Role of Duty Cycle in Burst-modulated Synthetic Jet Flow Control

Flow control plays a critical role in enhancing the performance and efficiency of aircraft, especially those operating at low Reynolds numbers. Aerodynamic stall due to flow separation results in a drastic loss of lift and an increase in drag, constraining the performance of airfoils. These challenges typically arise in low-speed, high-altitude aircraft used for surveying and stealth, gliders, electric aircraft, and wind turbine blades. Flow control techniques can modify the flow around an airfoil, reattaching separated flows during post-stall conditions, thereby expanding the airfoil’s operational envelope.

Flow control techniques can be broadly classified into passive and active methods. Passive techniques involve modifying the flow without adding energy, for example, modifying the wing shape, adding vortex generators [1], or incorporating roughness elements [2]. While passive flow control can enhance aerodynamic performance, these methods often incur parasitic drag in the portion of the operational envelope when they are not needed [3]. In contrast, active flow control (AFC) techniques can be selectively employed under specific conditions, minimizing adverse effects when inactive. Despite their advantages, AFC systems tend to increase the aircraft’s weight, which is especially problematic in the case of nano and micro air vehicles where weight and volume limitations are stringent [4]. Furthermore, AFC systems draw substantial electrical power, a significant concern for electric aircraft [4, 5]. Traditional continuous blowing methods, for instance, require plumbing systems that add weight and complexity [6]. In contrast, AFC using synthetic jet actuators (SJAs) does not require plumbing, making them an ideal choice for aircraft flow control.

Typically utilizing plasma actuators or piezoelectric diaphragms, SJAs are zero-net-mass-flux devices that cyclically ingest and expel fluid, forming a time-averaged jet that adds momentum to the flow [7, 8]. Furthermore, synthetic jets have been shown to outperform continuous jets in fluid entrainment and mixing [9, 10, 11]. The effectiveness of SJAs in flow control is largely due to the generation of coherent vortical structures. These vortices, induced by the cyclic actuation of SJAs, are convected downstream along the suction side of the airfoil, entraining high-momentum fluid from the freestream into the separated shear layer. This process of momentum transfer energizes the shear layer, enabling it to overcome the adverse pressure gradient, thereby facilitating flow reattachment [6, 12, 13, 14]. The ability of SJAs to control flow separation through this mechanism makes them particularly effective for enhancing aerodynamic performance. Recent advancements in SJA technology have led to the development of MEMS-based devices, which are lightweight and reliable, making them ideal for flow control applications [14]. Additionally, SJAs offer a cost-effective alternative to similar AFC devices [3]. Over the past few decades, SJAs have been extensively researched and have achieved a high technology readiness level of 7 due to their successful implementation in real flight tests [15, 4].

Slot-style SJAs have been studied extensively due to their advantages in fluid entrainment [16]. However, their installation requires significant modifications to the wing surface and often involves large cavities, introducing structural concerns and resulting in high power consumption. This has driven research into arrays of small, circular SJAs for flow control, which also have the advantage of low power requirements and minimal noise production compared to large cavity SJAs. For example, a previous study using a large cavity SJA required driving voltages up to 275 $\mathrm{V_{pp}}$ [17], while the effects of control fully saturated at only 20 $\mathrm{V_{pp}}$ using an array of microblowers under similar experimental conditions [14].

Many parametric studies have been conducted to optimize flow reattachment, reduce drag, enhance lift, and maximize the stability of aerodynamic forces. Research has examined various factors, such as the effect of chordwise actuation location [18, 19, 20], blowing angle [18, 21], and orifice geometry [22, 23]. For practical flight applications, the most easily adjustable parameters that affect control performance are related to the waveform driving the SJAs. For a burst-modulated signal, the three primary waveform parameters that can be adjusted are the modulation frequency, the blowing strength, and the burst duty cycle (DC). Power consumption is significantly impacted by the blowing strength, controlled by varying the applied voltage and the DC, which dictates the fraction of the period during which SJA is activated.

The blowing strength is a critical parameter for SJAs in flow control applications, often quantified by a non-dimensional blowing ratio $C_{B}=\overline{U_{j}}/U_{\infty}$, where $\overline{U_{j}}$ is the time-averaged jet velocity during expulsion and $U_{\infty}$ is the freestream velocity. The blowing strength of an SJA is dictated by the amplitude of the SJA’s actuation, which is controlled by the voltage amplitude of the input signal. Experimental studies have demonstrated that increasing the blowing ratio can result in reduced drag and increased lift [9, 18, 17, 20, 24]. However, the effectiveness eventually saturates, with no additional aerodynamic benefits from further increases in the blowing ratio. This saturation point corresponded to the transition from a laminar separation bubble to a fully reattached flow [25]. Prior flow visualizations revealed that an increase in the blowing ratio leads to a thinning of the shear layer, a decrease in wake width, and a downward shift of the wake [17]. These desirable flow characteristics observed at higher blowing ratios are attributed to the postponed dissipation of the coherent vortices induced by the SJA, which enhances momentum transport into the shear layer [26, 24]. It is important to note that the majority of findings in these studies have been based on data collected at the midspan. A recent study revealed that flow over an airfoil controlled by SJAs is highly three-dimensional, with control efficacy degrading significantly even at moderate distances from the midspan, though still within the extent of the SJA array [27]. Furthermore, Feero et al. [25] showed that while control effects may be saturated at midspan, further increases in the blowing ratio can improve the spanwise control authority, highlighting the need for comprehensive three-dimensional flow analysis.

For flow control applications, SJAs are often driven by a burst-modulated signal, allowing the SJA to operate at its optimal frequency while targeting global instabilities in the flow associated with significantly lower frequencies. An example of a burst-modulated waveform is displayed in figure 1. Burst modulation has proven to be an effective technique in flow control, as demonstrated by various experimental studies [28, 29, 30, 25, 20, 31, 32, 13, 33, 24, 34, 14]. Additionally, it offers significant advantages over continuous actuation; for example, Amitay and Glezer [28] showed that burst modulation, when tuned to the airfoil’s natural frequency, increased the lift coefficient by $400\text{\,}\mathrm{\char 37\relax}$ compared to continuous high-frequency actuation while operating at $25\text{\,}\mathrm{\char 37\relax}$ of the momentum coefficient. Similarly, Borghi et al. [31] showed that burst modulation of plasma SJAs was significantly more effective in recovering stall over continuous actuation. An et al. [32] demonstrated successful temporary flow reattachment following a four-pulse burst sequence from an SJA. Additionally, this technique has the benefit of reduced power consumption due to the SJA only being powered for a fraction of the signal’s period.

The DC of the burst-modulated signal is another critical parameter in optimizing SJA performance and power consumption. Low-DCs significantly reduce power input, as the actuator operates for only a fraction of the signal’s period. In a parametric study, Abdolahipour et al. [35] found that high-frequency synthetic jets achieve maximum mean exit velocities at low DCs, which is desirable for flow control applications. The study also revealed that high DCs cause successive vortex rings to converge; at excessively high DCs, they interact and destroy. Additionally, Taylor et al. [3] demonstrated that using $20\text{\,}\mathrm{\char 37\relax}$ and $60\text{\,}\mathrm{\char 37\relax}$ DCs reduced hysteresis in lift compared to continuous actuation for a dynamically pitching airfoil. Similarly, Rice et al. [13] improved many aspects of dynamic stall control by using a low-DC, consuming only $35\text{\,}\mathrm{\char 37\relax}$ of the power required for continuous actuation. Table 2 provides an overview of the discussed experimental studies utilizing burst modulation in synthetic jet flow control.

The fluidic performance of SJAs is often evaluated using the momentum coefficient, which quantifies the momentum imparted by the SJA relative to the freestream flow. Various definitions of the momentum coefficient have been proposed by different researchers. The momentum coefficient for burst-modulated SJAs is not only influenced by the peak-to-peak voltage ($\mathrm{V_{pp}}$) but also the DC, as highlighted by Margalit et al. [37]. While previous research has often focused on enhancing momentum addition through increased signal amplitude at a constant DC, the blowing ratio ($C_{B}$) and momentum coefficient ($C_{\mu}$) have often been used interchangeably as measures of jet strength. In this study, the momentum coefficient is defined as the ratio of the momentum imparted by the synthetic jet to the incoming flow momentum over the entire actuation cycle, aligning with the definition proposed by Taylor et al. [3]:

where $\rho_{\infty}$ is the freestream fluid density, $A_{f}$ is the projected control area for a single jet, and $\overline{I_{j}}$ is the time-averaged jet momentum given by:

where $A_{j}$ is the jet orifice area, $\tilde{u}_{j}$ is the phase-averaged jet velocity, $T$ is the cycle period, and $\tau$ is the SJA active duration, which is typically set to $\tau=DC\times T$. Therefore, the momentum coefficient is commonly scaled proportionally to the DC [18, 38, 39]. To summarize, in burst-modulated SJAs, the momentum coefficient depends on both the blowing ratio and the DC. With these definitions, the blowing ratio measures the jet’s mean velocity relative to the oncoming flow, while the DC is the fraction of the actuation period that the jet is active. While prior studies have demonstrated that a threshold momentum coefficient must be met to fully reattach the separated shear layer [17, 4], it remains uncertain whether altering the momentum coefficient by varying the DC has the same effect as varying it via the blowing ratio. This raises an important question: can short, intense jets achieve the same control efficacy as longer, less intense bursts when the time-averaged momentum imparted is equal?

This paper explores the aerodynamic effects of varying the DC and blowing ratio of an SJA array, with a focus on optimizing control efficiency and power consumption. Section 3.1 investigates how these parameters influence lift performance and power consumption, aiming to identify effective, power-efficient control strategies. The study also examines the effect of varying the DC on flow characteristics and vortical structures responsible for flow reattachment in Section 3.2. Finally, correlations between single-point pressure measurements and lift coefficients are explored in Section 3.3. This approach facilitates rapid evaluation of control parameters for lift characteristics, serving as a preliminary step before performing a detailed pressure study.

Experiments were conducted in the low-speed recirculating wind tunnel in the Department of Mechanical and Industrial Engineering at the University of Toronto (figure 2). The test section has dimensions of $5\text{\,}\mathrm{m}$ $\times$ $0.91\text{\,}\mathrm{m}$ $\times$ $1.22\text{\,}\mathrm{m}$ and features acrylic windows on the top and side walls for observation and measurement. The flow passes through seven screens and a 12:1 contraction before entering the test section. The wind tunnel is capable of producing speeds between 3–18 \unit[per-mode = symbol]\per with a turbulence intensity of less than $1\text{\,}\mathrm{\char 37\relax}$. The freestream velocity was measured with a pitot-static tube at the test section entrance connected to an MKS Baratron 226A differential pressure transducer with a range of $267\text{\,}\mathrm{Pa}$. The uncertainty of the freestream velocity is estimated to be less than $\pm$1\text{\,}\mathrm{\char 37\relax}$$. For the experiments conducted, the wind tunnel was operated at a freestream velocity of $U_{\infty}=5.1$ \unit[per-mode = symbol]\per, resulting in a chord-based Reynolds number of $\mathrm{Re_{c}}=10^{5}$.

A NACA 0025 airfoil was placed in the wind tunnel with the leading edge approximately $40\text{\,}\mathrm{cm}$ from the test section inlet (figure 3). Additionally, the coordinate axes are defined, with $z=0$ corresponding to the midspan. The aluminum wing has an aspect ratio of approximately 3, with a span of $b=885$ \unit\milli, and a chord length of $c=300$ \unit\milli. The wing spans the entire width of the test section and features circular end plates which isolate it from the boundary layer at the wind tunnel walls [20]. The wing comprises three parts, with a hollow center third to house the sensors and actuators. In the center, there is a $317\text{\,}\mathrm{mm}$ $\times$ $58\text{\,}\mathrm{mm}$ rectangular cutout where the microblower array is installed, with a flush $0.8\text{\,}\mathrm{mm}$ hole for the nozzle of each SJA. The angle of attack was set to $\alpha=$10\text{\,}\mathrm{\SIUnitSymbolDegree}$$, such that the flow separates at approximately $12\text{\,}\mathrm{\char 37\relax}$ chord with the specified flow parameters. Sixty-four pressure taps along the midspan of the airfoil were connected to a Scanivalve pressure scanner with pneumatic tubing. The surface pressure of the airfoil was measured using an MKS Baratron 226A pressure transducer, featuring a bidirectional range of $\pm 26.7$ \unit. For each measurement, 30,000 samples were collected at a sampling rate of $1\text{\,}\mathrm{kHz}$, yielding a lift coefficient with an error of less than $2\text{\,}\mathrm{\char 37\relax}$.

The SJAs used are the commercially available Murata MZB1001T02 microblowers, pictured in figure 4, and are embedded underneath the surface of the airfoil. The SJAs are equally spaced in the spanwise direction by $25\text{\,}\mathrm{mm}$. The array consists of two rows of 12 SJAs located at $10.7\text{\,}\mathrm{\char 37\relax}$ and $19.8\text{\,}\mathrm{\char 37\relax}$ chord. However, only the upstream row was activated in these experiments, as indicated by the arrows in figure 3. The SJA operates between 5–30 $\mathrm{V_{pp}}$ and has a drive resonant frequency between 24–27 \unit\kilo. The mean centerline velocity of the synthetic jet reached a maximum when driven at a frequency of $25.1\text{\,}\mathrm{kHz}$. However, due to the right-skewed velocity response, the carrier frequency was chosen as $f_{c}=25.5$ \unit\kilo to ensure a stable jet velocity [14]. The SJAs were burst modulated at an excitation frequency of $f_{m}=200$ \unit, corresponding to a non-dimensional frequency of $F^{+}=11.76$. Square waveforms were used for the carrier and modulation frequency. The DC was varied from $5\text{\,}\mathrm{\char 37\relax}$ to $95\text{\,}\mathrm{\char 37\relax}$ and the blowing ratio was varied from $C_{B}=1.9$ to $C_{B}=5.0$. The time-averaged jet velocities used to calculate the blowing ratio were measured previously by Chovet et al. [40]. These blowing ratios were achieved by varying the input voltage from 10–20 $\mathrm{V_{pp}}$. Prior visualizations showed that at 5 $\mathrm{V_{pp}}$, the flow region controlled by the SJA is highly asymmetric even at high-DCs [41]. This aligns with previous tests [14], which showed large variations in jet centerline velocity between microblowers operating below 8 $\mathrm{V_{pp}}$ and increased sensitivity in the velocity response within this low-voltage range. Consequently, this study focuses on operating voltages of 10 $\mathrm{V_{pp}}$ and above to ensure the analysis captures fluidic effects while minimizing random variations in the SJAs’ response. By varying the DC and the input voltage, the estimated momentum coefficients achieved range from $C_{\mu}=2\times 10^{-5}$ to $4\times 10^{-3}$. These estimates are derived from linearly scaling the measurements obtained at a $50\text{\,}\mathrm{\char 37\relax}$ DC from Xu et al. [14]. The experimental parameters are summarized in table 3 and the control parameters are summarized in table 4.

Figure 5 illustrates the setup in which the SJA array receives its input signal from a Rigol DG1022Z function generator, amplified by a YAMAHA HTR5470 amplifier. The signal is then routed through a 10 $\Omega$ resistor to prevent overloading before reaching the 12 SJAs wired in parallel. The power consumption of the SJA array was determined by measuring the power consumed by the amplifier while the SJAs were active ($P_{\mathrm{amp,active}}$) and subtracting the idle power consumption of the amplifier ($P_{\mathrm{amp,idle}}$) and the power dissipated by the resistor ($P_{\mathrm{resistor}}$):

The power consumption of the amplifier was measured using a consumer-grade wattmeter, which has an uncertainty of $\pm$$0.1\text{\,}\mathrm{W}$. A Rigol DS1202Z-E oscilloscope was used to measure the RMS voltage drop across the resistor. The power dissipated by the resistor was then calculated using the equation:

where $V_{\mathrm{RMS}}$ is the measured RMS voltage drop across the resistor, and $R$ is the resistance value. The uncertainty in this calculation was determined to be $\pm$$0.1\text{\,}\mathrm{W}$. Therefore, the total uncertainty in the power consumption of the SJAs was estimated to be $\pm$$0.2\text{\,}\mathrm{W}$.

Cross-sectional smoke flow visualization in the spanwise-transverse plane was performed with a single horizontal smoke wire upstream of the wing. The horizontal smoke wire was positioned just above the airfoil’s stagnation point to visualize the flow at the edge of the shear layer. The horizontal smoke wire was installed $9.5\text{\,}\mathrm{cm}$ upstream of the leading edge, as shown in blue in figure 3. The smoke wire length spanned slightly larger than the SJA array. Figure 3 shows how the horizontal wire (blue dashed line) is installed between two vertical support wires (yellow dash-dot lines). The horizontal wire was kept taut by making it slightly shorter than the distance between the vertical support wires so that they bowed inward. This also helped ensure the horizontal wire remained in the same position across all tests. The wire was coated with oil and then heated resistively to generate smoke streaks. A laser sheet, oriented perpendicular to the flow, illuminated the generated smoke at the trailing edge, providing a sectional visualization of the shear layer boundary (figure 6). A Nikon D7000 DSLR camera downstream of the airfoil and test section was used to image the smoke streaks. The camera was operated in burst mode, capturing up to six images per second, facilitating the capture of the smoke visualization at peak density. A long exposure time of 1/6 \unit (2.8 convective timescales) was used to provide a sense of the mean flow while capturing unsteady areas highlighted by motion blur. The camera was operated with an aperture of $f/$1.8, and an ISO of 4000. Additional details on the smoke visualization method can be found in Machado et al. [36, 27].

Particle image velocimetry (PIV) measured the streamwise-transverse velocity field above the airfoil. Neutrally, buoyant particles were introduced into the flow using a fog machine downstream of the test section. Two JAI SP-5000M-USB cameras, each with a resolution of 2560 $\times$ 2048, were positioned outside the test section and aligned with the airfoil’s chord. Composite images were created by stitching together the camera captures, resulting in a field of view (FOV) measuring $270\text{\,}\mathrm{mm}$ $\times$ $120\text{\,}\mathrm{mm}$, with a pixel resolution of $17\text{\,}\mathrm{p}\mathrm{i}\mathrm{x}\mathrm{e}\mathrm{l}\mathrm{s}\mathrm{/}\mathrm{m}\mathrm{m}$ (figure 7). The stitched FOV effectively captured the range $x/c\in[0.1,1]$ and $y/c\in[0,0.4]$, covering the area of interest above the airfoil. A Litron Bernoulli $200\text{\,}\mathrm{mJ}$ Nd-YAG laser with a wavelength of $532\text{\,}\mathrm{nm}$ was passed through converging and diverging cylindrical lenses ($f=1000$ \unit\milli and $f=-13.7$ \unit\milli, respectively) to create a thin laser sheet that illuminated the measurement plane. The image acquisition and laser pulses were synchronized using an NI PCIe-6323 data acquisition card (DAQ) at $10\text{\,}\mathrm{Hz}$, and 1000 image pairs were recorded for each measurement. The time delay between the frames in an image pair was set to $120\text{\,}\mathrm{\SIUnitSymbolMicro s}$. The random error in the mean velocity is estimated to be less than $0.01U_{\infty}$ based on a convergence study. For the control cases, phase-locked velocity measurements were achieved by synchronizing image acquisition at eight evenly spaced phases relative to the SJA modulation frequency, where a phase angle of $\phi=0$$\mathrm{\SIUnitSymbolDegree}$ represents the activation of the actuator. Coherent fluctuations are extracted from the velocity signal using the triple decomposition [42]. The streamwise velocity was decomposed as $u=\bar{u}+\tilde{u}+u^{\prime}$, where $\bar{u}$ is the time-averaged velocity, $\tilde{u}$ is the coherent velocity obtained from the phase-average, and $u^{\prime}$ is the fluctuation velocity [43]. Velocity vectors were obtained using open-source software OpenPIV-Python-GPU, utilizing a multi-pass cross-correlation algorithm to accurately record large and small displacements. The PIV process involved an initial iteration at an interrogation window size of 64 $\times$ 64 pixels, followed by two iterations at 32 $\times$ 32 pixels, and two iterations at 16 $\times$ 16 pixels. Linear window deformation was used to reduce correlation errors in high-shear regions.

This paper presents a comprehensive experimental investigation using a finite-span SJA array for flow reattachment on a stalled airfoil. The study focuses on the aerodynamic effects of two key control parameters: the blowing ratio (controlled by the input voltage) and the burst duty cycle, along with their interactions. Additionally, the power requirements of the tested control cases are measured to identify power-efficient strategies for synthetic jet flow control. Effective flow control was achieved with low-DC control strategies, leading to significant power savings compared to traditional methods that typically operate at a $50\text{\,}\mathrm{\char 37\relax}$ DC or with continuous actuation.

While it is widely established that increasing the momentum coefficient can improve lift characteristics, prior studies have primarily focused on controlling the momentum coefficient via the blowing ratio alone. A key finding of this paper is that the threshold momentum coefficient for reattachment can also be achieved by increasing the DC, which can trigger flow reattachment from a previously separated state at lower DCs. Additionally, higher blowing ratios were found to reduce the threshold DC required for flow reattachment. Increases in the momentum coefficient via either the DC or blowing ratio were found to improve the spanwise control authority and lift coefficient, however, these improvements were not consistent. A sharp initial increase in control effectiveness coincided with complete flow reattachment, after which further increases yielded diminishing returns, indicating that the control effects had saturated. The most power-efficient strategy for time-averaged lift recovery was found to involve low-DCs ($5\text{\,}\mathrm{\char 37\relax}$) at threshold blowing ratios, suggesting brief, strong perturbations are effective for reattachment while maintaining efficiency. Interestingly, employing high-power control strategies, operating at an order of magnitude higher wattage, did not significantly improve the spanwise control authority. The maximum spanwise control length achieved was limited to only $40\text{\,}\mathrm{\char 37\relax}$ of the array’s length. This highlights the challenges in achieving consistent control across the entire wing span with finite-span SJAs, which may be attributed to the impact of highly turbulent, uncontrolled flow beyond the extent of the array.

The study also investigates how the flow field, dynamics, and vortical structures vary across a wide range of DCs, offering insights into control effectiveness and lift force stability, which are crucial for aviation applications. With the blowing ratio held constant, the DC was varied from low ($5\text{\,}\mathrm{\char 37\relax}$) to medium ($50\text{\,}\mathrm{\char 37\relax}$) to high ($95\text{\,}\mathrm{\char 37\relax}$) values. Although all control cases achieved flow reattachment, differences were observed in the flow dynamics. Low-DCs resulted in unsteady control, while higher DCs produced a phase-invariant flow field and thus steady aerodynamic effects throughout the actuation period. This behaviour is explained by the analysis of the SJA-induced spanwise vortices, which serve as the primary mechanism in flow reattachment. At the low DC the vortices were larger, lifted off the airfoil surface, and dissipated earlier along the chord, reducing their effectiveness in transporting momentum from the freestream into the shear layer. Conversely, at high DCs, the vortices were smaller, yet stronger, and remained close to the suction surface, effectively transporting momentum and energizing the shear layer. Additionally, at low DCs, the chordwise dissipation point of vortices was found to be phase-dependent, explaining the variation in the shear layer dynamics across the actuation period. These results suggest that overly conservative flow control strategies with low DCs can lead to unstable aerodynamic effects.

Lastly, the study found a strong correlation between the lift coefficient and the strength of the suction peak, demonstrating that single-point pressure measurements can serve as reliable indicators of lift. This finding is particularly important for rapidly testing various control parameters, including modulation frequency, DC, and blowing ratio, to identify optimal combinations for different flow conditions.

This work was supported by the Natural Science and Engineering Research Council of Canada and the SciNet High Performance Computing consortium and the Canadian Microelectronics Corporation (CMC).