Effects of Fixed Leading-Edge DBD Plasma Actuation on Pressure-Derived Lift of a NACA 0012 Airfoil

Abstract

In this study, a dielectric barrier discharge (DBD) plasma actuator was placed at the leading edge of a National Advisory Committee for Aeronautics (NACA) 0012 airfoil to act on the separation initiation point, rather than on an already separated flow farther downstream on the upper surface. The aerodynamic response was examined using complementary measurements: (i) quiescent-air thrust characterization to quantify the actuator forcing level for two dielectric configurations under voltage and frequency sweeps, (ii) wind-tunnel surface-pressure measurements on the upper and lower surfaces over an angle-of-attack sweep, and (iii) smoke-wire flow visualization. To enable consistent actuator-OFF/ON comparisons despite non-matching tap locations, a pressure-derived lift coefficient was evaluated by integrating $C_{p,l}-C_{p,u}$ over the common instrumented chordwise interval $x/c = 0.2533~0.7620$ after linear interpolation onto a common grid. The results demonstrate that a single fixed leading-edge actuation setting is not universally beneficial across the angle of attack. The actuation effect on the lift increment is small at $\alpha =4°$ and $8°$ and should be interpreted cautiously, given the pressure coefficient resolution, whereas near stall and post-stall conditions exhibit a robust redistribution of the surface-pressure field and can yield strongly negative lift increments (e.g., $\alpha =18°$). These findings highlight the need for condition-dependent evaluation and design guidelines for leading-edge DBD actuation, based on measured pressure-field changes.

1. Introduction

Dielectric barrier discharge (DBD) plasma actuators have been investigated for more than two decades as a practical, all-electric approach to active flow control. The appeal of AC-DBD actuation lies in its surface-mounted implementation, absence of moving parts, and ability to induce a near-wall jet through electrohydrodynamic body forcing. Comprehensive reviews have summarized the actuator physics, operating modes, and representative aerodynamic applications, including airfoil separation control and stall mitigation [1,2]. In airfoil flows, the primary objective is often to delay the onset of flow separation or to reduce the extent of separated flow at elevated angles of attack, thereby improving lift performance and robustness under off-design conditions [3,4].

Despite these advantages, implementing AC-DBD plasma actuators in wind-tunnel and practical aerodynamic systems poses several challenges. Because the actuation authority is produced through near-wall electrohydrodynamic forcing, the achievable momentum addition is often limited and strongly dependent on the baseline boundary-layer state (transition/separation), actuator geometry and dielectric configuration, and the applied waveform and voltage/frequency settings; consequently, the outcome can be beneficial, neutral, or even adverse, depending on the operating condition [1,2,3,4,5,6]. In addition, the need for high-voltage hardware introduces practical constraints related to the electrical safety, insulation and arcing margins, electromagnetic interference, and long-term reliability of the dielectric and electrodes (e.g., aging, surface contamination, and discharge non-uniformity), while the energetic cost and the definition/normalization of “actuation strength” remain nontrivial for engineering comparison [1,2,7,8,9]. Relative to more conventional flow-control approaches—such as passive devices (e.g., vortex generators), mechanical devices, or fluidic methods (steady blowing/suction and synthetic/pulsed jets)—DBD actuation offers attractive features including surface-mounted integration, fast response, and the absence of moving parts and external plumbing; however, it may provide weaker momentum authority under some constraints and can exhibit stronger condition dependence than fluidic forcing designed to inject a prescribed mass/momentum flux [1,2,3,4]. Therefore, a key practical motivation is to evaluate DBD actuation in a reproducible manner under well-defined electrical settings and clearly stated performance metrics, while explicitly acknowledging the variability observed across operating conditions and measurement definitions.

State-of-the-art studies have demonstrated that plasma-based actuation can modify airfoil separation and stall characteristics, but the reported benefits vary widely across configurations and operating conditions. Early work established separation control at high angles of attack using AC-DBD actuation [3], and subsequent studies discussed broader turbulent-boundary-layer control perspectives and mechanisms [4]. For airfoil applications, actuator placement and implementation have been explored as critical design choices, including chordwise-location optimization to target separation behavior (e.g., on NACA 0015) [10], measurement methodologies and characterization metrics for thrust/power and actuator diagnostics [11,12,13], and approaches that alter airfoil loading through (virtual) Gurney-flap effects [14,15]. Related plasma-actuation studies have also reported stall-control outcomes at high angles of attack [6] and demonstrated leading-edge implementations intended to influence separation initiation [5]. Motivated by the literature, the present study adopts a fixed leading-edge AC-DBD setting to intentionally probe baseline-state dependence across an angle-of-attack sweep, while independently quantifying actuation strength using thrust-based characterization for repeatable comparison under practical electrical constraints [7,8,9,16,17,18].

A key design choice in airfoil applications is actuator placement along the chord and its intended interaction with the separation process. Several studies have optimized the actuation location to influence the separation behavior on airfoils (e.g., by moving the actuator downstream to act on a separation line that has shifted aft with the operating condition) [10]. Other work has demonstrated lift/drag changes and stall-control benefits using different actuator concepts and placements [11,12,13], including implementations that exploit (virtual) Gurney-flap effects to modify airfoil loading [14,15]. Stall control at high angles of attack has also been reported in related plasma-actuation studies [6]. From a physical standpoint, this placement choice determines whether the actuator is primarily attempting to (i) influence the boundary-layer response and separation triggering near the leading edge, or (ii) interact with an already developed separated shear layer farther downstream on the upper surface. These are not equivalent control targets: the former aims at the initiation mechanism, while the latter acts on the dynamics of an established separated region and its shear layer. Consistent with this distinction, wind-tunnel experiments using leading-edge SDBD plasma actuators have reported increased maximum lift and delayed stall, underscoring the relevance of targeting separation initiation near the leading edge [5].

In this context, the present study focuses on a leading-edge configuration because it is explicitly aligned with the earliest stage of separation development. In this study, the actuator was placed at the leading edge to act on the separation initiation point, rather than on an already separated flow farther downstream on the upper surface. This choice is particularly relevant for angle-of-attack sweeps that traverse attached, near-stall, and post-stall regimes, where a modest change in early boundary-layer behavior can produce a qualitatively different global flow state, pressure field, and load response. At the same time, the literature clearly indicates that DBD aerodynamic benefits are strongly condition-dependent. The reported outcomes vary with the baseline flow state, actuator geometry and dielectric configuration, driving waveform and amplitude, and the evaluation metric [3,4]. Similar sensitivity to boundary conditions and near-surface coupled transport has also been discussed in other surface-driven engineering systems (as a conceptual analogy) [19]. This perspective underscores the importance of accurately characterizing the imposed forcing when interpreting performance changes in DBD-aerodynamic applications. This conditionality becomes most critical near-stall and post-stall, where the separated shear layer is highly unsteady and its receptivity to forcing can change markedly with the angle of attack, potentially weakening suction enhancement or producing an unfavorable pressure shift even when the same actuation setting is applied.

In addition, pulse-modulated (burst-mode) actuation introduces further control parameters—most notably, the burst repetition frequency and duty cycle—that can strongly influence separation-control effectiveness. Prior airfoil studies using burst-mode driving have reported that the optimal burst settings depend on the baseline flow state and Reynolds number, and that the achievable benefit can change markedly across near-stall and post-stall regimes [20,21,22]. More recent wind-tunnel/flight-scale investigations likewise suggest that plasma-based stall control may yield only modest increases in maximum lift in some configurations, while still providing improvements in post-stall behavior and robustness, reinforcing that the net aerodynamic benefit is not universal but case-dependent [23].

Another practical issue is how to quantify actuation strength in a way that is repeatable and interpretable for wind-tunnel testing. While velocity-field diagnostics and body-force estimations are powerful, they may not always be available in early-stage experiments. Prior studies have established useful actuator-characterization measurements, including induced wall-flow measurements, thrust/power scaling, and diagnostics for comparing actuator configurations [7,9,16,17,18]. In particular, thrust measurements in quiescent air provide a simple, repeatable proxy for the net momentum imparted by an AC-DBD actuator, and methodology details—including the antithrust hypothesis and installation effects—have been carefully documented [8]. Accordingly, thrust-based characterization is adopted here as an experimentally grounded indicator of actuation strength that can be used to compare dielectric configurations under voltage/frequency sweeps.

A further methodological challenge arises when aerodynamic performance is evaluated from discrete surface-pressure measurements. Pressure integration is widely used to estimate lift from upper- and lower-surface pressure distributions. However, pressure-derived lift can be sensitive to pressure tap effects, tap layout, and the chosen integration interval, especially when comparisons are made across an angle-of-attack sweep or when the available tap coverage differs between the upper and lower surfaces [24,25]. This sensitivity is practically important for actuator experiments because actuator installation can partially occlude taps, alter the local surface condition, or lead to non-overlapping chordwise coverage between the upper and lower surfaces. Without consistent processing, apparent actuator-OFF/ON differences can be confounded by differences in sampling coverage, rather than reflecting a true actuation effect. To mitigate this issue, the present study evaluates pressure-derived lift by integrating the pressure difference over the common chordwise interval instrumented on both surfaces, following standard pressure-integration practice [26]. This approach enforces a consistent comparison basis across angles of attack and between actuator-OFF/ON cases.

The objective of this paper is to quantify how a fixed leading-edge DBD actuation setting modifies the surface-pressure field and the resulting pressure-derived lift of a NACA 0012 airfoil while independently characterizing actuation strength. The study proceeds in two steps. First, actuation strength is characterized in quiescent air with thrust measurements for two dielectric configurations under voltage and frequency sweeps, following established thrust-measurement practice [8]. Second, the actuator is applied in wind-tunnel tests, where upper- and lower-surface pressure distributions are measured over an angle-of-attack sweep. The pressure-derived lift is then evaluated by integrating the pressure difference over the common instrumented chordwise interval, enabling robust actuator-OFF/ON comparisons across angles [26]. Finally, the results are interpreted in the context of the known conditionality of plasma-based separation control near-stall and post-stall [3,4,6], with emphasis on clarifying when and why a fixed leading-edge setting can yield a positive lift response in attached flow yet become neutral or adverse as the baseline state transitions toward strong separation. In the present study, the actuator is operated in a single fixed electrical condition (continuous sinusoidal mode) to reflect practical constraints in early-stage wind-tunnel testing, where stable and reproducible settings are often prioritized over case-by-case tuning; this design therefore requires a condition-dependent interpretation supported by independent actuation-strength characterization.

The remainder of this paper is organized as follows. Section 2 describes the experimental setup, including the wind-tunnel facility, the airfoil model and DBD actuator configurations, the electrical driving conditions and thrust measurements, the surface-pressure measurements, the smoke-wire visualization procedure, and the data-processing method for pressure-derived lift over the common instrumented chordwise interval. Section 3 presents the thrust characteristics obtained in quiescent air and the measured surface-pressure distributions and pressure-derived lift results across the angle-of-attack sweep. Section 4 discusses the angle-of-attack-dependent actuation response in conjunction with the smoke-wire observations, and summarizes the implications, limitations, and recommended improvements for future measurements and evaluation.

2. Materials and Methods

2.1. Wind-Tunnel Facility and Test Conditions

Experiments were conducted in a low-speed wind tunnel (AF-100, TECQUIPMENT, Nottingham, UK) at the National Institute of Technology, Tsuyama College. An overview of the test-section setup and instrumentation is shown in Figure 1a; a photograph of the facility is provided in Figure 1d. The test section size was 305 × 305 × 600 mm (0.305 × 0.305 × 0.600 m). The tests were performed at a free-stream velocity of $U_{\infty } =5$ m/s. The angle of attack was set to $\alpha = 0°, 4°, 8°, 12°, 16°$, and $18°$. The coordinate system was defined such that $x$ is aligned with the free-stream direction and y is normal to the free stream; the positive $y$-direction corresponds to the upward direction, relative to the airfoil model.

The free-stream dynamic pressure was evaluated as $q_{\infty } = \left({\displaystyle \frac{1}{2}}\right)\rho U_{\infty }^2$, where $\rho$ is the air density. The Reynolds number based on the airfoil chord was ${Re}_c = {\displaystyle \frac{\rho U_{\infty }c}{\mu }}$, where $c$ is the chord length and $\mu$ is the dynamic viscosity. Unless otherwise noted, all measurements were conducted under identical wind-tunnel settings for the plasma-actuator-OFF and plasma-actuator-ON cases. The free-stream turbulence (velocity-fluctuation) intensity in the test section was measured at the test-section center, using a hot-wire anemometer (GM8903, Shenzhen Wintact Electronics, Guangdong, China) at $U_{\infty } = 5$ m/s. From three 60 s records logged at 1 Hz, the intensity was $T_{\mathrm{u}} = u_{\mathrm{r}\mathrm{m}\mathrm{s}}/U_{\infty } = 4.12\% \pm 1.23\%$ (mean ± SD, $n = 3$). Because the logging rate is 1 Hz, this value primarily reflects low-frequency freestream velocity fluctuations and may underestimate higher-frequency turbulence components; nevertheless, all actuator-OFF/ON cases were tested under identical wind-tunnel settings, so the present discussion focuses on robust relative differences between the two conditions.

As shown in Figure 1a, the pressure taps on the airfoil were connected via tubing to a multi-tube inclined water manometer (AFA1, TECQUIPMENT) located outside the test section, and the DBD plasma actuator was driven by a high-voltage power supply unit (PA Series, PSI, Kawagoe, Japan) placed outside the test section.

Figure 1. Wind-tunnel facility and experimental setup for surface-pressure measurement and smoke-wire visualization. (a) Side-view schematic of the wind-tunnel test section (305 × 305 × 600 mm) showing the NACA 0012 airfoil model ($c = 150$ mm), pressure tap tubing (upper 10 taps and lower 10 taps) connected to the multi-tube inclined water manometer (dotted ellipsis indicates omitted repeated tubes for clarity), and the high-voltage power supply; the free-stream direction $U_{\infty }$ and the viewing direction for smoke-wire visualization (normal to the side window; ⊗) are indicated. (b) Pressure tap distribution, actuator placement, and taps sealed by the actuator installation (×); the exposed electrode was installed in the immediate vicinity of the leading edge ($x/c \approx 0$). Chordwise tap locations are listed in Table 1. (c) Side-view arrangement of the smoke-wire visualization system (nichrome wire, ϕ0.26 mm) placed upstream of the leading edge and powered by a DC supply (50 V). (d) Photograph of the low-speed wind-tunnel facility used in this study.

Figure 1. Wind-tunnel facility and experimental setup for surface-pressure measurement and smoke-wire visualization. (a) Side-view schematic of the wind-tunnel test section (305 × 305 × 600 mm) showing the NACA 0012 airfoil model ($c = 150$ mm), pressure tap tubing (upper 10 taps and lower 10 taps) connected to the multi-tube inclined water manometer (dotted ellipsis indicates omitted repeated tubes for clarity), and the high-voltage power supply; the free-stream direction $U_{\infty }$ and the viewing direction for smoke-wire visualization (normal to the side window; ⊗) are indicated. (b) Pressure tap distribution, actuator placement, and taps sealed by the actuator installation (×); the exposed electrode was installed in the immediate vicinity of the leading edge ($x/c \approx 0$). Chordwise tap locations are listed in Table 1. (c) Side-view arrangement of the smoke-wire visualization system (nichrome wire, ϕ0.26 mm) placed upstream of the leading edge and powered by a DC supply (50 V). (d) Photograph of the low-speed wind-tunnel facility used in this study.

Table 1. Chordwise locations of pressure taps on the NACA 0012 airfoil.

No.	Upper Surface x/c	Lower Surface x/c
1	0.0051 ×	0.0101 ×
2	0.0254	0.0508 ×
3	0.0762	0.1016
4	0.1270	0.1524
5	0.2533	0.2743
6	0.4133	0.3963
7	0.5385	0.5182
8	0.6757	0.6401
9	0.8128	0.7620
10	0.9144	0.8636

Notes: × indicates pressure taps sealed by the actuator installation and thus excluded from the pressure-derived analysis.

Table 1. Chordwise locations of pressure taps on the NACA 0012 airfoil.

No.	Upper Surface x/c	Lower Surface x/c
1	0.0051 ×	0.0101 ×
2	0.0254	0.0508 ×
3	0.0762	0.1016
4	0.1270	0.1524
5	0.2533	0.2743
6	0.4133	0.3963
7	0.5385	0.5182
8	0.6757	0.6401
9	0.8128	0.7620
10	0.9144	0.8636

Notes: × indicates pressure taps sealed by the actuator installation and thus excluded from the pressure-derived analysis.

2.2. Airfoil Model and DBD Plasma Actuator Configuration

A NACA 0012 airfoil model was used in the present study. The chord length and span of the model were $c =0.150$ m and $b =0.300$ m, respectively. The model was mounted in the wind-tunnel test section described in Section 2.1, and the angle of attack was adjusted by rotating the model about the quarter-chord location.

A dielectric barrier discharge (DBD) plasma actuator was installed near the leading edge of the airfoil. The actuator consisted of an exposed electrode and an encapsulated (buried) electrode separated by a dielectric layer, forming a conventional single-sided DBD configuration. The electrodes were made of copper-foil tape (TERAOKA SEISAKUSYO, Tokyo, Japan) with a thickness of $t_{\mathrm{e}} =0.07$ mm. The exposed- and buried-electrode widths were $w_{\mathrm{e}} =1.5$ mm and $w_{\mathrm{b}} =15$ mm, respectively, and the spanwise electrode length was $L =150$ mm. The streamwise gap $g$, defined as the distance from the downstream edge of the exposed electrode to the upstream edge of the buried electrode, was set to approximately zero in the immediate vicinity of the leading edge. The dielectric layer was formed using polyimide tape (3M, St. Paul, MN, USA) with a nominal thickness of $t_{\mathrm{d}} =0.05$ mm per layer. Two actuator builds were considered in this study: a two-layer (“two-tape”, i.e., two-zone) configuration and a three-layer (“three-tape”, i.e., three-zone) configuration, corresponding to total nominal dielectric thicknesses of 0.10 mm and 0.15 mm, respectively. The three-tape actuator was used only for the standalone thrust characterization (mounted on an acrylic plate), whereas the two-tape configuration was used for the wind-tunnel experiments on the airfoil.

Surface-pressure taps were distributed on both the upper and lower surfaces. The pressure tap layout, actuator placement, and sealed taps are summarized in Figure 1b, and the chordwise tap locations are listed in Table 1. Taps sealed by the actuator assembly (marked by × in Table 1) were excluded from the pressure-derived analysis. In addition, the experimental arrangement for the smoke-wire flow visualization is shown in Figure 1c.

2.3. Electrical Driving Conditions and Thrust Measurement

The working principle of the single-sided DBD plasma actuator is illustrated in Figure 2. The actuator was driven by a sinusoidal high-voltage power supply. In this study, no burst (pulse) modulation was applied; it was operated in continuous sinusoidal mode throughout all measurements. The applied voltage is reported as the peak-to-peak value, $V_{\mathrm{p}\mathrm{p}}$, and the carrier (driving) frequency is denoted by $f$. The electrical power consumption was measured under the representative operating frequency used in the wind-tunnel sweep ($f \approx 3.4$ kHz; measured $f =3.525$ kHz). The measurement was repeated $n = 3$ times at each voltage, yielding $P =0.612\pm 0.033$ W at $V_{\mathrm{p}\mathrm{p}} =3$ kV, $P =1.411\pm 0.314$ W at $V_{\mathrm{p}\mathrm{p}} =5$ kV, and $P =4.322\pm 2.315$ W at $V_{\mathrm{p}\mathrm{p}} =7$ kV (mean ± 1 SD). The corresponding power–voltage sweep is provided in the Supplementary Materials (Table S1). According to the power-supply manual, the recommended operating frequency range is 5–10 kHz; however, in the present thrust characterization, stable and repeatable readings were obtained at $f =3.4$ kHz. Therefore, $f =3.4$ kHz was adopted as the reference condition for the thrust voltage sweep and as a representative fixed carrier frequency for the subsequent wind-tunnel angle-of-attack sweep, so that actuator-OFF/ON comparisons are not confounded by changes in electrical settings.

To quantify the actuation strength in a practical and repeatable manner, the actuator thrust was measured in quiescent air, using a standalone setup. For the thrust characterization, the actuator was mounted on an acrylic plate, and thrust was measured using a precision electronic balance (LIBROR AEG-202, SHIMADZU, Kyoto, Japan) with a readability of 1/10,000 g (0.1 mg). For each electrical setting, the balance reading was recorded after it visually stabilized. Two parameter sweeps were performed: (i) a frequency sweep at fixed $V_{\mathrm{p}\mathrm{p}} =1$ kV with $f = 3.4, 5.4, 7.4, 9.4$, and 11.6 kHz, and (ii) a voltage sweep at fixed $f =3.4$ kHz with $V_{\mathrm{p}\mathrm{p}} = 1, 3, 5$, and 7 kV. For the wind-tunnel measurements, $V_{\mathrm{p}\mathrm{p}} =7$ kV was selected as the highest voltage that could be operated reliably in our setup without arcing while maintaining repeatability over repeated runs. The thrust data are used as a proxy for the forcing level introduced by the actuator when interpreting changes in surface pressure and the smoke-wire visualization presented in Section 4.

2.4. Surface Pressure Measurement

Surface pressure was measured using discrete pressure taps distributed on the upper and lower surfaces (Figure 1b and Table 1). The pressure measurement and data-reduction procedure is summarized in Figure 3. For each test condition (angle of attack $\alpha$ and plasma-actuator state OFF/ON), the wind tunnel was first set to the target free-stream velocity and stabilized, while the ambient temperature $T$ and pressure $p_{\mathrm{a}}$ were recorded.

All pressure taps were connected via tubing to a multi-tube inclined water manometer placed outside the test section (Figure 1a). One reference tube was connected to the free-stream static port of a Pitot-static probe installed in the test section, so that the free-stream static pressure $p_{\infty }$ was captured in the same manometer image as the tap pressures. For each condition, the manometer was photographed, and the reading along the inclined tube $∆s$ was obtained from the photograph for each tap and for the reference tube.

The vertical height difference was computed from the inclined reading as

$$∆h=∆s \sin \theta \left(\theta =40°\right),$$

and the corresponding pressure difference for each tap was obtained as

$$∆p_{\mathrm{t}\mathrm{a}\mathrm{p}}={\rho }_{\mathrm{w}}g∆h=p_{\mathrm{t}\mathrm{a}\mathrm{p}}-p_{\infty },$$

where ${\rho }_{\mathrm{w}}$ is the water density and $g$ is the gravitational acceleration. The pressure coefficient was then computed as

$$C_{\mathrm{p}}={\displaystyle \frac{p_{\mathrm{t}\mathrm{a}\mathrm{p}}-p_{\infty }}{q_{\infty }}}={\displaystyle \frac{∆p_{\mathrm{t}\mathrm{a}\mathrm{p}}}{q_{\infty }}}, q_{\infty }={\displaystyle \frac{1}{2}}{\rho }_{\mathrm{a}}{U}_{\infty }^2.$$

Here, $U_{\infty }$ and $q_{\infty }$ were obtained from the Pitot-static probe, and the air density ${\rho }_{\mathrm{a}}$ was evaluated from the recorded $T$ and $p_{\mathrm{a}}$.

For each test condition, the manometer photograph was taken five times and the mean value was used for $C_{\mathrm{p}}$. Taps sealed by the actuator installation (marked by $\times$ in Table 1) were excluded from the pressure-derived analysis.

2.5. Smoke-Wire Flow Visualization

Qualitative flow visualization was conducted using the smoke-wire method to observe the near-airfoil flow field under plasma-actuator-OFF and plasma-actuator-ON conditions (the overall workflow is summarized in Figure 4). A thin nichrome wire (ϕ0.26 mm) was installed upstream of the airfoil at $x/c =-0.5$ (measured from the leading edge), spanning the test section at the mid-span location of the model. The wire was coated with a small amount of a liquid-paraffin/benzene mixture (5:1 by volume) and electrically heated to generate smoke streaks, which were convected through the airfoil region by the free-stream flow.

The visualization was performed at the same free-stream velocity as the pressure measurements, $U_{\infty } = 5$ m/s, and at the same angles of attack ($\alpha =0°,4°,8°,12°,16°,18°$). The smoke streaks were recorded using a digital camera (EOS Kiss X5, Canon, Tokyo, Japan) from the side window (side view) at a resolution of 1280 × 720 and an encoded frame rate of 59.94 fps ($\approx$60 fps). The visualization images presented in the Discussion section are time-averaged (mean-intensity) fields, computed by averaging 165 consecutive frames extracted from the recorded videos after selecting a time interval in which the smoke is clearly visible. For reference, the corresponding maximum-intensity projections (computed from the same 165 frames) are provided in the Supplementary Materials (Figures S1 and S2) to highlight the outer envelope of the smoke distribution and intermittently appearing structures. The procedural flow from condition-setting to frame-extraction and post-processing is outlined in Figure 4.

2.6. Data Processing and Pressure-Integrated Lift over the Common Instrumented Range

To quantify the net pressure-loading change due to actuation, a pressure-derived lift coefficient was estimated by integrating the pressure difference between the lower and upper surfaces over the chordwise region, where both surfaces were instrumented. Using the surface-pressure coefficients defined in Section 2.4, the pressure-derived lift over the common range is defined as

$$C_{L,\mathrm{p}}^{\left(\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{m}\mathrm{o}\mathrm{n}\right)}={\int }_{x/c=x_{\mathrm{m}\mathrm{i}\mathrm{n}}}^{x_{\mathrm{m}\mathrm{a}\mathrm{x}}}\left(C_{p,l}\left(x/c\right)-C_{p,u}\left(x/c\right)\right)d\left(x/c\right),$$

where $C_{p,u}$ and $C_{p,l}$ denote the upper- and lower-surface pressure coefficients, respectively. In the present setup, the leading-edge region is partially affected by the actuator installation and associated tap sealing, and the most downstream usable tap locations are not identical between the upper and lower surfaces. Therefore, integrating over the full tap coverage of either surface would require extrapolation or would introduce non-overlapping chordwise coverage, which can artificially bias the pressure-integrated lift and the actuator-OFF/ON comparison. For this reason, the integration limits $x_{\mathrm{m}\mathrm{i}\mathrm{n}} =0.2533$ and $x_{\mathrm{m}\mathrm{a}\mathrm{x}} =0.762$ were selected as the overlap of the usable (unsealed) pressure tap locations available on both surfaces (see Table 1 and Figure 1b), and this fixed common interval was applied to all angles of attack and both actuation conditions to ensure a consistent and unbiased comparison basis.

Because the pressure taps on the upper and lower surfaces are not located at identical $x/c$ positions, $C_{p,u}$ and $C_{p,l}$ were linearly interpolated onto a common $x/c$ grid prior to integration. To assess the uncertainty introduced by the linear interpolation, we performed a sensitivity check by repeating the integration using different common chordwise grids (coarser and finer; e.g., $∆\left(x/c\right) =0.02$ and 0.005), and confirmed that the resulting $C_{L,\mathrm{p}}^{\left(\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{m}\mathrm{o}\mathrm{n}\right)}$ and $∆C_L$ changed only marginally compared with the dominant trends discussed in this paper. Because both actuator-OFF and actuator-ON cases use the same pressure tap locations and are processed with an identical interpolation and integration procedure, the interpolation-related bias is expected to largely cancel out in $∆C_L$; therefore, the conclusions are not sensitive to the use of linear interpolation for mapping $C_{p,u}$ and $C_{p,l}$ onto a common $x/c$ grid. The integral was then evaluated using the trapezoidal rule. The actuation-induced change in the pressure-derived lift coefficient was defined as

$$∆C_L=C_{L,\mathrm{p},\mathrm{o}\mathrm{n}}^{\left(\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{m}\mathrm{o}\mathrm{n}\right)}-C_{L,\mathrm{p},\mathrm{o}\mathrm{f}\mathrm{f}}^{\left(\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{m}\mathrm{o}\mathrm{n}\right)},$$

where the subscripts “on” and “off” indicate the plasma-actuator-ON and plasma-actuator-OFF conditions, respectively.

Finally, as described in Section 2.4, the pressure coefficient resolution of the inclined manometer under $U_{\infty }=5$ m/s is approximately $∆C_p \approx 0.83$; thus, pressure coefficients reported as $C_p =0$ should be interpreted as indistinguishable from zero within this resolution. Accordingly, the present study focuses on robust trends (e.g., sign reversal and large $C_p$ redistributions), rather than subtle $C_p$ differences near the measurement resolution.

2.7. Measurement Uncertainty and Repeatability

This section summarizes the primary sources of uncertainty that are relevant to interpreting the present pressure- and thrust-based trends. Surface pressures were read using an inclined water manometer with a tube inclination of 40°. The smallest scale division is 2 mm along the tube; accounting for the inclination, this corresponds to a pressure resolution of $∆C_p \approx 0.83$ under $U_{\infty } =5$ m/s. This resolution is reported transparently, and it motivates a key point in how the dataset is interpreted: the present study is intended to support the interpretation of robust, condition-dependent changes (e.g., sign reversal and large redistribution of $C_p$ and $∆C_L$), rather than to resolve subtle $C_p$ differences near the measurement resolution. In addition, repeated readings occasionally returned as zero for some taps; these are treated as practical zeros within the measurement resolution, rather than as an exact zero pressure difference.

The free-stream reference pressures used for normalization (static pressure $p_{\infty }$ and dynamic pressure $q_{\infty }$) were obtained from a Pitot tube measurement. Because the same tunnel settings and normalization procedure were used consistently across actuator-OFF and actuator-ON cases at each angle of attack, the main conclusions are drawn from the relative differences and repeatable trends, rather than from the absolute $C_p$ values that may be sensitive to small systematic offsets in the reference quantities.

For the thrust characterization (Section 2.3), thrust was measured using a precision electronic balance with a readability of 0.1 mg. For each electrical setting, the value was recorded after the reading visually stabilized; thus, the reported thrust levels should be interpreted as practical, repeatable indicators of actuation strength, rather than as absolute force measurements with a fully quantified uncertainty budget. Accordingly, the uncertainty discussion in this paper is intended to support the interpretation of trends with angle of attack and actuation settings, rather than to provide a comprehensive metrological uncertainty analysis. Unless otherwise stated, the error bars in the surface-pressure plots indicate the minimum–maximum range over the repeated measurements.

3. Results

3.1. Thrust Characteristics of the DBD Plasma Actuator

Figure 5 summarizes the thrust measured in quiescent air as a function of the carrier (driving) frequency at a fixed voltage of $V_{\mathrm{p}\mathrm{p}} =1$ kV for the two-tape and three-tape actuators. The mean thrust increased monotonically with frequency for both configurations over the tested range ($f =3.4-11.6$ kHz). For the two-tape actuator, the mean thrust rose from 0.034 mN at 3.4 kHz to 0.188 mN at 11.6 kHz. For the three-tape actuator, the corresponding values increased from 0.028 mN to 0.134 mN. Across all tested frequencies, the two-tape actuator produced a larger mean thrust than the three-tape actuator. The run-to-run scatter, indicated by the (one-sided) error bars, becomes more pronounced at the higher-frequency conditions. The actuator was operated in continuous sinusoidal mode (no burst modulation) for all thrust measurements.

At higher carrier frequencies, the incremental thrust gain tends to diminish. This behavior is consistent with the fact that, under fixed $V_{\mathrm{p}\mathrm{p}}$, increasing $f$ does not necessarily yield a proportional increase in effective electrohydrodynamic forcing: surface-charge accumulation on the dielectric can partially shield the local electric field near the exposed-electrode edge, limiting further growth of the discharge and the induced wall-jet momentum. In addition, because the actuator behaves as a strongly capacitive load, the frequency-dependent impedance and phase characteristics of the power-supply/actuator system can constrain the discharge-current increase at higher $f$, so that part of the additional electrical input contributes to reactive/dielectric losses, rather than net thrust.

Figure 6 shows the thrust response to the applied voltage at a fixed frequency of $f =3.4$ kHz. As shown in the enlarged view (Figure 6a), both actuators exhibited a gradual increase in thrust from 1 to 3 kV, followed by a more rapid rise toward 5 kV. The two-tape actuator increased from 0.023 mN at $V_{\mathrm{p}\mathrm{p}} =1$ kV to 0.083 mN at 3 kV and 0.664 mN at 5 kV, while the three-tape actuator increased from 0.028 mN to 0.062 mN and 0.325 mN at the same voltages. Over the full range, up to 7 kV (Figure 6b), the mean thrust continued to increase strongly, reaching 4.03 mN for the two-tape actuator and 0.785 mN for the three-tape actuator at $V_{\mathrm{p}\mathrm{p}} =7$ kV. Overall, the voltage sweep indicates a markedly nonlinear response, with substantially larger thrust achieved by the two-tape actuator at higher voltages. Although both the two-tape and three-tape actuators share the same electrode planform geometry, they differ in dielectric thickness (two-tape: $t_{\mathrm{d}} =0.10$ mm; three-tape: $t_{\mathrm{d}} =0.15$ mm). For a given $V_{\mathrm{p}\mathrm{p}}$ and carrier frequency, a thicker dielectric reduces the effective electric field in the discharge region in a first-order sense and lowers the effective capacitance of the actuator, which tends to reduce the amount of charge transfer and the resulting electrohydrodynamic forcing. This provides a physically consistent explanation for the systematically smaller thrust measured for the three-tape configuration under the present electrical constraints and continuous sinusoidal operation (no burst/pulse modulation).

3.2. Surface Pressure Distributions

3.2.1. Surface Pressure Distributions at $\alpha =4°$

Figure 7 compares the chordwise surface-pressure distributions at $\alpha =4°$ for the actuator-OFF and actuator-ON conditions. In both cases, the upper-surface pressure coefficient is negative over the measured leading-edge to mid-chord region and approaches values near zero toward the aft tap locations, whereas the lower-surface pressure remains positive over the available tap range. Relative to the actuator-OFF case (Figure 7a), the actuator-ON case (Figure 7b) exhibits a more negative upper-surface pressure coefficient over the mid- to aft-chord tap locations ($x/c\gtrsim 0.4$), while the lower-surface pressure shows comparatively smaller changes. As a result, the pressure difference between the two surfaces increases over portions of the measured chord when the actuator is turned on.

3.2.2. Surface Pressure Distributions at $\alpha =8°$

Figure 8 compares the surface-pressure distributions at $\alpha =8°$ for the actuator-OFF and actuator-ON conditions. With actuation (Figure 8b), the upper-surface pressure coefficient becomes less negative near the leading-edge tap locations ($x/c\lesssim 0.2$) compared with the actuator-OFF case (Figure 8a), indicating a reduction in upper-surface suction over the forward portion of the measured chord. Downstream of mid-chord ($x/c\gtrsim 0.5$), the upper-surface pressure coefficients remain close to zero for both cases. The lower-surface pressure distributions show comparatively small changes between OFF and ON across the available tap locations.

3.2.3. Surface Pressure Distributions at $\alpha =18°$

Figure 9 compares the surface-pressure distributions at $\alpha =18°$ for the actuator-OFF and actuator-ON conditions. In the actuator-OFF case (Figure 9a), the upper-surface pressure coefficient remains negative over the measured chordwise range, whereas the lower-surface pressure is positive over the available tap locations, yielding a finite pressure difference between the two surfaces. In contrast, in the actuator-ON case (Figure 9b), both the upper- and lower-surface pressure coefficients collapse toward values near zero over most of the measured chord, indicating a substantially reduced pressure difference between the two surfaces within the available tap range.

Taken together, Figure 7, Figure 8 and Figure 9 show that the surface-pressure distributions and the resulting pressure difference between the upper and lower surfaces change markedly with the angle of attack. At $\alpha =4°$, the actuator-ON case exhibits an increase in upper-surface suction over the mid- to aft-chord tap locations, relative to the actuator-OFF case, while the lower-surface pressure changes remain comparatively small. At $\alpha =8°$, the actuator-ON case shows a reduction in upper-surface suction near the leading-edge tap locations, with smaller differences downstream. At $\alpha =18°$, the actuator-ON case shows both upper- and lower-surface pressure coefficients approaching values near zero over most of the measured chord, resulting in a substantially reduced pressure difference within the available tap range.

3.3. Pressure-Derived Lift Coefficient

Pressure-derived lift coefficients were obtained by integrating the pressure difference between the upper and lower surfaces. Because several pressure taps were unavailable due to the actuator installation, and the available tap ranges differ between the two surfaces, the integration was performed over the common chordwise interval where measurements are available on both surfaces. Figure 10 compares the resulting pressure-derived lift estimate, $C_{L,\mathrm{p}}^{\left(\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{m}\mathrm{o}\mathrm{n}\right)}$, for the actuator-OFF and actuator-ON conditions as a function of the angle of attack. The pressure-derived lift increases with $\alpha$ up to intermediate angles for both cases, while a marked decrease is observed for the actuator-ON condition at $\alpha = 18°$.

The actuator’s influence on the pressure-derived lift depends on the angle of attack. As summarized in Figure 11, the lift increment $∆C_L = C_{L.\mathrm{o}\mathrm{n}}-C_{L.\mathrm{o}\mathrm{f}\mathrm{f}}$, which is positive at low angles, becomes small at intermediate angles and is strongly negative at $\alpha =18°$.

3.4. Relationship Between Pressure Distribution and Pressure-Derived Lift

The trends in $C_{L,\mathrm{p}}^{\left(\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{m}\mathrm{o}\mathrm{n}\right)}$ (Figure 10) and $∆C_L$ (Figure 11) are consistent with the changes observed in the surface-pressure distributions (Figure 7, Figure 8 and Figure 9) within the available tap range. At $\alpha =4°$, the actuator-ON case exhibits more negative upper-surface $C_p$ over the mid- to aft-chord tap locations than the actuator-OFF case (Figure 7), corresponding to a positive $∆C_L$. At $\alpha =8°$, the actuator-ON case shows reduced upper-surface suction near the leading-edge tap locations compared with the actuator-OFF case (Figure 8), and the resulting $∆C_L$ is smaller. At $\alpha =18°$, the actuator-ON case shows both upper- and lower-surface $C_p$ approaching values near zero over most of the measured chord (Figure 9), corresponding to the large negative $∆C_L$.

3.5. Summary of Results

Across the tested angles of attack, the thrust measurements provide a repeatable indicator of actuation strength, and the surface-pressure measurements quantify how the actuator modifies the pressure field on both surfaces. The pressure distributions show that the actuator effect is strongly dependent on the angle of attack: at $\alpha =4°$, the actuator increases the upper-surface suction over the available tap range; at $\alpha =8°$, the actuator reduces the leading-edge suction; and at $\alpha =18°$, both upper- and lower-surface pressure coefficients approach values near zero over most of the measured chord. Consistent with these pressure changes, the pressure-derived lift estimate obtained from common-range integration increases at low angles, but it exhibits a large negative increment at $\alpha =18°$, as reflected in the corresponding $∆C_L$ trend.

4. Discussion

4.1. Key Findings and Focus of the Discussion

The present results show that a leading-edge DBD plasma actuator can markedly modify the aerodynamic loading of a NACA 0012 airfoil, and that the direction and magnitude of the response depend strongly on the angle of attack. The actuation strength was first characterized by thrust measurements in quiescent air (Figure 5 and Figure 6), and the same operating setting was then applied in the wind-tunnel tests. The surface-pressure measurements reveal that the pressure-field response differs across the tested angles (Figure 7, Figure 8 and Figure 9): at $\alpha =4°$, the actuation increases the upper-surface suction over the measured mid- to aft-chord region, whereas at $\alpha =8°$, it reduces the leading-edge suction, relative to the actuator-OFF case. At $\alpha =18°$, the actuator-ON case shows both upper- and lower-surface $C_p$ approaching values near zero over most of the measured chord, indicating a substantially reduced pressure difference within the available tap range. These changes are consistent with the pressure-derived lift estimates obtained via common-range integration (Figure 10 and Figure 11), including a positive $∆C_L$ at low angles and a strongly negative $∆C_L$ at $\alpha =18°$.

Accordingly, this discussion treats the tested angles ($\alpha =4°, 8°$ and $18°$) as distinct conditions that represent markedly different baseline states, without implying a universal benefit of actuation. The objective is to explain why a fixed electrical setting yields opposite pressure and loading responses depending on the baseline condition. We first relate the measured thrust trends to a practical measure of actuation strength (Section 4.2), then interpret the pressure-field changes observed at $\alpha = 4°$ and $\alpha = 8°$ (Section 4.3 and Section 4.4), and finally discuss the qualitatively different response at $\alpha = 18°$(Section 4.5). Throughout the discussion, interpretations are grounded in the present measurements—discrete surface-pressure taps and qualitative smoke-wire visualization; the resulting limitations and needed follow-on measurements are summarized in Section 4.6.

4.2. Actuation Strength and Why the Response Changes with the Angle of Attack

The thrust measurements provide a practical proxy for relative actuation strength under different electrical settings. For both actuator layouts, the measured thrust increases with the frequency at $V_{\mathrm{p}\mathrm{p}} =1$ kV and increases strongly with $V_{\mathrm{p}\mathrm{p}}$ at a fixed frequency (Figure 5 and Figure 6). At the same electrical setting, the two-tape configuration produces larger thrust than the three-tape configuration, and the two-tape actuator was therefore selected for the airfoil experiments.

DBD plasma actuators introduce momentum into the near-wall region by generating a wall-jet-like induced flow. Prior work has emphasized that actuation “strength” can be quantified using metrics beyond electrical settings alone (e.g., induced-flow velocity, momentum-based coefficients, thrust/power-related measures, or body-force estimates), and that the control outcome depends strongly on the baseline boundary-layer/separation state [1,2,3,4,5,11,12,13,14]. Thus, a single actuator can be beneficial in attached or marginally separated conditions, yet have limited authority—or even adverse coupling—in more strongly separated flows.

Consistent with this understanding, the present actuator setting should be interpreted as a fixed forcing level applied to three distinct baseline states as $\alpha$ is increased. As $\alpha$ increases, the suction-side boundary layer thickens and the separation tendency intensifies, so the relative authority of the same near-wall forcing decreases and its coupling mechanism can change—from energizing an attached boundary layer, to perturbing a near-stall shear layer, to interacting with a fully separated shear layer. This framework motivates interpreting the present results primarily as angle-of-attack-dependent responses to fixed forcing, and it highlights the need for future measurements that can connect the electrical setting to a nondimensional forcing metric and to resolved flow-field changes.

4.3. Attached-Flow Condition (α = 4°): Favorable Pressure-Field Modification

At $\alpha =4°$, the baseline pressure distribution indicates an attached-flow condition over the measured region, with strong suction near the leading edge followed by gradual recovery downstream (Figure 7a). With actuation, the upper-surface suction is strengthened over much of the measured chord, while the lower-surface pressure remains comparatively unchanged, resulting in a net increase in pressure-derived loading (Figure 7b).

This favorable redistribution is also reflected in the lift increment derived from the common-range integration, where $∆C_L$ is positive at a low angle of attack (Figure 11). Within the present measurement resolution and discrete tap coverage, the actuation at $\alpha =4°$ is therefore interpreted as a net energization of the suction-side boundary layer that enhances pressure loading, rather than as a qualitative change in the overall flow topology.

4.4. Near-Stall Condition (α = 8°): Suction Loss and Onset Separation

At $\alpha =8°$, the baseline pressure distribution shows increased suction compared with $\alpha =4°$, but also a more pronounced recovery toward mid-chord, indicating that the flow is closer to separation (Figure 8a). Under actuation, the measured upper-surface suction is weakened and the recovery occurs earlier, yielding a negative lift increment that is relative to the actuator-OFF case (Figure 8b and Figure 11).

Although the pressure taps cannot resolve the full unsteady and three-dimensional behavior, the time-averaged smoke-wire visualization provides qualitative context for this adverse response. As shown in Figure 12, the actuator-ON case exhibits an earlier departure of the streak lines from the upper surface and a distinct separation vortex compared with the actuator-OFF case, which is consistent with the actuation promoting or amplifying separation at this near-stall condition. A plausible explanation is that the forcing introduces disturbances that thicken the boundary layer or destabilize the shear layer in a way that reduces time-averaged suction; however, velocity-field measurements will be required to confirm this mechanism.

4.5. Post-Stall Condition (α = 18°): Separated-Flow Reorganization

In the post-stall condition at $\alpha =18°$, the pressure distribution indicates a largely separated suction-side flow: the upper-surface $C_p$ is close to zero over most of the measured chord, implying a diminished ability of the pressure field to generate useful loading (Figure 9a). When the actuator is turned on, the pressure-derived loading decreases further, and the common-range lift estimate drops sharply compared with the actuator-OFF case (Figure 9b and Figure 11). This behavior produces a strongly negative $∆C_L$ at $\alpha =18°$ (Figure 11).

The time-averaged smoke-wire visualization in Figure 13 suggests that actuation does not promote reattachment at this condition but instead reorganizes the separated flow into a large recirculation/vortex bubble near the leading edge. Such a response is qualitatively consistent with the actuator, forcing coupling to an already separated shear layer and sustaining large-scale unsteady structures, rather than restoring an attached boundary layer.

With the present measurements, we cannot determine whether this reorganization corresponds to changes in separation onset location, shear-layer frequency, or recirculation size, but the hypothesis provides a testable target for future PIV or time-resolved pressure measurements.

4.6. Implications and Limitations

Taken together, the pressure and visualization results indicate that a single fixed actuation setting can lead to beneficial, neutral, or adverse aerodynamic outcomes depending on the baseline state. In attached conditions, the actuator strengthens suction and increases pressure-derived lift ($\alpha =4°$), whereas near stall, it weakens suction and is associated with earlier separation ($\alpha =8°$), and in post-stall it appears to sustain a large separated structure with a substantial loss of pressure-derived lift over the common range ($\alpha =18°$).

Taken together, the pressure and visualization results indicate that a single fixed actuation setting can lead to beneficial, neutral, or adverse aerodynamic outcomes, depending on the baseline state. In attached conditions (e.g., α = 4°), the single-sided AC-DBD actuator introduces near-wall electrohydrodynamic forcing that is commonly interpreted as a wall-jet-like momentum addition which can enhance suction and strengthen the favorable pressure gradient over the forward chord, thereby increasing the pressure-derived lift over the common instrumented interval. Near stall (e.g., α = 8°), the baseline state is close to separation and highly sensitive to perturbations; under such conditions, the same forcing can modify the leading-edge boundary-layer development and the separated-shear-layer roll-up/reattachment tendency in a way that weakens suction and promotes earlier separation, which is consistent with the observed pressure redistribution and the smoke-wire visualization. In post-stall (e.g., α = 18°), where a large separated structure dominates, the actuation may reorganize or sustain the separated region and the associated suction-side pressure plateau, rather than reattach the flow, resulting in a further loss of pressure-derived lift over the common range. Importantly, the present actuator was operated in continuous sinusoidal mode (no burst/pulse modulation), and we intentionally used a single fixed electrical setting; therefore, the observed variations should be viewed as evidence of baseline-state dependence rather than contradictions with prior reports, whose Reynolds number, freestream turbulence, actuator geometry/placement, actuation mode, and evaluation metrics differ across studies [1,2,3,4,7,8,9].

While the present measurements focus on pressure loading and its lift implication over the common instrumented range, the pressure distributions still provide qualitative, pressure-based indications of drag trends. In near-stall and post-stall conditions, a suction-side pressure plateau and delayed pressure recovery are consistent with a widely separated flow state, which typically increases pressure drag. In our data, the actuator-ON cases that exhibit weakened suction and separation-related pressure redistribution therefore suggest a tendency toward higher pressure drag under those conditions. This inference is qualitative and limited to pressure effects over the instrumented interval, because viscous drag and the uninstrumented chordwise regions are not captured in the present setup.

A key limitation of the present study is the discrete and partially missing/overlapping pressure tap coverage (due to the actuator installation and sealed taps), which constrains the integration interval and can influence pressure-derived lift estimates and actuator-OFF/ON comparisons [24,25]. The smoke-wire visualization is qualitative and does not provide velocity or vorticity fields. Even with these constraints, the present dataset provides a consistent, measurement-based picture of the angle-of-attack-dependent actuation response through complementary pressure-derived lift (over the common instrumented range) and smoke-wire visualization evidence.

Future work should improve both the pressure-based loading evaluation and the flow-field diagnostics. On the pressure side, increasing the density of pressure taps and the chordwise overlap between the upper and lower surfaces would reduce the sensitivity to the limited common integration interval, and adopting a multi-channel pressure scanner would improve repeatability and temporal sampling; complementary direct force measurements (e.g., a force balance) would further strengthen the validation of the pressure-derived lift trends [24,25]. On the flow-diagnostics side, quantitative measurements of separation location and shear-layer dynamics are required; while PIV would be ideal for the velocity/vorticity fields, practical near-term alternatives that are compatible with the present setup include pointwise velocity measurements (e.g., hot-wire) at selected stations and time-resolved smoke-wire/video-based metrics to characterize unsteadiness and separation/reattachment behavior. These improvements will enable a more quantitative, mechanism-based interpretation of the pressure trends and visualization evidence that are reported here.

In comparison with public studies that also report results under fixed actuation settings, quantitative agreement is not necessarily expected, because the baseline flow state and the actuation definition/normalization differ substantially across experiments. Reported outcomes depend on the Reynolds number and freestream turbulence (which influence transition and separation), actuator geometry/placement, and the actuation mode and waveform (e.g., continuous sinusoidal AC-DBD versus pulsed/nanosecond actuation). In the present study, the actuator was operated in continuous sinusoidal mode (no burst/pulse modulation). In addition, the apparent “benefit” can vary with the chosen evaluation metric (force-balance coefficients versus pressure-derived loading over a specified integration interval) and how the forcing level is characterized (e.g., $V_{\mathrm{p}\mathrm{p}}$, carrier frequency, waveform, or electrical power). These factors can change the receptivity of the separated shear layer, especially near stall and post-stall, where the flow is highly unsteady. Therefore, differences from previous reports are likely attributable to variations in the baseline state (transition/separation), actuation mode, and the selected metric/normalization, rather than contradictions [1,2,3,4,7,8,9].

5. Conclusions

This study investigated the aerodynamic response of a NACA 0012 airfoil to a leading-edge DBD plasma actuator, using thrust characterization, surface-pressure measurements, and smoke-wire flow visualization. Here, “pressure-derived lift” refers to the pressure-derived lift over the common instrumented range, $C_{L,\mathrm{p}}^{\left(\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{m}\mathrm{o}\mathrm{n}\right)}$, obtained by integrating $C_{p,l}-C_{p,u}$ over $x/c = 0.2533$~0.7620 (see Section 2.6).

The actuator thrust increased with both the carrier (driving) frequency and the applied voltage. The voltage sweep showed a strongly nonlinear increase in thrust, and under the tested electrical constraints, the two-tape configuration consistently produced larger thrust than the three-tape configuration. Based on this practical actuation-strength characterization, wind-tunnel experiments were conducted by comparing actuator-OFF and actuator-ON cases under identical tunnel settings.

The surface-pressure response to actuation was strongly dependent on the angle of attack. At $\alpha =4°$, the actuation increased the upper-surface suction over the measured mid- to aft-chord region, whereas at $\alpha =8°$, it reduced leading-edge suction relative to the actuator-OFF case. Under the post-stall condition ($\alpha =18°$), both upper- and lower-surface $C_p$ approached values near zero over much of the measured chord, indicating a diminished pressure difference within the available tap range. Consistently, the pressure-derived lift estimate $C_{L,\mathrm{p}}^{\left(\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{m}\mathrm{o}\mathrm{n}\right)}$ and the lift increment $∆C_L = C_{L,\mathrm{p},\mathrm{o}\mathrm{n}}^{\left(\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{m}\mathrm{o}\mathrm{n}\right)}-C_{L,\mathrm{p},\mathrm{o}\mathrm{f}\mathrm{f}}^{\left(\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{m}\mathrm{o}\mathrm{n}\right)}$ indicated that the actuation effect was small at $\alpha =4°$ and $8°$ and should be interpreted cautiously, given the pressure coefficient resolution ($∆C_P \approx 0.83$ at $U_{\infty } = 5$ m/s). In contrast, a robust post-stall change was observed: $∆C_L$ became strongly negative at $\alpha = 18°.$

Smoke-wire visualization provided qualitative context for the pressure-field changes at higher angles. At $\alpha = 8°$, the actuator-ON case showed smoke streaks lifting off from the upper surface near the trailing edge, compared with the actuator-OFF case. At $\alpha = 18°$, visualization indicated immediate leading-edge separation and a larger separated region in the actuator-ON case, which was consistent with a separation-dominated pressure field. Overall, these results indicate that a fixed actuation setting is not universally beneficial across the angle of attack. Robust design guidelines—particularly for near-stall and post-stall applications—will require condition-dependent strategies and more quantitative diagnostics (e.g., denser surface-pressure measurements and time-resolved velocity/pressure data) to link the forcing level to separation behavior and integrated aerodynamic performance.