ = 3 kHz	Chord = 10 cm
	$l_{pl}$ = 3 mm	${\alpha }_{pl}$ = 0.3	Opt = 10%C		Inner surfaces
[165]	Shyy	$V_{pl}$ = 3 kV	NACA 0022	2.15	${60}^{\circ }$–${120}^{\circ }$
∗	$h_{pl}$ = 2.5 mm	$f_{pu}$ = 383 Hz	Chord = 10 cm
	$l_{pl}$ = 5 mm	Dc = 20%	Opt = 30%C
		${\alpha }_{pl}$ = 0.3			Suction surfaces
[167]	Shyy	$V_{pl}$ = 4 kV	NACA 0022	2	$0^{\circ }$–${360}^{\circ }$
∗	$h_{pl}$ = 1.5 mm	$f_{pu}$ = 1 kHz	Chord = 15 cm
	$l_{pl}$ = 3 mm	DC = 35%	Opt = 0.002%C
		$F^{+}$ = 7.1–21.4			Suction surfaces
[169]	Shyy	$V_{pl}$ = 6 kV	S-Blade	≤1	$0^{\circ }$–${360}^{\circ }$
∗	$h_{pl}$ = 10 mm	$f_{pl}$ = 3 kHz	Opt = 50%C
	$l_{pl}$ = 20 mm	${\alpha }_{pl}$ = 1			Outer surfaces
[166]	S-H	$V_{pl}$ = 20 kV	NACA 0021	2.4	$0^{\circ }$–${360}^{\circ }$
	$T_{pl,e}$ = $70 \mathsf{\mu }$m	$f_{pl}$ = 14 kHz	Chord = 8.5 cm
	$T_{pl,i}$ = 3 mm		Opt = 0%C
	$l_{pl,e}$ = 20 mm
	$l_{pl,c}$ = 5 mm				Inner surfaces

Table 10. Main characteristics of PAs when applied on micro scale VAWTs (Numerical).

Ref.	Theory	Excitation	Airfoil	TSR/$\mathbf{\Omega }$	Azimuth Angle and PA Location
[170]	Shyy	$V_{pl}$ = 4 kV	NACA 0016	200 rpm	Specific angular positions
∗	$h_{pl}$ = 1.5 mm	$f_{pl}$ = 3 kHz	Chord = 30 cm
	$l_{pl}$ = 3 mm	${\alpha }_{pl}$ = 1	Opt = 20%C		Both Surfaces
[171]	Shyy	$V_{pl}$ = 4 kV	NACA 0016	200 rpm	$0^{\circ }$–${360}^{\circ }$
	$h_{pl}$ = 1.5 mm	$f_{pl}$ = 3 kHz	Chord = 30 cm
	$l_{pl}$ = 3 mm	${\alpha }_{pl}$ = 1	Opt = 2%C		Pressure surfaces
[172]	Shyy	$V_{pl}$ = 4 kV	NACA 0016	1	$0^{\circ }$–${360}^{\circ }$
	$h_{pl}$ = 1.5 mm	$f_{pl}$ = 3 kHz	Chord = 30 cm
	$l_{pl}$ = 3 mm	${\alpha }_{pl}$ = 1	Opt = 20%C		Suction Surfaces
[163]	Shyy	$V_{pl}$ = 4 kV	NACA 0022	2.15	${55}^{\circ }$–${145}^{\circ }{/175}^{\circ }$–${265}^{\circ }$ and ${285}^{\circ }$–${15}^{\circ }$
∗	$h_{pl}$ = 1.5 mm	$f_{pl}$ = 3 kHz	Chord = 10 cm
	$l_{pl}$ = 3 mm	${\alpha }_{pl}$ = 0.3	Opt = 10%C		Inner surfaces
[164]	Shyy	$V_{pl}$ = 4 kV	NACA 0022	2.15	$0^{\circ }$–${30}^{\circ }{/240}^{\circ }$–${360}^{\circ }$
∗	$h_{pl}$ = 1.5 mm	$f_{pl}$ = 3 kHz	Chord = 10 cm
	$l_{pl}$ = 3 mm	${\alpha }_{pl}$ = 0.3	Opt = 10%C		Inner surfaces
[165]	Shyy	$V_{pl}$ = 3 kV	NACA 0022	2.15	${60}^{\circ }$–${120}^{\circ }$
∗	$h_{pl}$ = 2.5 mm	$f_{pu}$ = 383 Hz	Chord = 10 cm
	$l_{pl}$ = 5 mm	Dc = 20%	Opt = 30%C
		${\alpha }_{pl}$ = 0.3			Suction surfaces
[167]	Shyy	$V_{pl}$ = 4 kV	NACA 0022	2	$0^{\circ }$–${360}^{\circ }$
∗	$h_{pl}$ = 1.5 mm	$f_{pu}$ = 1 kHz	Chord = 15 cm
	$l_{pl}$ = 3 mm	DC = 35%	Opt = 0.002%C
		$F^{+}$ = 7.1–21.4			Suction surfaces
[169]	Shyy	$V_{pl}$ = 6 kV	S-Blade	≤1	$0^{\circ }$–${360}^{\circ }$
∗	$h_{pl}$ = 10 mm	$f_{pl}$ = 3 kHz	Opt = 50%C
	$l_{pl}$ = 20 mm	${\alpha }_{pl}$ = 1			Outer surfaces
[166]	S-H	$V_{pl}$ = 20 kV	NACA 0021	2.4	$0^{\circ }$–${360}^{\circ }$
	$T_{pl,e}$ = $70 \mathsf{\mu }$m	$f_{pl}$ = 14 kHz	Chord = 8.5 cm
	$T_{pl,i}$ = 3 mm		Opt = 0%C
	$l_{pl,e}$ = 20 mm
	$l_{pl,c}$ = 5 mm				Inner surfaces

5.2.2. Experimental Investigations

In this subsection, the most relevant experimental studies related to PAs applied on micro (laboratory scale) vertical axis wind turbines are presented.

Greenblatt et al. [173] investigated the impact of typical plasma actuators on a small Darrieus-WT with two blades. The plasma geometry used followed the empirical method presented by Post and Corke [70]. The actuators were implemented on the inner airfoil surface, close to the leading edge. Wind velocities studied ranged from 4.4 m/s to 7.1 m/s, and various values of TSRs were considered. They investigated the effect of pulsating frequency ($F^{+}={\displaystyle \frac{f_{pu}C}{U_{\infty }}}$) between 1 ≤ $F^{+}$ ≤ 5, and a wide range of Dc 1% ≤ Dc ≤ 50% was as well evaluated. Voltage was fixed at 8 kV (P-P). The actuators on the blades were turned on just in the upwind region. Based on the results, the optimum values of Dc and $F^{+}$ changed by TSR and wind speed. At TSR = 1.9, PAs with a $F^{+}=2$, and two duty cycles, Dc = 5 and 10% increased the output power of the WT by $31\%$ and $38\%$, respectively (versus the non-actuated case).

In a second study, Greenblatt et al. [174] implemented the actuators on the same turbine and in the same location as in the previously investigated WT [173]. The actuators were operated with a fixed pulsating frequency of 500 Hz and a fixed duty cycle of 20%, in the upwind region. All studies were performed at $U_{\infty }$ = 7 m/s, and when TSRs were <2, they observed that the power consumption of the PAs was higher than the power increase obtained by the WT. They noted this issue arose from the excitation parameters (duty cycle (Dc), applied voltage, and pulsating frequency) employed, and they reported that activating the PAs using a controller could effectively address this limitation. This hypothesis was tested in the author’s next studies [175,176].

Ben-Harav and Greenblatt [175] implemented PAs through a feed-forward controller, on the same wind turbine evaluated by [173,174]. The PAs’ design and location considered were the same as in [173]. A pulsating frequency of 500 Hz, a range of Dc between 1% and 20%, and a voltage of 8 kV (P-P) were considered. Experiments were performed at a $U_{\infty }$ = 7 m/s and a TSR = 1.38. Actuators were turned on just in the upwind region. When the actuators on the inner sides of the blades were activated at specific azimuth angles, the output power of the wind turbine was enhanced (with respect to the non-actuated case) by 12% and 7.5% for Dc = 5% and 10%, respectively. The optimum azimuth angular position, blade location and excitation parameters for each of the related studies are presented in

Table 11. PA on micro scale VAWTs (Experimental). The asterisk ∗ sign indicates that the output power was obtained based on an energy assessment.

Ref.	Model	Material	Voltage and Frequency	Azimuth Angle and PA Location
[173]	Post and Corke	Copper	$V_{pl}$ = 8 kV	$0^{\circ }$–${180}^{\circ }$
	$T_{pl,e}$ = $70 \mathsf{\mu }$m	Polyamide	$F^{+}=2$
	$T_{pl,i}$ = $150 \mathsf{\mu }$m		Dc = 5%	NACA 0015
			Power supply = 24 V	Chord = 15 cm
[174]	Post and Corke	Copper	$V_{pl}$ = 8 kV	$0^{\circ }$–${180}^{\circ }$
	$T_{pl,e}$ = $70 \mathsf{\mu }$m	Polyamide	$f_{pu}$ = 500 Hz
	$T_{pl,i}$ = $125 \mathsf{\mu }$m		Dc = 20%	NACA 0015
			Power supply = 24 V	Chord = 15 cm
[175]	Post and Corke	Copper	$V_{pl}$ = 8 kV	${70}^{\circ }$–${137}^{\circ }$
∗	$T_{pl,e}$ = $70 \mathsf{\mu }$m	Polyamide	$f_{pu}$ = 500 Hz
	$T_{pl,i}$ = $125 \mathsf{\mu }$m		Dc = 5%
			DC = 10%	NACA 0015
			Power supply = 24 V	Chord = 15 cm
[176]	Post and Corke	Copper	$V_{pl}$ = 8 kV	${60}^{\circ }$–${180}^{\circ }{/240}^{\circ }$–${360}^{\circ }$
∗	$T_{pl,e}$ = $125 \mathsf{\mu }$m	Polyamide	$f_{pu}$ = 500 Hz
	$T_{pl,i}$ = $125 \mathsf{\mu }$m		Dc = 20%
			Dc = 10%	NACA 0015
			Power supply = 24 V	Chord = 15 cm
[177]	-	Copper	$V_{pl}$ = 35 kV at $U_{\infty }$ = 6 m/s	$0^{\circ }$–${360}^{\circ }$
	$l_{pl,e}$ = 3.18 mm	RTV silicone	$V_{pl}=26$ to 35 kV at $U_{\infty }$ = 8 to 10 m/s
	$l_{pl,c}$ = 6.35 mm		$f_{pl}$ = 6.5 KHz	NACA 0018
	$T_{pl,i}$ = 3.18 mm			Chord = 10 cm

.

In a fourth experimental research, Greenblatt and Lautman [176] studied the PAs operation on the same wind turbine previously studied by [173,174,175]. The PAs considered were the same as in [173,175]. As already performed in their previous work [175], the PAs were integrated with an open loop (feed-forward) controller, but now the PAs were activated across the downwind and upwind regions. The aim behind the actuation in the downwind region was to mitigate the flow separation induced by the shaft. The actuation performance was tested at three wind speeds of 5, 6, and 7 m/s and at three ranges of TSRs, from 1.3 to 1.9. Excitation parameters were adjusted as in [174]. Results showed that at $U_{\infty }$ = 5 and 6 m/s and at two respective TSRs (1.45 and 1.5), actuating the PAs improved the output power of the wind turbine by 126% and 43% (when compared with the non-actuated case), respectively.

Jafari et al. [177] implemented the PAs on a Darrieus-WT with three blades. The PAs were located close to the leading edge and on the inner surface of three blades. They were operated in continuous mode with a constant frequency of 6.5 kHz and four voltages of 26, 29, 32, and 35 kV (P-P). Investigations were performed at $U_{\infty }$ = 6, 8, 10, and 12 m/s and at different ranges of TSRs. For a wind speed of $U_{\infty }$ = 6 m/s and at all TSRs, actuating the PA with maximum voltage increased the output power of the wind turbine against the non-actuated case. Under such conditions, the wind turbine exhibited a power increase of 28% (when compared with the non-actuated case). However, at wind speeds of 8, 10, and 12 m/s, and at high TSRs, regardless of the excitation parameters, the effect of the PAs on the output power of the WT was minimal in contrast to the non-actuated case; see Figure 32.

Table 11 summarizes the main characteristics of PAs’ experimental implementation on small-scale VAWTs. The applied voltage $V_{pl}$ is expressed in terms of its peak-to-peak (P-P) value. The final column reports the optimum azimuth angles and the location where the PAs were placed.

• Summary of the achievements of DBD plasma actuators applied to VAWTs

The previous experimental and numerical investigations demonstrate that PAs operate in both steady and pulsating modes and can be effectively applied to laboratory-scale VAWTs to enhance aerodynamic efficiency across a range of TSRs. In these WTs, the flow separation occurs under two primary conditions. The first is at low tip speed ratios (TSRs), corresponding to high angles of attack, where separation develops on the suction surfaces, specifically the inner surface in the upwind region and the outer surface in the downwind region. The second condition arises due to the presence of the central shaft, which disturbs the flow and induces additional separation at particular azimuth angles in the downwind region [166,176] as follows:

• The successful implementation of PAs on VAWTs using phenomenological models (numerical methods) such as the Shyy and S-H models depended on several key factors, including the chordwise placement, actuation at particular azimuth angles, excitation parameters such as the applied voltage and frequency, tip speed ratio (TSR), and airfoil type. In VAWTs, optimum actuation timing (when the PAs are turned on/off based on the azimuth angle) is the key factor to enhance the WT performance. And as specified in Table 10 and Table 11, operating the actuators at specific angular positions, whether in numerical studies [163,165,170] or in experimental investigations [175,176], results in a net power gain after performing the corresponding energy assessment. These optimum angular positions were dependent on the tip speed ratio (TSR) and airfoil type.
• In numerical simulations, a parametric study was conducted to find the optimum chordwise placement [163,165,167,169], and it was found to depend on the TSR and airfoil type. The actuators achieved a successful performance when placed between the leading edge (0%C) to 30%C in all laboratory-scale Darrieus-WTs. In contrast, for the Savonius WT (S-blade), the optimum placement was identified at the middle of the blade. None of the reviewed studies examined the upstream and downstream separation points in the baseline case. Regardless of the boundary layer separation point, operating the actuators near the leading edge and on the inner surface (suction surface) of the blades in both the downwind, and upwind regions was found to be beneficial in both numerical and experimental investigations.
• Owing to its simplicity, most of the numerical studies used the Shyy model. In the Shyy model, several parameters, including the discharge time ($\Delta t$ = $67 \mathsf{\mu }$m), distance between the electrodes (0.25 mm), charge of the electron ($e_{pl}$ = 1.602 × ${10}^{-19}$), and the net charge density (1$\times {10}^{11}{\mathrm{C}/\mathrm{c}\mathrm{m}}^3$), are held constant, while voltage and frequency are treated as variable parameters. An increase in the applied voltage leads to an expansion of the plasma region; consequently the PA based on the Shyy model is voltage-dependent.

6. Conclusions

This review compiles and analyzes existing studies on the use of dielectric barrier discharge (DBD) plasma in flow control applications involving flat plates, airfoils, and both vertical- and horizontal-axis wind turbines. Research trends show a growing interest in using these actuators to enhance the drag reduction, delay stall AoA, improve aerodynamic efficiency, and enhance turbine performance; however, most studies are still at laboratory scale with simplified test conditions.

The development of dielectric barrier discharge (DBD) plasma actuators has significantly advanced flow control strategies in aerodynamics, offering a novel approach to boundary layer manipulation. DBD plasma actuators influence the incoming flow mainly through momentum injection driven by the electrohydrodynamic (EHD) effect, or by generating compression waves resulting from rapid local Joule heating. Based on their driving mechanisms and operating principles, a new classification of DBD plasma actuators can be proposed as follows:

1. AC DBD plasma actuators (PA).

1.1 AC-pulsating DBD plasma actuator (PA).

2. Sliding DBD actuators (S-PA).

3. DC-pulsed nanosecond DBD actuators–McGowan approach (D-PA).

4. DC-pulsed nanosecond DBD actuators (P-PA).

5. AC-pulsed nanosecond DBD actuators (A-PA).

6. DC-pulsed nanosecond DBD actuators (P-PA) and S-PA (PS-PA).

In the following table, the first column presents the different classifications of the actuators, the second describes their operating principles, the third highlights key parameters obtained from both experimental and numerical studies, and the last column outlines their applications based on studied papers.

An overview of the present study
Actuators	Principle	Effective parameters	Application
PA	EHD	-Single and multiple location	-Flat plate
		-Gap between the electrodes	-Airfoil
		-Encapsulated electrode’s length	-HAWTs
		-DBD permittivity	-VAWTs
		-Duty cycle (Dc) and $F^{+}$
S-PA	EHD	-DC voltage (+/−)	-Flat plate
		-AC voltage
		-Periodic frequency
D-PA	Pressure wave	-${\lambda }_z^{+}$	-Flat plate
		-$W_{max}/u_{\tau }$
		-DBD permittivity
		-DC voltage
		-Actuator’s design
P-PA	Pressure wave	-Rise time	-Airfoil
		-Pulse width
		-DC voltage
A-PA	Pressure wave	Pulsating frequency	-Airfoil
		-Pulse width
		-AC voltage
PS-PA	Pressure wave	-Pulsating frequency	-Flat plate
		-DC voltage

The successful implementation of DBD plasma actuators in aerodynamic applications depends on several critical factors, including excitation parameters (voltage and frequency), material, geometry, installation location, and distance between the actuators in a multiple implementation strategy. The main conclusions can be summarized as follows:

• In PAs (typical), the DBD thickness and permittivity, geometry of exposed electrodes and length of the encapsulated electrode significantly influence the plasma actuator efficiency. At high applied voltages, materials with lower permittivity demonstrated superior discharge efficiency, while at lower voltages, materials with higher permittivity provided more favorable performance. Interestingly, at high voltages, the thickest DBD produced the highest velocity. This indicates that both the choice of material and the DBD thickness play an important role in overall performance. Moreover, when the gap between the electrodes exceeded a determined threshold, the electric field was reduced. To maximize the effect of the PAs on airfoils and WTs, a parametric study focused on evaluating a range of applied voltages, frequencies, and chordwise locations, in both single and multiple configurations, proved to be effective [115,119,146,163,165].
• In S-PA, the DC-actuated electrode had a strong influence on the velocity of the flow field when compared to a typical PA, accelerating the ionic wind [86,87] and allowing additional control over the flow direction [90,91].
• Applying the D-PA on flat plates effectively reduced drag at high wind speeds by producing a spanwise near-wall flow that suppressed streak lift-up. The degree of the drag reduction highly depended on two parameters, ${\lambda }_z^{+}={\displaystyle \frac{{\lambda }_z{u}_{\tau }}{\nu }}$, which characterizes the number of viscous wall units, and $W_{max}/u_{\tau }$, which represents the level of spanwise plasma-induced flow required relative to the local friction velocity. The optimal value of both parameters ($W_{max}/u_{\tau }$ and ${\lambda }_z^{+}$) varies depending on DC applied voltage.
• In P-PAs, the deposited energy was the key metric for characterizing nanosecond pulsed, and pressure wave intensity was directly correlated with the amplitude of the deposited energy. Reducing the rise time of the pulse enhanced the pressure wave due to faster energy deposition.
• Optimization of typical plasma actuators, whether operating in periodic or pulsating modes and/or in A-PAs, and with the focus on enhancing performance and reducing power consumption of the actuators, depended critically on the proper selection of the non-dimensional frequency $F^{+}$ in VAWTs [173], HAWTs [147,156], and on the shape of the airfoils [141,142].
• The comparison between the typical PAs and nanosecond DC pulsed actuators, such as D-PA on flat plates or P-PA on airfoils, serves to highlight the latter’s strengths. The typical plasma actuators (PA) are efficient and reliable at low to moderate wind speeds; however, their influence weakens at higher speeds. In contrast, nanosecond plasma actuators maintain strong control authority at high wind speeds and can effectively energize the boundary layer, making them particularly suitable for stall suppression at high angles of attack [101,137]. A particularly beneficial effect was observed in nanosecond AC-pulsed actuators [134,140,141]. To maximize the effect of these actuators, it is necessary to study the pulse width, rise/fall times, and the influence of these parameters on the deposited energy.
• Dielectric material choices such as Macor, ceramic, Teflon, and polyamide have influence on the operation of the actuator and thus need to be properly chosen before incorporating them into the plasma actuator design. In most of the published papers, polyamide was the material used due to its high dielectric strength and permittivity, as demonstrated by [178,179,180]. Furthermore, various types of Kapton (polyamide), including HN, MT, and other types, offer distinct electrical and mechanical properties that can affect the performance of DBD plasma actuators [181,182]. Furthermore, mica exhibited stable dielectric characteristics (electrical properties) that are resistant to arcing under ionized air conditions [99,101].
• In both VAWTs and HAWTs, a parametric study to implement the PAs in multiple locations, regardless of the separation point and under static and dynamic pitching state AoA, can significantly enhance the aerodynamic performance of the WTs. According to the numerical investigation conducted on large horizontal-axis wind turbines, activating the actuators around the mid-span region of the blade yielded greater aerodynamic benefits than actuating them near the hub. Moreover, numerical redesign of large horizontal-axis wind turbines to incorporate plasma actuators (PAs) with auxiliary devices—particularly near the blade tip—significantly reduced the damage-equivalent loads and improved the levelized cost of energy, especially at inflow velocities lower than rated speed $U_{\infty }\le 9.8$ m/s [149,152,154]. The performance of the actuators on vertical axis wind turbines was strongly influenced by factors such as chordwise placement (which varies with tip speed ratio and airfoil type), azimuthal actuation timing, and excitation parameters like voltage and frequency. From these, the precise timing of actuation relative to the azimuth angle proved to be the most crucial for enhancing turbine efficiency.